Identifying RNA regions for reverse transcription and PCR amplification

Abstract

A computational and analytical method identifies optimal regions within RNA molecules for efficient reverse transcription (RT) and polymerase chain reaction (PCR) amplification. The method introduces four new quantitative parameters: an RNA Accessibility Parameter (RAP), which integrates probability of base pairing (Pbp) with positional entropy (Spos) to quantify nucleotide accessibility; an Efficiency Reverse Transcription Score (ERTS), which combines RAP with Gibbs free energy (AG) of RNA-DNA hybridization to estimate per-nucleotide hybridization and initiation likelihood; a Region Reverse Transcription Score (RRTS). which sums ERTS across contiguous windows to rank primer-binding regions; and a threshold for each RRTS. which demarcates optimal regions and defines a Minimum Initiation Subregion (MIS) sufficient for initiating hybridization and reverse transcription. RNA regions with RRTS above the threshold are able to initiate primer binding and reverse transcription, even in partially structured RNA. Primers, primer pairs, probes, primer-probe sets, and kits containing them are also disclosed.

Description

IDENTIFYING RNA REGIONS FOR REVERSE TRANSCRIPTION AND PCR AMPLIFICATION CLAIM TO PRIORITY

[0001] This patent application claims the benefit of priority to Chilean Patent Application Number 202500003, filed January 2, 2025, and entitled “Method for Identifying Optimal RNA Regions for Efficient Reverse Transcription and PCR Amplification,” which is incorporated by reference herein in its entirety.INCORPORATION BY REFERENCE OF SEQUENCE LISTING

[0002] This application contains a Sequence Listing which has been submitted electronically in ST26 format and hereby incorporated by reference in its entirety. Said ST26 file, created on December 31, 2025, is named 6707002W01.xml and is 6,403 bytes in size.TECHNICAL FIELD

[0003] Disclosed herein are computer-implemented computational methods and systems for analyzing RNA structural ensembles to improve primer design for reverse-transcription-dependent nucleic-acid amplification.BACKGROUND

[0004] Reverse Transcription-Polymerase Chain Reaction (RT-PCR) is a molecular biology technique used for detecting and quantifying RNA. The process involves the conversion of RNA into complementary DNA (cDNA) using reverse transcriptase enzymes, followed by amplification through PCR. However, RNA molecules often form complex secondary structures (e.g., hairpins, loops, stems) that hinder primer binding and impede reverse transcription. These structural barriers significantly reduce RT-PCR efficiency and sensitivity, especially for structured RNAs such as viral genomes, non-coding RNAs, and regulatory transcripts.SUMMARY

[0005] The implementations described herein provide a computational and experimentally validated method for identifying RNA regions that support efficient reverse transcription and primer-mediated amplification. The implementations described herein integrate structural ensemble metrics and thermodynamic hybridization energy into a unified quantitative framework, enabling the prediction of nucleotide positions and regional segments that exhibit high accessibility and strong primer-binding performance. By combining basepairing probabilities, positional entropy metrics, RNA-DNA Gibbs free energy measures, and region-level aggregation, the implementations disclosed herein identify RNA segments that provide superior initiation of reverse transcription, including in highly structured or partially folded RNA molecules.

[0006] The implementations disclosed herein introduce quantitative metrics that characterize local accessibility using ensemble-derived structural information. The implementations disclosed herein also combine the local accessibility quantitative metrics with thermodynamic data to evaluate the likelihood of productive primer binding and reverse-transcription initiation at each nucleotide. In addition, region level quantitative measures are determined that aggregates nucleotide-based quantitative measures and metrics over a window to identify extended regions with consistently high efficiency. A regional threshold can enable the detection of an optimal binding region can be used to determine a minimal sub-region that can be used for robust initiation of reverse transcription.

[0007] The disclosed method provides a technical solution to the limitations of existing primer-design tools, which rely on single-structure predictions, simple thermodynamic heuristics, or sequence-based rules and therefore fail to capture the combined influence of accessibility, structural uncertainty, and hybridization energetics. By quantitatively integrating these elements, the method identifies optimal primer-binding regions that are not predictable using AG, GC content, Tm, or conventional design strategies alone.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and, together with the description, serve to explain the principles, structure, and operation of the disclosed methods and systems. It is to be understood that the drawings are provided for purposes of illustration only and are not intended to limit the scope of the invention as defined by the claims. Elements and features shown in the drawings may be simplified or not to scale for clarity of presentation.

[0009] Figure 1 illustrates an example framework to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations.

[0010] Figure 2 illustrates an example framework to generate metrics for individual nucleotides of an RNA sequence that can be used to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations.

[0011] Figure 3 illustrates an example of a two-dimensional (2D) secondary structure of a ribosomal RNA (rRNA) molecule from Escherichia coli.

[0012] Figure 4 illustrates a three-dimensional (3D) structural model of the 16S rRNA from Escherichia coli.

[0013] Figure 5 illustrates a graphic of ERTS values as a function of nucleotide position, with a dashed horizontal line representing the ERTS threshold.

[0014] Figure 6 is a flow diagram of an example process to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations.

[0015] Figure 7 illustrates a diagrammatic representation of a machine in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example implementation.DETAILED DESCRIPTION

[0016] The design of primers for amplification of complex RNA molecules faces several interrelated technical challenges arising from the intrinsic properties of RNA. For example, RNA molecules can be shaped into extensive secondary andtertiary structures. To illustrate, RNA molecules often fold into highly stable configurations involving long-range base pairing and pseudoknot formation. These structures shield portions of the RNA sequence from hybridization and prevent primers from annealing efficiently. Existing computational techniques for identifying potential regions of an RNA sequence that can be used in the design of reverse transcription primers typically assume linear accessibility and fail to account for this conformational complexity. These approaches can also focus on global minima and do not identify accessible regions for efficient primer annealing.

[0017] Additionally, RNA molecules have dynamic structural heterogeneity because RNA does not adopt a single static conformation but exists as an ensemble of structures that fluctuate depending on ionic strength, temperature, and local sequence context. This structural heterogeneity complicates the prediction of accessible sites for primer annealing and can lead to inconsistent amplification efficiency across replicates or reaction conditions. For example, existing computational techniques for RNA primer design do not quantify local pairing variability or accessibility in dynamic RNA conformations and do not identify accessible regions for efficient primer annealing.

[0018] Existing techniques for designing RNA reverse transcription primers also suffer from incomplete thermodynamic evaluations. Most primer design programs consider only DNA-DNA duplex stability during PCR, ignoring the RNA-DNA hybridization energetics that govern the initial reverse transcription step. The Gibbs free energy (AG) of RNA-DNA interactions differs substantially from that of DNA-DNA duplexes, resulting in inaccurate estimates of binding affinity when RNA structure is not explicitly modeled. Additionally, while AG predicts binding stability, it overlooks local accessibility and dynamic structure formation and may not be a good predictor of complex RNA amplification.

[0019] Further, existing frameworks for identifying regions of RNA molecules that can form the basis for reverse transcription primers lack integrative quantitative metrics. In particular, existing methods lack a unified metric to evaluate the combined impact of RNA accessibility and thermodynamic favorability. For example, various existing approaches can rely solely on probabilities of base pairing within RNA molecules to estimate unpaired regions,while neglecting positional entropy — a measure of structural flexibility — and the actual energy required to form an RNA-DNA hybrid. As a result, existing primer design approaches may select regions that appear accessible in silico but perform poorly in experimental conditions.

[0020] In still other situations, researchers often rely on trial-and-error optimization of reaction conditions, such as modifying enzyme conditions, using additives, or adjusting temperature profiles, to compensate for poor primer performance. This empirical process is time-consuming, costly, and inconsistent, particularly when working with structured RNAs such as viral genomes, long noncoding RNAs, and ribosomal RNA molecules. Additionally, these approaches do not address the root causes of reverse transcription inefficiencies, such as the structural and thermodynamic constraints of RNA molecules, and can be labor intensive and inconsistent, especially for long or complex RNAs and are not accurate predictors of complex RNA amplification.

[0021] The implementations described herein provide a computational and quantitative method capable of integrating both structural and thermodynamic determinants of RNA primer binding. The implementations described herein also directly addresses the limitations of existing techniques by introducing a framework that systematically identifies RNA regions that combine high structural accessibility indicated by low secondary structure and high entropy with favorable hybridization energetics indicated by relatively low AG values. This approach enables the rational design of primers and probes for reliable and efficient reverse transcription and amplification of even the most structurally complex RNA molecules.

[0022] In one or more aspects, computational systems and methods integrate basepairing probabilities, indicators of positional entropy RNA-DNA, and hybridization free energy (AG) computations for individual nucleotide positions of RNA molecules in conjunction with regional sliding-window aggregation into a unified scoring framework for identifying optimal reverse-transcription regions. In this way, the implementations described herein combine these ensemble-derived structural parameters with thermodynamic hybridization energy to compute a per-nucleotide score and a regional score that predicts reversetranscription efficiency. The implementations described herein also determine acontiguous high-efficiency zone required for robust initiation of reverse transcription. Further, the implementations described herein link RNA secondarystructure ensemble statistics to measurable laboratory outcomes such as threshold cycle (Ct) reduction or amplification performance to produce primers with superior experimental performance.

[0023] In various examples, a per-base efficiency metric is generated that integrates structural and thermodynamic factors that is used to produce a regionlevel reverse-transcription efficiency score. Additionally, a minimum length for initiation of reverse transcription can be quantified and primer-binding regions identified that specifically optimized for reverse-transcription initiation, rather than PCR binding alone.

[0024] Existing methods for improving reverse transcription efficiency — such as modifying enzyme conditions, using additives, or adjusting temperature profiles — do not address the root causes of reverse transcription inefficiencies: the structural and thermodynamic constraints of RNA molecules. Some RNA-focused computational approaches can estimate RNA secondary structures. Additionally, some RNA-focused computational techniques can determine various metrics or quantitative measures related to nucleotides in RNA sequences pairing with one another.

[0025] A number of computational methods exist for predicting RNA structure or designing oligonucleotides, including algorithms that compute base-pairing probabilities, positional entropy, unpaired-probability profiles, ensemble defect, AG of hybridization, or SHAPE-derived accessibility profiles. Other tools apply sliding-window analysis to identify regions of low predicted structure or favorable hybridization thermodynamics. Methods used for siRNA, antisense oligos, CRISPR guide RNAs, and mRNA accessibility prediction employ singleparameter or dual-parameter heuristics, such as minimum free energy structure, local unpaired probability, or AG-based binding prediction.

[0026] However, existing techniques for primer design do not quantitatively identify regions within RNA molecules that are both structurally accessible and energetically favorable for efficient reverse transcription and amplification. The implementations described herein overcome the longstanding challenge of predicting reverse-transcription efficiency in structured RNA molecules byintroducing a scoring framework grounded in ensemble-based structural analysis and thermodynamic modeling. In one or more examples, the computational method automatically calculates the following parameters do identify primer target regions:1. RNA Accessibility Parameter (RAP): A composite accessibility measure derived from base-pairing probability (Pbp), positional entropy (Spos), and equivalent metrics of structural openness.2. Efficiency Reverse Transcription Score (ERTS): A per-nucleotide efficiency value integrating RAP with the Gibbs free energy (AG) of RNA-DNA hybridization, providing a direct estimate of per-base favorability for primer binding.3. Region Reverse Transcription Score (RRTS): An aggregated efficiency score computed across a window of nucleotides, enabling identification and ranking of favorable multi-base primer-binding regions.4. Minimum Initiation Subregion (MIS): A quantitatively defined contiguous or non-contiguous subregion within a high-RRTS window, representing the smallest region sufficient to initiate productive reverse transcription.

[0027] This integrated framework produces practical, experimentally validated predictions of primer performance and can be implemented on a computer system comprising one or more processors and a non-transitory computer-readable medium storing instructions for executing each step of the method.

[0028] The implementations described herein can provide the following advantages with respect to existing techniques used for primer design:Predictive accuracy: The combined use of structural ensemble metrics and hybridization thermodynamics yields superior prediction of primer performance relative to traditional sequence-based methods.Increased sensitivity: Primers designed using the method exhibit markedly reduced Ct values and enhanced detection sensitivity, including in highly structured RNA targets.Automation-ready: The workflow is fully automatable and suitable for high-throughput primer design pipelines.Scalable to many RNA classes: Applicable to viral genomes, bacterial rRNA, long non-coding RNAs, messenger RNAs, and synthetic constructs.MIS-driven reliability: Explicit identification of a Minimum Initiation Subregion provides a robust indicator of initiation efficiency and enables reliable primer placement in partially folded regions.Industrial applicability: The method improves assay development in clinical diagnostics, food safety testing, environmental monitoring, research molecular biology, and any workflow requiring accurate primer design for structured RNA.DEFINITIONS

[0029] Base-Pairing Probability (Pbp©): The probability that nucleotide position i is base-paired in the RNA structural ensemble, derived from a partition-function computation. Equivalent or analogous metrics, such as probability of being unpaired, single-stranded propensity, or expected pairing frequency, may be used interchangeably.

[0030] Positional Entropy (SPos©): A measure of structural uncertainty at nucleotide position i reflecting the diversity of pairing states across the ensemble. Alternative ensemble-based metrics of structural variability (including Shannon entropy variants, structural diversity indices, or expected base-pair distance) are encompassed herein.

[0031] Hybridization Free Energy (AG©): The predicted Gibbs free energy for RNA-DNA hybridization at position i, calculated by the nearest-neighbor thermodynamic model or any equivalent thermodynamic approximation, including empirical or machine-leaming-derived hybridization estimates.

[0032] RNA Accessibility Parameter (RAP©): A composite measure of nucleotide accessibility derived from one or more structural metrics, including Pbp©, SPos®, or any equivalent measure of accessibility or structural openness. RAP may therefore be computed using single or combined inputs reflecting local structural flexibility.

[0033] Efficiency Reverse Transcription Score (ERTS©): A per-nucleotide score incorporating RAP and AG, or any equivalent combination of accessibility and thermodynamic predictors. ERTS is not limited to a particular algebraic form and may be computed by linear, nonlinear, or machine-learning models.

[0034] Region Reverse Transcription Score (RRTS©): An aggregated score over a region of length W, computed from ERTS© using an aggregation function, including sums, averages, weighted sums, maxima, probabilistic aggregations, or integrated metrics.

[0035] Minimum Initiation Subregion (MIS): A contiguous or non-contiguous set of nucleotide positions whose collective ERTS exceeds an initiation requirement, including threshold-based, cumulative, percentile, or weighted criteria. The MIS defines the minimal region supporting reverse-transcription initiation.PARAMETER DEFINITIONS AND RANGESWindow Length (W):

[0036] The window length used to compute RRTS may be predetermined, dynamically selected, or optimized based on the RNA target. In some embodiments, W is between 4-40 nucleotides, between 6-30 nucleotides, or between 8-20 nucleotides. Any window length suitable for aggregating ERTS values is encompassed herein.ERTS Threshold (T):

[0037] The threshold used to determine whether an ERTS value is considered “high” may be fixed, relative, or empirically defined. T may be a global threshold, a percentile-based threshold (e.g., top 10% of ERTS values), or a dynamic threshold computed from the distribution of ERTS values. All such thresholding approaches are covered.Regional Threshold (RT):

[0038] The threshold used to evaluate RRTS may be absolute, relative, normalized, or percentile-based, and may vary across RNA targets.AG Calculation Method:

[0039] AG values may be computed using nearest-neighbor thermodynamics, approximations thereof, modified models, or machine-learning thermodynamic predictors.Ensemble Computation Method:

[0040] Pbp and Sposmay be computed using partition-function algorithms, stochastic sampling of structural ensembles, or any equivalent ensemble-based structure-prediction method.Scoring Weight Parameters (a, f>. y):

[0041] Weighting terms used in RAP or ERTS calculations may be fixed, learned, or user-defined. These parameters may be optimized algorithmically or selected empirically.MIS Length Requirement (L):

[0042] The minimum length of the MIS may be determined relative to primer length, empirical RT efficiency, RRTS magnitude, or a combination thereof. L may be within >4, >5, >6, >8, >10, or >12 nucleotides depending on the implementation.

[0043] Figure 1 illustrates an example framework 100 to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations. The framework 100 can include a computing system 102. The computing system 102 can perform computational methods, processes, and techniques that can identify regions of RNA molecules that can be used to synthesize primers for reverse transcription of the RNA molecules and, in at least some situations, amplification. The computing system 102 can be implemented by one or more computing devices 104. The one or more computing devices 104 can include one or more server computing devices, one or more desktop computing devices, one or more laptop computing devices, one or more tablet computing devices, one or more mobile computing devices, or combinations thereof. In certain implementations, at least a portion of the one or more computing devices 104 can be implemented in a distributedcomputing environment. For example, at least a portion of the one or more computing devices 104 can be implemented in a cloud computing architecture.

