Concepts for training and using at least one machine learning model for modeling kinetic aspect of biological organism

Abstract

Examples relate to concepts of training and using at least one machine learning model for modeling a kinetic aspect of a biological organism, and in particular to methods, apparatuses, and computer programs for training at least one machine learning model for modeling a kinetic aspect of a biological organism, and various methods of using such at least one trained machine learning model. A method of training at least one machine learning model for modeling a kinetic aspect of a biological organism includes training the machine learning model based on training data. The training data is based on experimental data of a plurality of clones of the biological organism. The training data includes a subset of training data based on experimental data of a single clone. A first component of the at least one machine learning model is trained using training data, wherein the first component represents a generic dynamic behavior of the biological organism. A second component of the at least one machine learning model is trained using a subset of training data, the second component representing a clone-specific dynamic behavior of the biological organism.

Description

Technical Field

[0001] Examples relate to concepts of training and using at least one machine learning model for modeling dynamical aspects of a biological organism, and in particular to methods, apparatus, and computer programs for training at least one machine learning model for modeling dynamical aspects of a biological organism, and various methods of using such trained at least one machine learning model. Background Art

[0002] Today, digital twins are widely used in various industrial fields (such as the automotive industry) because digital twins can significantly improve and accelerate the design, optimization and control of machines, industrial products and supply chains. With its predictive capabilities, digital twins can be used to directly intervene in production or predict and improve the overall behavior of assets and supply chains. This helps monitor and optimize processes and control them to improve process robustness, product yield and quality.

[0003] Despite these advantages, digital twins are rarely applied to biotechnological production processes. The main reasons are the limited applicability of digital twins to different organisms and cell lines, process settings and scales, and the high requirements for measurement data. For example, during manufacturing, only a limited amount of data is available. Often, not all required measurement entities are available to generate digital twins with high predictive quality. Measurement noise may further limit the model’s predictive quality, which is desired for robust process control.

[0004] Although the mathematical model of biotechnology process has been developed in the past, these models can not handle different application situations, such as clone, product and process format.For each new application situation, it is necessary to generate new data and model.This has caused a large amount of resources and time cost.On the other hand, owing to lack of suitable model or software platform to realize the automatic integration of data and the generation and application of high-quality model, therefore process optimization is mainly completed by simple experimental design and the control via glucose curve and other quantities such as pH and temperature.The applicability of this model is limited, because for the situation that the data observed during manufacturing for example reduce and quality reduce, the prediction quality may be considered as not enough.Therefore, it can not be used for process monitoring and robust control usually.

[0005] An improved conception of digital twins for biotechnological production processes might be desired. Summary of the invention

[0006] This expectation is solved by the subject-matter of the independent claims.

[0007] Various embodiments of the present disclosure are based on the discovery that the problem of lack of experimental data necessary to generate digital twins can be overcome by using experimental data between multiple clones, cell lines and / or process forms to generate generalized digital twins, which can then be additionally adjusted to specific clones of cell lines. Due to the available additional experimental data, such digital twins can produce higher prediction quality than smaller digital twins specific to cell lines, clones and process forms. In the proposed concept, the generation of such digital twins includes training at least one machine learning model, which includes: a first component (e.g., a first machine learning model or a first multi-layer of a neural network), which is trained to model the general (i.e., non-clone-specific) dynamic aspects of the modeled biological organism; and a second component (e.g., a second machine learning model or a second multi-layer of a neural network), which is trained to model clone-specific aspects of the biological organism. For this training, training data is used, wherein only a clone-specific subset is used to train the clone-specific second component. Once trained, the trained parameters can be reused for the integration of new data sets, so that the digital twin can be extended and tuned to specific clones while reducing computational costs and data requirements. These digital twins can be used offline for process improvement or optimization (including clone selection, platform culture medium design) and online for monitoring and controlling biotechnological processes to improve process robustness, performance and product quality. Therefore, the proposed digital twin can be used, for example, during manufacturing to improve product quality or for process monitoring and control, because its high prediction quality can improve the estimation of the relevant system state despite the uncertainty of the measurement.

[0008] Therefore, the proposed concept can solve one or more of the above limitations by reusing data and model parameters from previous culture runs to reduce the data requirements for generating digital twins for new application scenarios (including different clones or process scales) while maintaining high prediction quality. Digital twins can be created by combining a general machine learning model and a clone-specific machine learning model (i.e., the first component and the second component described above) (e.g., a neural network) with metabolic functions and a reactor model, and the reactor model can be adapted to different process settings and scales (e.g., as shown in WO 2020 / 224779 A1) through a hybrid approach. The machine learning model contains general parameters and clone-specific parameters (i.e., the first component and the second component described above), which can be trained together or individually depending on the application specifications. This makes the method widely applicable to different cell lines, clones, and scales. The general parameters can be trained with all data sets and save general metabolic behaviors. On the other hand, the clone-specific parameters are only trained with a data set for a clone (clone-specific), and therefore clone-specific behaviors other than general behaviors can be learned. Digital twins based on these machine learning models can learn generic and clone-specific behaviors and can be embedded in control strategies including state estimation and model predictive control. The proposed digital twins can be used, for example, to improve product quality or for process monitoring and control during manufacturing, since their high prediction quality enables estimation of relevant system states despite measurement uncertainties.

[0009] Various aspects of the present disclosure relate to a method of training at least one machine learning model for modeling dynamic aspects of a biological organism. For example, the at least one machine learning model may be suitable for a digital twin of a biological organism or a bioreactor including a biological organism. The method includes training the machine learning model based on training data. The training data is based on experimental data of multiple clones of the biological organism. The training data includes a subset of training data based on experimental data of a single clone. A first component of the at least one machine learning model is trained using (all) the training data. The first component represents the general dynamic behavior of the biological organism. A second component of the at least one machine learning model is trained using the subset of training data. The second component represents clone-specific dynamic behavior of the biological organism. By training a first component representing general dynamic behavior (common to different clones, process scales, and / or cell lines) and a second component representing clone-specific behavior, additional experimental data can be used to train a first component with improved prediction quality, which is fine-tuned to a specific clone of interest by using the second component. This can result in a machine learning model with an overall improved prediction quality, and thus improve the prediction quality of a digital twin employing such a machine learning model.

[0010] In general, for example, in a supervised learning-based training method, the training data includes training input data and training output data. For example, the training input data may include a representation of an experimental environment of an organism. The training output data may represent kinetic properties (e.g., changes in concentration, concentration, or (flow)) observed in response to the corresponding experimental environment. Thus, data typically sampled during experiments involving biological organisms in bioreactors can be used to train the at least one machine learning model, for example, by some preprocessing to generate the input (and output) desired by the at least one machine learning model.

[0011] Training a machine learning model typically involves changing the machine learning model so that during training, the difference between the observed output of the machine learning model and the expected output of the machine learning model (e.g., as defined by the training output data) decreases over time. Thus, training the at least one machine learning model may include determining the deviation between the output of a function and the training output data, wherein the function is based on the at least one machine learning model, a first flux pattern set representing a common function of the plurality of clones of the biological organism, and a second flux pattern set specific to the single clone of the biological organism. For example, the output of the at least one machine learning model may be used as a parameter of the function together with the first flux pattern set and the second flux pattern set and then compared with the training output data, or the training output data may be preprocessed using the first flux pattern set and the second flux pattern set and then compared with the output of the at least one machine learning model. In a specific example, the training output data may be compared with a hybrid model (e.g., as discussed in WO 2020 / 224779 A1), which may be based on the at least one machine learning model, the first flux pattern set, the second flux pattern set, and optionally, one or more other models, such as a reactor model. For example, the flux pattern can be an elementary flux pattern (EFM) and a metabolic basic function (also referred to as a basic pattern). For example, for the generation of a metabolic basic function (e.g., biomass production, product formation, or the production of non-essential amino acids), a flux balance analysis can be applied. Further functions can be supplemented by elementary flux pattern analysis.

[0012] In some examples, the representation of the experimental environment (contained in the training input data) may include more information than is required for training purposes. Therefore, dimensionality reduction may be applied to the representation of the experimental environment. For example, the representation of the experimental environment may correspond to a compressed representation of the experimental environment that has a reduced dimensionality compared to an uncompressed representation of the experimental environment. This may coordinate input vectors between different data sets representing the experimental environment and also reduce the complexity of training, and therefore reduce the computational power required for training.

[0013] In many cases, the envisioned digital twin is used to improve the production process of the biological component of a pharmaceutical product. Therefore, the quality of the biological component can be another factor that the machine learning model can be trained on. For example, the training output data can also represent one or more biopharmaceutical product quality characteristics of the biological organism in the experimental environment. In fact, the at least one machine learning model and the digital twin based on the at least one machine learning model can also be used to predict the quality of the biological component being produced, and therefore can be used to select the environment of the biological organism so that the quality of the biopharmaceutical product is improved.

[0014] As described above, the training data is based on experimental data from multiple clones. In some embodiments, the multiple clones can be clones of the same cell line. In other words, the training data can be based on experimental data from multiple clones of the same cell line of the biological organism. Although based on a more limited training database, the use of multiple clones of the same cell line can improve the uniformity of the experimental results and thus improve the quality of prediction. Alternatively, the training data can be based on experimental data from multiple clones of multiple different cell lines of the biological organism. This can increase the pool of training data, thereby improving the quality of prediction, but if the behavior of the cell lines is not similar enough, it may cause problems (e.g., problems with the convergence of at least one machine learning model).

[0015] In addition, the training data can be based on experimental data from multiple different process scales (e.g., from a small experimental setup to full-scale production). This can improve the prediction quality of the at least one machine learning model when applied to predict the kinetic behavior of biological organisms at different process scales.

[0016] For example, the at least one machine learning model may include at least one deep neural network, wherein the first component includes a first plurality of layers of the at least one deep neural network, and the second component includes a second plurality of layers of the at least one deep neural network. For example, the first component and the second component may be implemented as different layers of the same neural network, or as two separate neural networks.

[0017] According to one example, the first component and the second component can be trained in a first stage of training, and the second component can be trained in a second stage of training after the first stage of training, wherein the first component is frozen during the second stage of training. In general, additional, clone-specific training may provide only limited benefit to the first component, so the first component can be frozen to reduce training complexity.

[0018] In various examples, the first component and the second component are trained based on the output of the corresponding other component. For example, the training output data can be compared with a combination of the corresponding outputs of the first component and the second component so that the outputs of the two components have an impact on the training of the corresponding other component.

[0019] In some examples, the at least one machine learning model may further include a third component that takes the output of the first component and the second component as its input. The method may include using the training data to train the third component of the at least one machine learning model. For example, the third component may be used to combine the output of the first component and the second component. Alternatively, the outputs may be combined (e.g., multiplied) as part of a (deterministic) function.

[0020] In various examples, the at least one machine learning model may further include a fourth component that represents one or more flux patterns not represented by the first component and / or the second component. The method may include training a fourth machine learning model using the training data. Thus, the fourth machine learning model may add support for clone-specific flux patterns not represented by the first machine learning model and the second machine learning model.

[0021] In various examples, a random algorithm can be used to train the at least one machine learning model. For example, a so-called ADAM algorithm can be used, which can be considered a stochastic gradient descent algorithm.

[0022] According to one example, the at least one machine learning model may form a machine learning model set. For example, the method may include training multiple machine learning model sets. The multiple machine learning model sets may be trained with different seed values, wherein the different seed values ​​affect at least one of the random initialization and random dropout of the parameters of the corresponding machine learning models. The method is referred to as an "ensemble method" and can be used to evaluate uncertainty in a predictive model by comparing and / or combining results generated by multiple different machine learning models that have received the same training (albeit with random differences in starting parameters and / or random dropout).

[0023] In some examples, the method further includes using transfer learning to adjust at least the clone-specific second component of the at least one machine learning model based on training data based on experimental data of an additional single clone. In this way, the computational effort already invested in generating a machine learning model for modeling the first clone can be reused to generate an additional machine learning model for modeling the second clone.

[0024] According to one example, the first component and the second component of the at least one machine learning model are separate machine learning models. Alternatively, the first component and the second component of the at least one machine learning model can be the first multi-layer and the second multi-layer of the same deep neural network. Both methods are applicable to the case of the present disclosure.

[0025] As described above, the training of the at least one machine learning model can be part of a process of generating a digital twin that can be used to model the behavior of a biological organism (e.g., a bioreactor including the biological organism). Thus, the method can also include using the trained at least one machine learning model to generate a digital twin of the biological organism. The digital twin can be used for many different purposes, as will be shown below.

[0026] For example, the digital twin may be used for experimental design purposes. For example, the method may include determining a plurality of experiments to be performed using the biological organism. For example, experiments may be determined so that previously unstudied environmental conditions are covered, or so that environmental conditions that lead to less accurate predictions are studied in more detail. Once the experiments have been conducted, the resulting experimental data may be used to continue training and thereby improve the prediction quality of the at least one machine learning model and thereby improve the prediction quality of the digital twin. In other words, the method may include continuing to train the at least one machine learning model based on additional training data, the additional training data being based on a plurality of experiments.

[0027] Another application of the generated digital twin is to determine target parameters for bioreactors containing biological organisms, such as culture medium composition, feeding strategy, etc. Therefore, some aspects of the present disclosure relate to a method for determining at least one target parameter of at least one bioreactor containing at least one biological organism (i.e., each bioreactor contains a biological organism). The method includes determining the at least one target parameter using at least one digital twin of at least one biological organism generated according to the above method and at least one corresponding cost function. For example, the at least one target parameter may include at least one of the following items: a target culture medium composition for the feed medium of the at least one biological organism; a target feeding strategy for the at least one biological organism; a target effluent strategy for the at least one biological organism; and a target initial condition for the at least one biological organism. Due to the improved prediction quality of the digital twin, the quality of the determined target parameters can also be improved. For example, at least two digital twins of at least two biological organisms can be used to jointly determine at least one target parameter of the at least two biological organisms (e.g., for a platform culture medium commonly used for a variety of different biological organisms).

[0028] In addition, such digital twins can be used to compare the characteristics of different clones, for example, for the purpose of clone selection. Therefore, some aspects of the present disclosure are related to a method for selecting clones of a biological organism. The method includes generating multiple digital twins of multiple clones of the biological organism using the above method. The method includes selecting clones by comparing one or more characteristics of the multiple digital twins. Similarly, the improved prediction quality of the digital twins can also improve the clone selection process.

