Computer-Implemented Method, Program, and Hybrid System for Observing Cellular Metabolic State

Abstract

The present application provides techniques for predicting the amount of at least one biological material produced or consumed by a biological system in a bioreactor. Process conditions and metabolite concentrations of the biological system are measured as a function of time. The metabolic rates of the biological system, including the specific consumption rate of metabolites and the specific production rate of metabolites, are determined. The process conditions and metabolic rates are provided to a hybrid system model configured to predict the production of the biological material. The hybrid system model includes a kinetic growth model configured to predict cell growth in the form of a function of time and a metabolic condition model based on the specific consumption rate or secretion rate of metabolites and selected process conditions. Wherein the metabolic condition model is configured to classify the biological system into a metabolic state. The amount of the biological material is predicted based on the hybrid system model.

Description

Technical Field

[0001] The present application relates to a computer-implemented method, program, and hybrid system for observing the metabolic state of cells, including a hybrid model. Specifically, the hybrid model can be used to provide observability of the metabolism of a bioreactor and / or optimize the reaction conditions of a biological process. Background Art

[0002] In biomanufacturing, biological systems are orchestrated to produce specific biomaterials. This process typically involves placing cells and / or microorganisms into a bioreactor that has a culture medium containing essential nutrients under controlled atmospheric conditions. The culture medium is consumed by the cells and used for growth and other metabolic functions, including the production of specific biomaterials and by-products.

[0003] Bioreactors contain instruments that continuously (e.g., once per second or minute) measure process conditions such as temperature, pH, and dissolved oxygen, as well as the addition of nutrients and gases, and the flow and content of the streams leaving the bioreactor. Typically, samples of the biological process are taken periodically (e.g., once or twice a day) to measure the content of a large number of fluids, including metabolites (e.g., glucose, glutamine, lactate, NH4, etc.), as well as cell concentration, the concentration of the biomaterial product (also known as titer), and the concentration of quality attributes (e.g., by-products, etc.). However, these methods rely on indirect measurements of the average cell metabolic behavior.

[0004] Techniques for modeling and analyzing cell behavior include flux balance analysis (FBA), which can be used to model and analyze cell metabolic behavior based on the specific consumption and production of measured metabolites. FBA calculates the flux of a given metabolite through the metabolic network, thereby allowing the prediction of the growth rate of an organism or the production rate of a metabolite. To prevent overfitting of the model, this type of analysis requires specific genetic knowledge of the cell line during the bioreactor process, as well as measurements of gene expression and metabolite levels measured during normal process development and manufacturing activities. Generally, observations of cell metabolism in process development and manufacturing are extremely limited, which restricts the use of this method.

[0005] In other cases, statistical methods are valuable in establishing regression models to relate measured process conditions and metabolites to predict titer and by-products. Although these methods are beneficial for prediction purposes, they have limited ability to understand which process variables (e.g., related to metabolic function) are responsible for good performance.

[0006] In other aspects, models such as the monomer kinetics model have been used to predict cell growth. This type of model effectively predicts the growth rate of cells based on the substrate concentration and inhibitory metabolites. However, this approach also does not consider the current state of the cells.

[0007] Accordingly, the lack of direct measurement of metabolic activity in process development creates a situation where a trial-and-error method is used to design process operations. Using this method, experiments are conducted in a mixed manner to determine the conditions for producing high-quality products with a relatively high yield.

[0008] Process development is challenging, and the ability to diagnose strange behavior or optimize the process is difficult. Typically, the biological relevant hypotheses for the observed metabolite profiles due to the metabolic state are left to subject matter experts (SMEs).

[0009] The monitoring of biomanufacturing processes is also challenging. Typically, control charts are generated for important process parameters and metabolites. This ensures that the process is in a controlled state relative to normal operation, but does not monitor the metabolism of biological cells. The diagnosis or prediction of abnormal metabolic operations is again left to SMEs.

