A method and system for determining dynamic parameters based on a digital microfluidic chip

Abstract

This invention discloses a method and system for determining kinetic parameters based on a digital microfluidic chip. The method includes: acquiring LSPR response data generated by the digital microfluidic chip during continuous injection of samples of multiple concentrations; acquiring droplet generation, fusion, transport, and arrival at the detection region events recorded by the chip control system; determining concentration switching nodes using droplet events and automatically segmenting the response data; establishing a global kinetic model and solving for parameters using a joint fitting method that shares the binding rate constant Kon, the dissociation rate constant Koff, and the maximum binding response value Rmax; and generating a fitting quality evaluation result. This invention directly uses the chip's own droplet manipulation events as concentration switching driving signals, avoiding traditional methods that rely on manual labeling or fixed timing, significantly improving the automation level and reliability of solving multi-concentration kinetic parameters.

Description

Technical Field

[0001] This invention relates to the field of digital microfluidic chips and biosensor data analysis technology, specifically to a method and system for measuring dynamic parameters based on digital microfluidic chips. Background Technology

[0002] Digital microfluidic chips utilize the dielectric wetting (EWOD) principle to manipulate the generation, transport, fusion, and splitting of discrete droplets, offering advantages such as low reagent consumption, high automation, and ease of integration with multiple functional units. In the fields of biopharmaceuticals and molecular diagnostics, digital microfluidic chips can integrate a full range of functional modules, including sample pretreatment, cell-free protein expression, magnetic bead purification, and localized surface plasmon resonance (LSPR) affinity detection.

[0003] LSPR sensing utilizes the resonant absorption phenomenon of metallic nanostructures to achieve label-free optical detection. Its resonant wavelength is highly sensitive to changes in refractive index near the sensing surface, enabling real-time monitoring of binding-dissociation kinetics between biomolecules. In a single-cycle, multi-concentration kinetic detection mode, analytes of different concentrations are sequentially injected into the same detection channel in ascending order, without surface regeneration between concentrations. Finally, affinity kinetic parameters are extracted through global fitting.

[0004] However, existing solutions have significant shortcomings in identifying multiple concentration switching nodes. Operators typically rely on manually marking injection time points or automatically dividing concentration segments according to a preset fixed time sequence. Manual marking is inefficient and heavily influenced by operator experience; the fixed time sequence method cannot adapt to unforeseen deviations in actual operation, such as droplet velocity fluctuations, electrode response delays, or microchannel blockages. If the concentration switching node is not accurately located, subsequent curve segmentation will produce errors, leading to significant deviations in key parameters such as Kon and Koff obtained from global fitting.

[0005] Therefore, there is an urgent need in the field for a technical solution that can automatically and reliably identify concentration switching nodes using the droplet manipulation event signals of the digital microfluidic chip itself, and based on this, complete the automatic segmentation of the response curve and the solution of global dynamic parameters. Summary of the Invention

[0006] To address the problem that existing technologies rely on manual labeling or fixed timing for concentration switching node identification, leading to inaccurate segmentation of multi-concentration LSPR response data and large deviations in kinetic parameter measurement, this invention provides the following technical solution.

[0007] The first aspect of this invention provides a method for determining dynamic parameters based on a digital microfluidic chip, comprising the following steps: S1. Acquire LSPR response data generated by the digital microfluidic chip during the continuous injection of multiple samples of different concentrations; S2. Obtain droplet events and corresponding event information recorded by the digital microfluidic chip control system. The droplet events include droplet generation events, droplet fusion events, droplet transport events, and droplet arrival at the detection area events. The event information includes event type, timestamp, and droplet identification. S3. Based on the timestamp of the droplet arrival event in the droplet event, determine the concentration switching nodes corresponding to samples of different concentrations; S4. The LSPR response data is automatically segmented according to the concentration switching node to obtain multiple concentration response segments and dissociation response segments; S5. Establish a global dynamic model that includes multiple concentration response zones; S6. The global dynamic model is solved by a joint fitting method using shared binding rate constant Kon, shared dissociation rate constant Koff, and shared maximum binding response value Rmax. S7 outputs the binding rate constant Kon, the dissociation rate constant Koff, and the equilibrium dissociation constant KD between target molecules.

[0008] Optionally, the determination of the S3 concentration switching node includes: A candidate concentration switching event sequence is established based on the timestamp of the droplet arriving at the detection area. The first derivative sequence of the sensor response curve obtained from the LSPR response data is calculated within a preset time window before and after the timestamp of the droplet arriving at the detection area. If there is a peak point within the window whose absolute value of the derivative exceeds a preset multiple standard and the deviation between the time corresponding to the peak point and the timestamp of the droplet arriving at the detection area is within a preset tolerance, then the time corresponding to the peak point is taken as the concentration switching node. If there is no peak point that meets the conditions or the deviation exceeds the limit within the window, the timestamp of the droplet arriving in the detection area plus the pre-calibrated system delay bias is used as the concentration switching node.

[0009] In some embodiments, step S4 uses an event-driven segmentation method to obtain at least two concentration response segments and a dissociation response segment from the sensing response curve obtained from the LSPR response data. The number of concentration response segments is automatically determined by the number of events where droplets arrive at the detection area.