[0029] Two further applications of such digital twins relate to monitoring and controlling biomanufacturing processes. For example, some aspects of the present disclosure relate to a method for monitoring a biomanufacturing process involving a biological organism. The method includes determining an estimated state of the biomanufacturing process using a digital twin of the biological organism generated according to the above method. For example, a rolling time domain method can be used to provide the digital twin with information about the environment of the biological organism. The method includes comparing the estimated state of the biomanufacturing process with the observed state of the biomanufacturing process. In this way, unexpected events can be detected during the manufacturing process.

[0030] For example, in comparing the estimated state of the biomanufacturing process to the observed state of the biomanufacturing process, a rolling horizon estimation algorithm may be used. This may enable estimation of unknown parameters, such as unknown metabolite concentrations, over time.

[0031] As described above, some aspects of the present disclosure relate to a method for controlling a biomanufacturing process involving a biological organism. The method includes using a digital twin of the biological organism generated according to the above method to continuously adjust the environment of the biomanufacturing process. The digital twin is provided with information about the environment of the biological organism using a backward time domain method. The method includes comparing an estimated state of the biomanufacturing process with a defined reference state trajectory of the biomanufacturing process. For example, the difference between the estimated state and the defined reference state trajectory can be used to perform continuous adjustments, for example, to change the state according to the state trajectory.

[0032] Various aspects of the present disclosure are directed to one or more computer systems including processing circuitry and memory circuitry, wherein the computer systems are configured to perform at least one of the above methods.

[0033] Similarly, various aspects of the present disclosure relate to a computer program with a program code for performing at least one of the above methods when said computer program is executed on a computer, a processor or a programmable hardware component. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Some examples of apparatus and / or methods will be described below, by way of example only, and with reference to the accompanying drawings, in which:

[0035] Figure 1 shows a schematic representation of a flux decomposition algorithm according to one example;

[0036] Figure 2a and Figure 2b A flow chart illustrating an example of a method of training at least one machine learning model for modeling dynamical aspects of a biological organism;

[0037] Figure 2c A schematic diagram showing an example of a computer system;

[0038] Figure 3 A flow chart illustrating an example of a method for determining at least one target parameter;

[0039] Figure 4 A flow chart illustrating an example of a method for monitoring a biomanufacturing process involving a biological organism;

[0040] Figure 5a and Figure 5b A schematic diagram of a rolling horizon estimation algorithm according to an example is shown;

[0041] Figure 6 A flow chart illustrating an example of a method for controlling a biomanufacturing process involving a biological organism;

[0042] Figure 7a and Figure 7b A schematic diagram of a model predictive control algorithm according to an example is shown;

[0043] Figure 8a and Figure 8b A schematic diagram of a model predictive monitoring and control algorithm is shown;

[0044] Fig. 9 A flow chart showing an example of a method for selecting a clone of a biological organism;

[0045] Fig.10 A regression plot demonstrating the prediction quality of one example is shown;

[0046] Fig.11 A schematic diagram showing a comparison of predictions with and without state estimation and corresponding measurement results; and

[0047] Fig.12 A schematic diagram demonstrating the process of deviation from the golden batch is shown. DETAILED DESCRIPTION

[0048] Some examples are now described in more detail with reference to the accompanying drawings. However, other possible examples are not limited to the features of the embodiments described in detail. Other examples may include modifications of these features and equivalent and replacement features of these features. In addition, the terms used to describe certain examples in this disclosure should not limit other possible examples.

[0049] Throughout the description of the accompanying drawings, the same or similar reference numerals refer to the same or similar elements and / or features, which may be implemented in the same or modified form while providing the same or similar functions. For clarity, the thickness of the lines, layers and / or regions in the drawings may also be exaggerated.

[0050] Unless explicitly defined otherwise in individual cases, when "or" is used to combine two elements A and B, this will be understood to disclose all possible combinations, i.e. only A, only B, and A and B. As another wording for the same combination, "at least one of A and B" or "A and / or B" can be used. The same applies to combinations of more than two elements.

[0051] If singular forms such as "a", "an", and "the" are used, and there is no explicit or implicit definition that the use of only a single element is mandatory, additional examples may use several elements to achieve the same function. If a function is described below as being implemented using multiple elements, additional examples may use a single element or a single processing entity to achieve the same function. It should also be understood that the terms "comprises" and / or "comprising" when used describe the presence of specific features, wholes, steps, operations, processes, elements, components, and / or combinations thereof, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, processes, elements, components, and / or combinations thereof.

[0052] In the present disclosure, the terms "optimization", "optimal", "best", "maximum", "minimum", etc. are used in a non-absolute manner. If something is optimized, the result is not necessarily the optimal result, but the best result or one of the best results given the constraints (such as limited running time, etc.). Therefore, even the "optimal" result does not necessarily mean the absolute optimal, but the best result or one of the best results given the above constraints. In the present disclosure, optimization refers to the process of finding better results, rather than determining a single best result.

[0053] Various examples of the present disclosure relate to methods for reusing data between multiple cell lines, clones, and projects for biotechnology process optimization and control. It provides a new method for automatically generating, validating, and simulating digital twins, such as between multiple cell lines, process forms (i.e., fed-batch and perfusion), scales, and products, and its application in the optimization, amplification, monitoring, and control of biotechnology production processes. Some examples of the concepts proposed by the present invention relate to cell culture methods and compositions thereof, which in one aspect improve the yield and quality of biotherapeutic proteins.

[0054] In the following, a brief introduction to digital twin models (of biological organisms) and metabolic network models is given. Digital twins, such as Insilico digital twins, typically use metabolic network models built based on biological knowledge. This ensures that (all) intracellular and extracellular fluxes are consistent with the available pathways and transformation steps for a given organism at any time point in the simulation. This can include considering the directionality of irreversible reaction steps. During simulations using digital twins, mass balance (i.e. element balance and charge balance) can be closed at (all) time points. In the following, the mathematical representation of the metabolic network model is explained in detail.

[0055] A metabolic network model is a mathematical representation of biochemical pathways within an organism. A pathway is a series of biochemical reactions in which a set of metabolic substrates is converted into a set of products. A typical pathway of a metabolic network may include one or more of the following: glycolysis; pentose phosphate pathway; amino acid metabolism; amino acid degradation; formation of DNA / RNA, proteins, lipids, carbohydrates; glycosylation; respiration; and transport steps between intracellular compartments and between the cytosol and the extracellular environment.

[0056] The construction of metabolic network models can include assembling available reactions into mathematical representations via stoichiometric matrices and validating the functionality of pathways expected to exist in cell lines based on prior biological knowledge. Genomic sequences form the basis of biochemical information used to reconstruct networks. Public databases like KEGG (Kyoto Encyclopedia of Genes and Genomes) and Biocyc bridge the gap between genomic sequences and biochemical reactions using genomic annotations.

[0057] Metabolic network models can include:

[0058] a) Elemental composition and molar mass of metabolites.

[0059] b) A stoichiometric matrix containing stoichiometric coefficients indicating the participation and role (reactants / products) of various metabolites in the chemical reactions of the metabolic network.

[0060] c) Reversibility index, which indicates whether the reaction is reversible.

[0061] d) The distribution of enzymes catalyzing the various reaction steps.

[0062] The stoichiometric matrix can be considered as the central part of the metabolic network model, where the stoichiometric matrix is ​​an m×n matrix containing the stoichiometric coefficients of m metabolites participating in n reactions. Each entry in the matrix is ​​a stoichiometric coefficient S that associates metabolite i with reaction j. i,j ,in:

[0063]

[0064] The stoichiometric matrix is ​​invariant and is usually sparse because most biochemical reactions involve only a few different metabolites. In each row of the stoichiometric matrix, the metabolites are balanced, and in each column, the chemical reactions are balanced with respect to the elements.

[0065] A reaction is defined as irreversible if it only proceeds in one direction and reversible if the reverse reaction can also occur. To define a metabolic model, reversibility R can be defined as an n-dimensional vector of Boolean values ​​for all reactions n of the metabolic model.

[0066]

[0067] The technology that is usually used in combination with the metabolic network model is flux balance analysis. Flux balance analysis (FluxBalance Analysis, FBA) is a mathematical method for analyzing the distribution of the reaction flux of a metabolic network model. It can be used to calculate the flux distribution based on the constrained linear optimization problem. Thus, under the condition that a group of constraints are applied to the metabolic network model, the flux can be optimized (that is, improved) by preferred metabolic reactions. Therefore, by optimizing (that is, improving) the metabolic reactions associated with biomass formation or product formation respectively, the production of biomass formation or biotechnology target products can be maximized (that is, improved).

[0068] The linear optimization problem solved by FBA can provide an improved or optimal specific flux distribution of the metabolic network, which maximizes (i.e., increases) the desired performance indicator / goal Z=c under the conditions of imposing a steady-state constraint (Sv=0) and lower / upper limits lb, ub and equality and inequality constraints g and h on the flux vector v. T v.

[0069] Mathematically, the whole problem can be expressed as follows:

[0070]

[0071] Constraint Sv = 0

[0072] lb≤v≤ub

[0073] g≤0

[0074] h=0

[0075] in,

[0076] Z=c T v is the objective function

[0077] c is a coefficient vector representing the weights of the reactions contributing to the objective function

[0078] S is the stoichiometric matrix

[0079] v is a flux vector describing all fluxes in the metabolic network, for example in units of mmol / (gDW·h), where gDW refers to grams dry weight.

[0080] lb is the lower limit vector containing the flux

[0081] Ub is the upper bound vector containing the flux

[0082] g is a vector of inequality constraints specific to the metabolic network model

[0083] h is a vector of equality constraints specific to the metabolic network model

[0084] The purpose of FBA is to maximize or minimize (i.e., increase or decrease) the objective function Z, so as to find a unique solution in the allowed solution space under the condition of being subject to a set of constraints. The objective function Z indicates which reactions can be maximized (i.e., increased) (positive weight c) or minimized (i.e., reduced) (negative weight c) by performing FBA. Vector c (which is a weight vector) is filled with zeros corresponding to uninteresting reactions and 1 corresponding to interested reactions. For example, if the production rate of a specific target product is of interest, the item of vector c for the specific reaction is 1, and is filled with zeros for all other reactions.

[0085] Z=c T v

[0086] The general mass balance for a biological process without reactions can be expressed as follows:

[0087] Input = Output + Accumulation

[0088] However, since FBA assumes mass balance at steady state, it means that the accumulation term becomes zero. Mathematically, this can be expressed in matrix form as follows:

[0089] Sv=0

[0090] Among them, S represents the stoichiometric matrix obtained from the metabolic network model as the core part, and v represents the flux vector describing the flux of all reactions of the metabolic network model. Usually, the number of reactions is higher than the number of metabolites associated with the metabolic network model. This means that the number of unknown variables exceeds the number of equations, and therefore, there is no unique solution for such a system.

[0091] Flux balance constraints narrow the space of possible solutions to the above equations. These flux balance constraints can be expressed as equations or inequalities. Equations numerically define the reaction input or output fluxes precisely, while inequalities simply impose boundaries on the solution space. These constraints can be set by modifying upper and lower limits on the fluxes.

[0092] lb≤v≤ub

[0093] Metabolic flux analysis (MFA) is another technique commonly used in metabolic network models. MFA is a constrained least squares minimization problem. It minimizes (i.e., reduces) the weighted mean square error between the resulting flux distribution and the given observed flux while considering various additional constraints. The weighted mean square error objective function is mathematically represented by Z as:

[0094]

[0095] Constraint Sv = 0

[0096] lb≤v≤ub

[0097] g≤0

[0098] h=0

[0099] in,

[0100] Z is the objective function

[0101] v is the flux vector describing all fluxes in the metabolic network, for example, the unit is mmol / (gDW·h)

[0102] e is the flux vector obtained from MFA

[0103] is the observed flux vector

[0104] W is included The diagonal matrix of the standard deviations of

[0105] S is the stoichiometric matrix

[0106] lb is the lower limit vector containing the flux

[0107] ub is the upper limit vector containing the flux

[0108] g is a vector of inequality constraints specific to the metabolic network model

[0109] h is a vector of equality constraints specific to the metabolic network model

[0110] Unlike the ordinary least squares error term, the weighted least squares error does not assume that all measurements have the same standard deviation. More accurate measurements have smaller standard deviation values ​​and thus larger weight values ​​(note that the weights are calculated as the element-by-element inversion of W. This is expressed in the above equation as ). This larger weight value forces the algorithm to preferentially fit more accurate measurements, i.e., those with lower standard deviations. If a measurement is inaccurate, it will have a correspondingly larger standard deviation value and thus a smaller weight value. Thus, the algorithm is less likely to fit such an inaccurate measurement. In summary, weighted least squares error can allow the MFA algorithm to produce more reliable results when faced with non-uniformly distributed standard deviations.

[0111] Including weighting factors in the objective function enables the algorithm to adapt to fluxes of different orders of magnitude (e.g., the consumption rate of small molecules (e.g., glucose) is much greater than the production rate of large molecules (e.g., glycoproteins)). To implement the MFA algorithm, for example, the simplex method from the CPLEX API (API (Application Programming Interface) for solving optimization problems) can be used.

[0112] Elementary flux pattern analysis (EFMA) is another technique commonly used in metabolic network models. The flux decomposition algorithm can decompose the metabolic flux distribution into elementary flux patterns (EFMs), which can be used to train at least one machine learning model of a digital twin (DT), as proposed in the present disclosure. EFM is generally considered to be the smallest functional unit in a metabolic network at steady state. This means that no reaction can be deleted from the EFM and still obtain a valid steady-state flux distribution. Using different sets of EFMs, all possible flux distributions in a metabolic network model can be described. Therefore, EFM can mathematically characterize the metabolic network structure.

[0113] In order to obtain EFM using the flux decomposition algorithm, a metabolic network model consisting of a stoichiometric matrix S and a reversibility vector R and a set of flux distributions (e.g., obtained via metabolic flux analysis (MFA) and / or (subsequent) flux balance analysis (FBA)) can be used. The flux decomposition algorithm used in the present disclosure is based on the work of Chan et al. ("Chan, SHJ, and Ji, P. (2011). Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks. Bioinformatics 27, 2256-2262"), with some modifications applied.

[0114] Figure 1 Schematic representation of a flux decomposition algorithm according to an example is shown. Initial condition 110, flux distribution V1, V2, ..., V n , set V i =V n At the beginning, you can use V i A variable called rest_flux is initialized 120. A flux decomposition algorithm may be performed 140 on rest_flux to obtain the EFM. Once the EFM is found, it may be added 150 to the stack of found EFMs and subtracted 160 from rest_flux. This process may be repeated until rest_flux meets a certain stopping criterion (see Section 2.4) 130. If this is the case, V may be terminated. i The flux is decomposed and can be used to determine V i+1 The same process 180 is performed. This cycle can continue until the final flux distribution (i.e., V n ) is completely decomposed 170. Finally, the complete stack of all found EFMs is the result of the flux decomposition algorithm and can be saved in the pattern matrix M 190. A possible prerequisite of the flux decomposition algorithm is to convert all reversible reactions into irreversible forms. This will be explained in detail below.