[0044] RNA sequence data 106 can be obtained by the computing system 102. In one or more examples, the RNA sequence data 106 can be obtained by the computing system 102 from one or more user devices. For example, the RNA sequence data 106 can be uploaded to the computing system 102. To illustrate, the RNA sequence data 106 can be uploaded to the computing system 102 via one or more application programming interface (API) calls supported by the computing system 102. Additionally, the RNA sequence data 106 can be uploaded to the computing system 102 via one or more user interfaces that are displayed by the one or more user devices. In one or more illustrative examples, the computing system 102 can provide a software package that is executable by the one or more user devices to display one or more user interfaces that are configured to capture the RNA sequence data 106 and make the RNA sequence data 106 accessible to the computing system 102. In still other examples, the RNA sequence data 106 can be stored by one or more data stores that are in electronic communication with the computing system 102. In one or more examples, the RNA sequence data 106 can be stored in a computer-readable file that is obtained by the computing system 102.

[0045] In at least some examples, the RNA sequence data 106 can comprise text data indicating one or more RNA nucleotide sequences. Individual RNA nucleotide sequences can include a string of alphanumeric characters representing nucleotides of an RNA molecule arranged in a specified order with individual nucleotides of the individual RNA nucleotide sequence corresponding to an individual position of the RNA molecule. In one or more illustrative examples, individual RNA nucleotide sequences included in the RNA sequence data 106 can include one or more instances of the letter ‘A’ to represent adenine in RNA nucleotide sequences, one or more instances of the letter ‘U’ to represent uracil in RNA nucleotide sequences, one or more instances of the letter ‘G’ to represent guanine in RNA nucleotide sequences, and one or more instances of the letter ‘C’ to represent cytosine in RNA nucleotide sequences. The RNA sequence data 106 can include additional information. For example, the RNA sequence data 106 can indicate an organism corresponding to one or more RNA nucleotides sequencesincluded in the RNA sequence data 106. The RNA sequence data 106 can also indicate a genus, species, or other taxonomical indicator corresponding to one or more RNA nucleotide sequences included in the RNA sequence data 106. In various examples, the RNA sequence data 106 can include ribosomal RNA sequences of a number of microbes. In one or more additional examples, the RNA sequence data 106 can include ribosomal RNA sequences comprising at least a portion of 16S ribosomal RNA and / or at least a portion of 23S ribosomal RNA of a number of microbes. In still other examples, the RNA sequence data 106 can include messenger RNA sequences of a number of microbes.

[0046] The computing system 102 can include a structure generating system 108 that generates RNA structural data 110 based on the RNA sequence data 106. In one or more examples, the structure generating system 108 can determine a plurality of secondary structural representations that correspond to individual RNA nucleotide sequences included in the RNA sequence data 106. For example, the structure generating system 108 can generate RNA structural data 110 indicating at least 10 secondary structural representations, at least 50 secondary structural representations, at least 100 secondary structural representations, at least 250 secondary structural representations, at least 500 secondary structural representations, at least 1000 secondary structural representations, at least 5000 secondary structural representations, at least 10,000 secondary structural representations, at least 25,000 secondary structural representations, at least 50,000 secondary structural representations, at least 100,000 secondary structural representations, at least 250,000 secondary structural representations, at least 500,000 secondary structural representations, at least 1,000,000 secondary structural representations, or more secondary structural representations that correspond to individual RNA nucleotide sequences included in the RNA sequence data 106. In various examples, the structure generating system 108 can generate RNA structural data 110 indicating no greater than 5,000,000 secondary structural representations, no greater than 2,000,000 secondary structural representations, no greater than 1,000,000 secondary structural representations, no greater than 500,000 secondary structural representations, or no greater than 100,000 the secondary structural representations. In at least some examples, the structure generating system 108 can generate RNA structural data 110 indicatingfrom 10 secondary structural representations to 5,000,000 secondary structural representations, from 10 secondary structural representations to 2,000,000 secondary structural representations, from 10 secondary structural representations to 1,000,000 secondary structural representations, from 10 secondary structural representations to 500,000 secondary structural representations, from 10 secondary structural representations to 100,000 secondary structural representations, from 10 secondary structural representations to 50,000 secondary structural representations, from 10 secondary structural representations to 25,000 secondary structural representations, from 10 secondary structural representations, to 10,000 secondary structural representations, from 10 secondary structural representations to 5000 secondary structural representations, from 10 secondary structural representations to 1000 secondary structural representations, from 10 secondary structural representations to 500 secondary structural representations, from 10 secondary structural representations to 250 secondary structural representations, or from 10 secondary structural representations to 100 secondary structural representations, from 100 secondary structural representations to 1,000,000 secondary structural representations, from 100 secondary structural representations to 100,000 secondary structural representations, from 100 secondary structural representations to 10,000 secondary structural representations, from 100 secondary structural representations to 5000 secondary structural representations, from 100 secondary structural representations to 1000 secondary structural representations, from 1000 secondary structural representations to 1,000,000 secondary structural representations, from 1000 secondary structural representations to 100,000 secondary structural representations, from 1000 secondary structural representations to 10,000 secondary structural representations, from 5000 secondary structural representations to 1,000,000 secondary structural representations, from 5000 secondary structural representations to 100,000 secondary structural representations, from 5000 secondary structural representations to 50,000 secondary structural representations, or from 5000 secondary structural representations to 10,000 secondary structural representations.

[0047] In one or more illustrative examples, the RNA structural data 110 can indicate a two-dimensional arrangement of nucleotides included in an RNA nucleotide sequence having a number of structural features. In various examples, the number of structural features for a given two-dimensional arrangement of nucleotides can include at least one of one or more stems, one or more pseudoknots, or one or more loops. In at least some examples, the number of structural features indicated by the RNA structural data 110 for two-dimensional arrangements of nucleotides included in an RNA nucleotide sequence can include one or more hairpin loops, one or more bridge loops, one or more internal loops, one or more bulge loops, or one or more branch loops. In one or more additional illustrative examples, the RNA structural data 110 can indicate that individual RNA nucleotide sequences have secondary structures that include at least 5 stems, loops, and / or branches; at least 10 stems, loops, and / or branches; at least 25 stems, loops, and / or branches; at least 50 stems, loops, and / or branches; at least 100 stems, loops, and / or branches, at least 250 stems, loops, and / or branches, at least 500 stems, loops, and / or branches, at least 750 stems, loops, and / or branches, at least 1000 stems, loops, and / or branches; at least 2500 stems, loops, and / or branches; at least 5000 stems, loops, and / or branches; at least 7500 stems, loops, and / or branches; at least 10,000 stems, loops, and / or branches; at least 25,000 stems, loops, and / or branches; at least 50,000 stems, loops, and / or branches; at least 75,000 stems, loops, and / or branches; or at least 100,000 stems, loops, and / or branches. In various examples, the RNA structural data 110 can indicate that individual RNA nucleotide sequences have secondary structures that include no greater than 1,000,000 stems, loops, and / or branches, no greater than 500,000 stems, loops, and / or branches, no greater than 100,000 stems, loops, and / or branches, no greater than 50,000 stems, loops, and / or branches, no greater than 25,000 stems, loops, and / or branches, no greater than 10,000 stems, loops, and / or branches, no greater than 5000 stems, loops, and / or branches, or no greater than 1000 stems, loops, and / or branches. In one or more illustrative examples, the RNA structural data 110 can indicate that individual RNA nucleotide sequences have secondary structures that include from 5 stems, loops, and / or branches to 1,000,000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 500,000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to100,000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 50,000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 10,000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 5000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 1000 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 500 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 250 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 100 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 50 stems, loops, and / or branches, from 5 stems, loops, and / or branches to 20 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 1,000,000 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 500,000 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 100,000 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 10,000, stems, loops, and / or branches, from 20 stems, loops, and / or branches to 1000 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 500 stems, loops, and / or branches, from 20 stems, loops, and / or branches to 100 stems, loops, and / or branches, from 100 stems, loops, and / or branches to 1,000,000 stems, loops, and / or branches, from 100 stems, loops, and / or branches to 500,000 stems, loops, and / or branches, from 100 stems, loops, and / or branches to 100,000 stems, loops, and / or branches, from 100 stems, loops, and / or branches to 10,000 stems, loops, and / or branches, from 100 stems, loops, and / or branches to 1000 stems, loops, and / or branches, or from 100 stems, loops, and / or branches to 500 stems, loops, and / or branches.

[0048] In one or more further illustrative examples, RNA structural data 110 can indicate that individual RNA nucleotide sequences have secondary structures that include at least 5 pseudoknots; at least 10 pseudoknots; at least 25 pseudoknots; at least pseudoknots; at least 100 pseudoknots, at least 250 pseudoknots, at least 500 pseudoknots, at least 750 pseudoknots, at least 1000 pseudoknots, at least 5000 pseudoknots, or at least 10,000 pseudoknots.

[0049] In still other examples, the structure generating system 108 can determine a plurality of tertiary structural representations that correspond to individual RNA nucleotide sequences included in the RNA sequence data 106. The tertiary structural representations can indicate a number of folding configurations forindividual RNA nucleotide sequences. For example, the structure generating system 108 can generate RNA structural data 110 indicating at least 10 tertiary structural representations, at least 50 tertiary structural representations, at least 100 tertiary structural representations, at least 250 tertiary structural representations, at least 500 tertiary structural representations, at least 1000 tertiary structural representations, at least 5000 tertiary structural representations, at least 10,000 tertiary structural representations, at least 25,000 tertiary structural representations, at least 50,000 tertiary structural representations, at least 100,000 tertiary structural representations, at least 250,000 tertiary structural representations, at least 500,000 tertiary structural representations, at least 1,000,000 tertiary structural representations, or more tertiary structural representations that correspond to individual RNA nucleotide sequences included in the RNA sequence data 106.

[0050] In one or more examples, the structure generating system 108 can generate the RNA structural data 110 by executing one or more thermodynamics-based computational models. For example, the structure generating system 108 can generate the RNA structural data 110 by executing one or more thermodynamic nearest neighbor models. In various examples, the structure generating system 108 can generate the RNA structural data 110 by executing one or more thermodynamics-based computational models as described in Hofacker IL. Vienna RNA secondary structure server. Nucleic Acids Res. 2003 Jul 1 ;31(13):3429-31 ; Gruber AR, Lorenz R, Bemhart SH, Neubock R, Hofacker IL. The Vienna RNA websuite. Nucleic Acids Res. 2008 Jul l;36(Web Server issue):W70-4; and Bellaousov S, Reuter JS, Seetin MG, Mathews DH. RNAstructure: Web servers for RNA secondary structure prediction and analysis. Nucleic Acids Res. 2013 Jul;41(Web Server issue):W471-4.

[0051] In one or more additional examples, the structure generating system 108 can generate the RNA structural data 110 by executing one or more machine learning models. For example, the structure generating system 108 can generate the RNA structural data 110 by executing a machine learning architecture that includes at least one of a number of convolutional layers, one or more recurrent neural networks, or one or more multilayer perceptron layers. In still other examples, the structure generating system 108 can generate the RNA structuraldata 110 by executing at least one of a long short term memory machine learning architecture or a transformer-based architecture. In at least some examples, the structure generating system 108 can execute machine learning models that have been trained using support vector machines. In one or more illustrative examples, the structure generating system 108 can generate the RNA structural data 110 by executing one or mor machine learning models described in Sato, K., Akiyama, M. & Sakakibara, Y. RNA secondary structure prediction using deep learning with thermodynamic integration. Nat Commun 12, 941 (2021); Fu L, Cao Y, Wu J, Peng Q, Nie Q, Xie X. UFold: fast and accurate RNA secondary structure prediction with deep learning. Nucleic Acids Res. 2022 Feb 22;50(3):el4; and Pearce, R., Omenn, G. S. & Zhang, Y. De novo RNA tertiary structure prediction at atomic resolution using geometric potentials from deep learning. Preprint at bioRxiv doi.org / 10.1101 / 2022.05.15.491755 (2022).

[0052] The computing system 102 can also include a nucleotide position computational pipeline 112 that determines a number of metrics and quantitative measures for individual positions included in RNA nucleotide sequences included in the RNA sequence data 106. The metrics and quantitative measures generated by the nucleotide position computational pipeline 112 for individual positions included in an RNA nucleotide sequence can be used to determine regions of the RNA nucleotide sequence that can be used in primer design and reverse transcription. For example, at operation 114, the nucleotide position computational pipeline 112 can generate quantitative measures for individual nucleotides of an RNA nucleotide sequence. To illustrate, the nucleotide position computational pipeline 112 can generate nucleotide pairing data 116. The nucleotide pairing data 116 can indicate, for individual positions of an RNA nucleotide sequence, a probability of the individual positions being paired with one or more additional positions of the RNA nucleotide sequence. In various examples, for a given RNA nucleotide sequence, the nucleotide pairing data 116 can be determined across a number of configurations of the RNA nucleotide sequence.

[0053] The nucleotide position computational pipeline 112 can also generate nucleotide accessibility data 118 for individual nucleotides of an RNA nucleotide sequence included in the RNA sequence data 106. The nucleotide accessibilitydata 118 can include quantitative measures that indicate the accessibility of an individual nucleotide for being coupled to a primer during the reverse transcription process. In at least some examples, the nucleotide accessibility data 118 can be determined based on a number of potential pairing states for individual nucleotides included in the RNA nucleotide sequence across a number of configurations of the RNA nucleotide sequence. In one or more illustrative examples, the nucleotide position computational pipeline 112 can generate at least one of the nucleotide pairing data 116 or the nucleotide accessibility data 118 using a partition function that can enumerate energetically feasible second structures and determine a Boltzmann-weighted probability for the individual configurations.

[0054] Additionally, the nucleotide position computational pipeline 112 can generate nucleotide thermodynamics data 120 for individual nucleotides of an RNA nucleotide sequence included in the RNA sequence data 106. The nucleotide thermodynamics data 120 can include a thermodynamic parameter indicating the energetic favorability of primer binding for a given position of an RNA nucleotide sequence. In various examples, the nucleotide position computational pipeline 112 can generate the nucleotide thermodynamics data 120 by determining Gibbs free energy of RNA-DNA hybridization for individual positions of an RNA nucleotide sequence.

[0055] Further, the nucleotide position computational pipeline 112 can generate positional reverse transcription (RT) data 122 for individual nucleotides of an RNA nucleotide sequence included in the RNA sequence data 106. The positional reverse transcription data 122 can indicate predicted favorability of initiating reverse transcription for individual nucleotides of the RNA nucleotide sequence. In at least some examples, the nucleotide position computational pipeline 112 can generate the positional reverse transcription data 122 based on the nucleotide pairing data 116, the nucleotide accessibility data 118, and the nucleotide thermodynamics data 120.

[0056] At operation 124, the nucleotide position computational pipeline 112 can generate quantitative measures for regions of the RNA nucleotide sequence by generating nucleotide region quantitative measures 126. The nucleotide region quantitative measures 126 can include a combination of the positional reverse transcription data 122 for a group of nucleotides included in an RNA nucleotidesequence. In one or more examples, the nucleotide region quantitative measures 126 can include an aggregation of the positional reverse transcription data 122 for a contiguous group of nucleotides included in an RNA nucleotide sequence. In one or more additional examples, the nucleotide region quantitative measures 126 can include an aggregation of the positional reverse transcription data 122 for a noncontiguous group of nucleotides included in an RNA nucleotide sequence. In various examples, the nucleotide region quantitative measures 126 can be determined by the nucleotide position computational pipeline 112 by aggregating positional reverse transcription data 122 for a plurality of groups of nucleotides included in an RNA nucleotide sequence. In at least some examples, individual groups of nucleotides for which the nucleotide region quantitative measures 126 are determined can be defined by a sliding window that traverses the RNA nucleotide sequence.

[0057] The computing system 102 can include a hybridization region identification system 128. The hybridization region identification system 128 can perform a computational analysis of the nucleotide region quantitative measures 126 to determine hybridization region data 130. The hybridization region data 130 can include regions of an RNA nucleotide sequence included in the RNA sequence data 106 that are favorable for reverse transcription reactions for the RNA nucleotide sequence. In one or more examples, the hybridization region identification system 128 can computationally analyze the nucleotide region quantitative measures 126 with respect to individual regions of nucleotides in relation to one or more criteria to determine the hybridization region data 130. In at least some examples, the one or more criteria can be different for different RNA nucleotide sequences included in the RNA sequence data 106. For example, the one or more criteria used by the hybridization region identification system 128 to computationally analyze a first RNA nucleotide sequence can be different from one or more additional criteria used by the hybridization region identification system 128 to analyze a second RNA nucleotide sequence. In various examples, the first RNA nucleotide sequence and the second RNA nucleotide sequence can be from different species or from different genera. In one or more illustrative examples, the hybridization region identification system 128 can determine the hybridization region data 130 based on rankings of the nucleotide regionquantitative measures 126. Additionally, the hybridization region identification system 128 can determine the hybridization region data 130 based on values of at least one of the nucleotide pairing data 116, the nucleotide accessibility data 118, the nucleotide thermodynamics data 120, or the positional reverse transcription data 122.