[0010] Optionally, the global dynamic model established in step S5 satisfies the following formula: dR(t) / dt=Kon·Ci·(Rmax-R(t))-Koff·R(t), Where Ci is the analyte concentration corresponding to the i-th concentration response segment, R(t) is the binding response value at time t, Kon is the binding rate constant, Koff is the dissociation rate constant, and Rmax is the maximum binding response value.

[0011] Furthermore, multiple concentration response segments share the same set of Kon, Koff, and Rmax parameters, and parameter fitting is completed simultaneously through a global optimization algorithm.

[0012] The global optimization algorithm includes one or more of the following: nonlinear least squares fitting algorithm, Levenberg-Marquardt algorithm, or trust region optimization algorithm.

[0013] In some embodiments, step S6 is followed by: generating a fitting quality evaluation result based on the fitting residuals, parameter stability, and model convergence, wherein the fitting quality evaluation result includes at least the goodness of fit R. 2 At least one of the following: root mean square error (RMSE) and coefficient of variation (CV).

[0014] A second aspect of the present invention provides a dynamic parameter measurement system based on a digital microfluidic chip, comprising: The data acquisition module is used to acquire LSPR response data generated by the digital microfluidic chip during the continuous injection of multiple samples of different concentrations; The droplet event acquisition module is used to acquire droplet events and corresponding event information recorded by the digital microfluidic chip control system. The droplet events include droplet generation events, droplet fusion events, droplet transport events, and droplet arrival at the detection area events. The event information includes event type, timestamp, and droplet identification. The concentration switching identification module is used to determine the concentration switching nodes corresponding to different concentration samples based on the timestamp of the droplet arrival in the detection area in the droplet event. The concentration switching nodes are determined by jointly judging the change rate of the sensing response curve obtained from the LSPR response data based on the timestamp of the droplet arrival in the detection area. The automatic curve segmentation module is used to automatically segment the sensing response data according to the concentration switching node to obtain at least two concentration response segments and a dissociation response segment. The global dynamics modeling module is used to build a global dynamics model that includes multiple concentration response regions; The joint fitting module is used to solve the parameters of the global dynamic model by using a joint fitting method that shares the binding rate constant Kon, the dissociation rate constant Koff, and the maximum binding response value Rmax. The quality evaluation module is used to generate fitting quality evaluation results based on fitting residuals, parameter stability, and model convergence. The results output module is used to output the binding rate constant Kon, the dissociation rate constant Koff, and the equilibrium dissociation constant KD between target molecules.

[0015] Furthermore, the system is communicatively connected to the digital microfluidic chip control module and receives droplet scheduling event information.

[0016] Compared with the prior art, the present invention has at least the following beneficial effects: (1) Use droplet manipulation events instead of manual marking or fixed timing as the driving signal for concentration switching. The digital microfluidic chip control system generates state events with precise timestamps and droplet identity information every time it performs droplet generation, fusion, and transport operations. These events are directly used for concentration switching node identification, eliminating the delay and deviation introduced by manual operation, and fundamentally improving the accuracy and repeatability of switching node positioning.

[0017] (2) The event-driven segmentation mechanism does not rely on a preset fixed timing sequence and automatically adapts to timing fluctuations in actual operation. Even if the droplet movement speed is deviated due to the influence of ambient temperature, chip surface aging or sample viscosity changes, as long as the event is correctly triggered when the detection area is reached, the positioning of the concentration switching node remains accurate.

[0018] (3) The joint fitting strategy of sharing Kon, Koff and Rmax for multiple concentrations is adopted, which effectively reduces the degree of freedom of parameter estimation and has better statistical reliability than the traditional method of fitting each concentration independently. It is especially suitable for the analysis of trace samples in single-cycle multi-concentration detection mode. Attached Figure Description

[0019] Exemplary embodiments of the present invention can be more fully understood by referring to the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain the present invention and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0020] Figure 1 This is a schematic flowchart of a method for determining dynamic parameters based on a digital microfluidic chip, provided in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram illustrating the correspondence between droplet events and LSPR response data provided in an embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram illustrating the automatic identification of concentration switching nodes based on droplet events, provided in an embodiment of the present invention.

[0023] Figure 4 This is a schematic diagram of the dynamic parameter measurement system based on a digital microfluidic chip provided in an embodiment of the present invention.

[0024] Figure Labels 10—Data Acquisition Module; 20—Droplet Event Acquisition Module; 30—Concentration Switching Recognition Module; 40—Automatic Curve Segmentation Module; 50—Global Dynamics Modeling Module; 60—Joint Fitting Module; 70—Quality Evaluation Module; 80—Result Output Module. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0026] Those skilled in the art should understand that in the embodiments of this application, "a plurality of" can refer to two or more, and "at least one" can refer to one, two, or more. Techniques, methods, and devices known to those skilled in the art are not discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification.

[0027] Furthermore, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn to actual scale. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. Moreover, the technical features involved in the different embodiments of the invention described below can be combined with each other as long as they do not conflict with each other.

[0028] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the term "digital microfluidics (DMF)" refers to microfluidic technology that utilizes the principle of dielectric wetting to apply voltage to an electrode array on the surface of a chip to drive nanoliter to microliter droplets for generation, transport, fusion, and splitting. A typical digital microfluidic chip uses a glass substrate, a high dielectric constant material as the dielectric layer, and a low surface energy fluoropolymer as the hydrophobic layer. The chip operates through oil-phase encapsulation to suppress the evaporation of nanoliter droplets during long-term operation.