[0115] To perform flux decomposition, the reactions in the metabolic network model can be converted into irreversible forms. Reversible reactions can be divided into two irreversible reactions (forward + and reverse j - ), the stoichiometric coefficient and the flux value have opposite signs. This can be expressed by the following equation:

[0116]

[0117] in,

[0118] i∈I is a metabolic compound (e.g. ATP (adenosine triphosphate))

[0119] j∈J is the reaction (e.g. ATPase 1)

[0120] c∈C is the cultivation process (e.g., cultivation 1)

[0121] t∈T is the time point during the culture period (e.g., 12.0[h])

[0122] R j is the reversibility vector term of reaction j

[0123] is the reversibility vector term of the irreversible forward reaction form of reaction j

[0124] is the reversibility vector term of the irreversible reverse reaction form of reaction j

[0125] S i,j is the stoichiometric matrix term for compound i and reaction j

[0126] is the stoichiometric matrix term for compound i and forward reaction j

[0127] is the stoichiometric matrix term for compound i and reverse reaction j

[0128] is the FBA flux of reaction j for culture c at time t

[0129] is the FBA flux of the forward reaction j for culture c at time t

[0130] is the FBA flux of the reverse reaction j for culture c at time t

[0131] In order to convert the reversible reaction into an irreversible form, the next task can be to identify the EFM in the metabolic network model. In general, in order to define p as an EFM defined by the flux distribution v, the following five different constraints can be considered:

[0132] 1. The elementary flux pattern p must satisfy the steady-state condition

[0133] Sp=0

[0134] where S is the stoichiometric matrix.

[0135] 2. For each reaction j, there is a binary integer variable a j , which determines that reaction j occurs (ON) (i.e., a j=1) or does not occur (OFF) (i.e., a j =0). Binary variable a j The inequality terms must be satisfied

[0136] 0.1a j ≤p j ≤Qδ j a j

[0137] where Q is a large positive number, δ j is also a binary variable indicating the activity function of the flux to be decomposed. If v j >0, then δ j =1, otherwise δ j =0(v j indicates the flux of reaction j). According to the second constraint, if a j = 0 (i.e., reaction j does not occur), then p j = 0, and thus does not involve reaction j. However, if a j =1 (i.e. reaction j occurs), then p j ≥0.1, so reaction j must have a positive flux.

[0138] Binary variable δ j is a unique feature of the second constraint, which means that if δ j =1, then p j and a j is forced to zero. In other words, this means that if v j =0, then p j = 0. The variable Q should be large enough to allow all flux patterns defined by v to satisfy the above constraints. Q can be interpreted as the maximum stoichiometric ratio allowed within a flux pattern p.

[0139] 3. To ensure that p is non-trivial (i.e., it has at least one non-zero flux):

[0140]

[0141] 4. As mentioned before, the primitive flux pattern p must be bounded by v. To ensure this, the number of non-zero fluxes in p must be smaller than the number of non-zero fluxes in v:

[0142]

[0143] 5. The fifth constraint is that all fluxes must be positive. This should be the case because all reactions are irreversible:

[0144] p j ≥0

[0145] The above constraints may be sufficient to ensure that the primitive flux pattern p is defined by v. Therefore, each objective function can be used, so the objective function is set to max(). The goal of the improvement or optimization algorithm is to maximize (i.e., increase) zero a j The number of values. This can enhance the sparsity of the algorithm so that the system can be described by a minimal (or reduced) set of non-zero fluxes. The above five constraints and the optimization objective function can be used to construct a mixed integer linear problem. If any feasible solution is found for a primitive flux pattern v, then v is still decomposable, otherwise v can be considered as an EFM.

[0146] After a new EFM is identified, it can be added to the stack of already solved modes. In an optimization (ie, improvement) problem, these modes are subtracted from the current residual flux by maximizing (ie, increasing) the coefficients of the positive linear combination of these modes.

[0147]

[0148] in,

[0149] j∈E represents only the observed exchange reaction

[0150] m is the number of metabolites in the stoichiometric matrix S

[0151] n is the number of reactions (converters) in the stoichiometric matrix S

[0152] S is the stoichiometric matrix

[0153] m mod is the number of elementary flux modes found

[0154] M is the matrix of the elementary flux patterns that have been found based on the stack

[0155] v rest is the remaining flux in the current iteration

[0156] r is a weight vector with coefficients of linear combinations of primitive patterns from the pattern matrix M to describe v rest

[0157] v rest* is the residual between the residual flux and the linear combination of EFM

[0158] In order for the algorithm to stop interpreting even small residual fluxes caused by noise A stopping criterion can be defined. This stopping criterion ∈ can be calculated as the residual v between the residual flux and the linear combination of EFM rest* Divide by the standard deviation σ of the initial FBA flux distribution v, square it and take the average (weighted mean square error, WMSE):

[0159]

[0160] in,

[0161] ∈ is the stopping criterion

[0162] is the residual between the residual flux and the linear combination of EFM for the exchange reaction j∈E

[0163] σ j is the corresponding standard deviation of the initial FBA flux distribution for the exchange reaction j∈E

[0164] e is the number of exchange reactions.

[0165] To make exchange flux results comparable for metabolites with significantly different molar masses (i.e., comparison of CO2 to biomass or product), for each exchange flux, the flux can be multiplied by its respective molar mass (molecular weight w j ):

[0166]

[0167] in,

[0168] v j is the initial FBA flux distribution of the observed exchange flux j∈E

[0169] w j is the corresponding molecular weight of the metabolite with observed exchange flux j∈E

[0170] is the observed initial FBA flux distribution for exchange flux j∈E weighted by the corresponding molecular weight

[0171] m mod is the number of elementary flux modes found

[0172] M is the matrix of the elementary flux patterns that have been found based on the stack

[0173] r is the weight vector with coefficients of linear combinations of primitive patterns from the pattern matrix M

[0174] is the flux distribution explained by the largest positive linear combination of EFMs weighted by molar mass

[0175] If the stopping criterion is reached, the remaining flux v rest*may not be further decomposed, and new FBA fluxes from the FBA stack can be used to find new EFMs. The stopping criterion is a suitable tool for defining the number of EFMs found by flux decomposition. By default, it can be set to a predefined low value, such as 0.0001.

[0176] The result of the flux decomposition may be an elementary flux pattern matrix M, which includes (all) the identified EFMs. The dimensionality of M is defined by the number of reactions (converters) of the metabolic network model and the number of identified EFMs.

[0177] In various examples of the present disclosure, a concept called a metabolic base function (MBF) (also called a base node) can be used. The digital twin can learn the impact of its inputs (e.g., a representation of the environment of the biological organism, such as one or more of the following: concentration, reactor volume, feed, sampling, additional inputs such as pH, temperature, and expression level) on the metabolic rate through primitive flux model (EFM) activities. In general, EFMs can be obtained via EFMA, which can use the observed exchange fluxes through metabolic flux analysis (MFA) and subsequent flux balance analysis (FBA) to estimate exchange rates. In other methods, the workflow may be run from scratch for each new project or data, which can result in higher costs. In addition, the quality of the estimated rates may be impaired due to limited data availability and the presence of measurement noise.

[0178] It is a finding of the proposed concept that for the same organism or cell line, a large number of metabolic functions are common between projects. Examples may include biomass and product formation, production of non-essential amino acids, and degradation of certain metabolites. As part of the generation of the metabolic network model, certain (required) metabolic functions may have been defined, which are a subset of these common functions. They can be derived by targeted flux balance analysis (FBA) and can be further extended by applying expert knowledge. An example is the conversion of an amino acid to another amino acid. These basic metabolic functions can be attached to the EFM or can be used as a starting point for subsequent EFMAs and reduce the number of required EFMs, which can reduce the computational time of flux decomposition algorithms or address data reduction challenges. In digital twins, EFMs and metabolic basic functions can be reused between projects.

[0179] For example, the above-mentioned metabolic basic function can be obtained via target flux balance analysis (FBA), for example, by setting constraints in the following manner: the exchange flux of the expected substrate can be constrained to be negative, the exchange flux of the product can be constrained to be positive (usually also the main substrate is fixed to a constant value to meet the unbounded problem), and other exchange fluxes can be constrained to zero. In addition, known yields can be fixed, for example, for the known substrate requirements formed by the product.

[0180] For example, for the metabolic base function "glucose degradation", the exchange flux of glucose can be set to -1, the exchange fluxes of CO2, H2O, and H can be unconstrained, while all other exchange fluxes are constrained to zero.

[0181] Optionally, a flux decomposition can be run to supplement missing functionality.

[0182] In the following, an example of a reactor model for a bioreactor (containing biological organisms) is given. The reactor model can represent (any) concentration and volume changes in the bioreactor due to influx (i.e., feed) and outflow (e.g., sampling, permeate outflow with cell entrapment during perfusion and bleed flux without cell entrapment). The change in volume V(t) can be described using the following differential equation:

[0183]

[0184] represents the volume increase due to feeding from medium i. I (t) is considered as the row vector of all feed rates. is the effluent rate and can be defined as the volume reduction due to the continuous withdrawal of medium from the bioreactor. O (t) is considered as the row vector of all outflow rates.

[0185] The biomass concentration X(t) changes relative to the existing biomass concentration due to the outflow of cells.

[0186]

[0187] Each outflow j has its own cell retention factor R j,X , R j,X Indicates how much biomass is trapped. This means that a cell retention factor of 0 corresponds to no retention at all, while a cell retention factor of 1 corresponds to complete retention. Within a time step, the cell retention factor is considered constant.

[0188] The concentration of non-biomass metabolites C(t) varies with the feed and outflow (with a factor r j The changes due to the given cutoff):

[0189]

[0190] in is the vector of metabolite concentrations in feed i.

[0191] In addition to the reactor model, the digital twin can also use the extracellular reaction model. Extracellular reactions are usually chemical degradation reactions that occur in the culture medium and are independent of the biomass concentration. An example of such a reaction is the degradation of glutamine to 5-oxoproline and ammonia. Variations in concentration can be simulated using mass action kinetics. Overall, the rate k of the abiotic degradation reaction of substrate S to product P is deg It can be expressed mathematically as:

[0192]

[0193] As another component, the digital twin can include a general osmotic concentration model. The osmotic concentration of a solution is the number of solute particles dissolved in 1 kg of a given solution. In the pharmaceutical industry, osmotic concentration is an important control and quality check parameter throughout the development and production of biologics. Monitoring osmotic concentration values ​​helps ensure cell health and reduce the risk of process failure. Thus, osmotic concentration can be considered when training a digital twin (DT), in particular when training at least one machine learning model of a DT. To this end, an osmotic concentration model (or sub-model) can be trained and included in the digital twin. Such an osmotic concentration model can predict experimentally measured osmotic concentration values. This makes it possible to control the osmotic concentration of a process improved by DT optimization. In this way, it is possible to support ensuring cell health in the optimized process and to reduce the risk of process failure.

[0194] For example, the osmotic concentration model can be a linear regression model, which is mathematically described as:

[0195]

[0196] in:

[0197] y N (t) is the normalized experimentally measured osmotic concentration value at time point t (ie, N stands for normalization).

[0198] The normalization type is maximum value normalization

[0199] α i is the coefficient corresponding to metabolite i

[0200] is the normalized experimentally measured concentration of metabolite i in the bioreactor at time point t. The type of normalization is maximum normalization in terms of metabolites. Biomass, dead biomass and glycoproteins are excluded.

[0201] β is the intercept

[0202] The linear regression model can be of the "Lasso" type, which can be trained based on L1 regularization. The algorithm can use normalized experimentally measured compound concentrations (i.e., ) and predict the normalized experimentally measured osmotic concentration value at time point t (i.e., y N (t)). This can be done by estimating the optimal α i value and the optimal β value.

[0203] In many cases, the osmotic concentration of a solution can be calculated as a weighted sum of the concentrations of the compounds in the solution, taking into account that the weights are positive. Therefore, in the Lasso algorithm, α i The values ​​(herein referred to as weights or coefficients) are forced to be positive. Once the normalized osmotic concentration values ​​are predicted, i.e., y N (t), denormalization can be applied and the actual osmotic concentration estimate derived.

[0204] The trained osmotic concentration model can be used in process improvement or optimization (see e.g. Fig. 9 ) in which the concentration of the compound in the culture medium and / or the feeding strategy are improved or optimized, respectively. The culture medium and / or feeding optimization may result in simulated time-resolved bioreactor concentration profiles that differ from experimental measurements. Estimation of α i After β and β, using the above equation, the time-resolved osmotic concentration value corresponding to the optimized process can be estimated. To this end, the modified or optimized time-resolved bioreactor concentration curve can be used in the above equation, that is, To estimate the corresponding osmotic concentration value, that is, t N (t). Such normalized osmotic concentration values ​​can be denormalized so that the actual time-resolved osmotic concentration values ​​can be estimated. This helps to keep the osmotic concentration of the improved or optimized method within a certain (reasonable) range, so that cell health is supported or ensured, and the improved or optimized method is at a lower risk of failure.

[0205] In practice, it may not be possible to measure bioreactor concentrations for every individual time point. If a measured concentration of a metabolite is missing at a particular time point, Incomplete (i.e., metabolite i at time point t ). Therefore, the corresponding osmotic concentration value at that specific time point may not be predicted.

[0206] To solve this problem, a downsampling method can be applied. When using the downsampling method, the time resolution of the data is set to a higher value (for example, Δt=24h). Then, the average of all measured concentration values ​​between t and t+Δt can be calculated and set as the measured concentration at time point t+Δt. The same method also applies to the osmotic concentration values ​​measured between t and t+Δt. In this way, even if one or more concentration measurements are not available during the time period between t and t+Δt, it is still possible to obtain a value at t+Δt (i.e., the downsampled value). In this way, The chance of being complete at more time points increases, thus using more data points to train the osmotic concentration values. The more time points available in the data, the better the trained osmotic concentration model is generally.

[0207] If for a certain metabolite the proportion of concentration measurements at all time points (over the entire process) is less than 50%, then the metabolite can be discarded from the permeate concentration prediction procedure.