[0058] In one or more illustrative examples, the hybridization region data 130 can include start and end coordinates of the nucleotide region determined by the hybridization region identification system 128. The hybridization region data 130 can also include the nucleotide sequence of the region identified by the hybridization region identification system 128 and one or more suggested primer sequences that correspond to the identified coordinates. Additionally, the hybridization region data 130 can include optional probe sequences or partner primers. Further data generated by the computing system 102 can be accessible to users of the computing system 102. For example, metadata related to at least one of the nucleotide pairing data 116, the nucleotide accessibility data 118, the nucleotide thermodynamics data 120, or the positional reverse transcription data 122. In still other examples, quality indicators and / or confidence scores related to the hybridization regions determined by the hybridization region identification system 128 can also be output by the computing system 102. Data output by the computing system 102 can be accessible via one or more user interfaces. Data output by the computing system 102 can also be accessible by one or more data stores and / or data storage media. In one or more illustrative examples, the data output by the computing system 102 can be stored in a structured format such as JavaScript Object Notation (JSON), extensible markup language (XML), FASTA, and / or SEQ ID NO format.

[0059] The framework 100 can also include, at step 132, producing primers 134 based on the hybridization region data 130. In one or more examples, the hybridization region data 130 can include one or more segments of nucleotides of an RNA nucleotide sequence included in the RNA sequence data 106 indicated by the hybridization region identification system 128 as having one or more characteristics that are favorable for binding a primer. The one or more primers 134 can be produced by one or more enzymatic oligonucleotide synthesismethods. Additionally, the one or more primers 134 can be produced using one or more phosphoramidite-based solid phase oligonucleotide synthesis methods.

[0060] In various examples, the one or more primers 134 can have a length of at least 3 nucleotides, at least 5 nucleotides, at least 8 nucleotides, at least 10 nucleotides, at least 12 nucleotides, at least 15 nucleotides, at least 18 nucleotides, at least 20 nucleotides, at least 22 nucleotides, at least 25 nucleotides, at least 28 nucleotides, or at least 30 nucleotides. Additionally, the one or more primers can have a length no greater than 50 nucleotides, no greater than 48 nucleotides, no greater than 45 nucleotides, no greater than 42 nucleotides, no greater than 40 nucleotides, no greater than 38 nucleotides, no greater than 35 nucleotides, or no greater than 32 nucleotides. In one or more illustrative examples, the one or more primers 134 can have a length from 2 nucleotides to 50 nucleotides, from 5 nucleotides to 40 nucleotides, from 5 nucleotides to 35 nucleotides, from 5 nucleotides to 30 nucleotides, from 5 nucleotides to25 nucleotides, from 5 nucleotides to 20 nucleotides, from 5 nucleotides to 15 nucleotides, from 10 nucleotides to 40 nucleotides, from 10 nucleotides to 35 nucleotides, from 10 nucleotides to 30 nucleotides, from 10 nucleotides to 25 nucleotides, from 10 nucleotides to 20 nucleotides, from 20 nucleotides to 40 nucleotides, from 20 nucleotides to 35 nucleotides, from 20 nucleotides to 30 nucleotides, from 25 nucleotides to 40 nucleotides, from 25 nucleotides to 35 nucleotides, or from 30 nucleotides to 40 nucleotides.

[0061] Additionally, the framework 100 can include, at step 136, performing analyte detection using the one or more primers 134. In one or more examples, the one or more primers 134 can be added to a sample to bind to target molecules included in the sample that correspond to the one or more primers 134. At least a portion of the sample can then undergo an amplification process to produce an amplification product that includes amplicons of the target molecules that are bound to the one or more primers 134. The amplification product can be produced by subjecting at least a portion of the sample to one or more sequencing processes. The one or more sequencing processes can include one or more next-generation sequencing processes.

[0062] The one or more primers 134 can be used in diagnostic real-time polymerase chain reaction assays, including clinical, veterinary, environmental,and food microbiology applications. Additionally, the one or more primers 134 can be used in high-throughput screening platforms requiring scalable primer design for large RNA panels or genomic targets. Further, the one or more primers 134 can be used in the manufacturing of detection kits for viral, bacterial, fungal, or eukaryotic RNA targets. In still other examples, the one or more primers 134 can be used in next-generation sequencing (NGS) library preparation, particularly for RNA-based metagenomics or microbiome analyses. The one or more primers 134 can also be used in bioprocessing and industrial fermentation monitoring, where rapid RNA-based detection is implemented for contamination control. In addition, the one or more primers 134 can be used in research applications in transcriptomics, ribosome profiling, and RNA structure-function studies.

[0063] In various examples, the processes implemented by the framework 100 can be integrated into laboratory workflows to enabling efficient and reliable primer selection. In at least some examples, framework 100 can be deployed as a cloud service, integrated into laboratory software, embedded into automated PCR workflow systems, and / or incorporated into commercial assay development pipelines.

[0064] In one or more illustrative examples, The analyte detection performed at step 136 can be performed to identify the presence of E. coli in one or more samples using primers generated from one or more E. coli RNA sequences included in the RNA sequence data 106. Additionally, the analyte detection performed at step 136 can be performed to identify the presence of Lactobacillus spp.in one or more samples using primers generated from one or more Lactobacillus spp. RNA sequences included in the RNA sequence data 106. Further, the analyte detection performed at step 136 can be performed to identify the presence of Salmonella spp. in one or more samples using primers generated from one or more Salmonella spp. RNA sequences included in the RNA sequence data 106. In various examples, the analyte detection performed at step 136 can be performed to identify the presence of Listeria spp. in one or more samples using primers generated from one or more Listeria spp. RNA sequences included in the RNA sequence data 106. In still other examples, the analyte detection performed at step 136 can be performed to identify the presence of a number of microbes using RNA sequences included in the RNA sequence data selected from a groupcomprising: Pediococcus spp., Brettanomyces spp., Zygosaccharomyces spp., Saccharomyces cerevisiae var. diastaticus, Alicyclobacillus spp., Enterobacteria, Aspergillus spp.,Penicillium spp., Bacillus spp., Staphylococcus aureus, Bacillus cereus, Cronobacter sakazakii, Candida spp., Pseudomonas spp., Listeria monocytogenes, Pseudomonas aeruginosa, Burkholderia cepacian, V. cholerae, V.vulnificus, V.parahaemolyticus, one or more yeasts, one or more molds, or one or more combinations thereof.

[0065] Figure 2 illustrates an example framework 200 to generate metrics for individual nucleotides of an RNA sequence that can be used to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations. The framework 200 can include a number of components of the computing system 102 described with respect to Figure 1. For example, the framework 200 can include the structure generating system 108, the nucleotide position computational pipeline 112, and the hybridization region identification system 128. The structure generating system 108 can obtain the RNA sequence data 106. The RNA sequence data 106 can include an RNA nucleotide sequence 202 that includes a number of positions that correspond to an arrangement of nucleotides.

[0066] The structure generating system 108 can produce secondary structural representations 204 that correspond to secondary structures of the RNA nucleotide sequence 202. The secondary structural representations 204 can indicate two-dimensional structural configurations of the RNA nucleotide sequence 202 that include at least one of one or more stems, one or more loops, or one or more pseudoknots. In various examples, the secondary structural representations 204 can indicate tens, hundreds, thousands, up to millions of secondary structural configurations of the RNA nucleotide sequence 202. In addition, the structure generating system 108 can produce tertiary structural representations 206. The tertiary structural representations 206 can indicate three-dimensional structures of the RNA nucleotide sequence 202. For example, the tertiary structural representations 206 can indicate folding configurations of the RNA nucleotide sequence 202. In one or more illustrative examples, the tertiary structural representations 206 can indicate tens, hundreds, thousands, up to millions of tertiary structural configurations of the RNA nucleotide sequence 202. In one ormore examples, the secondary structural representations 204 and the tertiary structural representations 206 can correspond to the RNA structural data 110 described with respect to Figure 1.

[0067] The nucleotide position computational pipeline 112 can include a nucleotide pairing system 208 that generates quantitative measures and metrics related to individual nucleotides of the RNA nucleotide sequence 202. The nucleotide pairing system 208 can determine quantitative measures and metrics related to individual nucleotides of the RNA nucleotide sequence 202 based on at least one of the secondary structural representations 204 and the tertiary structural representations 206. In one or more examples, the nucleotide pairing system 208 can determine quantitative measures and metrics related to probability of individual nucleotides included in the RNA nucleotide sequence 202 pairing with at least one additional nucleotide of the RNA nucleotide sequence 202. For example, the nucleotide pairing system 208 can determine a nucleotide pairing probability 210 for individual nucleotides of the RNA nucleotide sequence 202. The nucleotide pairing probability 210 can indicate a probability that an individual nucleotide of the RNA nucleotide sequence 202 pairs with another nucleotide of the RNA nucleotide sequence 202.

[0068] In one or more illustrative examples, the nucleotide pairing system 208 can determine the nucleotide pairing probability 210 of a first nucleotide 212 of the RNA nucleotide sequence 202. The nucleotide pairing probability 210 for the first nucleotide 212 can be based on a number of pairing probabilities of the first nucleotide 212 with respect to other nucleotides of the RNA nucleotide sequence 202. In at least some examples, the nucleotide pairing probability 210 for the first nucleotide 212 can be determined based on a probability of the first nucleotide 212 pairing with each other nucleotide of the RNA nucleotide sequence 202. To illustrate, the nucleotide pairing probability 210 can be determined based on a number of base pairing probabilities, such as a first probability of a first pairing 214 between the first nucleotide 212 and a second nucleotide 216, a second probability of a second pairing 218 between the first nucleotide 212 and a third nucleotide 220, and a third probability of a third pairing 222 between the first nucleotide 212 and a fourth nucleotide 224.

[0069] The nucleotide pairing system 208 can also determine a nucleotide pairing state metric 226. The nucleotide pairing state metric 226 can indicate a number of different pairing states for individual nucleotides of the RNA nucleotide sequence 202. In at least some examples, the nucleotide pairing state metric 226 can correspond to a distribution of pairing states for the individual nucleotides of the RNA nucleotide sequence 202.

[0070] In one or more additional illustrative examples, the nucleotide pairing system 208 can determine an RNA secondary structure ensemble based on the secondary structural representations 204 using a partition-function-based algorithm. For example, RNA molecules exhibit complex two-dimensional secondary structures characterized by multiple helices, multi-branch loops, interior loops, bulges, and long-range interactions. These architectural features fluctuate across an ensemble of possible conformations rather than existing in a single, fixed fold. To accurately characterize this ensemble, the nucleotide position computational pipeline can compute an RNA partition function using a thermodynamic folding algorithm. Examples of thermodynamic folding algorithms can include the ViennaRNA package and the RNAstructure software. The partition function can enumerate at least a portion of the energetically feasible secondary structures and assigns each conformation a Boltzmann-weighted probability.

[0071] From the partition-function calculation, the method derives two ensemblelevel structural descriptors for each nucleotide position i: the nucleotide pairing probability 210, which can be referred to herein as the base-pairing probability Pbpi and the nucleotide pairing state metric 226, which can be referred to herein as the positional entropy Sposi. The base-pairing probability represents the likelihood that nucleotide i, such as the first nucleotide 212, is paired across all structures in the ensemble, while positional entropy quantifies the structural uncertainty at that position by measuring the distribution of alternative pairing states. Together, these parameters provide a quantitative description of local accessibility and structural variability, offering information beyond what can be inferred from a single predicted structure.

[0072] The advantages of using an ensemble of configurations to determine the nucleotide pairing probability 210 and the nucleotide pairing state metric 226 bythe nucleotide pairing system 208 can be indicated by Figure 3, which depicts an example of a two-dimensional (2D) secondary structure of a ribosomal RNA (rRNA) molecule from Escherichia coli. RNA. These RNA molecules exhibit complex two-dimensional secondary structures characterized by multiple helices, multi-branch loops, interior loops, bulges, and long-range interactions. These architectural features fluctuate across an ensemble of possible conformations rather than existing in a single, fixed fold. Figure 3 exemplifies the complexity of natural RNA secondary structures and illustrates the structural environment that the disclosed method analyzes computationally when determining base-pairing probabilities, positional entropy, RNA accessibility parameters, and downstream efficiency metrics. The depiction highlights the intrinsic multi-branch and multiloop organization of rRNA molecules, underscoring the need for automated, algorithmic analysis of thousands of potential structural interactions and accessibility states. Figure 3 shows secondary structures of the 16S rRNA of Escherichia coli (E. coli) as described in Williamson JR. Assembly of the 30S ribosomal subunit. Q Rev Biophys. 2005 Nov;38(4):397-403. The reference numbers indicate approximate positions of nucleotides that are numbered from the 5’ end to the 3’ end.

[0073] In addition, the advantages of using an ensemble of configurations to determine the nucleotide pairing probability 210 and the nucleotide pairing state metric 226 by the nucleotide pairing system 208 can be indicated by Figure 4, which depicts the three-dimensional tertiary fold of the 16S rRNA of E. coli. The figure illustrates the complex tertiary fold of the molecule, including its numerous helices, loops, and long-range interactions. This depiction illustrates the structural complexity that underlies RNA behavior and emphasizes that evaluating accessibility, entropy, and base-pairing probabilities requires computational analysis rather than manual inspection. Because tertiary interactions influence the pairing landscape indirectly through their impact on local secondary-structure populations, the use of ensemble-derived quantities Pbpi and Sposi is implemented for accurately estimating RNA accessibility. An example of the tertiary structure of E. Coli 16S rRNA can be found in Tung, Chang-Shung & Joseph, Simpson & Sanbonmatsu, Kevin. (2002). All-atom homology model of the Escherichia coli 30S ribosomal subunit. Nature structural biology. 9. 750-5. 10.1038 / nsb841.

[0074] The computation of Pbpi and Sposi requires evaluating thousands to millions of potential structures depending on sequence length, with time complexity on the order of O(n3) and memory complexity on the order of O(n2). It is not feasible for these computations to be performed manually and inherently require execution on one or more processors, ensuring the method is rooted in computational implementation rather than mental analysis. The resulting ensemble-derived metrics form the structural foundation for subsequent calculations of other quantitative measures and metrics that may be referred to herein as the RNA Accessibility Parameter (RAP), the Efficiency Reverse Transcription Score (ERTS), and the Region Reverse Transcription Score (RRTS).

[0075] In one or more examples, the nucleotide position computational pipeline 112 can include a nucleotide accessibility metric system 228. For individual nucleotides of the RNA nucleotide sequence 202, the nucleotide accessibility metric system 228 can generate a nucleotide accessibility metric 230 based on the nucleotide pairing probability 210 and the nucleotide pairing state metric 226 for the individual nucleotides. In various examples, the nucleotide accessibility metric 230 can correspond to the RNA Accessibility Parameter (RAPi) that provides a composite measure of the structural openness of nucleotide position i within the RNA molecule corresponding to the RNA nucleotide sequence 202. RAPi integrates ensemble-derived metrics to estimate the likelihood that a nucleotide is accessible for hybridization and can therefore support initiation of reverse transcription. In its primary form, RAPi is computed from (i) the base-pairing probability Pbp. representing the likelihood that position i is paired across the RNA ensemble, and (ii) the positional entropy Spos., quantifying the structural uncertainty and diversity of pairing states at that position. Positions with low pairing probability and high structural entropy exhibit higher accessibility and correspondingly higher RAP values.

[0076] In one or more illustrative examples, RAPi is defined according to a weighted function of these ensemble metrics, such as:RAPi = (1 “ Pbp^ ' (Spost)!3(Equation 1)where a and f> are weighting factors. In one or more examples, a and f> can be user-defined. In one or more additional examples, a and f> can be empirically determined for a given RNA nucleotide sequence 202, one or more RNA nucleotide sequences corresponding to one or more species, or one or more RNA nucleotide sequences corresponding to one or more genera.

[0077] Although, RAPi can be determined based on the illustrative example of Equation 1, RAPi can also be determined using other methods that integrate one or more ensemble-derived indicators of structural accessibility, local structure uncertainty, and / or local structural openness. In one or more additional examples, RAPi can be determined using probabilities of individual nucleotides of the RNA nucleotide sequence 202 being unpaired (PU) or using a measure of singlestranded propensity. In one or more additional examples, RAPi can be determined based on ensemble defect or expected base-pair distance for individual nucleotides of the RNA nucleotide sequence 202. In one or more further examples, RAPi can be determined using Shannon entropy variants and / or based on solventaccessibility estimates derived from 3D models. In still other examples, RAPi can be determined based on local structural diversity indices and / or machine-leaming-based accessibility predictors. In various examples, RAPi can be calculated directly from partition-function probabilities, stochastic sampling of structural ensembles, or hybrid ensemble methods. The ensemble computation required to obtain these metrics inherently involves evaluation of a large number of possible RNA structures and is unable to reasonably be performed manually.