[0029] The term "localized surface plasmon resonance (LSPR)" refers to the resonant absorption phenomenon generated by the collective oscillation of localized surface plasmons in a metallic nanostructure under incident light irradiation. The resonance wavelength is extremely sensitive to changes in refractive index in the nanoscale range near the sensing surface, and can be used for real-time, label-free monitoring of biomolecule binding-dissociation dynamics.

[0030] The term "droplet event" refers to the operational events recorded in a structured format by the digital microfluidic chip control system during the execution of droplet manipulation commands. Droplet events, functionally categorized, include at least the following four types: droplet generation events (recording the droplet's identifier, target volume, generation electrode position, and generation completion timestamp); droplet fusion events (recording the identifiers of participating droplets, the fused droplet's identifier, the fusion electrode position, and the fusion completion timestamp); droplet transport events (recording the droplet's identifier, starting electrode, target electrode, and arrival timestamp); and droplet arrival in the detection area events (recording the droplet's identifier, the detection area inlet electrode position, and arrival timestamp). Each droplet event carries at least three pieces of information: an event type label, an occurrence timestamp, and a droplet identifier.

[0031] The term "global kinetic model" refers to a modeling approach that integrates the kinetic processes of multiple concentration response regions under a unified mathematical model framework, describing them holistically using shared kinetic parameters (Kon, Koff, Rmax). Compared to independent fitting at each concentration, the global kinetic model reduces the degrees of freedom in fitting and improves the statistical reliability of parameter estimates by constraining the kinetic parameters of the same analyte-ligand system to remain constant at different concentrations.

[0032] The term "concentration switching node" refers to the time boundary at which different concentrations of analyte samples arrive at the LSPR detection region and begin to exert a detectable influence on the sensing signal. In multi-concentration continuous injection experiments, samples of different concentrations enter the detection channel sequentially, and the concentration switching node is used to determine the segment boundaries of each concentration response segment in the LSPR response data. The accuracy of the concentration switching node location directly determines the accuracy of subsequent curve segmentation and the reliability of kinetic parameter fitting.

[0033] The term "joint fitting" refers to a fitting strategy in which the binding rate constant Kon, the dissociation rate constant Koff, and the maximum binding response value Rmax are set as global parameters shared by all concentration ranges when fitting Langmuir kinetic model data for multi-concentration LSPR response data, and the optimal global parameter estimates are obtained simultaneously through a single optimization process.

[0034] The term "sensor response curve" refers to the response signal curve obtained by changing LSPR response data over time, with time on the horizontal axis and the amplitude of the optical response signal reflecting the bonding-dissociation process of the sensing surface on the vertical axis.

[0035] The term "event-driven segmentation" refers to a segmentation method that uses the timestamp of droplet manipulation events (especially the event of droplets arriving at the detection area) as the segmentation boundary driving signal to automatically divide the LSPR response data sequence into multiple concentration response segments and dissociation response segments without relying on manual labeling or fixed timing.

[0036] The term "single-cycle multi-concentration (SCK) mode" refers to a detection mode in which different concentrations of analytes are continuously injected into the same detection channel in ascending order during a single experimental cycle, without sensor surface regeneration between concentrations, and the kinetic parameters are finally extracted through global fitting.

[0037] The term "multi-cycle kinetics (MCK) mode" refers to a detection mode in which each concentration corresponds to an independent binding-dissociation cycle, and the cycles include a regeneration step of the sensing surface (e.g., elution with low pH glycine buffer). The response data of each cycle can be incorporated into the detection mode for global fitting or independent fitting.

[0038] Please see Figure 1 A method for determining dynamic parameters based on a digital microfluidic chip, comprising: Step S1: Obtain LSPR response data generated by the digital microfluidic chip during the continuous injection of multiple samples of different concentrations.

[0039] Specifically, the raw spectral signal I_sample transmitted through the LSPR detection area is continuously acquired using a miniature spectrometer at a preset sampling frequency. Simultaneously, a light source intensity reference spectrum I_ref is acquired through a light source reference fiber. The following preprocessing sub-steps are performed sequentially on each frame of spectral data: (a) Dark current subtraction—Based on the dark current spectrum I_dark obtained by averaging the preset number of frames collected under the condition of blocking the light source before the experiment, perform I_sample'=I_sample-I_dark on each frame of the original spectrum; (b) Light source fluctuation normalization—The spectrum after dark current subtraction is normalized according to the formula I_norm=(I_sample'-I_dark) / (I_ref-I_dark) to eliminate the interference of low-frequency drift of light source intensity over time on the LSPR signal; (c) Smoothing filter—Apply a digital smoothing filter to the normalized spectrum to suppress high-frequency random noise while preserving the shape characteristics of the resonance peaks.

[0040] After preprocessing, the resonant peak wavelength is calculated using a peak tracking algorithm.