[0010] Traditional batch-fed processes operate under relatively safe conditions with rich nutrients, resulting in titers typically around 2 to 6 grams per liter. To optimize the yield (e.g., product formation) to achieve higher yields (e.g., 20 grams per liter and above), longer run times may be required, but this may also result in by-products. However, without knowledge of cell metabolism, optimizing productivity is difficult and is done in a mixed manner. Summary of the Invention

[0011] According to one aspect of the present application, there are provided computer-implemented methods, computer program products, and systems for observing the cell metabolic state, including a hybrid model for optimizing bioprocess reaction conditions. From a process control perspective, the observability of cell metabolism enables a large volume of fluid to be maintained under the correct conditions, such as controlling the nutrients in a large volume of fluid to maximize metabolic activity towards product production while minimizing undesired activities (e.g., producing by-products, excessive cell growth, etc.). Observability is a term in advanced process control that refers to the ability to generate visibility of the measured or in this case unmeasured potential drivers of a system (e.g., a bioreactor).

[0012] According to one aspect, a computer-implemented method is provided that uses observations of the metabolic state of a biological system to predict the amount of at least one biomaterial produced or consumed by the biological system in a bioreactor. The method includes: measuring the process conditions of the biological system and the change in metabolite concentration over time; determining the metabolic rate of the biological system, including the specific consumption rate of metabolites and the specific production rate of metabolites; providing the process conditions and the metabolic rate to a hybrid system model configured to predict the production of the biomaterial, where the hybrid system model includes: a kinetic growth model configured to predict cell growth as a function of time, and a metabolic condition model configured to select process conditions based on the specific consumption rate or secretion rate of metabolites, where the metabolic condition model is further configured to classify the biological system into a metabolic state; and predicting the amount of biomaterial based on the hybrid system model.

[0013] The metabolic condition model, when used in a real-time environment, is a type of state observer.

[0014] Further, according to the above method, the kinetic model can be configured to predict viable cell density.

[0015] Further, according to the above method, the kinetic model can be configured to reference lysed cells.

[0016] Further, according to the above method, a metabolic state observer for metabolites can be constructed to provide a prediction result of the internal metabolic state of the biological system.

[0017] Further, according to the above method, the method further includes: obtaining the current measurement result of the metabolite; using the metabolic state observer to determine the consumption rate of the metabolite; and using the metabolic state observer and the current measurement result to predict the future concentration of the metabolite.

[0018] Further, according to the above method, cell state classification can be performed using the metabolic state observer to predict the specific consumption rate or specific production rate of the metabolite.

[0019] Further, according to the above method, the predicted specific consumption rate or the predicted specific production rate is determined using training data.

[0020] Further, according to the above method, the method further includes: classifying the internal metabolic state into an optimal or sub-optimal category for biomaterial production; and sending a notification to the user when the internal metabolic state is classified as the sub-optimal category.

[0021] Further, according to the above method, the kinetic growth model includes a monomer kinetic model or a saturation kinetic model.

[0022] Further, according to the above method, the cell density or cell viability in the form of a time function for the biological system can be measured.

[0023] Further, according to the above method, the kinetic growth model is also configured to predict the growth of microbial cells in the form of a time function.

[0024] Further, according to the above method, the metabolic condition model includes one or more of the following: a machine learning model, a deep learning model, a principal component analysis (PCA) model, a partial least squares (PLS) model, a partial least squares discriminant analysis (PLS-DA) model, and an orthogonal partial least squares discriminant analysis (OPLS-DA) model.

[0025] Further, according to the above method, the method further includes: obtaining a test sample from the bioreactor; and determining whether the amount of the biological material in the test sample is within the range predicted by the hybrid model.

[0026] Further, according to the above method, the parameters of the hybrid system model are updated when the hybrid system model is running, where the parameters include the metabolic rate and coefficients associated with the hybrid system model.