[0078] In addition, the nucleotide position computational pipeline 112 can include a hybridization thermodynamics system 232. The hybridization thermodynamics system 232 can combine the nucleotide accessibility metric 230 and thermodynamics data 234 for individual nucleotides of the RNA nucleotide sequence 202 to generate a thermodynamics metric 236. In one or more examples, the thermodynamics data 234 can include Gibbs Free energy of hybridization for the individual nucleotides of the RNA nucleotide sequence 202. In at least some examples herein the thermodynamics metric 236 can correspond to ERTSi. For example, RAPi can be combined with thermodynamic hybridization energy (AGi) to yield an integrated predictor of primer-binding favorability at individual nucleotide positions of the RNA nucleotide sequence 202.

[0079] In at least some examples, to complement the structural accessibility estimate provided by RAPi, the nucleotide position computational pipeline 112 can determine the Gibbs free energy of RNA-DNA hybridization (AGi) at individual nucleotide positions i of the RNA nucleotide sequence 202. This thermodynamic parameter captures the energetic favorability of primer binding and provides an independent quantitative dimension that, when combined with structural accessibility, yields an accurate predictor of reverse-transcription efficiency.

[0080] In one or more examples, AGi can be determined using the nearest-neighbor thermodynamic model, such as parameter sets from SantaLucia, Turner, or equivalent hybridization models. These models quantify the stability of RNA-DNA duplex formation by evaluating at least one of dinucleotide stacking interactions, base pairing, helix initiation terms, or salt-concentration effects. AGi can be determined for single nucleotide positions, for each possible primer offset, or for sliding windows corresponding to one or more primer lengths.

[0081] In one or more additional examples, other thermodynamic estimation methods can be used by the nucleotide position computational pipeline 112 to determine the thermodynamics data 234. For example, the thermodynamics data 234 can be determined using modified nearest-neighbor parameter sets and / or empirical thermodynamic predictors. In still other examples, the thermodynamics data 234 can be determined based on salt-corrected hybridization functions and / or melting-temperature-based AG estimators. In various examples, the thermodynamics data 234 can be determined by implementing at least one of machine-leaming-derived RNA-DNA hybridization predictors or thermodynamic models calibrated for non-canonical bases or chemically modified primers.

[0082] The combination of AGi with RAPi is different from existing primerdesign tools that evaluate AG independently of structural accessibility and therefore identify regions of RNA sequences that are energetically favorable but structurally inaccessible. In contrast, the framework 200 uses AGi as a thermodynamic complement to RAPi, to determine regions of RNA sequences that are both energetically stable and structurally open as evidenced by the nucleotideposition computational pipeline 112 determining relatively high efficiency scores for these regions.

[0083] Computing AGi profiles across the full RNA nucleotides sequence 202 is performed by multiple iterations of evaluating thermodynamic models, often across thousands of possible hybridization positions. This computation must be performed by a computer, as it involves iterative evaluation of local sequence contexts and integration with ensemble-derived metrics. The thermodynamic modeling step therefore contributes directly to the algorithmic nature of the method and establishes that the disclosed workflow cannot be executed manually.

[0084] The resulting AGi values form the thermodynamic component of the Efficiency Reverse Transcription Score (ERTSi), in which AG and RAP are integrated to produce a per-nucleotide prediction of primer-binding favorability. The Efficiency Reverse Transcription Score (ERTSi) provides an integrated pernucleotide estimate of the likelihood that reverse transcription can successfully initiate at nucleotide position i. ERTSi combines the structural accessibility of a nucleotide (represented by RAPi) with the thermodynamic favorability of primer binding (represented by AGi). This dual integration of structural and energetic factors is a central feature of the disclosed method and enables accurate prediction of primer performance in highly structured RNA molecules.

[0085] In one or more examples, ERTSi is computed as a function of RAPi and AGi, such as:ERTS[=RAP[ ■ f ( Gi) (Equation 2)where f(AGi) is a thermodynamic weighting function that increases for more favorable (more negative) Gibbs free energies. In one or more illustrative examples, the thermodynamic weighting function can include at least one of one or more exponential weighting functions, one or more logistic weighting functions, one or more linear weighting functions, or one or more power-law transformations of AGi. Additional models that integrate structural accessibility with hybridization energetics can also be used for the thermodynamic weighting function.

[0086] In still other examples, ERTSi can be determined by a weighted combination of RAPi and AGi. ERTSi can be determined based on nonlinear relationships between accessibility and energetics. In various examples, ERTSi can be determined using machine-learning models trained on empirical RT efficiency datasets. Additional thermodynamic parameters, such as stacking energies, helix initiation penalties, and / or salt corrections, can also be used to determine ERTSi. Further, additional structural metrics, such as ensemble defect, solvent accessibility, and / or 3D proximity data, can be used to determine ERTSi.

[0087] ERTSi therefore represents a flexible yet structured framework for quantifying the local suitability of each nucleotide for primer-mediated reverse transcription. The calculation of ERTSi requires processor-based integration of ensemble-derived variables and thermodynamic models across potentially thousands of sequence positions. Because the ERTSi profile results from iterative computation of data-derived accessibility metrics and energy functions, the method cannot be performed manually, reinforcing its computational nature.

[0088] The nucleotide position computational pipeline 112 can include a reverse transcription (RT) likelihood system 238 that determines regional reverse transcription metrics 240 based on the thermodynamics metrics 236 for a number of individual nucleotides of the RNA nucleotide sequence 202. In one or more examples, the reverse transcription likelihood system 238 can determine the regional reverse transcription metrics 240 for groups of continuous nucleotides of the RNA nucleotide sequence 202 included in a sliding window 242. In various examples, the sliding window 242 can include a number of nucleotides that corresponds to a number of nucleotides included in primers that can be designed using the framework 200. In at least some examples, the sliding window 242 can traverse the RNA nucleotide sequence 202 at a specified intervals. For example, with each iteration of computations performed by the reverse transcription likelihood system 238, the sliding window 242 can shift by at least one nucleotide, at least two nucleotides, at least three nucleotides, at least four nucleotides, at least five nucleotides, at least eight nucleotides, or at least ten nucleotides along the RNA nucleotide sequence 202. In one or more illustrative examples, the sliding window 242 can traverse the RNA nucleotide sequence 202 from a 3’ end to a 5’end. In one or more additional illustrative examples, the sliding window 242 can traverse the RNA nucleotide sequence 202 from a 5’ end to a 3’ end.

[0089] ERTSi constitutes the per-base foundation for the Region Reverse Transcription Score (RRTSj). While RAP and AG characterize local structural and energetic properties, ERTS synthesizes these parameters into a single integrated predictor of initiation efficiency. By aggregating ERTS values across windows of length W, the framework 200 can be implemented to determine extended regions appropriate for primer placement and determines the Minimum Initiation Subregion (MIS) required to initiate reverse transcription.

[0090] The Region Reverse Transcription Score (RRTSj) provides a regional measure of the predicted reverse-transcription efficiency for a contiguous segment of the RNA beginning at position). Whereas ERTSi quantifies local favorability at individual nucleotide positions, RRTSj aggregates these values across a defined window length W to identify extended regions that collectively support efficient primer binding and extension.

[0091] In one or more examples, RRTSj can be determined by aggregating the ERTSi values across a sliding window of width W nucleotides, such as the sliding window 242:RRTSj = i = jj+W~1ERTSi(Equation 3)The window W can correspond to the minimum primer length, an experimentally determined initiation region, or any suitable aggregation interval. In various examples, the window W can include larger or smaller numbers of nucleotides than the minimum primer length. Additionally, the window W can be overlapping or non-overlapping with respect to groups of nucleotides included in the RNA nucleotide sequence 202. Further, the window W can have variable lengths or adaptive region sizes. In at least some examples, the length of the sliding window 242 can be based on features of an organism from which the RNA nucleotide sequence 202 is derived. For example, the length of the sliding window 242 can be based on at least one of a species or genera of an organism from which the RNA nucleotide sequence 202 is derived.

[0092] The window-based aggregation of regional reverse transcriptase thermodynamics metrics 236 can transform the per-nucleotide landscape into aregional efficiency profile, revealing extended segments that maintain consistently high scores rather than isolated favorable nucleotides.

[0093] In one or more additional examples, RRTSj may alternatively be determined using weighted sums of ERTSi values. In various examples, the RRTSj values can be determined using moving averages as the sliding window 242 moves across the RNA nucleotide sequence 202. In still other examples, the reverse transcription likelihood system 238 can determine RRTSj values based on at least one of geometric or harmonic means or ERTSi values. In one or more further examples, the reverse transcription likelihood system 238 can determine RRTSj values using nonlinear or machine-learning aggregation models. In addition, the RRTSj values can be determined based on percentile-based or rank-based aggregation of ERTSi values. The RRTSi values can also be determined using contiguous-but-non-linear windows (e.g., excluding structurally hindered sites).

[0094] In one or more examples, the regional reverse transcription metrics 240 can be computationally analyzed by the hybridization region identification system 128 to determine regions of the RNA nucleotide sequence 202 that can form the basis for primer design with respect to the RNA nucleotide sequence 202. In various examples, the hybridization region identification system 128 can apply a regional threshold to the regional reverse transcription metrics 240, such as the RRTS profile, to distinguish optimal from suboptimal regions. A region is considered favorable when its RRTSj value exceeds the threshold for at least the minimum number of consecutive positions required to identify a functional initiation region.

[0095] In one or more illustrative examples, the threshold can be an absolute value for RRTS. In one or more additional illustrative examples, the threshold can be determined relative to the median or mean RRTS. In one or more further illustrative examples, the threshold can be a percentile-based threshold. For example, the threshold can be based on the regions having the highest RRTS values, such as the top 1% of regions, the top 5% of regions, the top 10% of regions, the top 15% of regions, or the top 20% of regions. In still other examples, the threshold can be determined dynamically for individual RNA target molecules. In various examples, the threshold can be determined based on distributions of at least one of ERTS or RAP values. The use of a threshold by the hybridizationregion identification system 128 can provide an objective and reproducible method for automatically identifying regions suitable for primer binding.

[0096] Regions determined by the hybridization region identification system 128 having RRTSj values that meet or exceed the threshold correspond to segments exhibiting both structural accessibility and favorable hybridization energetics across an extended region. These segments are designated as potential regions for primer-binding site selection. RRTSj therefore serves as a region-level efficiency predictor, integrating the combined contributions of structural ensemble characteristics and hybridization thermodynamics across a multi-nucleotide interval.

[0097] Computing RRTSj across an RNA molecule requires iterative aggregation of ERTSi values at each nucleotide offset, often numbering thousands of possible windows. These operations are implemented by electronic computation and are unable to be performed manually, reinforcing that the operations performed with respect to the framework 200 are to be executed by one or more processors

[0098] RRTSj can be used by the hybridization region identification system to determine extended, high-efficiency regions and serves as the precursor to identifying a minimum initiation subregion (MIS). In at least some examples, the MIS can be included in the hybridization region data 130 produced by the hybridization region identification system 128. While ERTSi captures local efficiency, RRTSj identifies broader regions capable of supporting robust initiation of reverse transcription and thereby directly informs the selection of primer-binding sites.

[0099] The Minimum Initiation Subregion (MIS) can represent a smallest contiguous or non-contiguous subset of nucleotide positions within a high-RRTS region that is sufficient to initiate productive primer binding and reverse transcription. While RRTSj identifies extended segments of the RNA that are globally favorable, the MIS captures the local core of the initiation process — the minimal structural and thermodynamic requirements necessary for a primer to successfully anneal and extend.

[0100] As shown in Figure 5, a region may exhibit high RRTS values but include a limited sub-interval that is favorable to trigger hybridization and extension. The plot displays ERTS values as a function of nucleotide position,with a dashed horizontal line representing the ERTS threshold. A contiguous window of ERTS values exceeding this threshold is indicated as being “bigger than MIS,” meaning that this segment is sufficiently long and accessible to support efficient reverse-transcription initiation. The MIS corresponds to this minimal functional unit. It is defined by selecting the shortest subset of nucleotide positions whose ERTSi values exceed a predetermined initiation threshold, such that the aggregate initiation requirement is satisfied.

[0101] In one or more examples, the MIS is computed by scanning the high-RRTS region for the shortest consecutive sequence of positions where:^init (Equation 4)where Tinit is an initiation threshold distinct from — or derived from — the RRTS regional threshold. By using Tinit, the MIS can capture the initiation-driving nucleotides within a broader favorable region.

[0102] In various examples, the MIS can include a contiguous group of nucleotides of the RNA nucleotide sequence 202. In one or more additional examples, the MIS can include a non-contiguous group of nucleotides of the RNA nucleotide sequence 202. In scenarios where the MIS includes a non-contiguous group of nucleotides, one or more structurally obstructed positions in a region of the RNA nucleotide sequence 202 can be excluded. In various examples, the size of the MIS window can have a variable length for different RNA nucleotide sequences. In these situations, the MIS window can be determined based on distributions of ERTS values. In still other examples, the hybridization region data 130 can include multi-segment MIS regions. In at least some examples, multisegment MIS regions can be determined for RNA molecules with complex local accessibility patterns. In one or more further examples, the MIS can be determined based on percentile-based ERTS cutoffs or machine-leaming-optimized thresholds. In one or more instances, the methods and processes implemented by the hybridization region identification system 128 can determine a minimal effective region even in situations where structural accessibility is unevenly distributed.

[0103] The hybridization region identification system 128 can determine boundaries for the MIS by identifying a smallest number of nucleotides meetingthe initiation condition. Additionally, the hybridization region identification system 128 can determine the boundaries of the MIS by selecting positions with ERTS values above a high-efficiency percentile. Further, the hybridization region identification system 128 can determine the MIS by determining a contiguous region of peak accessibility within a high-RRTS window. The hybridization region identification system 128 can also optimize MIS length relative to primer design constraints (e.g., minimum anchoring bases). In one or more illustrative examples, the MIS length can be at least 6, 7, 8, 9, 10, 11, 12, 13, 14 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or 25 nucleotides. The length of the MIS can be based on reaction conditions, primer chemistry, and RNA structural context.

[0104] The MIS provides a quantitative and experimentally validated measure of the minimal nucleotide requirement for efficient initiation, thereby enabling automated, scalable, and highly reliable primer design. While a high RRTS region ensures overall suitability for primer placement, the MIS identifies the precise nucleotides to be included within a primer to enable reliable initiation of reverse transcription. In one embodiment, any primer designed for the region must overlap with the MIS to ensure efficient binding. Thus: RRTSj identifies the region of interest and MIS identifies the minimal portion that governs initiation. Primer-binding sites can be selected to fully or partially overlap the MIS.

[0105] Determining the MIS requires iterative evaluation of ERTSi values within each high-RRTS value region and application of thresholding algorithms to identify minimal functional subsets. These operations are performed using processor-based computation and are unable to be performed manually due to the number of potential subregions and the combinatorial nature of ERTS distribution across structured RNA molecules.

[0106] Once the optimal region and its corresponding Minimum Initiation Subregion (MIS) have been identified, one or more primer-binding regions suitable for reverse transcription and subsequent amplification can be determined. This step translates the computational outputs (ERTSi, RRTSj, MIS boundaries) into actionable primer-design coordinates that can be used directly in RT or RT-PCR assays. The primer-binding region is selected such that it fully or partially overlaps the MIS, ensuring that the primer incorporates the minimal nucleotide set required for efficient initiation. In one or more examples, the primer-bindingregion begins upstream or downstream of the MIS by a variable offset, allowing flexibility in primer length and positioning while preserving overlap with the essential initiation core. The primer-binding region can also be determined based on minimum and / or maximum primer lengths that can be different from the MIS length. Additionally, the primer binding region can be determined based on melting-temperature ranges for the primers. Further, the primer binding region can be determined based on GC content limits. In still other examples, the primer binding region can be determined by avoiding regions having a threshold number of consecutive nucleotides of the same type (e.g., homopolymeric runs) or repetitive motifs. The primer binding region can also be determined by avoiding regions that can result in predicted primer-dimer or hairpin structures. In addition, the primer binding region can be determined based on compatibility with target assay chemistry (e.g., hydrolysis probes, intercalating dyes, modified nucleotides). These criteria can be applied through rule-based filters, scoring functions, or machine-learning predictors.