[0041] Preferably, the centroid method can be used to calculate the weighted average wavelength within a preset wavelength window (e.g., ±20~50 nm) near the nominal resonance peak, using the normalized intensity at each wavelength point as the weight. The centroid method features subwavelength accuracy and insensitivity to local noise. By calculating the resonance peak wavelength frame by frame, time-series data R(t) of the LSPR response is formed, which reflects the real-time binding-dissociation kinetics between analyte molecules and ligand molecules on the sensing surface. The wavelength range, optical resolution, and sampling rate of the spectrometer can be selected according to specific experimental requirements, such as using a miniature fiber optic spectrometer with a wavelength range of 400~1000 nm and an optical resolution better than 1 nm.

[0042] Step S2: Obtain the droplet events and corresponding event information recorded by the digital microfluidic chip control system.

[0043] For details, please refer to Figure 2 and Figure 3 The firmware of the digital microfluidic chip control system synchronously records droplet manipulation event logs during experimental operation. The logs are organized in structured data formats (e.g., JSON, Protocol Buffers, or a custom binary format), with each record corresponding to one droplet manipulation operation. Event log generation occurs synchronously with the execution of droplet manipulation commands; the firmware writes the logs immediately upon command completion, independent of operator marking or external triggering. Droplet generation events record the droplet's identifier, target volume, generation electrode position, and generation completion timestamp; droplet fusion events record the identifiers of participating droplets, the fused droplet's identifier, the fusion electrode position, and the fusion completion timestamp; droplet transport events record the droplet identifier, starting electrode, target electrode, and timestamp of arrival at the target electrode; and droplet arrival at the detection area events record the droplet identifier, the detection area inlet electrode position, and the arrival timestamp. Event timestamps are generated by the chip controller's hardware timer with millisecond-level precision.

[0044] For an experimental run containing N analyte samples of different concentrations, the chip generates sample droplets of each concentration in ascending order and transports them to the LSPR detection area.

[0045] Accordingly, the droplet event log contains N sets of droplet manipulation event sequences. Each set of sequences includes: the generation event of the sample droplet of this concentration (recording the droplet ID and the time of generation completion), one or more transport events (recording the arrival time of each segment of transport along the path from the generation location to the detection area), the fusion event when the buffer or reference solution needs to be mixed, and the final droplet arrival event in the detection area (recording the precise time when the droplet enters the inlet electrode of the detection area).

[0046] Compared with the traditional method of manually recording injection time by the operator, the event log generated by the chip firmware has at least the following advantages: the timestamp accuracy is in the millisecond range, there is no delay in human response, the association between the event and the droplet identity is automatically maintained by the system, and there is a complete event traceability chain.

[0047] Step S3: Determine the concentration switching nodes corresponding to samples of different concentrations based on droplet events.

[0048] Specifically, the timestamps of all droplet arrival events in the detection area are extracted from the event log of step S2 to obtain the timestamp sequence {t_arrive_i} (i=1,2,...,N) of candidate switching nodes. To further improve the node positioning accuracy, a joint judgment mechanism based on the signal characteristics of the sensor response curve itself is introduced. For each candidate timestamp t_arrive_i, the first derivative dR / dt sequence of the sensor response curve is calculated within a preset time window before and after it. The injection of analyte causes a step change in the refractive index of the sensing surface, resulting in obvious positive or negative peaks in dR / dt at the moment of switching. The mean and standard deviation of dR / dt within this window are calculated, and peaks whose absolute values ​​exceed a preset multiple of the mean are identified.

[0049] The final concentration switching node t_switch_i is determined using the following dual rules: Rule 1: If there is a sampling point within the window that meets the above peak conditions, and the absolute deviation between the time corresponding to the peak point and the candidate event timestamp t_arrive_i is within the preset tolerance (e.g., ±1~5 seconds), then the time corresponding to the peak point is taken as t_switch_i. At this time, the droplet event and the rate of change of the sensing response curve signal mutually confirm each other, and the node positioning confidence is the highest. Rule 2: If there is no peak point that meets the conditions within the window, or if the peak point deviation exceeds the limit, the candidate event timestamp plus a pre-calibrated system delay bias is used as t_switch_i. This bias can be calibrated through pre-experimentation, that is, the average delay time between the droplet entering the inlet electrode of the detection area and the start of the sensing signal generating a detectable change is determined in advance.

[0050] Typical scenarios that cause a fallback from Rule 1 to Rule 2 include: in the high-concentration range, the derivative spike at the moment of switching is not obvious due to the response approaching saturation; or in the low-concentration range, the spike is submerged by noise due to the low signal-to-noise ratio. These dual rules ensure the robustness of this method under different concentration ranges and different signal-to-noise ratios; under conditions of complete event logs and good signal-to-noise ratio, most nodes are determined by Rule 1; in a few abnormal cases, it automatically falls back to Rule 2, avoiding interruption of the entire analysis process due to the absence of individual nodes.

[0051] Step S4: The LSPR response data is automatically segmented according to the concentration switching node to obtain multiple concentration response segments and dissociation response segments.

[0052] Specifically, based on the N concentration switching nodes {t_switch_i} determined in step S3, the LSPR response data sequence R(t) is automatically divided into N+1 segments. Segmentation is indexed by timestamps, eliminating the need for manual specification of the number of segments or boundary positions. The first N segments are concentration response segments—the time range of the i-th segment extends from t_switch_i to the next node, corresponding to the binding-dissociation response process of the i-th concentration analyte sample; the N+1-th segment is the dissociation response segment, corresponding to the dissociation process after the last concentration analyte injection is completed. The response data of this segment is used to fit the dissociation rate constant Koff.