[0208] Some examples of the present disclosure relate to product quality attributes (PQA). Product quality attributes (such as glycosylation and charge variants of the product) are modeled as a percentage of the total product titer:

[0209]

[0210] in:

[0211] C varj is the concentration of PQAj

[0212] p varj,％ is the percentage value of the contribution of PQAj to the total product titer

[0213] C P is the product concentration (titer)

[0214] In the following, the so-called generalized kinetic cell model (GKCM), a general pattern matrix, a clone-specific pattern matrix as well as general parameters and clone-specific parameters are discussed. These can be used in combination to simulate dynamical aspects of biological organisms. The general parameters and clone-specific parameters can correspond to components of at least one machine learning model, for example to layers of one or more artificial neural networks, or to different machine learning models. In the following, the application of the GKCM, including the general parameters and clone-specific parameters, is presented, followed by training.

[0215] The generalized kinetic cell model (GKCM) uses differential equations to simulate concentration changes caused by cell metabolism. The differential equation that can be used for biomass concentration X(t) is:

[0216]

[0217] As shown in the above equation, biomass concentration may depend on the current biomass concentration, the biomass growth rate (often just called growth rate) and the linear constant k 死亡 In the example below, a single rate to describe the growth (μ(t)>0) and death (μ(t)<0) of biomass.

[0218] For metabolite concentrations, the equation may be different since changes in metabolite concentrations may depend on biomass concentration and biomass-specific consumption / production rates r(t). This can be represented mathematically by the following differential equation:

[0219]

[0220] The growth rate and biomass-specific consumption / production rate may depend on the current biomass concentration and metabolite concentration. The variable C(t) here refers to all concentrations c i The rates μ(t), r(t) are possible outputs of the kinetics given by a machine learning model (e.g., a neural network, see below for different architecture types) and stoichiometry (given by EFM and / or metabolic base functions). The general mathematical description can be given by:

[0221] [μ(t),r(t)] T =f 动力学 (M 通用 ,M 特定于克隆 ,t,x 环境 (t),θ 通用 ,θ 特定于克隆 )

[0222] in,

[0223] f 动力学 (·) is the kinetic relationship trained in the neural network combined with stoichiometry from the metabolic network model

[0224] M 通用 is a matrix containing elementary flux patterns (EFMs) and / or metabolic base functions with a defined order. In particular, the functions and order of the patterns are identical in each clone (thus universal). Only the biomass and product synthesis patterns may differ between clones due to differences in biomass or product composition.

[0225] M 特定于克隆 is a matrix containing clone-specific numbers of elementary flux patterns (EFMs) and / or metabolic basal functions with clone-specific functions

[0226] x 环境(t)[X(t),c(t),p(t)] t

[0227] p(t) is a vector of additional parameters (e.g. pH and temperature) that can be used as additional inputs to the kinetic cell model

[0228] θ 通用 is a collection of general kinetic cell model parameters that can be trained with data from a large number of clones and shared among clones

[0229] θ 特定于克隆 is a set of clone-specific kinetic cell model parameters trained only on clone-specific data

[0230] General pattern matrix M 通用 Elementary flux patterns or basic metabolic functions with defined functions and orders can be included. In particular, the functions and orders of the patterns can be the same in each clone. Due to differences in biomass or product composition, only the fluxes within the synthesis patterns of biomass and products may be different between clones. Although there are differences in the individual fluxes in these patterns, these patterns may have the same function and be located at the same position in the matrix between clones. Therefore, the universal kinetic model can be trained for the functions it represents.

[0231] Clone-specific pattern matrix M 特定于克隆 Can contain any (i.e., clone-specific) number of patterns with any (i.e., clone-specific) functionality

[0232] In the following, generic parameters and clone-specific parameters will be discussed. They may correspond to a first component and a second component of at least one machine learning model for modeling the dynamics of a biological organism.

[0233] θ 通用 (For example, it can be used as The first component and / or the third component of the at least one machine learning model is formed by a set of parameters calibrated using data from (all) available processes in the GKCM training set (e.g., from all training data). 特定于克隆 (For example, it can be used as The second component and / or fourth component forming at least one machine learning model is a different set of parameters in the training data that may exist for each clone and may be different for each clone because it is calibrated only using training data corresponding to the corresponding clone (e.g., a subset of training data based on experimental data of a single clone).

[0234] In some cases, especially when initially generating GKCMs, θ can be trained in parallel on a large number of datasets from different clones.通用 and θ 特定于克隆 In other cases, for example, when the GKCM was previously trained with historical data and only a reduced dataset is available for the new clones (without historical data), a warm start can be applied, i.e., θ can be loaded from the previously trained GKCM. 通用 , and remain unchanged, while calibrating the clone-specific parameters θ corresponding to the new clones on the new data 特定于克隆 .

[0235] Optionally, a generic compression can be used to handle measurement vectors of different sizes. In general, it is recommended to use a low-dimensional representation of the input vector (which can represent the environment of the biological organism), which can include (all) factors that can affect the state of the organism. The input vector can be defined as

[0236] x 环境 =[X,c,p] T

[0237] This low-dimensional representation (which may correspond to a compressed representation of the environment) can be achieved, for example, using linear methods such as PCA or using the compression part of an autoencoder. In general, the mapping function can be defined as

[0238]

[0239] where θ 压缩 is θ 通用 A subset of .

[0240] In various examples, some general constraints can be applied to f 动力学 In the rate equation f 动力学 In the above notation, the sum of the fluxes through any mode can (must) be positive. Negative mode fluxes can reverse the flux of an irreversible reaction, resulting in a thermodynamically infeasible flux. In addition, in the above notation, the mode matrix can contain exchange reactions (which are uniquely mapped to extracellular compounds with a factor of 1), that is, can contain stoichiometric mappings to extracellular compounds. In addition, matrix multiplication of the mode matrix with the stoichiometric matrix can be used to map the mode fluxes to growth rates and exchange rates.

[0241] In some examples, regularization can be used. In the context of training a GKCM, it may be advisable to specifically tune the clone-specific parts (e.g., M 特定于克隆 and θ 特定于克隆 The flux of

[0242] f 动力学 A specific example

[0243]

[0244] In the following, the term ANN i Used to describe different artificial neural networks (e.g. feedforward neural networks) as a function of a specified input. Since the output of these neural networks is usually constrained, for example, between 0 and 1, it is usually associated with a positive scalar, vector or matrix (which is represented here as H i ) are multiplied.

[0245] The following examples are given with respect to ANN (Artificial Neural Network) as a specific example of a machine learning model. However, other types of machine learning models may also be used.

[0246] In the following, two examples of architectures for combining the generic part and the clone-specific part of the GKCM are given. As will become apparent later, depending on the chosen architecture, the training of at least one machine learning model can be appropriately adjusted. Furthermore, the proposed concept is not limited to the two architectures given below.

[0247] In the first architecture example, multiplication is used to combine the common and clone-specific parts of the GKCM. The common part f1 and the clone-specific part f2 can be combined using the following architecture

[0248]

[0249] where f1 is

[0250]

[0251] f2 is

[0252]

[0253] and f4 is

[0254]

[0255] In the first architecture, a cell model with a first component f1 (including the parameters of the general dynamic cell model ), the second component f2 (including clone-specific kinetic cell model parameters ) and the fourth component f4 (comprising clone-specific kinetic cell model parameters ).

[0256] In a second architecture, the first component and the second component of at least one machine learning model are combined using a third component of at least one machine learning model. In the second architecture, the general part f1 and the clone-specific part f2 are combined using the following architecture f3:

[0257]

[0258] where f1 is

[0259]

[0260] and f2 is

[0261]

[0262] and f4 is

[0263]

[0264] In the second architecture, a kinetic cell model with a first component f1 (including the parameters of the general kinetic cell model ), the second component f2 (including clone-specific kinetic cell model parameters ), the third component f3 (including the general dynamic cell model parameters ) and the fourth component f4 (comprising clone-specific kinetic cell model parameters ).

[0265] In both examples above, depending on x 环境 The available measurements of the elements in (t), May be generated by different general purpose compressions:

[0266]

[0267] in, Include the corresponding intersection of the available measurements as a subset of the x environment in the data from all clones (input of the common part f1) or in the data of the corresponding clone (input of the clone-specific parts f2 and f4), respectively. Note that in the simplest case,

[0268] In some examples, data augmentation for interpretable common behaviors can be used. Data augmentation can be used to make the common parts of the model easier to interpret. Typically, process data is associated with a specific clone. However, the process data can be augmented so that each process is replicated, resulting in an original set of processes associated with a specific clone and another set of processes not associated with a specific clone. For processes not associated with a specific clone, the outputs of f2 and f4 can be 0. Therefore, common behaviors can be identified as the combination of the outputs of f1 and f3 with f2=f4=0.

[0269] In the following, examples of mathematical descriptions of digital twins are given. In various examples, the overall mathematical description of the digital twin is as follows:

[0270]

[0271] in,

[0272] U is an index of metabolites involved in extracellular reactions

[0273] S is an index of substrates involved in extracellular reactions

[0274] P is an index of the product involved in the extracellular reaction

[0275] as well as

[0276] [μ(t),r(t)] T =f 动力学 (M 通用 ,M 特定于克隆 ,t,x 环境 (t),θ 通用 ,θ 特定于克隆 ).

[0277] In other words, the GKCM and therefore at least one machine learning model having first, second, and optionally third and / or fourth components may be used to determine the rate [μ(t), r(t)] T As part of the digital twin.

[0278] The functions included in the pattern matrix can be metabolically based functions and / or EFMs derived from flux distributions from MFA regarding observed exchange rates that can be obtained via rate estimation (e.g., via a digital twin with a black-box (data-driven) kinetic cell model).

[0279] In the following, the training of a digital twin is discussed. This includes the training of at least one machine learning model, which can be used as part of the GKCM.

[0280] Figure 2a and Figure 2b A flow chart of an example of a method for training at least one machine learning model for modeling dynamic aspects of a biological organism is shown. The method includes training a machine learning model based on training data (step 210). The training data is based on experimental data of multiple clones of the biological organism. The training data includes a subset of training data based on experimental data of a single clone (or multiple subsets of experimental data based on individual clones). The method includes training a first component of at least one machine learning model using the training data (e.g., all of the training data) (step 211). The first component represents the general dynamic behavior of the biological organism. The method includes training a second component of at least one machine learning model using (only) the subset of training data (step 212). Thus, the second component represents clone-specific dynamic behavior of the biological organism.

[0281] Figure 2cSchematic diagram of an example of a computer system 20 is shown. The computer system 20 includes circuits configured to provide the functionality of the computer system 20. For example, Figure 2c The computer system 20 includes (optional) interface circuitry 22, processing circuitry 24, (optional) memory circuitry 26, and storage circuitry 28. For example, the processing circuitry 24 may be coupled to the interface circuitry 22, the memory circuitry 26, and the storage circuitry 28. For example, the processing circuitry 24 may be configured to provide the functionality of the computer system 20 in combination with the interface circuitry 22 (for example, for exchanging information with other components of the computer system or external to the computer system), the memory circuitry 26 (for temporarily storing information, such as machine-readable instructions), and the storage circuitry 28 (for permanently or semi-permanently storing information, such as machine-readable instructions). In general, the functionality of the processing circuitry 24 may be implemented by the processing circuitry 24 executing machine-readable instructions. Therefore, any features attributed to the processing circuitry 24 may be defined by one or more of a plurality of machine-readable instructions. The computer system 20 may include a plurality of machine-readable instructions, for example, within the memory circuitry 26 or within the storage circuitry 28.

[0282] In some examples, computer system 20 is configured to perform Figure 1 a and / or Figure 1 b. Alternatively or additionally, the computer system 20 may be configured to Figure 3 , Figure 4 , Figure 6 and Fig. 9 at least one of the methods.

[0283] In general, machine learning refers to algorithms and statistical models that computer systems can use to perform specific tasks without using explicit instructions but relying on models and inferences. For example, in machine learning, data transformations inferred from the analysis of historical data and / or training data can be used instead of rule-based data transformations. For example, a machine learning model can be used or a machine learning algorithm can be used to analyze image content. In order for a machine learning model to analyze image content, the machine learning model can be trained using training images as input and training content information as output. By training the machine learning model with a large number of training images and associated training content information, the machine learning model "learns" to recognize image content, so the machine learning model can be used to recognize image content that is not contained in the training image. The same principle can also be used for other types of data: by training a machine learning model using training data and expected outputs, the machine learning model "learns" the transformation between data and output, which can be used to provide output based on non-training data provided to the machine learning model.

[0284] In the present case, at least one machine learning model is trained to model the dynamic aspects of a biological organism. In this context, the biological organism may be a cell (or more precisely, multiple cells of the same clone of a cell line) hosted in a bioreactor. However, the proposed concept is not limited to cells. Different types of biological organisms can be supported. "Dynamic aspects" refers to the metabolism of the biological organism, i.e. how a given metabolite influx and a given environment (extracellular metabolite concentration, temperature, etc.) lead to a certain outflow (which is based on the metabolism of the biological organism). In the context of GKCM (which can be based on at least one machine learning model), rates μ(t) and r(t) are used instead of inflow and outflow, where μ(t) refers to the biomass growth rate (adjusted for cell death) and r(t) is a consumption / production rate specific to the biomass. The rates μ(t), r(t) are possible outputs of the dynamics given by the machine learning model and stoichiometry, as shown in the first and second architectures introduced above. In other words, at least one machine learning model can be combined with the flux pattern of the biological organism to model the dynamics of the biological organism. This is achieved by f 动力学 To indicate that f 动力学 is a kinetic relationship trained in at least one machine learning model in combination with stoichiometry from a metabolic network model, wherein

[0285] [μ(t),r(t)] T =f 动力学 (M 通用 ,M 特定于克隆 ,t,x 环境 (t),θ 通用 ,θ 特定于克隆 ).

[0286] In this formula, M 通用 Regarding the general flux model, M 特定于克隆 Regarding clone-specific flux patterns, x 环境 (t) represents the environment of the biological organism and is therefore the input to at least one machine learning model. 通用 and θ 特定于克隆 is a trainable parameter and is therefore the training object of at least one machine learning model, and therefore also the training object of GKCM and DT.

[0287] The training algorithm can be used to adjust (and improve) the (trainable) variables of the digital twin (DT) so that it can accurately predict the experimental data of all given processes (e.g., the time-resolved concentration of a compound). The learning procedure can include, in particular, adjusting and improving parameters from a generalized kinetic cell model (i.e., at least one machine learning model). This trained DT is then able to predict the dynamics of the cell based on the cell's environment (mainly extracellular metabolite concentrations). The machine learning model (e.g., a neural network) receives data for a certain time step and adjusts its weights and biases to predict the experimental data for that particular time step. This may result in a cyclic approach being used at all time steps. Therefore, in some examples, the machine learning model can be considered to be a cyclic metabolic network. More information about cyclic metabolic networks can be found in WO 2020 / 224779A1.