[0107] In implementations that use two primers (forward and reverse) and an optional probe, the framework 200 can be repeated with respect to the RRTS / MIS analysis on the complementary strand or opposite direction of the RNA molecule. In one or more additional examples, the method may select the partner primer using sequence-based heuristics while ensuring that the MIS-overlapping primer is the initiation-region component. For probe-based assays (e.g., TaqMan), a probe-binding region can be determined such that the probebinding region is located downstream of the primer-binding region while avoiding structured domains or regions with low RAP or ERTS values.

[0108] In various examples, multiple candidate primers can be determined that are ranked by a composite score. The composite score can be determined based on overlap with MIS. Additionally, the composite score can be determined based on aggregate ERTS or RRTS values for the primer region. Further, the composite score can be determined based on AG stability. In still other examples, the composite score can be determined according to a predicted absence of secondary structures. The composite score can also be determined based on assayspecific constraints (e.g., amplicon length requirements). The ranking of primer candidates can enable fully automated primer selection. Determination of primer-binding regions requires integration of the MIS boundaries, RRTS profde, sliding-window calculations, and thermodynamic and sequence-based constraints. These operations are performed electronically and are unable to be executed manually due to the number of possible offsets, sequence permutations, and structural conformations involved.

[0109] The identification and output of the primer-binding region provides the actionable design parameters needed to synthesize primers that target structurally accessible, thermodynamically favorable, and experimentally validated regions of an RNA molecule. This enables rapid, reliable, and scalable primer selection for use in reverse-transcription and PCR-based detection assays. In at least some examples, data generated by the framework 200 can be accessible by an application programming interface (API) or graphical user interface (GUI) enabling. In one or more examples, the API and / or graphical user interfaces can enable users to upload RNA sequences. Additionally, the API and / or graphical user interfaces can enable users to visualize quantitative measures and metrics, such as Pbp, Spos, RAP, ERTS, and RRTS profdes. The API and / or graphical user interfaces can also enable users to view and inspect MIS boundaries and / or review automatically generated primer candidates. In still other examples, the API and / or graphical user interfaces can enable the export of results of the framework 200 to laboratory information systems or primer-ordering platforms. In one or more further examples, the framework 200 can integrate with laboratory automation platforms for end-to-end assay development, enabling rapid experimental validation of computationally predicted primers. Execution of the framework 200 is performed by processor-based computation due to the large number of ensemble states, thermodynamic evaluations, and sliding-window operations involved. These computations are unable to be performed manually. The system and medium therefore provide a technical effect by enabling automated identification of optimal primer-binding regions that produce experimentally validated improvements in reverse-transcription efficiency.

[0110] The frameworks 100 and 200 provide a concrete technical effect by enabling the accurate identification of RNA regions that support efficient primer hybridization and reverse-transcription initiation. By integrating RNA structural ensemble parameters (base-pairing probability and positional entropy)with thermodynamic hybridization energy (AG) into a unified scoring system (RAP —> ERTS —> RRTS), the method produces a quantitative prediction of initiation efficiency that was not achievable using existing techniques. The technical effects achieved by the frameworks 100 and 200 include improved prediction of primer-RNA hybridization success, derived from the integration of ensemble-derived accessibility and per-nucleotide AG values. Additionally, the frameworks 100 and 200 provide accurate localization of extended RNA segments that facilitate reverse-transcription initiation, based on regional aggregation of per-nucleotide efficiency scores (RRTS). Further, the frameworks 100 and 200 identify a Minimum Initiation Subregion (MIS), representing a minimal nucleotide subset for efficient primer engagement. The frameworks 100 and 200 also provide enhanced sensitivity and lower Ct values in RT-PCR assays, as experimentally demonstrated in Example 4 described below. In still other examples, the frameworks 100 and 200 provide robustness across RNA molecules with complex secondary and tertiary structure, including rRNA, viral RNA, and long non-coding RNA. These effects provide measurable improvements in the detection of analytes, including faster amplification, higher sensitivity, more consistent primer performance, and improved detection in low-RNA or partially degraded samples. The workflow therefore produces a tangible and reproducible technical improvement over existing primer-design methodologies.

[0111] The methodology described above provides a systematic and quantitative approach to identifying optimal RNA regions for efficient reverse transcription and amplification. By introducing the RNA Accessibility Parameter (RAP), the Efficiency Reverse Transcription Score (ERTS), and the Region Reverse Transcription Score (RRTS) — together with the Minimum Binding Region Determination — the implementations described herein provide advantages with respect to the limitations of existing primer design strategies. Through the integration of structural accessibility, thermodynamic stability, and regional scoring, implementations described herein achieve sensitivity, reproducibility, and predictive power in RT-PCR assay development, that are not found in existing techniques, particularly when dealing with highly structured RNA molecules.

[0112] The implementations described herein produce a technical effect by enabling the accurate identification of RNA regions that support efficientreverse transcription and primer-mediated amplification. This technical effect can be based on the combination of one or more methods and processes described herein, such as ensemble-based structural metrics (Pbp, Spos), thermodynamic hybridization energy (AG), and regional aggregation scoring (ERTS and RRTS), and the identification of a Minimum Initiation Subregion (MIS). Unlike existing primer-design heuristics, this integrated approach predicts experimentally measurable improvements in cDNA yield and amplification efficiency. The implementations described herein thus improve laboratory performance in molecular detection assays.

[0113] The implementations described herein are industrially applicable to fields requiring sensitive and reliable detection of RNA, including clinical diagnostics, pathogen detection, environmental monitoring, food-safety testing, industrial fermentation, biodefense, and research assay development. The computational pipeline enables rapid design of primers for diverse RNA targets, supports high-throughput processing of multiple sequences, and integrates seamlessly into automated assay-development workflows. As the output of the methods and processes directly determines primer sequences used in biochemical reactions, the implementations described herein provide reproducible and scalable improvements to molecular testing workflows in industrial, clinical, and research settings.

[0114] The implementations described herein provide an unexpected advantage over existing technologies in that the predicted optimal regions produce reverse-transcription primers with dramatically improved amplification performance, even when existing primer-design parameters such as GC content, melting temperature, sequence length, and AG do not differ substantially between the improved and baseline primer sets. This demonstrates that the disclosed integration of ensemble-derived structural metrics and thermodynamic modeling captures determinants of reverse-transcription efficiency that are neither recognized nor predictable by existing techniques.

[0115] The implementations described herein are applied to biological macromolecules and produce a concrete, real-world result: identification of primer-binding regions suitable for laboratory use. The method is therefore not an abstract idea but a specific technical solution to the problem of inefficient reversetranscription in structured RNA molecules. The output of the implementations described herein is used directly in a tangible laboratory procedure — namely, the design of primers and probes for initiating reverse transcription and PCR amplification. The computational results are thus applied to a concrete biotechnological process.

[0116] In certain embodiments, the implementations described herein provide primers, primer pairs, and probes that have been identified using computational methods and processes. A “forward primer” binds to the antisense (template) strand and copies the sense strand, while the “reverse primer” binds to the sense (non-template) strand and copies the antisense strand, working from opposite ends to define the target region. For example, in one or more examples, a forward primer comprises a nucleotide sequence as set forth in SEQ ID NO: 4 and a reverse primer comprises a nucleotide sequence as set forth in SEQ ID NO: 5, the primers being configured to prime reverse transcription and amplification of a region of the 23 S rRNA of Escherichia genus. In various examples, the primer pair is used in combination with a hydrolysis probe comprising a nucleotide sequence as set forth in SEQ ID NO: 6.

[0117] In one or more additional examples, primers and probes designed by the implementations described herein include variants having at least 90%, at least 95%, or at least 98% sequence identity to SEQ ID NO: 4, SEQ ID NO: 5, SEQ ID NO: 6, or SEQ ID NO: 4-6, provided that such variants retain the ability to specifically hybridize to the corresponding target region and support efficient reverse transcription and amplification under standard reaction conditions. The stringency during hybridization is known to be a function of temperature, salt concentration, primer strand length, GC content of the nucleotide sequence of the primer and the concentration of the chaotropic agent in the hybridization buffer. As the stringent conditions, the conditions described in Sambrook, J. et al. (1998) Molecular Cloning: A Laboratory Manual (2nd ed.), Cold Spring Harbor Laboratory Press, New York and the like can be used. The stringent temperature condition is not less than about 30°C., more preferably not less than about 37°C., most preferably not less than about 42°C. Other conditions include hybridization time, concentration of washing agents (e.g., SDS), presence or absence of carrierDNA and the like, and various stringencies can be determined by combining these conditions.

[0118] The primers and probes described herein may be supplied individually, as primer pairs, or as part of a kit further comprising one or more of: a reverse transcriptase, a DNA polymerase, reaction buffers, dNTPs, and instructions for performing reverse-transcription PCR or real-time PCR using the primers and / or probes.

[0119] The primer or probe is a nucleic acid, and the nucleic acid is preferably a single-stranded nucleic acid. “Nucleic acid” means a molecule in which a number of nucleotides are polymerized in a nucleotide sequence, for example, in DNA, RNA and / or a polymer of RNA and DNA. Nucleotides come in two main types (purines and pyrimidines) and carry bases like Adenine (A), Guanine (G), Cytosine (C), Thymine (T in DNA), and Uracil (U in RNA). The length of each primer or probe is not particularly limited as long as each primer can specifically recognize the corresponding specific recognition region, and hybridization between primers does not occur. The length of each primer is can be 15 bases or more and 40 bases or less. In at least some examples, the lower limit of each primer length is 16 bases or more, 17 bases or more, or 18 bases or more. In addition, the upper limit of each primer length can be 39 bases or less, 38 bases or less, or 37 bases or less.

[0120] The primer or probe can be produced by one or more chemical synthesis methods. For example, primers and / or probes can be produced using an enzyme such as nuclease and the like, or can also be produced using a commercially available DNA / RNA automatic synthesizer (Applied Biosystems, Beckman Instruments etc.). In these primers or probes, the constituting nucleic acid can be further modified freely. For example, in the primer or probe, the 5'-terminal or 3 '-terminal can contain a labeling substance (e.g., fluorescent molecule, dye molecule, radioisotope, organic compound such as digoxigenin or biotin, and the like) and / or an addition sequence (loop primer part used in LAMP method and the like) to facilitate detection or amplification of the primer. The primer or probe can be phosphorylated or aminated at the 5 '-terminal. The primer or probe can contain only natural bases or can include one or more modified bases. Examples of a modified base include, but are not limited to, deoxyinosine,deoxy uracil, phosphorothioated base and the like. Furthermore, the primer or probe can contain any oligonucleotide derivative containing a phosphorothioate bond, a phophoroamidate bond and the like, or can contain peptide-nucleic acid (PNA) containing a peptide nucleic acid bond.

[0121] The primer or probe can be isolated or purified. Being “isolated or purified” means that an operation to eliminate components other than the object component from a natural or synthesized state is applied. The purity of the isolated or purified primer or probe (percentage of target primer or probe contained in total nucleic acid) in (w / w) % is generally not less than 50%, preferably not less than 70%, more preferably not less than 90%, most preferably not less than 95% (e.g., 100%). The purity of the primer or probe can be appropriately changed according to the solvent and the state of solid or liquid. The unit of the purity can be (w / v) % or (v / v) %, and the desirable purity can be calculated as appropriate, taking into consideration the above-mentioned definition of purity in (w / w) %.

[0122] These primers and probes can be provided as a solid in a dry state or in the state of alcohol precipitation, or can also be provided by being dissolved in water or a suitable buffer (e.g., TE buffer and the like).

[0123] Figure 6 is a flow diagram of an example process 600 to identify regions of RNA molecules that can be sites for hybridization in reverse transcription processes, in accordance with one or more example implementations. In at least some examples, the operations performed with respect to the process 600 can be implemented by the frameworks 100 and 200 described in relation to Figures 1 and 2, respectively.

[0124] The process 600 can include, at operation 602, receiving an input RNA sequence of interest. The RNA sequence of interest can correspond to an RNA molecule. In one or more examples, the RNA molecule can include ribosomal RNA, viral RNA, bacterial RNA, eukaryotic mRNA, or long noncoding RNA.

[0125] The process 600 can also include, at operation 604, computing the RNA secondary-structure ensemble using a partition-function-based algorithm. From this ensemble, the process 600 can proceed to operation 606 to generate derives base-pairing probabilities (Pbpi) and positional entropy (Spos) for each nucleotide position i, characterizing the structural accessibility and uncertaintyinherent to the RNA. These ensemble-derived parameters form the structural foundation upon which subsequent scoring calculations are performed.

[0126] At each nucleotide position, the process 600 next computes, at operation 608, the RNA Accessibility Parameter (RAPi), a composite metric reflecting the likelihood that the nucleotide is structurally available for hybridization. In one or more examples, RAPi can be computed as a weighted function of (1 -Pbpi) and Spos.. In one or more additional examples, RAPi can comprise at least one of: unpaired probability, ensemble defect, Shannon entropy, solvent accessibility, or a machine-leaming-based accessibility score. In various examples, RAPi can be computed and used to identify a primer-binding region without computing AGi.

[0127] Thermodynamic contributions are then incorporated into the process 600, at operation 610, by calculating the RNA-DNA hybridization Gibbs free energy (AG) for each position using a nearest-neighbor model or equivalent thermodynamic predictor. In various examples, AGi can also be predicted by a machine-learning model.

[0128] The structural and thermodynamic parameters are integrated to produce the Efficiency Reverse Transcription Score (ERTSi) at operation 612, which quantifies the predicted favorability of initiating reverse transcription at nucleotide i. The ERTSi can be computed using a nonlinear integration of RAPi and AGi. Additionally, ERTSi can be computed using a model trained on reversetranscription efficiency data without direct AG calculation.

[0129] The ERTSi values are subsequently aggregated, at operation 614, across a sliding window of length W to compute the Region Reverse Transcription Score (RRTSj) for each candidate region starting at position). This regional score identifies extended segments that maintain consistently high reverse-transcription efficiency. In one or more examples, RRTSj can be computed using a sliding window of length between 4 and 40 nucleotides. In one or more additional examples, RRTSj can be computed using a nonlinear aggregation of ERTSi values such as a geometric mean, harmonic mean, or percentile-based function. In one or more further examples, ERTSi can be computed without normalizing for primer length, thereby covering implementations that omit length-dependent corrections.

[0130] A regional threshold is then applied, at operation 616, to RRTSj values to identify optimal regions for primer binding. Within each region exceeding the threshold, determines the Minimum Initiation Subregion (MIS), defined as the smallest contiguous or non-contiguous set of nucleotides whose ERTSi values collectively satisfy an initiation requirement sufficient to trigger robust reverse transcription. In one or more examples, the MIS can comprise a contiguous subregion of an RNA nucleotide sequence. In one or more additional examples, the MIS can comprise a non-contiguous subset of nucleotide positions of an RNA nucleotide sequence. In at least some examples, multiple candidate primer-binding regions can be ranked based on RRTSj, MIS size, AGi, or primer design constraints. In one or more additional examples, MIS can be determined as the smallest subset of nucleotides for which ERTSi exceeds an initiation threshold independent of the window-based RRTS calculation. In one or more further examples, MIS can be computed using a machine-learning classifier trained on experimentally validated initiation regions.

[0131] At operation 618, the process 600 includes determining the efficiency of the nucleotide region, such as a primer binding region, for primer-mediated amplification. In one or more examples, the nucleotide region that overlaps at least part of the MIS. The primer-binding region can be used to design a primer, a probe, or both. In one or more examples, the primer-binding region is used to design primers for reverse-transcription quantitative PCR (RT-qPCR), digital PCR, LAMP, or RNA amplification In various examples, operation can be optional and the outputted primer-binding region can be determined based on RAPi without the use of RRTSj. In still other examples, operation can be optional and the primer-binding region is determined based on ERTSi without requiring computation of RRTSj. In one or more illustrative examples, MIS can be computed based on ERTSi without using RRTSj At least one primer comprising a nucleotide sequence overlapping the identified region can be used to design a primer that is configured for laboratory reverse transcription processes.

[0132] The primer-binding region can be selected by maximizing RAPi, ERTSi, or RRTSj individually or in combination. Additionally, the primer-binding region encompasses nucleotides corresponding to a top-ranked RAPi region, thereby covering primer selection based solely on RNA accessibility. Further, theprimer-binding region can be selected using ERTSi values even when RAPi values are not explicitly reported to the user. The primer-binding region can also selected using a version of RRTS computed using variable window sizes, adaptive windows, or windows of unequal length. In at least some examples, MIS can be defined as any subset of contiguous or non-contiguous nucleotides whose aggregate ERTSi value exceeds an initiation threshold, thereby covering alternative MIS definitions. MIS can also be computed by integrating both structural ensemble descriptors and RNA-DNA hybridization thermodynamics, and no prior accessibility measure may be used to independently identify the MIS.