[0053] After segmentation, baseline zeroing is performed on each concentration response segment: the mean value of R(t) within a preset short-time window before the segment's start time t_switch_i is used as the baseline offset for that segment, and baseline subtraction is performed on the response values ​​of all sampling points within the segment. Baseline zeroing ensures that each concentration response segment starts from a unified zero response value, eliminating potential baseline drift differences between concentration segments and improving the numerical stability of subsequent joint fitting. The baseline zeroing process for the dissociation response segment is similar to that for the concentration response segment, but the actual response level carried over from the last concentration segment is retained to accurately reflect the dissociation process.

[0054] In an alternative implementation, the data integrity of each segment can be checked after segmentation: if a segment has missing response data or a low signal-to-noise ratio due to droplet manipulation anomalies (e.g., droplet loss or path error), the system automatically marks the segment as invalid and excludes it from subsequent joint fitting. This anomaly segment detection can be based on a combination of anomaly event records in the droplet event log (e.g., droplet loss events or droplet positioning failure events) and statistical characteristics of the response data.

[0055] Step S5: Establish a global dynamic model that includes multiple concentration response zones.

[0056] Based on the 1:1 reversible binding reaction A + L = AL between analyte molecule A and fixed ligand molecule L, the Langmuir pseudo-first-order kinetic model is adopted: dR(t) / dt=Kon·Ci·(Rmax-R(t))-Koff·R(t); Where Ci is the analyte concentration in the i-th concentration response segment, R(t) is the response value at time t, and Kon is the binding rate constant (M). -1 s -1 Koff is the dissociation rate constant (s). -1Rmax is the maximum binding response value, Ci is determined by the experimental design, and Kon, Koff and Rmax are the fitting parameters to be solved.

[0057] Kon, Koff, and Rmax were set as shared global parameters across all N concentration response ranges. The physicochemical basis for this setting is that the microscopic binding rate constant and dissociation rate constant between the same analyte and the same ligand are determined by the properties of the molecule itself and do not change with analyte concentration under the same temperature and buffer conditions (law of mass action). Meanwhile, in a single experiment, the number of ligands immobilized on the sensing surface does not change significantly between concentration transitions, therefore Rmax is also a fixed value. By using the above three parameters as shared variables, response data from all concentration ranges are simultaneously included in the fitting process, effectively reducing the degrees of freedom in the fitting and improving the statistical reliability of parameter estimation compared to traditional methods that fit each concentration range independently.

[0058] In alternative implementations, other kinetic models can be selected and the shared parameter set adjusted accordingly based on the actual molecular binding mode. For example, for binding reactions involving mass transfer constraints, the mass transfer coefficient can be added as a global or local parameter; for two-site binding modes, two sets of parameters (Kon, Koff, Rmax) can be set to describe high-affinity and low-affinity sites respectively; for cases requiring description of ligand surface isomerism, the Gaussian distribution or the Langmuir-Freundlich model can be used.

[0059] Step S6: Solve the parameters of the global dynamic model by using a joint fitting method of shared Kon, shared Koff, and shared Rmax.

[0060] Specifically, a global optimization algorithm is used for joint fitting, and the objective function for optimization is the weighted sum of squared residuals between the model predictions and observed values ​​across all concentration response segments: χ 2 =ΣiΣj[(R_obs,ij-R_fit,ij) 2 / σ_ij 2 ]+χ 2 _dissoc; Where R_obs,ij and R_fit,ij are the observed value and model predicted value of the j-th data point in the i-th concentration segment, respectively, and σ_ij 2 χ is the noise variance at that point (which can be estimated from the local signal fluctuations in the neighborhood of that point). 2 _dissoc is the sum of squared residuals for the dissociated response segment.

[0061] In some embodiments, the optimization algorithms that can be used include nonlinear least squares fitting algorithms, such as the Levenberg-Marquardt algorithm and trust region optimization algorithms. The Levenberg-Marquardt algorithm adaptively adjusts the weight parameters between gradient descent and the Gaussian-Newton step size. It quickly approximates the optimal solution using gradient descent when the parameter space is far from it, and switches to Gaussian-Newton to achieve quadratic convergence when it is close to the optimal solution. It is particularly suitable for scenarios with a small number of fitting parameters (only 3 shared parameters). Trust region optimization algorithms determine the search direction and step size by solving constraint subproblems in the neighborhood of the current parameter point, and have advantages in handling parameter boundary constraints.

[0062] Regarding algorithm parameter settings, the parameter search boundary is used to prevent the fit from diverging (for example, Kon can set the lower search bound to 10). 1 M -1 s -1 and the upper realm 10 9 M -1 s -1 Koff sets the lower bound to 10. -7 s -1 and the upper realm 10 0 s -1 Rmax is set with a lower bound of 0 and an upper bound that is a preset multiple of the maximum observed response; the initial guesses for the parameters can be set based on prior knowledge or heuristic rules (for example, the initial value of Rmax can be the mean response of the latter half of the highest concentration region, and the initial values ​​of Kon and Koff can be the typical order of magnitude for that protein type); the iteration termination condition is χ². 2 The relative change is lower than a preset threshold (e.g., 10). -6 (or reach the preset maximum number of iterations (e.g., 200~1000 times).)