[0027] Further, according to the above method, the process conditions include one or more of the following: pH, temperature, dissolved oxygen, osmotic pressure, the process flow leaving the bioreactor, the growth medium, by-products, amino acids, metabolites, oxygen flow rate, nitrogen flow rate, carbon dioxide flow rate, air flow rate, and stirring speed.

[0028] Further, according to the above method, the growth medium includes nutrients having amino acids, sugars, or organic acids.

[0029] Further, according to the above method, the by-products include amino acids, sugars, organic acids, or ammonia.

[0030] Further, according to the above method, the method further includes: determining optimal process conditions for the bioreactor based on the hybrid system model; measuring the experimental process conditions in the form of a time function of the bioreactor using one or more sensors; monitoring the measured experimental process conditions to detect deviations from the optimal process conditions; and when a deviation is detected, sending a notification to the user.

[0031] Further, according to the above method, the method further includes: determining optimal process conditions for the bioreactor based on the hybrid system model; measuring the experimental process conditions in the form of a time function of the bioreactor using one or more sensors; monitoring the measured experimental process conditions to detect deviations from the optimal process conditions; and providing feedback to the controller controlling the bioreactor to automatically adjust the experimental process conditions to minimize the deviation from the optimal process conditions.

[0032] In some aspects, the method further includes: determining optimal process conditions for the bioreactor based on the hybrid system model; measuring the experimental process conditions in the form of a time function of the bioreactor using one or more sensors; monitoring the measured experimental process conditions to detect deviations from the optimal process conditions; when a deviation is detected, sending a notification to the user; and providing feedback to the controller controlling the bioreactor to automatically adjust the experimental process conditions to minimize the deviation from the optimal process conditions.

[0033] Further, according to the above method, the method further includes: simulating, using the hybrid system model, a prediction of at least one biological material, wherein the hybrid system model is initialized with the process conditions; and determining one or more states of the biological system based on the simulation.

[0034] Further, according to the above method, the method further includes: adjusting the process conditions based on an optimization method to determine a configuration of process conditions for optimizing the prediction trajectory, product quantity (titer), and / or product quality.

[0035] According to one aspect, the method includes calibrating a hybrid system model for predicting a biomaterial produced by a biological system in a bioreactor. The method includes: obtaining experimental data including measurements of one or more process conditions, one or more metabolite concentrations, and cell counts for a plurality of bioreactor batches, where each batch is associated with a given configuration of process conditions; using a kinetic model of the hybrid system model to determine a growth rate under optimal conditions based on the experimental data; using the kinetic model to determine cell lysis parameters based on the growth rate under optimal conditions and the growth rate from the experimental data; determining a metabolite specific productivity or specific consumption rate; determining kinetic parameters of a growth inhibitory factor to minimize the gap between the growth rate under optimal conditions and the growth rate from the experimental data; and providing the determined kinetic parameters, the cell lysis parameters, the growth rate, and the metabolite specific productivity or specific consumption rate to a metabolic condition model of the hybrid system model to classify the biological system into a metabolic state associated with a given productivity of the biomaterial produced by the biological system, based on the measured specific consumption rate or measured secretion rate of the metabolite.

[0036] Further, according to the above method, a parameter configuration can be provided to an optimization module, where the parameter configuration includes the growth rate under optimal conditions, the metabolite specific consumption rate and specific productivity, and new process conditions, to determine process conditions for optimizing the production of the biomaterial.

[0037] Further, according to the above method, the method further includes monitoring batch properties of the bioreactor using principal component analysis (PCA).

[0038] Further, according to the above method, the output of the bioreactor is predicted using partial least squares (PLS).

[0039] Further, according to the above method, the output is the amount of the biomaterial.

[0040] In the present application, the biomaterial may include metabolites, cells, desired proteins, antibodies, immunoglobulins, toxins, one or more by-products, target molecules, or any other type of molecule produced using a bioreactor. There may be more than one biomaterial of interest, including products, target biologics.

[0041] In the present application, the growth inhibitory factor may include matrix limitation inhibiting growth, temperature or pH change, or metabolite.