[0133] In still other examples, RAP, ERTS, or RRTS may not be computed by any single-parameter accessibility metric selected from the group consisting of unpaired probability, ensemble defect, minimum free energy structure, or AG-only windows. In at least some examples, RRTSj can identify a region that could not be detected using AG-only or unpaired-probability-only methods. In various examples, the combination of RAP, ERTS, RRTS, and MIS can produce an experimentally measurable reduction in Ct value relative to primers selected using existing methods.

[0134] In one or more examples, the process 600 can be used to synthesize a primer comprising the nucleotide sequence of SEQ ID NO:4. In one or more additional examples, the process 600 can be used to synthesize a primer comprising the nucleotide sequence of SEQ ID NO:5. In one or more further examples, the process 600 can be used to synthesize a probe comprising the nucleotide sequence of SEQ ID NO:6. In various examples, the process 600 can be used to synthesize a primer pair comprising SEQ ID NO:4 and SEQ ID NO:5. In still other examples, the process 600 can be used to synthesize a primer-probe set comprising SEQ ID NO:4, SEQ ID NO:5, and SEQ ID NO:6. In one or more illustrative examples, a sample can be contacted with a primer pair comprising SEQ ID NO:4 and SEQ ID NO:5; reverse transcription and amplification can be performed; and detecting amplification using a probe comprising SEQ ID NO:6 can be performed. In one or more additional illustrative examples, 23 S rRNA of Escherichia coli can be detected using a kit comprising a primer comprising SEQ ID NO:4, a primer comprising SEQ ID NO:5, and a probe comprising SEQ ID NO:6; optionally together with buffers, enzymes, or instructions. Escherichia spp.(including E. coli) 23S rRNA can also be detected using a primer comprising SEQ ID NO:4, SEQ ID NO:5, or SEQ ID NO:6.

[0135] Figure 6 illustrates the computational flow from structural ensemble analysis to MIS identification. Once an optimal region and its MIS are identified, the method outputs the nucleotide coordinates and sequence of the recommended primer-binding region. These computational results may be used directly to design primer and probe sequences for reverse transcription and PCR amplification. Because the workflow integrates structural, thermodynamic, and regional scoring information, it provides a quantitative and experimentally validated prediction of primer performance that surpasses existing sequence-based methods.

[0136] Figure 7 illustrates a diagrammatic representation of a machine in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example implementation. Figure 7 illustrates a diagrammatic representation of a computing device 700 in the form of a computer system within which a set of instructions may be executed for causing the computing device 700 to perform any one or more of the methodologies discussed herein, according to an example, according to an example implementation. Specifically, Figure 7 shows a diagrammatic representation of the computing device 700 in the example form of a computer system, within which instructions 702 (e.g., software, a program, an application, an applet, an app, or other executable code) for causing the computing device 700 to perform any one or more of the methodologies discussed herein may be executed. For example, the instructions 702 may cause the computing device 700 to implement the frameworks 100, 200, described with respect to Figures 1 and 2, respectively, and to execute the process 600 described with respect to Figure 6.

[0137] The instructions 702 transform the general, non-programmed computing device 700 into a particular computing device 700 programmed to carry out the described and illustrated functions in the manner described. In alternative implementations, the computing device 700 operates as a standalone device or may be coupled (e.g., networked) to other machines. In a networked deployment, the computing device 700 may operate in the capacity of a servermachine or a client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The computing device 700 may comprise, but not be limited to, a server computer, a client computer, a personal computer (PC), a tablet computer, a laptop computer, a netbook, a set-top box (STB), a personal digital assistant (PDA), an entertainment media system, a cellular telephone, a smart phone, a mobile device, a wearable device (e.g., a smart watch), a smart home device (e.g., a smart appliance), other smart devices, a web appliance, a network router, a network switch, a network bridge, or any machine capable of executing the instructions 702, sequentially or otherwise, that specify actions to be taken by the computing device 700. Further, while only a single computing device 700 is illustrated, the term “machine” shall also be taken to include a collection of computing devices 700 that individually or jointly execute the instructions 702 to perform any one or more of the methodologies discussed herein.

[0138] Examples of computing device 700 can include logic, one or more components, circuits (e.g., modules), or mechanisms. Circuits are tangible entities configured to perform certain operations. In an example, circuits can be arranged (e.g., internally or with respect to external entities such as other circuits) in a specified manner. In an example, one or more computer systems (e.g., a standalone, client or server computer system) or one or more hardware processors (processors) can be configured by software (e.g., instructions, an application portion, or an application) as a circuit that operates to perform certain operations as described herein. In an example, the software can reside (1) on a non-transitory machine readable medium or (2) in a transmission signal. In an example, the software, when executed by the underlying hardware of the circuit, causes the circuit to perform the certain operations.

[0139] In an example, a circuit can be implemented mechanically or electronically. For example, a circuit can comprise dedicated circuitry or logic that is specifically configured to perform one or more techniques such as discussed above, such as including a special-purpose processor, a field programmable gate array (FPGA) or an application-specific integrated circuit (ASIC). In an example, a circuit can comprise programmable logic (e.g., circuitry, as encompassed within a general-purpose processor or other programmable processor) that can betemporarily configured (e.g., by software) to perform the certain operations. It will be appreciated that the decision to implement a circuit mechanically (e.g., in dedicated and permanently configured circuitry), or in temporarily configured circuitry (e.g., configured by software) can be driven by cost and time considerations.

[0140] Accordingly, the term “circuit” is understood to encompass a tangible entity, be that an entity that is physically constructed, permanently configured (e.g., hardwired), or temporarily (e.g., transitorily) configured (e.g., programmed) to operate in a specified manner or to perform specified operations. In an example, given a plurality of temporarily configured circuits, each of the circuits need not be configured or instantiated at any one instance in time. For example, where the circuits comprise a general-purpose processor configured via software, the general-purpose processor can be configured as respective different circuits at different times. Software can accordingly configure a processor, for example, to constitute a particular circuit at one instance of time and to constitute a different circuit at a different instance of time.

[0141] In an example, circuits can provide information to, and receive information from, other circuits. In this example, the circuits can be regarded as being communicatively coupled to one or more other circuits. Where multiple of such circuits exist contemporaneously, communications can be achieved through signal transmission (e.g., over appropriate circuits and buses) that connect the circuits. In implementations in which multiple circuits are configured or instantiated at different times, communications between such circuits can be achieved, for example, through the storage and retrieval of information in memory structures to which the multiple circuits have access. For example, one circuit can perform an operation and store the output of that operation in a memory device to which it is communicatively coupled. A further circuit can then, at a later time, access the memory device to retrieve and process the stored output. In an example, circuits can be configured to initiate or receive communications with input or output devices and can operate on a resource (e.g., a collection of information).

[0142] The various operations of method examples described herein can be performed, at least partially, by one or more processors that are temporarily configured (e.g., by software) or permanently configured to perform the relevantoperations. Whether temporarily or permanently configured, such processors can constitute processor-implemented circuits that operate to perform one or more operations or functions. In an example, the circuits referred to herein can comprise processor-implemented circuits.

[0143] Similarly, the methods described herein can be at least partially processor implemented. For example, at least some of the operations of a method can be performed by one or processors or processor-implemented circuits. The performance of certain of the operations can be distributed among the one or more processors, not only residing within a single machine, but deployed across a number of machines. In an example, the processor or processors can be located in a single location (e.g., within a home environment, an office environment or as a server farm), while in other examples the processors can be distributed across a number of locations.

[0144] The one or more processors can also operate to support performance of the relevant operations in a "cloud computing" environment or as a "software as a service”

[0145] (SaaS). For example, at least some of the operations can be performed by a group of computers (as examples of machines including processors), with these operations being accessible via a network (e.g., the Internet) and via one or more appropriate interfaces (e.g., Application Program Interfaces (APIs).)

[0146] Example implementations (e.g., apparatus, systems, or methods) can be implemented in digital electronic circuitry, in computer hardware, in firmware, in software, or in any combination thereof. Example implementations can be implemented using a computer program product (e.g., a computer program, tangibly embodied in an information carrier or in a machine readable medium, for execution by, or to control the operation of, data processing apparatus such as a programmable processor, a computer, or multiple computers).

[0147] A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a software module, subroutine, or other unit suitable for use in a computing environment. A computer program can be deployed to be executed on one computer or on multiple computers at onesite or distributed across multiple sites and interconnected by a communication network.

[0148] In an example, operations can be performed by one or more programmable processors executing a computer program to perform functions by operating on input data and generating output. Examples of method operations can also be performed by, and example apparatus can be implemented as, special purpose logic circuitry (e.g., a field programmable gate array (FPGA) or an application-specific integrated circuit (ASIC)).

[0149] The computing system can include clients and servers. A client and server are generally remote from each other and generally interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. In implementations deploying a programmable computing system, it will be appreciated that both hardware and software architectures require consideration. Specifically, it will be appreciated that the choice of whether to implement certain functionality in permanently configured hardware (e.g., an ASIC), in temporarily configured hardware (e.g., a combination of software and a programmable processor), or a combination of permanently and temporarily configured hardware can be a design choice. Below are set out hardware (e.g., computing device 700) and software architectures that can be deployed in example implementations.

[0150] In an example, the computing device 700 can operate as a standalone device or the computing device 700 can be connected (e.g., networked) to other machines.

[0151] In a networked deployment, the computing device 700 can operate in the capacity of either a server or a client machine in server-client network environments. In an example, computing device 700 can act as a peer machine in peer-to-peer (or other distributed) network environments. The computing device 700 can be a personal computer (PC), a tablet PC, a set-top box (STB), a Personal Digital Assistant (PDA), a mobile telephone, a web appliance, a network router, switch or bridge, or any machine capable of executing instructions (sequential or otherwise) specifying actions to be taken (e.g., performed) by the computing device 700. Further, while only a single computing device 700 is illustrated, theterm “computing device” shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

[0152] Example computing device 700 can include a processor 704 (e.g., a central processing unit CPU), a graphics processing unit (GPU) or both), a main memory 706 and a static memory 708, some or all of which can communicate with each other via a bus 710. The computing device 700 can further include a display unit 712, an alphanumeric input device 714 (e.g., a keyboard), and a user interface (UI) navigation device 716 (e.g., a mouse). In an example, the display unit 712, input device 714 and UI navigation device 716 can be atouch screen display. The computing device 700 can additionally include a storage device (e.g., drive unit) 718, a signal generation device 720 (e.g., a speaker), a network interface device 722, and one or more sensors 724, such as a global positioning system (GPS) sensor, compass, accelerometer, or another sensor.

[0153] The storage device 718 can include a machine readable medium 726 on which is stored one or more sets of data structures or instructions 702 (e.g., software) embodying or utilized by any one or more of the methodologies or functions described herein. The instructions 702 can also reside, completely or at least partially, within the main memory 706, within static memory 708, or within the processor 704 during execution thereof by the computing device 700. In an example, one or any combination of the processor 704, the main memory 706, the static memory 708, or the storage device 718 can constitute machine readable media.

[0154] While the machine readable medium 726 is illustrated as a single medium, the term "machine readable medium" can include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that configured to store the one or more instructions 702. The term “machine readable medium” can also be taken to include any tangible medium that is capable of storing, encoding, or carrying instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure or that is capable of storing, encoding or carrying data structures utilized by or associated with such instructions. The term “machine readable medium” can accordingly be taken to include, but not belimited to, solid-state memories, and optical and magnetic media. Specific examples of machine-readable media can include non-volatile memory, including, by way of example, semiconductor memory devices (e.g., Electrically Programmable Read-Only Memory

[0155] (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM)) and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks.

[0156] The instructions 702 can further be transmitted or received over a communications network 728 using a transmission medium via the network interface device 722 utilizing any one of a number of transfer protocols (e.g., frame relay, IP, TCP, UDP, HTTP, etc.). Example communication networks can include a local area network (LAN), a wide area network (WAN), a packet data network (e.g., the Internet), mobile telephone networks (e.g., cellular networks), Plain Old Telephone (POTS) networks, and wireless data networks (e.g., IEEE 802.11 standards family known as Wi-Fi®, IEEE 802.16 standards family known as WiMax®), peer-to-peer (P2P) networks, among others. The term “transmission medium” shall be taken to include any intangible medium that is capable of storing, encoding or carrying instructions for execution by the machine, and includes digital or analog communications signals or other intangible medium to facilitate communication of such software.

[0157] As used herein, a component can refer to a device, physical entity, or logic having boundaries defined by function or subroutine calls, branch points, APIs, or other technologies that provide for the partitioning or modularization of particular processing or control functions. Components may be combined via their interfaces with other components to carry out a machine process. A component may be a packaged functional hardware unit designed for use with other components and a part of a program that usually performs a particular function of related functions. Components may constitute either software components (e.g., code embodied on a machine-readable medium) or hardware components. A "hardware component" is a tangible unit capable of performing certain operations and may be configured or arranged in a certain physical manner. In various example implementations, one or more computer systems (e.g., astandalone computer system, a client computer system, or a server computer system) or one or more hardware components of a computer system (e.g., a processor or a group of processors) may be configured by software (e.g., an application or application portion) as a hardware component that operates to perform certain operations as described herein.

[0158] In view of the above-described implementations of subject matter this application discloses the following list of examples, wherein one feature of an example in isolation or more than one feature of an example, taken in combination and, optionally, in combination with one or more features of one or more further examples are further examples also falling within the disclosure of this application.

[0159] Example 1. A computer-implemented method for identifying an optimal primer-binding region within an RNA molecule, comprising: receiving, by one or more processors, an RNA nucleotide sequence; computing, using a partition-function-based structural ensemble algorithm, for each nucleotide position i in the sequence, a base-pairing probability Pbp. and a positional entropy Spos. computing, for each nucleotide position i, an RNA Accessibility Parameter (RAPi) based on Pbp. and Spos., computing, for each nucleotide position i, a Gibbs free energy value AGi representing predicted RNA-DNA hybridization stability; computing, for each nucleotide position I, an Efficiency Reverse Transcription Score (ERTSi) based on RAPi and AGi; computing, for each region j of length W, a Region Reverse Transcription Score (RRTSj) based on an aggregation of ERTSi values within the region; identifying one or more regions for which RRTSj exceeds a regional threshold; determining, within each identified region, a Minimum Initiation Subregion (MIS) comprising a smallest subset of nucleotide positions whose ERTSi values satisfy an initiation threshold; outputting a primerbinding region that overlaps at least part of the MIS; and designing a primer comprising a nucleotide sequence overlapping the identified region, the primer being configured for laboratory reverse transcription.

[0160] Example 2. A system for identifying an optimal primer-binding region within an RNA molecule, comprising: one or more processors; and a non-transitory computer-readable medium storing instructions that, when executed bythe one or more processors, cause the system to perform the method of Example 1.

[0161] Example 3. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method of Example 1.

[0162] Example 4. The method of any one of Examples 1-3, wherein RAPi is computed as a weighted function of (1 -Pbpi) and Spos..

[0163] Example 5. The method of any one of Examples 1-4, wherein RAPi further comprises at least one of: unpaired probability, ensemble defect, Shannon entropy, solvent accessibility, or a machine-leaming-based accessibility score.

[0164] Example 6. The method of any one of Examples 1-5, wherein AGi is computed using a nearest-neighbor thermodynamic model.

[0165] Example 7. The method of any one of Examples 1-6, wherein AGi is predicted by a machine-learning model.

[0166] Example 8. The method of any one of Examples 1-7, wherein ERTSi is computed using a nonlinear integration of RAPi and AGi.

[0167] Example 9. The method of any one of Examples 1-8, wherein RRTSj is computed using a sliding window of length between 4 and 40 nucleotides.

[0168] Example 10. The method of any one of Examples 1-9, wherein the MIS comprises a contiguous subregion.

[0169] Example 11. The method of any one of Examples 1-10, wherein the MIS comprises a non-contiguous subset of nucleotide positions.

[0170] Example 12. The method of any one of Examples 1-11, further comprising ranking multiple candidate primer-binding regions based on RRTSj, MIS size, AGi, or primer design constraints.

[0171] Example 13. The method of any one of Examples 1-12, wherein the primer-binding region is used to design a primer, a probe, or both.

[0172] Example 14. The method of any one of Examples 1-13, wherein the primer-binding region is used to design primers for reverse-transcription quantitative PCR (RT-qPCR), digital PCR, LAMP, or RNA amplification.

[0173] Example 15. The method of any one of Examples 1-14, wherein the RNA molecule is ribosomal RNA, viral RNA, bacterial RNA, eukaryotic mRNA, or long non-coding RNA.

[0174] Example 16. The method of any one of Examples 1-15, wherein the outputted primer-binding region is determined based solely on RAPi without the use of RRTSj.