[0063] In an alternative implementation, Bayesian inference methods can be used instead of point estimation optimization. For example, samples can be generated from the posterior distribution of the parameters using Markov chain Monte Carlo (MCMC) sampling, obtaining the optimal parameter estimate along with the uncertainty distribution (posterior probability density). This method, by introducing a prior distribution of the parameters (e.g., an empirical distribution based on historical experimental data), can still provide relatively robust parameter interval estimates even with poor data quality or a limited number of concentration points, and naturally provides uncertainty quantification indicators such as the parameter coefficient of variation.

[0064] Step S7: Output the binding rate constant Kon, dissociation rate constant Koff, and equilibrium dissociation constant KD between target molecules, where KD = Koff / Kon.

[0065] First, the fitting quality evaluation results are generated based on the fitting residuals, parameter stability, and model convergence.

[0066] Specifically, after the joint fitting converges, one or more of the following fitting quality evaluation indicators are calculated to help the operator judge the reliability and usability of the results: Goodness-of-fit metrics, such as the coefficient of determination R. 2 =1-SS_res / SS_tot, where SS_res is the residual sum of squares, SS_tot is the total sum of squares, and R 2 The closer R is to 1, the higher the model's interpretability of the data. 2 If the value is below a preset threshold (e.g., 0.90 or 0.95), a warning message will be displayed indicating that the model may have mismatch or data quality issues.

[0067] Root mean square error (RMSE) = sqrt[Σ(R_obs - R_fit)] 2 / (N_total-p)], where N_total is the total number of data points involved in the fitting, p is the number of fitting parameters, and RMSE measures the magnitude of the prediction error in the same units as the original response data. Normalized RMSE can also be used to eliminate the influence of signal amplitude differences on index interpretation.

[0068] The coefficient of variation (CV) of each fitted parameter is calculated by extracting the standard error of the parameter from the diagonal elements of the covariance matrix. CV = std(parameter estimate) / parameter estimate. If the CV of Kon and Koff is too high, it indicates that the parameter lacks sufficient observation data constraints and the estimation result is unreliable.

[0069] Statistical tests on residual distribution: Perform statistical tests on the fitted residual sequence to determine whether it is randomly distributed. Optional test methods include the runs test (used to detect non-random trends in the residual sequence) or the Durbin-Watson test (used to detect first-order autocorrelation of the residuals). If the test p-value is lower than the preset significance level, it indicates that there is a systematic bias in the residuals, which may be caused by model mismatch, baseline drift, or outlier data points.

[0070] Based on the comparison results of the above indicators with their respective preset thresholds, a comprehensive evaluation conclusion is generated. The evaluation conclusion is divided into at least three categories: "Pass," indicating that all key indicators meet the preset thresholds, the system automatically outputs parameters, and the operator can use the results for downstream analysis without further verification; "Review," indicating that some indicators are in the boundary region (e.g., R...). 2 If the value is between 0.88 and 0.95, or Kon's CV is between 30% and 50%, the system outputs parameters along with clear diagnostic information (specifically listing which indicators have not reached the ideal level and the possible reasons). It is recommended that the operator manually review the output to decide whether to adopt the results. Invalid results indicate that the key indicators have seriously deviated from the preset threshold (e.g., R0). 2If the value is <0.80 or Kon's CV is >80%, the system will not output any parameters or will only output parameters with invalid flags. At the same time, it will output the reason for the failure and possible improvement suggestions (such as suggesting to increase the number of concentration gradients, extend the monitoring time of each concentration range, check the abnormal event records of the droplet manipulation process, or investigate the activity of ligands on the sensor surface).

[0071] The aforementioned quality evaluation system ensures the comparability of results between different experimental batches, and the accumulated evaluation data can serve as a basis for automatic optimization of subsequent experimental parameters. For example, if invalid conclusions from multiple consecutive batches of experiments are concentrated in the low concentration range, the system can suggest that the operator increase the volume of the lowest concentration or extend the monitoring time in the low concentration range in subsequent experiments.

[0072] Then, the binding rate constant Kon, the dissociation rate constant Koff, and the equilibrium dissociation constant KD between the target molecules are output, where KD = Koff / Kon.

[0073] Specifically, when the evaluation conclusion is "pass," the system outputs Kon, Koff, KD, and a complete fit quality evaluation report (including numerical values ​​for each indicator). The output format can be selected as structured text (e.g., JSON, CSV, XML) or directly written to a database (e.g., SQLite, PostgreSQL), facilitating automatic retrieval by downstream informatics systems (e.g., candidate molecule ranking, structure-activity relationship analysis, machine learning model training). When the evaluation conclusion is "review," the output parameters are accompanied by clear confidence level markers and diagnostic information, allowing the operator to review the data and make a final decision based on the diagnostic suggestions. When the evaluation conclusion is "invalid," a detailed analysis report of the failure reasons is output, including specific indicators of non-compliance, possible experimental problem diagnoses, and specific improvement suggestions, helping the operator quickly locate the problem and reduce the blindness of repeated experiments.

[0074] As a preferred approach, this method can be extended in several dimensions to adapt to different experimental needs and application scenarios.