[0288] The at least one machine learning model is trained with experimental data to learn the cell culture dynamics over time through an optimization program. The experimental data is the training data mentioned above, wherein at least one machine learning model is trained with training input data. A popular method for training machine learning models is called "supervised learning", which can also be used to train at least one machine learning model. In supervised learning, a machine learning model is trained using multiple training samples, each of which includes multiple input data values ​​(i.e., training input data) and one or more expected output values ​​(i.e., training output data), i.e., each training sample is associated with an expected output value. By specifying both training input data and training output data, the machine learning model "learns" which output data to provide based on input data similar to the samples provided during training.

[0289] In the proposed concept, the training data may include such training input data and training output data. In this case, the training input data may include a representation of an experimental environment of the organism. The training output data may represent the dynamic characteristics observed in response to the corresponding experimental environment. As described above, this representation of the dynamic characteristics observed in response to the corresponding experimental environment may correspond to rates μ(t), r(t). However, these rates may not be directly output by at least one machine learning model (e.g., by a first component and a second component). Instead, the first component and the second component may be embedded in a function (e.g., f 动力学 ), where the general flux pattern and the clone-specific flux pattern M 通用 ,M 特定于克隆 And the representation of the experimental environment (x 环境 (t)), the first component and the second component are part of the function (e.g., as parameters of a kinetic cell model )). Two examples of possible architectures for implementing such a function are referred to above as the first architecture and the second architecture. For example, the first component and the second component of the at least one machine learning model may correspond to f1 (including the general dynamic cell model parameters ) and f2 (including clone-specific kinetic cell model parameters At least one of the machine learning models further includes a third component f3 (including the general kinetic cell model parameters ) and / or a fourth component f4 (comprising clone-specific kinetic cell model parameters ). In some cases, it is assumed that the first component, the second component, the third component, and the fourth component include separate machine learning models (e.g., ANN). However, these components may also be implemented as separate layers of the same machine learning model (e.g., ANN). Therefore, the first component and the second component (and optionally the third component and the fourth component) of at least one machine learning model may be separate machine learning models, or the first component and the second component (and optionally the third component and the fourth component) of at least one machine learning model may be the first and second (and optionally the third and fourth) layers of the same deep neural network. In both cases, at least one machine learning model may include at least one deep neural network, wherein the first component, the second component, the (optional) third component, and the (optional) fourth component include the first, second, third, and fourth layers of the at least one deep neural network.

[0290] Supervised learning is generally based on supervised learning algorithms, such as classification algorithms, regression algorithms, or similarity learning algorithms. In the context of the present specification, a regression algorithm may be used because it can be used when the output may have any value (within a certain range).

[0291] Alternatively, reinforcement learning can be used to train at least one machine learning model. In reinforcement learning, one or more software actors (referred to as "software agents") are trained to take actions in an environment. Based on the actions taken, rewards are calculated. Reinforcement learning is based on training one or more software agents to select actions that increase the cumulative reward, resulting in the formation of software agents that are better at performing a given task (as evidenced by increased rewards).

[0292] Both supervised learning and reinforcement learning are based on gradually reducing the deviation between the desired output of at least one machine learning model and the output provided by the at least one machine learning model during training. In the context of the present specification, the output is input into the above formula so that training can be based on gradually reducing the deviation between the desired output of a function (including at least one machine learning model) and the output provided by the function during training. Thus, training at least one machine learning model may include determining the deviation between the function and the training output data, wherein the function is based on at least one machine learning model, a first set of flux patterns (e.g., M) representing common functions of multiple clones of a biological organism, and a first set of flux patterns (e.g., M) representing common functions of multiple clones of a biological organism. 通用 ) and a second set of throughput modes specific to individual clones of an organism (e.g., M 特定于克隆 ) (which is also part of the above function). In other words, training the at least one machine learning model can include determining a deviation between an output of the function and the training output data (the rates observed during the experiment), wherein the function is based on the at least one machine learning model, a first set of flux patterns (e.g., M ) representing common functions of a plurality of clones of a biological organism, and a training output data (the rates observed during the experiment). 通用 )) and a second set of throughput modes specific to individual clones of an organism (e.g., M 特定于克隆 ). For example, the first flux pattern set and the second flux pattern may include primitive flux patterns and / or metabolic basic functions.

[0293] In the example generally discussed in WO 2020 / 224779 A1, the above function can be based on or correspond to a hybrid model, wherein the hybrid model includes at least one machine learning model, a first flux pattern set and a second flux pattern set, and other components (e.g., a reactor model).

[0294] In various examples of the present disclosure, the first component and the second component are both functions (eg, f 动力学 ), wherein a deviation is determined between the training output data and the function. Thus, the output of the first component also influences the training of the second component (and vice versa). The same is true for the optional third and fourth components. Thus, the first and second (and optional third and fourth) components can be trained based on the outputs of the corresponding other components.

[0295] In the second architecture described above, the outputs of the first and second components (f1 and f2, respectively) are input to another component f3 of at least one machine learning model, which includes the kinetic cell model parameters The component may be a third component of at least one machine learning model that takes as its input the outputs of the first component and the second component. Thus, the method may further include training the third component of the at least one machine learning model using the training data (using the same techniques as described in conjunction with the first component and the second component) (step 213). Additionally or alternatively, the at least one machine learning model may further include a fourth component (e.g., including the kinetic cell model parameters). f4), which represents one or more flux patterns not represented by the first component and / or the second component. Similarly, the method may include training a fourth machine learning model using the training data (step 214).

[0296] The training of at least one machine learning model is based on reducing the deviation between the desired output of the at least one machine learning model (or in the present case, the function) and the training output data. The deviation can be used as part of a loss function (in the case of supervised learning), where the larger the deviation, the higher the loss, or the deviation can be used as part of a reward function (in the case of reinforcement learning), where the smaller the deviation, the higher the reward.

[0297] In the following, the focus is on supervised learning and the corresponding loss functions. However, similar results can be achieved using reinforcement learning with the corresponding reward functions.

[0298] In various examples, at least one machine learning model can be trained using a random algorithm. For example, a stochastic gradient descent algorithm can be used to reduce or minimize the result of a loss function. In each training iteration, the parameters of the machine learning model (e.g., the gradients of at least one layer of a neural network) are calculated using a subset of the experimental data / training data (a "batch" in machine learning terms). For example, the parameters / gradients can be updated by reducing or minimizing the following loss function:

[0299]

[0300] in,

[0301] c 预测 is the concentration calculated by the mixture model

[0302] c 测量 is the experimentally measured concentration

[0303] c 测量,std is the standard deviation of the experimentally measured concentrations

[0304] p is the training operation (i.e. process)

[0305] t is the measurement time point

[0306] m i It is a metabolite

[0307] m 交换,i Exchange metabolites

[0308] Δt is the time interval between two adjacent points on the time grid

[0309] λ is the weighting factor that regularizes the synaptic weights

[0310] |W l | is the L1 norm of the synaptic weights between layers in a neural network

[0311] V is the volume of the bioreactor

[0312] γ is the weighting factor of negative regularization

[0313] relu is the rectifier function

[0314] is the exchange metabolite m in culture run p at time point t 交换,i The predicted rate

[0315] c rr is the rate change regularization penalty factor

[0316] In the example above, The above deviations can be expressed.

[0317] The first and second (and optional third and fourth) components are trained using training data, which are experimental data based on multiple clones of a biological organism. Therefore, the training data is not based on the experimental data of a single clone but is generated based on the experimental data of multiple different clones. These clones can all be clones of the same cell line. In other words, the training data can be based on the experimental data of multiple clones of the same cell line of a biological organism. Alternatively, clones of two or more different cell lines (e.g., one or more clones of each cell line, such as multiple clones of each cell line) can be used. In other words, the training data can be based on the experimental data of multiple clones of multiple different cell lines of a biological organism. In addition, in order to further increase the breadth of the training data, training data representing different process scales can be used (e.g., experimental data from small-scale experiments, experimental data from medium-scale experiments, and data from large-scale production operations). In other words, the training data can be based on experimental data from multiple different process scales.

[0318] For training the second (and optionally the fourth) component, only a limited subset of the training data is used, i.e., a subset of the training data based on the experimental data of a single clone. Thus, the one or more components are trained to represent clone-specific (i.e., of the clone represented by the subset of training data) dynamic behavior of the biological organism. For example, when at least one machine learning model is trained with training data outside of the subset, i.e., when training is performed that does not involve the single clone, the second component and the optional fourth component can be frozen (i.e., set to a non-trainable state).

[0319] In this disclosure, the experimental environment is represented by (x 环境 (t)) may be an input (e.g., of the first component, the second component, and the fourth component) of at least one machine learning model, and f1, f2, f3, and f4 may be corresponding outputs of the first component, the second component, the third component, and the fourth component, which are in f 动力学 In some examples, the representation may be compressed. Thus, the representation of the experimental environment may correspond to a compressed representation of the experimental environment (e.g., ), which has a reduced dimensionality compared to the uncompressed representation of the experimental environment.

[0320] In the previous examples, the rates μ(t), r(t) were the main focus of the discussion. However, DTs can be particularly useful when used as part of biopharmaceutical production planning and improvement or optimization. Thus, the training output data can also represent one or more biopharmaceutical product quality characteristics (e.g., the PQAs described above) of the biological organisms in the experimental environment.

[0321] In some examples of the present disclosure, a so-called ensemble approach may be employed. An ensemble approach is a method of evaluating the uncertainty of a predictive model. In this method, a collection of models may be trained using the same training data set instead of training a single model. In order to impose variability between different models, a randomly selected seed value may be set corresponding to each model. This results in variability in model training / prediction despite having exactly the same training set for all models within the ensemble. This variability in model predictions can then be interpreted as uncertainty in the model. Although ensemble approaches are computationally expensive due to multiple trainings, this is a simple way to quantify the uncertainty of a predictive model.

[0322] In general, random features lead to variability between trained models when more than one training is performed (each with a randomly selected seed value). This variability between trained models can be used to quantify training uncertainty. A trained digital twin (DT) can include one or more random features, such as:

[0323] Optimization (stochastic gradient descent)

[0324] Random initialization of DT parameters (e.g., sampling from a uniform distribution)

[0325] Random dropout (randomly shutting down some neurons)

[0326] In order to quantify the uncertainty of the trained DT (especially at least one machine learning model of the GKCM), multiple (e.g., 10) generalized dynamic cell models can be trained using the best hyperparameters found in the greedy hyperparameter search and using exactly the same data set. Here, the entire data set is used (i.e., no training test or training validation split is performed, so 100% of the data set is used). Each training is performed considering a randomly selected seed value. Therefore, at least one machine learning model (e.g., a first component, a second component, an optional third component, and an optional fourth component) can form a machine learning model set. The method may include training multiple machine learning model sets (step 210). For example, multiple machine learning model sets can be recursively trained with different seed values. For example, different seed values ​​can affect at least one of the random initialization of parameters and the random inactivation of the corresponding machine learning model. The random characteristics of the DT lead to variability between these multiple trained dynamic cell models. This leads to variability in DT predictions. The overall DT prediction (i.e., descriptive quality) can be considered as the average of the predictions made by ten dynamic cell models. Then, the uncertainty of the trained DT can be defined as the standard deviation of the predictions made by the ten dynamic cell models.

[0327] The results of the ensemble approach can be a trained DT (which includes multiple generalized kinetic cell models), a quantification of the descriptive quality of the trained DT, and a quantification of the uncertainty of the DT predictions.

[0328] In various examples of the present disclosure, transfer learning is used. Machine learning (ML) algorithms iteratively train statistical models to describe the correlation between input and output variables. Typically, this is done by providing the model with multiple input data sets (i.e., training input data) with known outputs (i.e., training output data). Based on the difference between the expected output value and the calculated output value, the parameters of the ML model can be updated in each iteration until convergence is achieved.

[0329] Training machine learning models is very expensive in terms of time and cost due to the need for large qualitative datasets of variables and the computational effort that increases with the amount of data and the number of trainable parameters. The latter grows with the number of variables in the model.

[0330] Transfer learning with warm start reduces these efforts by reusing parts of the model, thereby reducing the amount of necessary data and computational cost while providing better generalization capabilities of the ML model. This will significantly save time and cost of the project and improve the quality of predictions.

[0331] In the context of artificial neural networks (ANNs), this can mean, for example, first training a source model with a certain task, and then using the resulting weights and biases of that network as an initialization (warm start) to train a target model with a different task using the same network structure. Typically, only a portion of the ANN for a new problem is initialized using a previously trained model, or a new portion can be added to a pre-existing ANN to solve a new problem. Ideally, this can result in a significant reduction in the training time of the ANN for the second problem, because the training starts closer to an improved or optimal set of parameters for the entire network. This also means that less data is needed in the second training to obtain good training results.

[0332] Transfer learning can be applied to the generalized kinetic cell model (GKCM). Different use cases can be considered here. The first one is actually an inherent part of the conception of the GKCM, namely that all clones share information between each other using the common layers of the ANN. Therefore, even training a GKCM from scratch will always include aspects of transfer learning between datasets, resulting in less data required per clone while maintaining good generalization capabilities and high prediction accuracy. This approach of training multiple models simultaneously is also called multi-task learning and is an approach typically used for heterogeneous transfer learning problems.

[0333] Because after training, it is possible to distinguish between generic and clone-specific behaviors. Since the layers are separated, it is possible to add additional clones to an existing GKCM using a combination of clone-specific layers and transfer learning and warm starting. In other words, Figure 2b As further shown in , the method can also include using transfer learning to adjust at least a clone-specific second component of at least one machine learning model based on training data based on experimental data of another single clone (step 240). Such use of transfer learning in GKCM can greatly speed up the training of new clones, and also enable training with less data (compared to the project's standalone "standard" DT) because most of the common layers (and common behaviors) have already been trained on other datasets. In such a scenario, the component of at least one machine learning model representing the common component (i.e., the first component) can be further trained, or, to speed up training, it can be frozen (i.e., set to be non-trainable).

[0334] Three examples for transfer learning and / or warm start are given below. In the first setting, the complete GKCM (generic layers and clone-specific layers) can be (re)trained with the same (or optionally, enhanced) dataset. Application cases include continuing stopped training (e.g. due to cloud instance loss), improving an existing GKCM when new data for the same clone is available, or version upgrades of software.

[0335] In a second setting, the full GKCM (general layer and clone-specific layer) can be trained again with a new clone-specific dataset. The advantage of this approach is that training can be run using only the reduced dataset. However, when using this approach, the general layer may not continue to benefit from adding more data to the GKCM. In this case, the first component and the second component (and optionally the third component and the fourth component) can be trained in a first stage of training, and the second component (and optionally the fourth component) can be trained in a second stage of training (which follows the first stage of training), wherein the first component is frozen during the second stage of training.