[0175] Example 17. The method of any one of Examples 1-16, wherein the primer-binding region is determined based solely on ERTS1without requiring computation of RRTSj.

[0176] Example 18. The method of any one of Examples 1-17, wherein the primer-binding region is determined based on RRTSj without requiring computation of MIS.

[0177] Example 19. The method of any one of Examples 1-18, wherein MIS is computed based on ERTSi alone without using RRTSj.

[0178] Example 20. The method of any one of Examples 1-19, wherein MIS is determined as the smallest subset of nucleotides for which ERTSi exceeds an initiation threshold independent of the window-based RRTS calculation.

[0179] Example 21. The method of any one of Examples 1-20, wherein MIS is computed using a machine-learning classifier trained on experimentally validated initiation regions.

[0180] Example 22. The method of any one of Examples 1-21, wherein ERTSi is computed using a model trained on reverse-transcription efficiency data without direct AG calculation.

[0181] Example 23. The method of any one of Examples 1-22, wherein RAPi is computed and used to identify a primer-binding region without computing AGi.

[0182] Example 24. The method of any one of Examples 1-23, wherein RRTSj is computed using a nonlinear aggregation of ERTS1values such as a geometric mean, harmonic mean, or percentile-based function.

[0183] Example 25. The method of any one of Examples 1-24, wherein ERTS1is computed without normalizing for primer length, thereby covering implementations that omit length-dependent corrections.

[0184] Example 26. The method of any one of Examples 1-25, wherein the primer-binding region is selected by maximizing RAPi, ERTSi, or RRTSj individually or in combination.

[0185] Example 27. The method of any one of Examples 1-26, wherein the primer-binding region encompasses nucleotides corresponding to a top-ranked RAPi region, thereby covering primer selection based solely on RNA accessibility.

[0186] Example 28. The method of any one of Examples 1-27, wherein the primer-binding region is selected using ERTSi values even when RAPi values are not explicitly reported to the user.

[0187] Example 29. The method of any one of Examples 1-28, wherein the primer-binding region is selected using a version of RRTS computed using variable window sizes, adaptive windows, or windows of unequal length.

[0188] Example 30. The method of any one of Examples 1-29, wherein MIS is defined as any subset of contiguous or non-contiguous nucleotides whose aggregate ERTSi value exceeds an initiation threshold, thereby covering alternative MIS definitions.

[0189] Example 31. The method of any one of Examples 1-30, wherein RAP, ERTS, or RRTS is not computed by any single-parameter accessibility metric selected from the group consisting of unpaired probability, ensemble defect, minimum free energy structure, or AG-only windows.

[0190] Example 32. The method of any one of Examples 1-32, wherein the MIS is computed by integrating both structural ensemble descriptors and RNA-DNA hybridization thermodynamics, and wherein no prior accessibility measure can independently identify the MIS.

[0191] Example 33. The method of any one of Examples 1-32, wherein RRTSj identifies a region that could not be detected using AG-only or unpaired-probability-only methods.

[0192] Example 34. The method of any one of Examples 1-33, wherein the combination of RAP, ERTS, RRTS, and MIS produces an experimentally measurable reduction in Ct value relative to primers selected using existing methods.

[0193] Example 35. A primer comprising the nucleotide sequence of SEQ ID NO:4.

[0194] Example 36. A primer comprising the nucleotide sequence of SEQ ID NO:5.

[0195] Example 37. A probe comprising the nucleotide sequence of SEQ ID NO:6.

[0196] Example 38. A primer pair comprising SEQ ID NO:4 and SEQ ID NO:5.

[0197] Example 39. A primer-probe set comprising SEQ ID NO:4, SEQ ID NO:5, and SEQ ID NO:6.

[0198] Example 40. A kit comprising: a primer comprising SEQ ID NO:4; a primer comprising SEQ ID NO:5; and a probe comprising SEQ ID NO:6; optionally together with buffers, enzymes, or instructions for detecting Escherichia coli 23 S rRNA.

[0199] Example 41. A method for detecting 23S rRNA of Escherichia spp. (including E. coli). comprising: contacting a sample with a primer pair comprising SEQ ID NO:4 and SEQ ID NO:5; performing reverse transcription and amplification; and detecting amplification using a probe comprising SEQ ID NO: 6.

[0200] Example 42. Use of a primer comprising SEQ ID NO: 4, SEQ ID NO:5, or SEQ ID NO:6 for detecting Escherichia spp. (including E. coli) 23S rRNA.

[0201] Example 43. A method for determining an optimized region within an RNA molecule, comprising integrating ensemble-derived structural metrics with RNA-DNA hybridization thermodynamics and identifying a minimal subregion sufficient to initiate reverse transcription.

[0202] Example 44. A method comprising: obtaining, by one or more computing devices each including one or more processors and memory, ribonucleic acid (RNA) sequence data indicating an RNA nucleotide sequence; generating, by the one or more computing devices, a plurality of secondary structural representations, individual secondary structural representations of the plurality of secondary structural representations indicating a plurality of secondary structures formed by the RNA nucleotide sequence; determining, by the one or more computing devices and based on the plurality of secondary structural representations, a nucleotide pairing probability metric indicating aprobability of individual nucleotides included in the RNA nucleotide sequence being paired with at least one additional nucleotide included in the RNA nucleotide sequence; determining, by the one or more computing devices, a first quantitative measure for the individual nucleotides included in the RNA nucleotide sequence, the first quantitative measure indicating an accessibility of the individual nucleotides of the RNA nucleotide sequence for being coupled to a primer during a reverse transcription process; determining, by the one or more computing devices, a second quantitative measure for the individual nucleotides of the RNA nucleotide sequence, the second quantitative measure being based on the nucleotide pairing probability metrics for the individual nucleotides, the first quantitative measure for the individual nucleotides, and thermodynamics data for the individual nucleotides; determining, by the one or more computing devices, a plurality of nucleotide region quantitative measures for a plurality of groups of nucleotides included in the RNA nucleotide sequence, individual nucleotide region quantitative measures of the plurality of nucleotide region quantitative measures being determined by aggregating the second quantitative measures for the individual nucleotides included in an individual group of nucleotides of the plurality of groups of nucleotides; determining, by the one or more computing devices, a group of nucleotides having a nucleotide region quantitative measure that satisfies one or more criteria; and synthesizing one or more primers that correspond to at least a portion of the group of nucleotides.

[0203] Example 45. The method of Example 44, wherein the plurality of secondary structures of the individual secondary structural representations include at least one of one or more stems, one or more loops, or one or more branches.

[0204] Example 46. The method of Example 44 or 45, wherein the first quantitative measure is determined with respect to a number of pairing states for the individual nucleotides of the RNA nucleotide sequence based on the plurality of secondary structural representations.

[0205] Example 47. The method of any one of Examples 44-46, wherein at least one of the nucleotide pairing probability for the individual nucleotides of the RNA nucleotide sequence or the first quantitative measure for the individual nucleotides of the RNA nucleotide sequence are determined by executing one or more partition functions.

[0206] Example 48. The method of any one of Examples 44-47, comprising: determining a nucleotide accessibility metric for the individual nucleotides of the RNA nucleotide sequence based on a weighted function comprising (i) a first component that corresponds to the nucleotide pairing probability and having a first weighting factor and (ii) a second component that corresponds to the first quantitative measure for the individual nucleotides of the RNA nucleotide sequence and having a second weighting factor.

[0207] Example 49. The method of any one of Examples 44-48, wherein the thermodynamics data for the individual nucleotides is determined by determining a Gibbs free energy of RNA-DNA hybridization for the individual nucleotides.

[0208] Example 50. The method of Example 49, wherein the Gibbs free energy of RNA-DNA hybridization for the individual nucleotides is determined based on a nearest neighbor thermodynamics model.

[0209] Example 51. The method of any one of Examples 44-50, wherein the group of nucleotides having the nucleotide region quantitative measure that satisfies the one or more criteria includes from 4 nucleotides to 40 nucleotides.

[0210] Example 52. The method of any one of Examples 44-51, wherein the plurality of nucleotide region quantitative measures are determined using a sliding window that traverses the RNA nucleotide sequence.

[0211] Example 53. The method of Example 52, comprising: determining a first nucleotide region quantitative measure in response to the sliding window overlapping a first group of nucleotides of the RNA nucleotide sequence; and determining a second nucleotide region quantitative measure in response to the sliding window overlapping a second group of nucleotides of the RNA nucleotide sequence that includes at least one nucleotide that is different from nucleotides included in the first group of nucleotides.

[0212] Example 54. The method of any one of Examples 44-53, wherein the group of nucleotides having the nucleotide region quantitative measure includes at least a minimum number of nucleotides to initiate a reverse transcription process for the RNA nucleotide sequence.

[0213] Example 55. The method of any one of Examples 44-54, comprising: performing a reverse transcription process using the one or more primers to determine a presence of one or more analytes in a sample.

[0214] Example 56. The method of Example 55, wherein the sample comprises a food sample or a beverage sample.

[0215] Example 57. A computing system comprising: one or more hardware processors; and memory storing computer-readable instructions that, when executed by the one or more hardware processors, perform operations comprising: obtaining ribonucleic acid (RNA) sequence data indicating an RNA nucleotide sequence; generating a plurality of secondary structural representations, individual secondary structural representations of the plurality of secondary structural representations indicating a plurality of secondary structures formed by the RNA nucleotide sequence; determining, based on the plurality of secondary structural representations, a nucleotide pairing probability metric indicating a probability of individual nucleotides included in the RNA nucleotide sequence being paired with at least one additional nucleotide included in the RNA nucleotide sequence; determining a first quantitative measure for the individual nucleotides included in the RNA nucleotide sequence, the first quantitative measure indicating an accessibility of the individual nucleotides of the RNA nucleotide sequence for being coupled to a primer during a reverse transcription process; determining a second quantitative measure for the individual nucleotides of the RNA nucleotide sequence, the second quantitative measure being based on the nucleotide pairing probability metrics for the individual nucleotides, the first quantitative measure for the individual nucleotides, and thermodynamics data for the individual nucleotides; determining a plurality of nucleotide region quantitative measures for a plurality of groups of nucleotides included in the RNA nucleotide sequence, individual nucleotide region quantitative measures of the plurality of nucleotide region quantitative measures being determined by aggregating the second quantitative measures for the individual nucleotides included in an individual group of nucleotides of the plurality of groups of nucleotides; and determining a group of nucleotides having a nucleotide region quantitative measure that satisfies one or more criteria.

[0216] Example 58. The computing system of Example 57, wherein the memory stores additional computer-readable instructions that, when executed by the one or more hardware processors, perform additional operations comprising: generating at least 500 secondary structural representations by executing one or more thermodynamic nearest neighbor models or one or more machine learning models.

[0217] Example 59. A computer-implemented method for identifying an optimal primer-binding region within an RNA molecule, comprising: receiving, by one or more processors, an RNA nucleotide sequence; computing, using a partition-function-based structural ensemble algorithm, for each nucleotide position i in the sequence, a base-pairing probability Pbp. and a positional entropy Spos. computing, for each nucleotide position I, an RNA Accessibility Parameter (RAPi) based on Pbp. and Spos. ; and determining, based on RAPi for each nucleotide position, a primer-binding region.

[0218] Example 60. The method of Example 59, comprising: computing, for each nucleotide position i, a Gibbs free energy value AGi representing predicted RNA-DNA hybridization stability; computing, for each nucleotide position I, an Efficiency Reverse Transcription Score (ERTSi) based on RAPi and AGi; computing, for each region j of length W, a Region Reverse Transcription Score (RRTSj) based on an aggregation of ERTSi values within the region; identifying one or more regions for which RRTSj exceeds a regional threshold; determining, within each identified region, a Minimum Initiation Subregion (MIS) comprising a smallest subset of nucleotide positions whose ERTSi values satisfy an initiation threshold; and outputting the primer-binding region that overlaps at least part of the MIS.

[0219] Example 61. The method of Example 59 or 60, comprising designing a primer comprising a nucleotide sequence overlapping the identified region, the primer being configured for laboratory reverse transcription.

[0220] Example 62. A computer-implemented method for identifying an optimal primer-binding region within an RNA molecule, comprising: receiving, by one or more processors, an RNA nucleotide sequence; computing, using a partition-function-based structural ensemble algorithm, for each nucleotideposition i in the sequence, a base-pairing probability Pbp. and a positional entropy Spos. computing, for each nucleotide position I, an RNA Accessibility Parameter (RAPi) based on Pbp. and Spos. computing, for each nucleotide position i, a Gibbs free energy value AGi representing predicted RNA-DNA hybridization stability; computing, for each nucleotide position I, an Efficiency Reverse Transcription Score (ERTSi) based on RAPi and AGi; and determining, based on ERTSi for each nucleotide position, a primer-binding region.

[0221] Example 63. The method of Example 62, comprising: computing, for each region j of length W, a Region Reverse Transcription Score (RRTSj) based on an aggregation of ERTSi values within the region; identifying one or more regions for which RRTSj exceeds a regional threshold; determining, within each identified region, a Minimum Initiation Subregion (MIS) comprising a smallest subset of nucleotide positions whose ERTSi values satisfy an initiation threshold; and outputting a primer-binding region that overlaps at least part of the MIS.

[0222] Example 64. The method of Example 62 or 63, comprising designing a primer comprising a nucleotide sequence overlapping the identified region, the primer being configured for laboratory reverse transcription.

[0223] Example 65. A computer-implemented method for identifying an optimal primer-binding region within an RNA molecule, comprising: receiving, by one or more processors, an RNA nucleotide sequence; computing, using a partition-function-based structural ensemble algorithm, for each nucleotide position i in the sequence, a base-pairing probability Pbpiand a positional entropy Spos. computing, for each nucleotide position I, an RNA Accessibility Parameter (RAPi) based on Pbp. and Spos. computing, for each nucleotide position i, a Gibbs free energy value AGi representing predicted RNA-DNA hybridization stability; computing, for each nucleotide position I, an Efficiency Reverse Transcription Score (ERTSi) based on RAPi and AGi; computing, for each region) of length W, a Region Reverse Transcription Score (RRTSj) based on an aggregation of ERTSi values within the region; identifying one or more regions for which RRTSj exceeds a regional threshold; and determining, based on identified RRTSj regions that exceed the regional threshold value, a primer-binding region.

[0224] Example 66. The method of Example 65, comprising: determining, within each identified region, a Minimum Initiation Subregion (MIS) comprising a smallest subset of nucleotide positions whose ERTSi values satisfy an initiation threshold; and outputting the primer-binding region that overlaps at least part of the MIS.

[0225] Example 67. The method of Example 65 or 66, comprising designing a primer comprising a nucleotide sequence overlapping the identified region, the primer being configured for laboratory reverse transcription.EXAMPLESExample 1: Comparison with AG-Based PredictionObjective

[0226] To demonstrate that AG alone (thermodynamic stability of the RNA-DNA duplex) cannot accurately predict reverse-transcription efficiency, especially in structured RNA regions where strong hybridization may occur at inaccessible sites.Calculated Parameters

[0227] The table below presents the calculated values of Positional Entropy (Spos), Probability of Base Pairing (Pbpi), RNA Accessibility Parameter (RAPi), Gibbs Free Energy Change (AG), and the resulting Efficiency Reverse Transcription Score (ERTSi) for selected nucleotide positions within the structured RNA sequence.Note: For simplicity, only selected nucleotide positions are included in this example.Experimental Design

[0228] To validate the predictive accuracy of ERTS and RRTS. two primers were designed — each corresponding to Region 1 (nucleotide range 512-532) and Region 2 (nucleotide range 540-560).

[0229] Both primers were synthesized and used to perform reverse transcription reactions under identical experimental conditions in the complex RNA molecule. Importantly, both primers were matched for similar melting temperatures (Tm) to ensure that any observed performance differences originated solely from structural accessibility rather than thermodynamic mismatch.

[0230] Both primers were chemically synthesized using solid-phase phosphoramidite oligonucleotide synthesis and purified prior to use. Reverse transcription and real-time PCR amplification were performed in a single-tube, one-step RT-qPCR reaction under identical experimental conditions using a complex structured RNA molecule as the template. Each reaction comprised 10 ng of RNA, 0.2 pM of each primer, 0.2 pM of a sequence-specific hydrolysisprobe labeled at the 5' end with a FAM fluorescent reporter and at the 3' end with a quencher, lx one-step RT-qPCR buffer, 3 mM MgCk 0.2 mM of each dNTP, and a combined reverse transcriptase / DNA polymerase enzyme system, in a total reaction volume of 25 pL.

[0231] The one-step RT-qPCR protocol included an initial reverse transcription step at 50 °C for 30 minutes, followed by enzyme activation and initial denaturation at 95 °C for 2 minutes, and PCR amplification comprising 40 cycles of denaturation at 95 °C for 15 seconds and combined annealing / extension at 60 °C for 30 seconds, during which fluorescence from the FAM-labeled probe was measured in real time. A final extension step was performed at 72 °C for 5 minutes.