[0075] Regarding the adaptive number of concentration segments, the number N of concentration segments is automatically determined by the number of droplet arrival events in the droplet event log, without requiring pre-specification by the operator. This means that this method is inherently compatible with different experimental channels on the same chip using different numbers of concentration gradients. For example, channel A performs fine characterization with 5 concentration gradients, while channel B performs rapid initial screening with 2 concentration gradients. The system automatically completes its segmentation and fitting based on the independent event logs of each channel.

[0076] Regarding compatibility with the Multi-Period Kinetics (MCK) mode, each concentration in MCK mode corresponds to an independent binding-dissociation cycle, with regeneration steps of the sensing surface (e.g., elution with low-pH glycine buffer) between cycles. In this mode, the droplet event log contains both operational events of the regenerated droplets and operational events of sample droplets at each concentration. The concentration switching recognition module achieves correct node identification in MCK mode by filtering by event type (extracting only arrival events of concentration sample droplets and excluding events related to the regenerated droplets). The response data for each cycle, after being segmented, can be included in global fitting or independent fitting respectively. The node identification method in MCK mode is similar to that in SCK mode, which will not be elaborated further here.

[0077] Regarding the expansion of detection modes, this method is also applicable to other real-time sensing and detection modes based on digital microfluidic chips, such as surface plasmon resonance (SPR), biolayer interference (BLI), fluorescence resonance energy transfer (FRET), or electrochemical impedance spectroscopy. As long as the detection system generates continuous time-series response data and the chip control system synchronously records droplet manipulation events, the droplet event-driven segmentation and joint fitting strategy of this method can be applied.

[0078] For combined verification of droplet event types, other droplet event types can be introduced for redundant verification. For example, by combining the timestamp of the droplet generation event and the preset transport path length, the estimated time for the droplet to reach the detection area from the generation location can be estimated, and this estimated time can be cross-checked with the timestamp of the actual droplet arrival event. If the deviation exceeds a preset threshold, an alarm is triggered, indicating that there may be an abnormal droplet path or transport delay. In this case, a conservative segmentation strategy can be adopted (e.g., expanding the uncertainty interval near the node, or reducing the fitting weight of the data in that segment).

[0079] Regarding event-driven baseline drift correction, in long-term experiments, LSPR sensors may drift slowly due to surface aging, light source attenuation, or temperature fluctuations. The system can periodically (e.g., at several concentration intervals) inject blank buffer control droplets into the detection channel and record their arrival at the detection area, using the blank control response data to track and correct baseline drift. The timing of blank control droplet injection is autonomously maintained by the event log and does not interfere with concentration switching events.

[0080] Please see Figure 4 A dynamic parameter measurement system based on a digital microfluidic chip includes a data acquisition module 10, a droplet event acquisition module 20, a concentration switching recognition module 30, an automatic curve segmentation module 40, a global dynamic modeling module 50, a joint fitting module 60, a quality evaluation module 70, and a result output module 80.

[0081] Specifically, the data acquisition module 10 establishes a connection with the spectrometer via a communication interface (e.g., USB or Ethernet), acquiring spectral data streams in real time using a callback or polling method. This shields the differences in underlying communication protocols between spectrometers from different manufacturers, providing a unified data format to the upper-layer modules. The droplet event acquisition module 20 connects to the digital microfluidic chip control module via a serial interface (e.g., SPI or UART) or USB, receiving droplet event packets pushed in real time by the chip firmware. It parses the binary event packets into a unified structured event object (containing fields such as event type, timestamp, and droplet ID), and maintains an event queue sorted by timestamp.

[0082] The concentration switching identification module 30 subscribes to the event stream and response data stream of the droplet event acquisition module 20, maintains a sliding time window buffer, and automatically triggers the dual verification process described in step S3 when a droplet arrival event is detected. This module can maintain a state machine internally, with states including idle (waiting for events), verification in progress (performing derivative spike analysis), confirmed (node ​​determined), and abnormal (event missing or verification failed). The automatic curve segmentation module 40 receives the confirmed node sequence output by the concentration switching identification module 30, performs segmentation and baseline zeroing on the buffered response data according to the method described in step S4, and outputs the segmentation results in the form of a segment object array.

[0083] The global dynamics modeling module 50 and the joint fitting module 60 work closely together. The modeling module constructs the objective function and parameter constraints based on the number of segments and the corresponding concentration values ​​of the segments, while the fitting module calls the selected optimization algorithm library to perform numerical optimization. These two modules can be implemented based on scientific computing libraries (such as Python's NumPy / SciPy or C++'s Ceres Solver / GSL), using ODE numerical integrators, such as LSODA or RK45, to solve the differential equations corresponding to each concentration segment, generating model prediction values ​​for each iteration step. The quality evaluation module 70 and the result output module 80 generate evaluation and output results according to the method described in step S7 above.

[0084] The modules described above can be implemented as software modules, running on embedded processors or general-purpose computers. Data exchange between modules can occur through mechanisms such as message buses, shared memory, or function calls. In one implementation, the data acquisition module 10 and the droplet event acquisition module 20 run as independent background threads, each maintaining its own data buffer. Upper-level modules consume data using event-driven or timed polling methods. This asynchronous architecture avoids the processing delay of a single module blocking the data acquisition stream. Further details about this system can be found in the descriptions of the methods described above, and will not be repeated here.