[0336] In the third setting of completely retraining the GKCM with another new clone, the full training dataset (from the new clone and the pre-existing process data) can be utilized. It is also proposed to continue training the clone-specific layers for the pre-existing clones to compensate for the changes in the general layers. These pre-existing clone layers can be warm-started like the general layers. The main advantage of the present disclosure is that the generalization ability of the GKCM is further improved.

[0337] Once at least one machine learning model, and therefore a GKCM, is trained, it can be used to generate a corresponding digital twin comprising at least one machine learning model. Figure 2b As shown in , the method may also include generating a digital twin of the biological organism using at least one trained machine learning model (step 220). In addition to the at least one machine learning model, other components may also be included in the digital twin, such as the remaining components of the GKCM (e.g., flux pattern), the extracellular reaction model, and the osmotic concentration model.

[0338] Machine learning algorithms are typically based on machine learning models. In other words, the term "machine learning algorithm" may refer to an instruction set that can be used to create, train, or use a machine learning model. The term "machine learning model" may refer to a data structure and / or rule set that represents knowledge learned, for example, based on training performed by a machine learning algorithm. In an embodiment, the use of a machine learning algorithm may mean the use of an underlying machine learning model (or multiple underlying machine learning models). The use of a machine learning model may mean training a machine learning model by a machine learning algorithm and / or a data structure / rule set that serves as a machine learning model.

[0339] For example, the machine learning model may be an artificial neural network (ANN). ANN is a system inspired by biological neural networks, such as those found in the brain. ANN includes a plurality of interconnected nodes and a plurality of connections (so-called edges) between the nodes. There are usually three types of nodes, input nodes that receive input values, hidden nodes that are (only) connected to other nodes, and output nodes that provide output values. Each node may represent an artificial neuron. Each edge may transfer information from one node to another. The output of a node may be defined as a (non-linear) function of the sum of its inputs. The input of a node may be used in the function based on the "weight" of the edge or node that provides the input. The weights of nodes and / or edges may be adjusted during the learning process. In other words, the training of an artificial neural network may include adjusting the weights of nodes and / or edges of the artificial neural network, i.e., achieving a desired output for a given input. In at least some embodiments, the machine learning model may be a deep neural network, such as a neural network including one or more hidden node layers (i.e., hidden layers), preferably multiple hidden node layers.

[0340] Alternatively, the machine learning model can be a support vector machine. A support vector machine (i.e., a support vector network) is a supervised learning model with an associated learning algorithm, which can be used to analyze data, for example, in classification or regression analysis. A support vector machine can be trained by providing a plurality of training input values ​​belonging to one of two categories to the input. A support vector machine can be trained to assign new input values ​​to one of two categories. Alternatively, the machine learning model can be a Bayesian network, which is a probabilistic directed acyclic graph model. A Bayesian network can use a directed acyclic graph to represent a set of random variables and their conditional dependencies. Alternatively, the machine learning model can be based on a genetic algorithm, which is a search algorithm and heuristic technique that mimics a natural selection process. Alternatively, the machine learning model can be based on a Gaussian process, which is a random process.

[0341] The interface circuit 22 or the means for communicating 22 may correspond to one or more inputs and / or outputs for receiving and / or transmitting information within a module, between modules, or between modules of different entities, which information may be a digital (bit) value according to a specified code. For example, the interface circuit 22 or the means for communicating 22 may include a circuit configured to receive and / or transmit information.

[0342] For example, the processing circuit 24 or the means for processing 24 may be implemented using one or more processing units, one or more processing devices, any means for processing (e.g., a processor), a computer, or a programmable hardware component that can be run with corresponding adapted software. In other words, the functions of the processing circuit 24 or the means for processing may also be implemented by software, which is then executed on one or more programmable hardware components. Such hardware components may include general purpose processors, digital signal processors (DSPs), microcontrollers, etc.

[0343] For example, memory circuit 26 or memory 26 may include volatile or non-volatile memory, such as circuitry for providing volatile or non-volatile memory. For example, memory circuit or memory 26 may be random access memory (RAM), such as dynamic random access memory (DRAM) or static random access memory (SRAM), or persistent memory (PMEM). For example, at least a portion of the memory circuit may be part of the processing circuit (e.g., a register of the processing circuit).

[0344] For example, the storage circuit 28 or the device 28 for storing information may include at least one element from the group of computer-readable storage media such as magnetic or optical storage media, such as a hard disk drive, a flash memory, a floppy disk, a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electronically erasable programmable read-only memory (EEPROM), or a network storage.

[0345] For example, computer system 20 may be a workstation computer system (eg, a workstation computer system used for scientific computing).

[0346] In combination with the proposed concept or one or more examples described above or below (for example, Figure 1 , Figures 3 to 12 ), mentioning more details and aspects of the training of at least one machine learning model (and thus, the training of GKCM and DT). The training of at least one machine learning model (and thus, the training of GKCM and DT) may include one or more additional optional features corresponding to one or more aspects of the proposed concept or one or more examples described above or below.

[0347] In the following, some examples of applications of such digital twins are given, which may include combining Figure 2a and Figure 2b At least one machine learning model trained as shown.

[0348] In some examples, digital twins can be used for process improvement or optimization.

[0349] In general, there are different methods for process improvement or optimization. Using, for example, a trained digital twin (DT) from an integrated approach, one (e.g., single) or multiple processes can now be improved or optimized, for example, by performing culture medium improvement or optimization and / or feed improvement or optimization. The better the prediction quality of the trained DT, the more reliable the improved optimization results. The improvement or optimization of culture medium involves improving or optimizing the concentration of the compound in the feed medium and / or the basal medium, with the aim of reducing or minimizing the cost function subject to a set of feasibility constraints. The improvement or optimization of feed involves improving or optimizing the feed strategy (i.e., deciding when to feed and how much to feed), with the aim of reducing or minimizing the cost function subject to a set of feasibility constraints.

[0350] Furthermore, the trained DT can be used to perform model-based design of experiments (MbDoE). Figure 2b As further shown in , the method may include determining a plurality of experiments to be performed using the biological organism (step 230), and continuing to train at least one machine learning model based on additional training data from the plurality of experiments (steps 210, 211, 212, 213, 214). Model-based experimental design may also be referred to as digital twin-based experimental design (DTDoE), and may perform simultaneous media and feed improvements or optimizations and design of new experiments. Thus, the determination of the plurality of experiments (step 230) may also be Figure 3 In both cases, a set of feasibility constraints can be applied to ensure that a practically feasible solution is obtained.

[0351] In the former case (feed / medium improvement or optimization), the goal can be to reduce or minimize the cost function (as in the case of medium and feed optimization), while in the latter case (model-based experimental design), the experimental data can be richer in terms of its information content. Ideally, the experimental data covers a wide range of variable dynamics during the process. Using such information-rich experimental data to train the DT helps to build a better DT in terms of its descriptive / predictive quality. After training the DT, for example, using an integrated method, the trained DT can be used to perform a DTDoE, taking into account the experimental design constraints. The result of the DTDoE is a guide to designing experiments proposed for experimental implementation. The designed experiments may include changes in feeding strategies and / or culture medium composition. Then, the experts responsible for implementing the experiment can implement the designed experiments according to the guidance, and the obtained experimental data can be provided for continuing to train at least one machine learning model. These experimental data can be integrated into the existing experimental data originally used to train the DT. Training the DT using this expanded data set can result in a better DT in terms of its descriptive / predictive quality.

[0352] As mentioned above, DT can be used to identify target parameters such as feeding strategy, medium composition, etc.

[0353] Figure 3 A flow chart of an example of a method for determining at least one target parameter of at least one bioreactor containing at least one biological organism is shown. The method comprises using a method according to the above ( Figure 2b At least one digital twin of at least one biological organism generated by the method of (step 310) and at least one corresponding cost function are used to determine at least one target parameter (step 310). Such target parameters may, for example, include at least one of the following: a target medium composition for a feed medium for at least one biological organism; a target feeding strategy for at least one biological organism; a target effluent strategy for at least one biological organism; and a target initial condition for at least one biological organism (all of which may affect the medium containing the biological organism). For example, the target parameter can be determined so that one or more characteristics of the resulting process (e.g., product quality, yield of a target product, etc.) are improved compared to other values ​​of the target parameter. Obviously, the method may also include generating a DT (step 220) as a preparatory task.

[0354] In some examples, at least one target parameter may be determined for a single clone. For this purpose, a single digital twin representing a single clone may be sufficient. Alternatively, at least one target parameter may be determined for multiple clones of the same cell line or different cell lines (e.g., for an entire platform for hosting different clones). In this case, at least two digital twins of at least two biological organisms may be used to jointly determine at least one target parameter for at least two biological organisms (i.e., determining the same one or more parameters for two or more different biological organisms, i.e., two or more different clones).

[0355] Examples of corresponding cost functions for determining target medium compositions and / or feeding strategies, as well as corresponding constraints for the respective target parameters, are given below. For example, a respective cost function can be calculated, for example, for a given clone or clone set of a biological organism and can be used to select the best performing clone in a given clone set of a biological organism (e.g., as combined with Fig. 9 ). For example, the method may include computing and scaling a culture medium composition cost function for each model of a digital twin of a biological organism so as to determine an improved or optimal target parameter (e.g., culture medium composition) across all models of the digital twin.

[0356] In various examples, some feasibility constraints are applied to facilitate determining at least one target parameter.

[0357] For example, constraints on the culture medium (or multiple culture media) can be applied. The metabolite concentration in the culture medium (i.e., c m ) may be subject to certain lower and upper limits, as follows:

[0358] LB m ≤c m ≤UB m

[0359] Default lower and upper limits for basal and feed medium compositions can be defined using the following rules, for example:

[0360]

[0361] in,

[0362] m represents a metabolite in the feed medium (i.e., basal medium or feed medium)

[0363] LB m Refers to the lower limit of basal / feed medium concentration

[0364] UB m Refers to the upper limit of basal / feed medium concentration

[0365] LBF m Refers to the weight / factor used to adjust the lower limit of basal / feed medium composition

[0366] UBF m Refers to the weight / factor used to adjust the upper limit of basal / feed medium composition

[0367] SF m Refers to the solubility factor of all metabolites present in the feed / basal medium

[0368] S refers to the solubility of all metabolites present in the feed / basal medium

[0369] Refers to the feed / basal medium concentration

[0370] Please note that the lower and upper values ​​represent only default values ​​and can be easily adjusted by the user as per the project specifications.

[0371] For example, constraints on feeding can be applied. For example, the bolus shot volume can be constrained by specific lower and upper limits, which can be specified as follows:

[0372] LB≤v 进料 ≤UB

[0373] Similar to the medium composition, default limits for feed volume can be defined as follows, for example:

[0374] LB=LBF*v ref

[0375] UB=UBF*v ref

[0376] in,

[0377] LB refers to the lower limit of feed volume

[0378] UB is the upper limit of feed volume

[0379] LBF is a factor used to define the lower limit of feed volume.

[0380] UBF is a factor used to define the upper limit of feed volume.

[0381] v ref Refers to the reference feed volume

[0382] Note that just like the medium constraints, the user can easily adjust the boundaries to match project requirements.

[0383] In the following, examples of loss functions for media and feed improvement or optimization are given. For example, a loss function may include an objective and a penalty term:

[0384]

[0385] in,

[0386] c m (p,t) is the concentration of metabolite m in process p at time t.

[0387] c m (p, t) may, for example, represent the last time point (i.e., c) corresponding to a given process p. m (p,t end )) product concentration.

[0388] α is the mapping function of the target term. It may take any of the following values:

[0389]

[0390] V i is the penalty term i.

[0391] The penalty term describes the amount by which the process specification (e.g., concentration, volume, permeate concentration, etc.) deviates from the desired range or target value. Mathematically, this can be expressed as follows:

[0392] V i =w i ·D i

[0393] in,

[0394] w i Refers to the penalty imposed on deviations from process specifications i

[0395] D i It refers to the amount of deviation.

[0396] Different deviation terms may include one or more of the following:

[0397] Negative concentration bias: This ensures that metabolite concentrations remain positive and therefore realistic.

[0398] Vessel Volume Upper and Lower Limit Deviation: This ensures that the bioreactor volume remains within or very close to the specified range defined by the upper / lower limits.

[0399] • Upper and lower concentration deviations: This ensures that the concentration of the compound in the bioreactor remains within or very close to the specified range defined by the upper / lower limits.

[0400] Medium Deviation Bias: This ensures that the concentration of compounds in the feed medium does not deviate unnecessarily from the reference value, thus ensuring that only the concentrations of metabolites that have a significant impact on the loss function are changed during optimization. This can help eliminate redundant changes in feed medium optimization.

[0401] c0 Deviation: This ensures that the concentrations of compounds in the basal medium do not deviate unnecessarily from the reference values, thus ensuring that only the concentrations of metabolites that have a significant impact on the loss function are changed during optimization. This can help eliminate redundant changes in basal medium optimization.

[0402] lm output deviation: This ensures that the osmotic concentration of the optimized culture medium remains below a predefined value. High osmotic concentration values ​​may pose a risk to cell health.

[0403] Feed Deviation Deviation: This ensures that the feed volume does not deviate unnecessarily from the reference value, allowing only those areas of the feed curve that have a significant impact on the loss function to be changed during optimization. This can help eliminate redundant changes in feed optimization.

[0404] Total Feed Volume Deviation: This ensures that the total feed volume remains within or very close to the specified range defined by the upper / lower limits.

[0405] In the following, an example of the loss function of the experimental design (i.e., MbDoE / DTDoE) is given. The loss function can be defined as:

[0406]

[0407] Among them, ρ m,n is the correlation factor between the predicted concentrations of metabolites m and n, which is mathematically defined as:

[0408]

[0409] in,

[0410] c m (p,t) and c n (p,t) are the predicted concentrations of metabolites m and n

[0411] and are the mean metabolite concentrations of metabolites m and n calculated across processes and time points.

[0412] Where α and V i The definition of is the same as in the previous section.

[0413] Improvement or optimization problems can be solved using a computational optimizer, such as the ADAM optimizer (Kingma, DP and Ba, J., 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv: 1412.6980), which can be used to solve the above-mentioned improvement or optimization problems. The solution of this problem can involve one or more of the following three parts: 1) integrated optimization, 2) multiple starting points, and 3) piecewise constant improvement or optimization, each of which will be discussed below.