[0232] This control ensures that the observed differences in Ct values directly reflect true accessibility effects rather than artifacts of primer stability or GC content.Regional ScoringInterpretation

[0233] If AG alone were used as the predictor, Region 1 — having a more negative free energy — would appear as the optimal site for primer design due to its apparently stronger hybridization potential. However, this region is structurally buried, reflected in its low RAP and low RRTS, resulting in poor reversetranscription performance.

[0234] In contrast, Region 2. though exhibiting slightly less favorable AG, shows significantly higher accessibility (RAP) and a long contiguous MIS. These characteristics enable rapid primer annealing, effective strand invasion, and efficient reverse transcription, evidenced by the much lower Ct value.

[0235] This experiment confirms that AG alone is insufficient to predict primer efficiency in structured RNAs and that the combined use of RAP, ERTS, and RRTS offers a far more accurate and mechanistically meaningful prediction of reverse-transcription success.Example 2: RRTS prediction powerObjective

[0236] To demonstrate the predictive ability of the Region Reverse Transcription Score (RRTS) parameter, primers were designed to bind two distinct regions of the same complex RNA molecule, each characterized by markedly different RRTS values.

[0237] This comparison assesses whether RRTS can accurately distinguish between regions that support efficient versus inefficient reverse transcription, independent of thermodynamic strength.Calculated Parameters

[0238] The table below presents the calculated values of Positional EntropyProbability of Base Pairing (PbPi), RNA Accessibility Parameter (RAPi), Gibbs Free Energy Change (AG), and the resulting Efficiency Reverse Transcription Score (ERTSi) for selected nucleotide positions within the structured RNA sequence.Note: For simplicity, only selected nucleotide positions are included in this example.Experimental design

[0239] Two primers were designed — each corresponding to one of the evaluated regions (Region 1 and Region 2) — based on their respective RRTS profiles.

[0240] Both primers were synthesized and tested under identical reaction conditions on the same RNA molecule to ensure comparability.

[0241] Importantly, both primers were matched for equivalent melting temperatures (Tm). GC content, and length. This design ensures that observeddifferences in reverse-transcription efficiency arise solely from RNA structural accessibility, rather than differences in primer thermodynamics or sequence composition.Experimental results.Interpretation

[0242] This example highlights the strong predictive performance of RRTS in identifying functionally optimal regions for reverse transcription.

[0243] Although both primers share similar AG values and equivalent Tm, their experimental outcomes differ dramatically.Region 1 (low RRTS = 12.2). characterized by low cumulative accessibility and a short or absent Minimum Initiation Subregion (MIS), exhibited inefficient amplification with a high Ct value (26).Region 2 (high RRTS = 25.2). encompassing a long contiguous MIS and high ERTS values across the region, produced rapid and efficient amplification with a low Ct value (15).

[0244] The observed correspondence between high RRTS and low Ct confirms that RRTS serves as a reliable, quantitative indicator of true reversetranscription efficiency.

[0245] This validation demonstrates that regional cumulative accessibility, rather than AG alone, governs the kinetic feasibility of primer annealing and extension in complex RNA structures.Example 3: Importance of the Minimum Region Required to Initiate HybridizationObjective

[0246] To demonstrate the importance of the Minimum Initiation Subregion (MIS) — the minimum contiguous portion of the primer-binding site required to initiate hybridization and reverse transcription.

[0247] Two primers were designed within the same RNA structural context:Primer 1 (positions 390-410) contains a long MIS that exceeds the ERTS threshold (TERTS).Primer 2 (positions 396-415) overlaps the same region but contains only a short MIS. insufficient to sustain stable hybridization initiation.

[0248] Both primers were synthesized and tested under identical reversetranscription conditions.

[0249] Importantly, they were matched for equivalent length. GC content, and melting temperature (Tm), ensuring that any observed performance differences are attributable exclusively to structural accessibility (as reflected by ERTS and MIS length), and not primer thermodynamics.Calculated Parameters

[0250] The following table presents calculated values for Positional Entropy (Spos), Probability of Base Pairing (Pbpi), RNA Accessibility Parameter (RAPi), Gibbs Free Energy Change (AG), and the resulting Efficiency Reverse Transcription Score (ERTSi) for nucleotide positions 390-420.Note: For simplicity, only selected nucleotide positions are included in this example.Experimental Design

[0251] To evaluate the impact of MIS length on reverse-transcription efficiency, two primers were tested:

[0252] Primer 1 (positions 390-410) includes a long contiguous MIS spanning positions 391-399, where ERTSi > TERTS throughout nine consecutive nucleotides. This region combines high RAP and highly favorable AG values, predicting strong accessibility and rapid initiation.

[0253] Primer 2 (positions 396-415) overlaps part of the same RNA structure but includes only a short MIS (positions 396-398, four consecutive nucleotides above TERTS). Despite similar AG and Tmvalues, this primer is predicted to perform poorly due to its limited initiation subregion.

[0254] Both primers were used for reverse-transcription reactions on the same RNA molecule under identical experimental conditions, with matching primer length, GC content, and Tm.Experimental results.Interpretation

[0255] This example demonstrates the critical importance of the Minimum Initiation Subregion (MIS) for successful primer binding and reverse transcription.

[0256] Although both primers share nearly identical thermodynamic parameters (AG and Tm), only the primer encompassing a long MIS (>6 nt) achieved efficient reverse transcription.

[0257] Primer 1 (positions 390-410) maintained a contiguous region of high ERTS values well above the TERTS threshold, enabling rapid nucleation, strand invasion, and full duplex formation.

[0258] Primer 2 (positions 395-415) lacked a sufficiently long contiguous favorable subregion, resulting in unstable initiation and poor amplification efficiency.

[0259] This finding confirms that a minimum contiguous length of favorable nucleotides (MIS) is essential for primer seeding and extension — demonstrating that ERTS and MIS jointly determine true initiation competence, beyond thermodynamic binding energy alone.Example 4: Primers and probe designed for Escherichia genus 23S rRNA using the RAP / ERTS / RRTS method.

[0260] In this example, the disclosed method was applied to the 23S rRNA of Escherichia coli in order to identify an optimal region for reverse transcription and subsequent amplification.

[0261] The full-length 23 S rRNA sequence of several species of Escherichia (around 2,900 nucleotides) was provided as input. Their secondarystructure ensemble was computed using a partition-function algorithm at 37 °C and 1 M monovalent salt concentration. For each nucleotide position i, the probability of base pairing Pbp.and the positional entropy Spos. were determined and used to compute the RNA Accessibility Parameter RAPi. In parallel, the Gibbs free energy of RNA-DNA hybridization Delta Gi was calculated for candidate primers of length 18-29 nucleotides.

[0262] The accessibility and thermodynamic parameters were integrated into an Efficiency Reverse Transcription Score ERTSi for each position. Sliding windows of 18-29 nucleotides were then evaluated to obtain the Region ReverseTranscription Score RRTSj. The region with the highest RRTSj and containing a Minimum Initiation Subregion (MIS) was selected. This region differed from the conventional method region despite similar GC content and similar melting temperatures, confirming that the computational scoring and not trivial sequence properties identified the improved region.

[0263] Within this region, the method selected primers (Escherichia F2, Escherichia R2) and one probe (Escherichia S2). The sequences are represented as SEQ ID NO: 4-6.

[0264] The results of these new primers and probe were compared directly with an existing primer-probe set targeting the 23S rRNA of Escherichia spp (Escherichia Fl, Escherichia Rl, Escherichia SI; SEQ ID NO: 1-3) that had been previously designed using conventional approaches.

[0265] Both primer sets were tested using the same DNA / RNA extract, taken from the same sample, and under identical RT-PCR conditions, including the same RT-PCR master mix, standard cycling parameters, reaction volumes, enzyme concentrations, and thermocycler program, The only difference between the two assays was the primer and probe sequences.

[0266] The amplification performance was evaluated by comparing Ct values. The original primer-probe set produced a Ct value of 23, whereas the method-designed primer-probe set produced a substantially lower Ct value of 12 under the same conditions, demonstrating a marked increase in amplification efficiency and improved reverse-transcription initiation.

[0267] These results confirm that the computational strategy disclosed herein produces primers targeting regions with higher structural accessibility and thermodynamic favorability, resulting in more efficient amplification of the same target RNA.Original primer and probe set (conventional set).Method-designed primers and probe set (implementations described herein)Interpretation

[0268] This dramatic performance difference demonstrates that:the region selected by the algorithm is structurally more accessible, provides more favorable RT initiation, andresults in substantially improved amplification efficiency.

[0269] The higher RRTS (30.5 vs. 7.9) and ~11-cycle Ct improvement (Ct 12 vs. Ct 23) cannot be attributed to changes in laboratory conditions, which were identical. The only difference was the region chosen based on structural ensemble computation (RAP / ERTS / RRTS pipeline). This directly supports the practical effectiveness of the computational method.

[0270] Such a dramatic Ct improvement is unexpected because the compared primers have similar Tm, GC%, length, and AG. Therefore, the improvement is attributable solely to the novel structural-ensemble scoring approach. Accordingly, the superior performance of the method-designed primers cannot be attributed to trivial sequence properties or standard thermodynamic rules. Instead, the observed improvement directly results from the structural-ensemble-based scoring (RAP, ERTS, and RRTS) and the MIS criteria disclosed herein, which identify regions of the RNA that are not apparent from AG, GC%, Tm, or primary sequence analysis alone.

[0271] Thus, the performance enhancement was unexpected and could not have been predicted by a person skilled in the art using known primer-design approaches.

[0272] These results confirm that the disclosed computational method transforms complex RNA structural parameters into concrete laboratory outcomes, producing primer and probe sequences that exhibit significantly improved biological performance. As the laboratory conditions and sample material were identical for both primer sets, the performance difference is attributable solely to the region identified by the computational method, demonstrating a real-world technical application beyond abstract computation.

Claims

CLAIMSWhat is claimed is:

1. A computer-implemented method for identifying an optimal primer-binding region within an RNA molecule, comprising:receiving, by one or more processors, an RNA nucleotide sequence; computing, using a partition-function-based structural ensemble algorithm, for each nucleotide position i in the sequence, a base-pairing probability Pbp. and a positional entropy Spos.computing, for each nucleotide position I, an RNA Accessibility Parameter (RAPi) based on Pbp. and Spos.computing, for each nucleotide position i, a Gibbs free energy value AGi representing predicted RNA-DNA hybridization stability;computing, for each nucleotide position I, an Efficiency Reverse Transcription Score (ERTSi) based on RAPi and AGi;computing, for each region j of length W, a Region Reverse Transcription Score (RRTSj) based on an aggregation of ERTSi values within the region;identifying one or more regions for which RRTSj exceeds a regional threshold;determining, within each identified region, a Minimum Initiation Subregion (MIS) comprising a smallest subset of nucleotide positions whose ERTSi values satisfy an initiation threshold;outputting a primer-binding region that overlaps at least part of the MIS; anddesigning a primer comprising a nucleotide sequence overlapping the identified region, the primer being configured for laboratory reverse transcription.

2. A system for identifying an optimal primer-binding region within an RNA molecule, comprising:one or more processors; anda non-transitory computer-readable medium storing instructions that, when executed by the one or more processors, cause the system to perform the method of claim 1.

3. A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to perform the method of claim 1.

4. The method of claim 1, wherein RAPi is computed as a weighted function of (1 ~^bpi) ^md Spos^.

5. The method of claim 1, wherein RAPi further comprises at least one of: unpaired probability, ensemble defect, Shannon entropy, solvent accessibility, or a machine-leaming-based accessibility score.

6. The method of claim 1, wherein AGi is computed using a nearest-neighbor thermodynamic model.

7. The method of claim 1, wherein AGi is predicted by a machine-learning model.

8. The method of claim 1, wherein ERTSi is computed using a nonlinear integration of RAPi and AGi.

9. The method of claim 1 , wherein RRTSj is computed using a sliding window of length between 4 and 40 nucleotides.

10. The method of claim 1, wherein the MIS comprises a contiguous subregion.

11. The method of claim 1, wherein the MIS comprises a non-contiguous subset of nucleotide positions.

12. The method of claim 1, further comprising ranking multiple candidate primerbinding regions based on RRTSj, MIS size, AGi, or primer design constraints.

13. The method of claim 1, wherein the primer-binding region is used to design a primer, a probe, or both.

14. The method of claim 1, wherein the primer-binding region is used to design primers for reverse-transcription quantitative PCR (RT-qPCR), digital PCR, LAMP, or RNA amplification.

15. The method of claim 1, wherein the RNA molecule is ribosomal RNA, viral RNA, bacterial RNA, eukaryotic mRNA, or long non-coding RNA.

16. The method of claim 1, wherein the outputted primer-binding region is determined based solely on RAPi without the use of RRTSj.

17. The method of claim 1, wherein the primer-binding region is determined based solely on ERTSi without requiring computation of RRTSj.

18. The method of claim 1, wherein the primer-binding region is determined based on RRTSj without requiring computation of MIS.

19. The method of claim 1, wherein MIS is computed based on ERTSi alone without using RRTSj.

20. The method of claim 1, wherein MIS is determined as the smallest subset of nucleotides for which ERTSi exceeds an initiation threshold independent of the window-based RRTS calculation.

21. The method of claim 1, wherein MIS is computed using a machine-learning classifier trained on experimentally validated initiation regions.

22. The method of claim 1, wherein ERTSi is computed using a model trained on reverse-transcription efficiency data without direct AG calculation.

23. The method of claim 1, wherein RAPi is computed and used to identify a primer-binding region without computing AGi.

24. The method of claim 1, wherein RRTSj is computed using a nonlinear aggregation of ERTSi values such as a geometric mean, harmonic mean, or percentile-based function.

25. The method of claim 1, wherein ERTSi is computed without normalizing for primer length, thereby covering implementations that omit length-dependent corrections.

26. The method of claim 1, wherein the primer-binding region is selected by maximizing RAPi, ERTSi, or RRTSj individually or in combination.

27. The method of claim 1, wherein the primer-binding region encompasses nucleotides corresponding to a top-ranked RAPi region, thereby covering primer selection based solely on RNA accessibility.

28. The method of claim 1, wherein the primer-binding region is selected using ERTSi values even when RAPi values are not explicitly reported to the user.

29. The method of claim 1, wherein the primer-binding region is selected using a version of RRTS computed using variable window sizes, adaptive windows, or windows of unequal length.

30. The method of claim 1, wherein MIS is defined as any subset of contiguous or non-contiguous nucleotides whose aggregate ERTSi value exceeds an initiation threshold, thereby covering alternative MIS definitions.

31. The method of claim 1, wherein RAP, ERTS, or RRTS is not computed by any single-parameter accessibility metric selected from the group consisting of unpaired probability, ensemble defect, minimum free energy structure, or AG-only windows.

32. The method of claim 1, wherein the MIS is computed by integrating both structural ensemble descriptors and RNA-DNA hybridization thermodynamics, and wherein no prior accessibility measure can independently identify the MIS.

33. The method of claim 1, wherein RRTSj identifies a region that could not be detected using AG-only or unpaired-probability-only methods.

34. The method of claim 1, wherein the combination of RAP, ERTS, RRTS, and MIS produces an experimentally measurable reduction in Ct value relative to primers selected using existing methods.

35. A primer comprising the nucleotide sequence of SEQ ID NO:4.

36. A primer comprising the nucleotide sequence of SEQ ID NO:5.

37. A probe comprising the nucleotide sequence of SEQ ID NO:6.

38. A primer pair comprising SEQ ID NO:4 and SEQ ID NO:5.

39. A primer-probe set comprising SEQ ID NO:4, SEQ ID NO: 5, and SEQ ID NO: 6.

40. A kit comprising:• a primer comprising SEQ ID NO:4;• a primer comprising SEQ ID NO:5; and• a probe comprising SEQ ID NO: 6;optionally together with buffers, enzymes, or instructions for detecting Escherichia coli 23 S rRNA.

41. A method for detecting 23S rRNA of Escherichia spp. (including E. coli). comprising:• contacting a sample with a primer pair comprising SEQ ID NO:4 and SEQ ID NO:5;• performing reverse transcription and amplification; and• detecting amplification using a probe comprising SEQ ID NO: 6.

42. Use of a primer comprising SEQ ID NO:4, SEQ ID NO:5, or SEQ ID NO:6 for detecting Escherichia spp. (including E. coll) 23 S rRNA.

43. A method for determining an optimized region within an RNA molecule, comprising integrating ensemble-derived structural metrics with RNA-DNA hybridization thermodynamics and identifying a minimal subregion sufficient to initiate reverse transcription.

Images