[0085] Finally, it should be understood that the embodiments described in this specification are merely illustrative of the principles of the embodiments described herein. Other variations may also fall within the scope of this specification. Therefore, alternative configurations of the embodiments described herein are intended to be illustrative rather than limiting, and should be considered consistent with the teachings of this specification. Accordingly, the embodiments described herein are not limited to those explicitly introduced and described herein.

Claims

1. A method for determining dynamic parameters based on a digital microfluidic chip, characterized in that, Includes the following steps: S1. Acquire LSPR response data generated by the digital microfluidic chip during the continuous injection of multiple samples of different concentrations; S2. Obtain droplet events and corresponding event information recorded by the digital microfluidic chip control system. The droplet events include droplet generation events, droplet fusion events, droplet transport events, and droplet arrival at the detection area events. The event information includes event type, timestamp, and droplet identification. S3. Based on the timestamp of the droplet arrival event in the droplet event, determine the concentration switching nodes corresponding to samples of different concentrations; S4. The LSPR response data is automatically segmented according to the concentration switching node to obtain multiple concentration response segments and dissociation response segments; S5. Establish a global dynamic model that includes multiple concentration response zones; S6. The global dynamic model is solved by a joint fitting method using shared binding rate constant Kon, shared dissociation rate constant Koff, and shared maximum binding response value Rmax. S7 outputs the binding rate constant Kon, the dissociation rate constant Koff, and the equilibrium dissociation constant KD between target molecules.

2. The method for determining kinetic parameters according to claim 1, characterized in that, The method for determining the concentration switching nodes corresponding to samples of different concentrations in S3 includes: A candidate concentration switching event sequence is established based on the timestamp of the droplet arriving at the detection area. The first derivative sequence of the sensor response curve obtained from the LSPR response data is calculated within a preset time window before and after the timestamp of the droplet arriving at the detection area. If there is a peak point within the window whose absolute value of the derivative exceeds a preset multiple standard and the deviation between the time corresponding to the peak point and the timestamp of the droplet arriving at the detection area is within a preset tolerance, then the time corresponding to the peak point is taken as the concentration switching node. If there is no peak point that meets the conditions or the deviation exceeds the limit within the window, the timestamp of the droplet arriving in the detection area plus the pre-calibrated system delay bias is used as the concentration switching node.

3. The method for determining kinetic parameters according to claim 1, characterized in that, In step S4, the event-driven segmentation method is used to automatically divide the sensing response curve obtained from the LSPR response data to obtain at least two concentration response segments and a dissociation response segment. The number of concentration response segments is automatically determined by the number of events of droplets arriving at the detection area.

4. The method for determining kinetic parameters according to claim 1, characterized in that, The global dynamic model established in step S5 satisfies: dR(t) / dt=Kon·Ci·(Rmax-R(t))-Koff·R(t); Where: Ci is the analyte concentration corresponding to the i-th concentration response segment; R(t) is the binding response value at time t; Kon is the binding rate constant; Koff is the dissociation rate constant; and Rmax is the maximum binding response value.

5. The method for determining dynamic parameters according to claim 4, characterized in that, Multiple concentration response ranges share the same set of Kon, Koff, and Rmax parameters, and parameter fitting is completed simultaneously through a global optimization algorithm.

6. The method for determining dynamic parameters according to claim 5, characterized in that, The global optimization algorithm includes one or more of the following: nonlinear least squares fitting algorithm, Levenberg-Marquardt algorithm, or trust region optimization algorithm.

7. The method for determining kinetic parameters according to claim 1, characterized in that, Step S6 is followed by: generating a fitting quality evaluation result based on the fitting residuals, parameter stability, and model convergence, wherein the fitting quality evaluation result includes at least the goodness of fit R. 2 At least one of the following: root mean square error (RMSE) and coefficient of variation (CV).

8. A dynamic parameter measurement system based on a digital microfluidic chip, characterized in that, include: The data acquisition module is used to acquire LSPR response data generated by the digital microfluidic chip during the continuous injection of multiple samples of different concentrations; The droplet event acquisition module is used to acquire droplet events and corresponding event information recorded by the digital microfluidic chip control system. The droplet events include droplet generation events, droplet fusion events, droplet transport events, and droplet arrival at the detection area events. The event information includes event type, timestamp, and droplet identification. The concentration switching identification module is used to determine the concentration switching nodes corresponding to different concentration samples based on the timestamp of the droplet arrival in the detection area in the droplet event. The concentration switching nodes are determined by jointly judging the change rate of the sensing response curve obtained from the LSPR response data based on the timestamp of the droplet arrival in the detection area. The automatic curve segmentation module is used to automatically segment the LSPR response data according to the concentration switching node to obtain at least two concentration response segments and a dissociation response segment. The global dynamics modeling module is used to build a global dynamics model that includes multiple concentration response regions; The joint fitting module is used to solve the parameters of the global dynamic model by using a joint fitting method that shares the binding rate constant Kon, the dissociation rate constant Koff, and the maximum binding response value Rmax. The quality evaluation module is used to generate fitting quality evaluation results based on fitting residuals, parameter stability, and model convergence. The results output module is used to output the binding rate constant Kon, the dissociation rate constant Koff, and the equilibrium dissociation constant KD between target molecules.

9. The dynamic parameter measurement system according to claim 8, characterized in that, The system is communicatively connected to the digital microfluidic chip control module and receives droplet scheduling event information.

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