[0414] In the following, more details on the integrated optimization or improvement technique are given. As mentioned earlier, a trained DT can be adopted as part of an improvement or optimization framework. When an integrated approach is adopted, the trained DT includes several kinetic cell models. In a general setting, the optimization problem can be solved for each of these kinetic cell models, thereby obtaining multiple different improved or optimal solutions. The next task will then be to combine these solutions in order to obtain a single overall improved or optimal solution. However, this is not trivial and may result in a significant loss of information, thereby providing a suboptimal solution.

[0415] To avoid this problem, an ensemble-based optimization approach can be employed. This also involves the use of multiple kinetic cell models in the trained DT obtained from the ensemble method. However, instead of solving an optimization problem for each of these models in a sequential manner, all kinetic cell models can be merged as part of a single improvement or optimization framework. This can be done by defining an overall objective of the proposed improvement or optimization framework, which can be a function of multiple objective function values ​​obtained from multiple kinetic cell models. Therefore, the problem now may be to find an improved or optimal solution that reduces or minimizes the combined cost function. Mathematically, this can be stated as follows:

[0416] Overall loss = f(loss1, loss2,…, loss N )

[0417] Where loss i is the loss function calculated using the kinetic cell model model i. Typically, function f is an average function, so the total loss of N kinetic cell models can be expressed as follows:

[0418]

[0419] In addition, the aforementioned multiple starting point method can be used. The multiple starting point method can form the second component of the improvement or optimization framework. As the name indicates, this means that multiple initial starting points of the improvement or optimization problem are used. For example, these initial points can be generated with the help of quasi-random Sobol sequences. Assuming that these are K points, this leads to K improvement or optimization problems, each problem starting from a different initial value of the concentration of the culture medium component. The multiple starting point method can improve the exploration of the design space, and therefore avoid being trapped in the local optimum region. Therefore, the higher the number of initial points, the better the coverage of the design space, and therefore improves the probability of finding a global improvement or optimal solution.

[0420] In some examples, piecewise constant improvement or optimization can be used. Unlike the multi-start method, piecewise constant improvement or optimization is only applicable to the improvement or optimization of time-resolved components (such as feeding strategies). Therefore, it may only be applicable to feeding optimization and experimental design. This strategy involves discretizing the design space into one / multiple parts. It is then assumed that the design points located in these parts remain unchanged, i.e., fixed at specific values. This helps to reduce the complexity of the improvement or optimization problem because it may result in a significant reduction in the number of decision variables or the size of the design space. In addition, the method can help obtain a more practical solution in which the number of changes over the entire feeding curve is less or more controllable.

[0421] Considering a single feed with 10 bolus volumes, an improvement or optimization of the feeding strategy can produce improved or optimal values ​​for these bolus volumes. Using a piecewise constant strategy, the algorithm can discretize the 10 time points into groups, and then a constant feed volume can be assumed in each of these groups. Therefore, this can reduce the number of decision variables from the number of boluses to the number of groups. The complexity of this problem may vary depending on the number of groups for a particular feed.

[0422] In some examples, glucose control may be performed. Typically, glucose feed may not be modified or optimized because most cell culture processes are operated with threshold-based glucose control. Glucose concentration in the bioreactor may affect the performance of the bioprocess. Therefore, an accurate description of the control mechanism applied in the actual process may be important for the accuracy of the predicted optimized bioprocess.

[0423] Glucose control feed is usually applied from a culture medium consisting of concentrated glucose. In order to prevent the limitation of glucose in a given bioprocess, glucose can be fed once the glucose concentration in the bioreactor drops below a given threshold. The corresponding volume of glucose feed is added depending on the glucose concentration in the feed medium and the desired bioreactor glucose concentration (set point). Glucose control is usually applied to a certain control period (i.e., between "control start" and "control end") during the process, and has a certain control frequency (e.g., daily control).

[0424] Glucose can also be present in other feed mediums (that is, other mediums except glucose medium). Therefore, when the feeding from these other mediums can be applied, the glucose concentration in the bioreactor increases. When other feedings and glucose control feeding are applied simultaneously, other feedings are used as the possible basis of calculating the required glucose feed volume addition. As a result, glucose control feeding can make the remaining gap approach the set point.

[0425] In this way, the glucose concentration can be maintained between the threshold and set point values ​​for a certain period of time during the process. Of course, each control cycle during the running process can adopt its own threshold and set point values. It is also possible to extend the control cycle to the entire process duration.

[0426] Some aspects of the present disclosure may relate to model prediction monitoring and control. Even a well-controlled manufacturing process may encounter unknown variables and deviate from an acceptable range. These deviations are usually detected only after they occur, so there is almost no chance to implement corrective and / or preventive measures (CAPA). In addition, measurements may only be available on different time scales (online, offline, atline, inline), which makes it difficult to track the process in real time. Model prediction monitoring and control can enable processing of different time scales of measurements, estimating the state of a bioprocess, predicting the performance of a bioprocess based on real-time measurements (monitoring), and improving or optimizing the process within a defined reference curve ("golden batch") to provide control suggestions.

[0427] Figure 4 A flow chart showing an example of a method for monitoring a biomanufacturing process involving a biological organism. The method includes using a Figure 1 b) using a digital twin of the biological organism generated by method b to determine an estimated state of the biological manufacturing process (step 410). Information about the environment of the biological organism (i.e., a representation of the environment) is provided to the digital twin using a rolling horizon method. The method includes comparing the estimated state of the biological manufacturing process with the observed state of the biological manufacturing process (step 420). For example, in comparing the estimated state of the biological manufacturing process with the observed state of the biological manufacturing process, a rolling horizon estimation algorithm can be used. Obviously, Figure 4 The method may also include generating a digital twin (step 220).

[0428] For state estimation, a rolling horizon estimation (MHE) can be applied, where the trained DT is used to obtain predictions that are reconciled based on the difference between predicted and measured metabolite concentrations and the trust in the model or measurements. This allows the prediction to be run in a time-point-by-time manner from measurement to measurement by taking into account model uncertainty in terms of model-plant mismatch and measurement noise, as well as estimates of unmeasured metabolite concentrations.

[0429] MHE is a backward time domain improvement or optimization technique for multivariate estimation that uses a dynamic reactor model, past measurement traces, and a cost function to be minimized. The improvement or optimization can be performed over a time interval (i.e., time domain), which moves forward in time (i.e., rolling time domain) as new measurements become available (e.g., for a process that takes 14 days, the MHE time domain is 6 days (d), the time grid is 24 hours, and one optimization can be performed from 0-1d, 0-2d, ..., 0-6d, 1d-7d, 2d-8d, ..., 8d-14d) (see Figure 5).

[0430] Figure 5a and Figure 5b A schematic diagram of a rolling horizon estimation (MHE) algorithm with a horizon of 6 days according to an example is shown. The algorithm performs a reconciliation (estimated state, star points) taking into account the measured values ​​(rectangular points) and the predicted values ​​from the digital twin (triangular points). During the optimization, the state noise for time points outside the rolling horizon window can be kept fixed, while the state noise for time points within the rolling horizon window can be changed. MHE also allows estimating unmeasured states, for example, see day 3 or day 7. After improvement or optimization and new input measurements, the window moves forward and the procedure can be repeated.

[0431] For example, the mathematical problem can be defined as follows:

[0432]

[0433] stc k+1 =f(c k ,u k ,p k )+w k

[0434] c k ∈C,u k ∈U,p k ∈P,w k ∈W

[0435] in,

[0436] w is the state noise (describing model mismatch),

[0437] L MHE Cost function,

[0438] c is a vector of metabolite concentrations including biomass,

[0439] C is the set of feasible concentrations resulting from the constraints,

[0440] k time (point),

[0441] uDigital twin inputs other than reactor concentrations, i.e., feeds and samples,

[0442] U is the set of feasible inputs resulting from the constraints,

[0443] f(·) is the functional relationship between the concentration, input and additional parameters and the concentration at the next time point (digital twin model),

[0444] p is a vector of additional parameters (pH, T, osmolarity, ...),

[0445] P is the set of feasible parameters resulting from the constraints,

[0446] c k ,p k ,u k Concentrations, parameters, and inputs at time point k.

[0447] Model mismatch (referred to as state noise in the following) as well as noisy measurements and inputs (feed, samples) are assumed to exist.

[0448] For example, the cost function can be defined as (adapted from Morabito, Bruno, et al. "Multi-mode Model Predictive Control and Estimation for Uncertain Biotechnological Processes." IFAC-Papers On Line 52.1 (2019): 709-714)

[0449]

[0450] in,

[0451] m∈M is the number of prediction models of DT

[0452] is the vector of state noise of model m at time point i,

[0453] is a vector of measured concentrations at time point i (can also be a subset of metabolites as required by DT),

[0454] is the vector of concentrations predicted by model m at time point i,

[0455] N MeE is the time domain length of the state estimation (in hours),

[0456] Q MHE is the weighting matrix of the state noise

[0457] R MHE is the weighting matrix of the stage cost (measurement noise)

[0458] and the matrix-vector norm

[0459] In some examples, model predictive control (MPC) can be performed. Given a reference trajectory of metabolite concentrations, improvements or optimizations during cultivation can be performed to obtain improved or optimized inputs (e.g., feeds, sampling) that can keep the process close to the reference while keeping the control effort reduced or minimized even in the presence of deviations in the process run. This can reduce risk during manufacturing while maintaining product quality.

[0460] Figure 6 A flow chart showing an example of a method for controlling a biomanufacturing process involving a biological organism. The method includes using a Figure 1 b) to continuously adjust the environment of the biomanufacturing process using a digital twin of the biological organism generated by method b (step 610), wherein information about the environment of the biological organism (i.e., a representation of the environment) is provided to the digital twin using a backward time domain method. The method includes comparing an estimated state of the biomanufacturing process with a defined reference state trajectory of the biomanufacturing process (step 620). For example, a model predictive control algorithm is used in comparing the predicted state of the biomanufacturing process with the defined reference state trajectory of the biomanufacturing process. Based on the comparison, the environment can be continuously adjusted (step 610). For example, the environment can be adjusted based on the comparison. Figure 4 The state estimation can be performed according to Figure 3 Methods to perform improvements or optimizations of an environment (i.e., target parameters of the environment). For example, Figure 6 The method may also include generating a digital twin (step 220).

[0461] Figure 7a and Figure 7b A schematic diagram illustrating a model predictive control (MPC) algorithm with a horizon of 6 days according to one example is shown. Figure 7a and Figure 7b In Figure 1, the algorithm is used to improve or optimize the control input (e.g., feed volume or rate) by reducing or minimizing the deviation between the reference (solid line) and the prediction (star points) of the digital twin, so that the improved or optimized prediction trajectory (dark funnel around the prediction points) follows the reference (solid line). In addition, the control effect and the deviation of the terminal cost (here: final titer) can be improved or optimized ( Figure 7a and Figure 7b ). Improvement or optimization can be performed on future predictions within a defined time domain moving forward during the culture time. Improved or optimized control inputs outside of this time domain window can remain fixed (or be implemented or optimized in the future).

[0462] MPC is a finite backoff horizon optimization technique that uses a dynamic reactor model, a reference trajectory, and a cost function to be reduced or minimized relative to the control input. Improvements or optimizations can be made over the entire planned cultivation time, but only the control at the next time point in the plant is applied. Improvements or optimizations are then made again, and so on.

[0463] For example, the mathematical problem can be defined as follows:

[0464]

[0465] stc k+1 =f(c k ,u k , p k )

[0466] c k ∈C,u k ∈U,p k ∈P

[0467] in,

[0468] L MPC is the cost function,

[0469] c is a vector including the metabolite concentrations of biomass,

[0470] C is the set of feasible concentrations resulting from the constraints,

[0471] k is the time (point),

[0472] uDigital twin inputs other than reactor concentrations, i.e., feeds and samples,

[0473] U is the set of feasible inputs resulting from the constraints,

[0474] f(·) is the functional relationship between the concentration, input and additional parameters and the concentration at the next time point (digital twin model),

[0475] p is a vector of additional parameters (pH, T, osmotic concentration, ...),

[0476] P is the set of feasible parameters resulting from the constraints,

[0477] c k , p k ,u k are the concentration, parameters and input at time point k.

[0478] For example, the cost function can be defined as (adapted from Morabito, Bruno, et al. "Multi-mode Model Predictive Control and Estimation for Uncertain Biotechnological Processes." IFAC-Papers On Line 52.1 (2019): 709-714.)

[0479]

[0480] in,

[0481] m∈M is the prediction model set of DT

[0482] i∈N MPC is up to a finite time domain N MPC (End of culture) time point

[0483] is the vector of metabolite concentrations at time point i predicted by DT m

[0484] is the vector of reference metabolite concentrations at time point i

[0485] u i is the input to DT, here: feed (the sampling will remain in the reference process)

[0486] is predicted by DT m at time point N MPC vector of metabolite concentrations at (here, final titer), and

[0487] At time point N MPC Vector of reference metabolite concentrations at (here final titer)

[0488] Q MPC is the weighting matrix of the reference deviations (covariance)

[0489] R MPC is the weighting matrix (covariance) of the control effects

[0490] E MPC is the weighted matrix (covariance) of terminal costs

[0491] and the matrix-vector norm

[0492] In the following, the overall improvement or optimization problem is discussed.

[0493] Figure 8a and Figure 8b A schematic diagram of the model predictive monitoring and control algorithm with a state estimation horizon of 7 days and a control horizon of 5 days is shown. The algorithm takes into account the measured values ​​( Figure 8a rectangle 830 in ) and the predictions from the digital twin ( Figure 8a The MHE also allows for the estimation of unmeasured states. The state estimate at the most recent time point can then be used as the initial condition for the MPC. The MPC algorithm can be optimized by reducing or minimizing the golden batch (solid line 850, Figure 8a ) and the prediction of the digital twin (the star 840 and area 845 on the right side of the second time domain line 820, Figure 8a ) to improve or optimize the control input (e.g., feed volume or rate) such that the improved or optimized predicted trajectory (star 860 and area 865 to the right of first time domain line 870, Figure 8b ) follows the golden batch (solid line 880, Figure 8b In addition, the control effect and the deviation of the terminal cost (here: final titer) can be improved or optimized ( Figure 8a and Figure 8b ). Improvement or optimization can be performed on future predictions within a defined time domain moving forward during the culture time. Improved or optimized control inputs outside of this time domain window can remain fixed (or be implemented or optimized in the future).

[0494] Model predictive monitoring and control algorithms can combine state estimation via rolling horizon estimation and model predictive control. At each new input measurement, the state estimator can run the MHE algorithm to obtain the latest state estimate in the MHE horizon (e.g., Figure 4 The currently estimated state can then be used as the initial condition for the prediction of the MPC controller, which improves or optimizes the control input according to the MPC objective in the MPC time domain (see Figure 6 , Figure 8a and Figure 8b ).

[0495] For example, the mathematical problem can be defined as follows:

[0496]

[0497] stc l+1 =f(c l ,u l , p l )

[0498] c l ∈C,u l ∈U,p l ∈P, l∈[t; t+N MPC ]

[0499]

[0500] W k ∈W, k∈[tN MHE ; t]

[0501]

[0502] in,

[0503] is a vector containing the estimated metabolite concentrations of the biomass

[0504] As combined Figure 3 As outlined, one task during improvement or optimization of a process may be the selection of promising clones. Fig. 9 A flow chart showing an example of a method for selecting clones of a biological organism. For the purpose of clone selection, the method comprises using Figure 1 b generates multiple digital twins of multiple clones of a biological organism (step 220). The method includes selecting clones (step 910) by comparing one or more characteristics of multiple digital twins, such as product quality, yield of target product (or more generally clonal potential or clonal plasticity, which may include yield of target product and / or platform matching of clones), etc. In general, clonal potential or clonal plasticity is a characteristic of clones that can vary between clones and refers to the potential change in clonal performance (e.g., titer / product yield) after changes in process conditions. It can be used as one of the characteristics of clone selection criteria. For example, the potential to increase titer can be evaluated through process improvement or optimization (feeding strategy and / or feed medium composition) for each clone. Therefore, it can be based on Figure 3 The method determines the target parameters to select one or more features. Fig. 9 The method may also include determining at least one target parameter for each clone using the multiple digital twins and the corresponding cost function (step 310), wherein the clone selection (step 910) is based on the determined target parameter.

[0505] In the following, a practical example of the proposed concept is given. In this example, it is demonstrated that a digital twin can be trained using data across clone and process scales and can be used for model predictive monitoring and control during manufacturing.

[0506] First, the experimental data used for digital twin generation is discussed. In this example, an industrial recombinant Chinese hamster ovary (CHO) cell line expressing IgG monoclonal antibody (mAb) through a glutamine synthetase (GS) expression system is used. The amino acid composition of the monoclonal antibody (in mol-%) is: Ala 5.0, Arg 2.9, Asn 4.0, Asp 4.0, Cys 2.4, Glu 4.8, Gln 4.7, Gly 6.5, His 2.0, Ile 2.3, Leu 7.4, Lys 6.8, Met 0.8, Phe 3.5, Pro 7.0, Ser12.7, Thr 8.0, Trp 1.7, Tyr 4.5, Val 9.0.

[0507] The experimental data used for digital twin generation included data sets from 15 ml and 250 ml scales (thus two different process scales), a total of 263 cultures and 31 clones, cultivated in fed-batch mode to produce IgG antibodies, including complete amino acid analysis, organic acids, cell counts, product titers, NH4 and glucose concentrations. For most clones, 4 cultures were provided, however, in some cases up to 46 cultures were provided.

[0508] The genome-scale CHO-K1 metabolic network model based on Hefzi et al. was used (Hefzi, Hooman, et al. "A consensus genome-scale reconstruction of Chinese hamster ovary cellmetabolism." Cell systems 3, 5 (2016): 434-443). The database was further sorted to obtain 3700 reactions and transport steps. Important metabolic functions were verified and other pathways such as glycosylation, mAb production, growth and cell lysis were added.

[0509] The following basic metabolic functions were deduced: synthesis of non-essential amino acids from glucose and NH4; degradation of amino acids to CO2; synthesis of cysteine ​​from methionine; synthesis of proline from arginine; degradation of glucose to CO2; synthesis of pyruvate and lactate from glucose; degradation of pyruvate and lactate to CO2; degradation of serine to pyruvate; synthesis of biomass and mAbs, synthesis of tyrosine from phenylalanine; and cell death and lysis.

[0510] For the extracellular network, abiotic degradation of glutamine to 5-oxoproline (and NH4, H) was considered.

[0511] In the following, the specific architecture used in the GKCM in this example to describe the growth and exchange rates of the measured metabolites is discussed.i Used to describe, for example, feed-forward neural networks as a function of specified inputs.

[0512]

[0513] where f3 is

[0514]

[0515] where f1 is

[0516]

[0517] and f2 is

[0518]

[0519] ANN1 (e.g., the first component of at least one machine learning model) is a feed-forward neural network with 2 hidden layers, each with 100 neurons, and an output dimension of 100. A 20% dropout is used for the hidden layers, and parametric relu is used as the activation function in the hidden layers. The activation function of the output layer is a sigmoid function. H1 is a positive scalar.

[0520] ANN2 (e.g., the second component of at least one machine learning model) is a feed-forward neural network with 2 hidden layers, each with 40 neurons, and an output dimension of 100. A 20% dropout is used for the hidden layers, and parametric linear rectification is used as the activation function in the hidden layers. The activation function of the output layer is the tanh function. H2 is a positive scalar.

[0521] Matrix H3 is a 100×1253 matrix, where

[0522] In this example, GKCM only uses the general mode M 通用 , no clone-specific mode M is used 特定于克隆 Therefore, f4 is zero in this example. In other words, the fourth component is unnecessary.

[0523] Furthermore, no explicit representation of the input vector in the low-dimensional space is used, i.e.

[0524] In the following, the training and validation of digital twins are discussed. Data augmentation is used so that each process is replicated, resulting in a set of original processes associated with a specific clone and another set of processes not associated with a specific clone. For processes not associated with a specific clone, the output of f2 is 0. Therefore, the common behavior can be identified as a combination of the outputs of f1 and f3 with f2=f4=0.

[0525] The predictive power of the digital twin was evaluated using a 4-fold cross validation set (see Figure 5). Each validation and training set always contained at least 1 culture of each clone. That is, if a clone had 4 cultures available, there would be 3 cultures in each training set and 1 culture in the validation set.

[0526] Fig.10 A regression plot showing the quality of GKCM predictions for each metabolite is shown. The plot compares the measured validation data with the predicted values ​​from GKCM. 2 A value of 1.0 indicates perfect prediction.

[0527] Model predictive monitoring and control was implemented on the basis of Cedex Bio HT (Roche) data to keep the reference culture on an improved or optimal target trajectory with respect to biomass and IgG concentrations by improving or optimizing the feeding profile. State estimation was based on the entire available Cedex Bio HT (Roche) dataset, taking into account uncertain initial concentrations, as well as uncertainties in the feeding and sampling information by allowing these variables to be varied during optimization.

[0528] In this specific example, the goal of model predictive control is to keep the culture on a reference trajectory by relying on predictions and state estimates from the digital twin. The state estimates are significantly closer to the actual measurements than the DT predictions alone, where the R 2 The values ​​were improved as follows: biomass from 0.63 to 0.9, glutamate from 0.9 to 0.96, glutamine from 0.67 to 0.87, pyruvate from 0.8 to 0.84, glucose from 0.5 to 0.83, and glycoprotein (IgG) from 0.85 to 0.98. The biomass and glycoprotein concentrations could be maintained at a level lower than that without control (biomass R 2 =-5.09, glycoprotein R 2 =0.93) is closer to the reference trajectory (biomass R 2 =0.79, glycoprotein R 2 =0.98).

[0529] This example shows that the digital twin proposed by the proposed concept can have high prediction quality on the validation set and provide a reliable estimate of the current state ( Fig.11 ), while keeping the process on the target trajectory ( Fig.12 ), thus enabling robust manufacturing.

[0530] Fig.11A schematic diagram comparing GKCM predictions with and without state estimation and the corresponding measurements from a process with state estimation and control is shown. The GKCM predictions with state estimation are closer to the actual measurements than the predictions without state estimation, demonstrating the improvement achieved through state estimation.

[0531] Fig.12 A schematic diagram of a process that deviates from the golden batch is shown (comparing measurements of a controlled and uncontrolled process). Through control and state estimation, the process was recovered and a trajectory close to the golden batch was obtained. The controller targets the biomass and glycoprotein trajectories. However, it can be seen that the trajectories of other metabolites can also be improved.

[0532] The aspects and features described with respect to a specific example in the foregoing examples may also be combined with one or more aspects and features of another example to replace the same or similar features of the other example, or to additionally introduce these features into the other example.

[0533] The example may also be or relate to a (computer) program including a program code to perform one or more of the above methods when the program is executed on a computer, a processor or other programmable hardware component. Therefore, the steps, operations or processes of the different methods in the above methods may also be performed by a programmed computer, a processor or other programmable hardware component. The example may also include a program storage device (e.g., a digital data storage medium) that is readable by a machine, a processor or a computer and encodes and / or contains programs and instructions that are executable by a machine, a processor or a computer. The program storage device may, for example, include or may be a digital storage device, a magnetic storage medium such as a disk and a tape, a hard drive or an optically readable digital data storage medium. Other examples may also include a computer, a processor, a control unit, a (field) programmable logic array ((F)PLA), a (field) programmable gate array ((F)PGA), a graphics processor unit (GPU), an application specific integrated circuit (ASIC), an integrated circuit (IC) or a system on a chip (SoC) system that is programmed to perform the steps of the above methods.

[0534] It should also be understood that, unless explicitly stated in individual cases or necessary for technical reasons, the disclosure of several steps, processes, operations or functions disclosed in the specification or claims should not be interpreted as implying that these operations must rely on the described order. Therefore, the above description does not limit the execution of several steps or functions to a certain order. In addition, in other examples, a single step, function, process or operation may include and / or may be decomposed into several sub-steps, sub-functions, sub-processes or sub-operations.

[0535] If some aspects have been described with respect to a device or system, these aspects should also be understood as descriptions of the corresponding methods. For example, blocks, devices, or functional aspects of a device or system may correspond to features (e.g., method steps) of the corresponding methods. Therefore, aspects described with respect to methods should also be understood as descriptions of corresponding blocks, corresponding elements, attributes, or functional features of the corresponding device or system.

[0536] The following claims are hereby incorporated into the detailed description, where each claim can stand alone as a separate example. It should also be noted that although in the claims a dependent claim refers to a specific combination with one or more other claims, other examples may also include a combination of a dependent claim with the subject matter of any other dependent claim or independent claim. Such combinations are explicitly proposed here, unless it is stated in individual cases that a specific combination is not intended. In addition, even if a claim is not directly defined as dependent on any other independent claim, the features of the claim should be included for the other independent claim.

Claims

1. A method of training at least one machine learning model for modeling dynamical aspects of a biological organism, the method comprising: training (210) the machine learning model based on training data, wherein the training data is based on experimental data of a plurality of clones of the biological organism, the training data comprising a subset of the training data based on experimental data of a single clone, wherein a first component of the at least one machine learning model is trained using the training data (211), the first component representing a general dynamic behavior of the biological organism, and Wherein a second component of the at least one machine learning model is trained using the training data subset (212), the second component representing clone-specific kinetic behavior of the biological organism.

2. The method according to claim 1, wherein: The method includes providing the machine learning model as part of a digital twin model for at least one of: a) determining at least one target parameter of at least one bioreactor containing at least one biological organism; b) selecting clones of the biological organism; c) controlling a biomanufacturing process involving the biological organism; and d) monitoring a biomanufacturing process involving the biological organism.

3. The method according to any one of claims 1 or 2, wherein: The training data includes training input data and training output data, the training input data including a representation of an experimental environment of the organism, and the training output data representing dynamic characteristics observed in response to the corresponding experimental environment.

4. The method according to claim 3, wherein: Training the at least one machine learning model includes determining a deviation between an output of a function and the training output data, wherein the function is based on the at least one machine learning model, a first set of flux patterns representing common functions of the multiple clones of the biological organism, and a second set of flux patterns specific to the single clone of the biological organism.

5. The method according to any one of claims 3 or 4, wherein: The representation of the experimental environment corresponds to a compressed representation of the experimental environment having a reduced dimensionality compared to an uncompressed representation of the experimental environment.

6. The method according to any one of claims 1 to 5, wherein: The training data is based on experimental data of multiple clones of the same cell line of the biological organism, or wherein the training data is based on experimental data of multiple clones of multiple different cell lines of the biological organism.

7. The method according to any one of claims 1 to 6, wherein: The training data is based on experimental data from a number of different process scales.

8. The method according to any one of claims 1 to 7, wherein: The at least one machine learning model further comprises a third component that takes as its input the output of the first component and the second component, the method comprising training the third component of the at least one machine learning model using the training data, And / or wherein the at least one machine learning model further comprises a fourth component representing one or more flux patterns not represented by the first component and / or the second component, and the method comprises training the fourth machine learning model using the training data.

9. The method according to any one of claims 1 to 8, wherein: The at least one machine learning model forms a machine learning model set, and the method includes training multiple machine learning model sets, wherein the multiple machine learning model sets are trained using different seed values, and the different seed values ​​affect at least one of the random initialization and random inactivation of parameters of the corresponding machine learning models.

10. The method according to any one of claims 1 to 9, wherein: The method also includes using transfer learning to adjust (230) at least the second clone-specific component of the at least one machine learning model based on training data from experimental data of additional individual clones.

11. The method according to any one of claims 1 to 10, wherein: The method also includes generating (220) a digital twin of the biological organism using the trained at least one machine learning model.

12. The method according to claim 11 also includes determining (230) a plurality of experiments to be performed using the biological organism, and continuing to train (210; 211; 212; 213; 214) the at least one machine learning model based on additional training data according to the plurality of experiments.

13. A method for determining at least one target parameter of at least one bioreactor comprising at least one biological organism, the method comprising: The at least one target parameter is determined (310) using at least one digital twin of at least one biological organism generated according to claim 11 and at least one corresponding cost function.

14. The method according to claim 13, wherein: At least two digital twins of at least two biological organisms are used to jointly determine the at least one target parameter of the at least two biological organisms.

15. A method for selecting clones of a biological organism, the method comprising: generating (220) a plurality of digital twins of a plurality of clones of the biological organism using the method of claim 11; and The clone is selected (910) by comparing one or more characteristics of the plurality of digital twins.

16. A method for controlling a biomanufacturing process involving a biological organism, the method comprising: continuously adjusting (610) the environment of the biofabrication process using a digital twin of the biological organism generated according to claim 11, wherein information about the environment of the biological organism is provided to the digital twin using a backward time domain method; and The estimated state of the biomanufacturing process is compared to a defined reference state trajectory of the biomanufacturing process (620).

17. A computer system (20) comprising processing circuitry (24) and storage circuitry (28), the computer system being configured to perform at least one of the method according to any one of claims 1 to 12, the method according to claim 13 or 14, the method according to claim 15, and the method according to claim 16.

18. A computer program having a program code for performing at least one of the methods according to any one of claims 1 to 12, the method according to claim 13 or 14, the method according to claim 15 and the method according to claim 16 when the computer program is executed on a computer, a processor or a programmable hardware component.

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