[0042] In the present application, the given productivity refers to the amount of product produced per cell.

[0043] In this application, process optimization refers to determining the optimal adjustment or setting of a process. This is described in more detail in the following detailed description.

[0044] Metabolites can include any suitable analyte, including but not limited to: amino acids (e.g., alanine, arginine, aspartic acid, asparagine, cysteine, cystine, glutamic acid, glutamine, glycine, histidine, hydroxyproline, isoleucine, leucine, lysine, methionine, phenylalanine, proline, serine, threonine, tryptophan, tyrosine, valine, etc.), saccharides (e.g., fucose, galactose, glucose, glucose-1-phosphate, lactose, mannose, raffinose, sucrose, xylose, etc.), organic acids (e.g., acetic acid, butyric acid and 2-hydroxybutyric acid, 3-hydroxybutyric acid, citric acid, formic acid, fumaric acid, isovaleric acid, lactic acid, maleic acid, propionic acid, pyruvic acid, succinic acid, etc.), and other organic compounds (e.g., acetone, ethanol, pyroglutamic acid, etc.).

[0045] Embodiments of this application can be implemented as a method or a system, and / or one or more computer program products. Embodiments of this application can be implemented as a machine-readable medium, where the medium is contained in one or more information carriers, such as a CD-ROM, a DVD-ROM, a semiconductor memory, or a hard disk. Such a computer program product can cause a data processing device to execute one or more operations described in the application program.

[0046] In addition, embodiments of this application can also be implemented as a system including a processor and a memory coupled to the processor. The memory can encode one or more programs to cause the processor to execute one or more methods described in the application. In some examples, the system can be a dedicated computer system including an embedded system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Details of one or more embodiments are set forth in the following exemplary drawings and description. Other features will be apparent from the description, the drawings, and the claims. However, it should be understood that even though the embodiments are described separately, the individual features of different embodiments can be combined into further embodiments.

[0048] Figure 1 An example of a computing environment of a hybrid model configured for observing the cell metabolic state provided by an embodiment of this application is shown.

[0049] Figure 2 An example of a state observer with state correction provided by an embodiment of this application is shown.

[0050] Figure 3A A flowchart of a simple metabolic state observer provided by an embodiment of this application is shown.

[0051] Figure 3B Another flowchart of the simple metabolic state observer provided by the embodiments of the present application is shown.

[0052] Figure 4A A flowchart of the complete metabolic state observer provided by the embodiments of the present application is shown.

[0053] Figure 4B A flowchart of the input and output of the complete metabolic state observer provided by the embodiments of the present application is shown.

[0054] Figure 5 A flowchart of the operations of the digital twin simulation using the hybrid model provided by the embodiments of the present application is shown.

[0055] Figure 6 A flowchart of calibrating the kinetic growth model provided by the embodiments of the present application is shown.

[0056] Figure 7 A flowchart of calibrating the metabolic regulation model provided by the embodiments of the present application is shown.

[0057] Figure 8 A flowchart of calibrating the hybrid model provided by the embodiments of the present application is shown.

[0058] Figure 9A The data flow path through the hybrid model provided by the embodiments of the present application is shown.

[0059] Figure 9B The data flow path of PCA / PLS for the metabolic condition model provided by the embodiments of the present application is shown.

[0060] Figure 10 Various process runs provided by the embodiments of the present application to determine the optimal parameters are shown.

[0061] Figure 11 The measurement trajectory (e.g., center point) for glucose concentration and the cell density for typical experimental data provided by the embodiments of the present application are shown.

[0062] Figure 12A An example of calculating the specific consumption rate of metabolites (e.g., glucose) from experimental data provided by the embodiments of the present application is shown. Figure 12B The output of the state observer for metabolites (such as glucose) that compares the predicted metabolite state with the measured value is shown. In this example, the predicted state (estimate) of the metabolic state observer is related to the experimental measurement value.

[0063] Figures 13A to 13C An example output of the cell state classification of the hybrid model provided by the embodiments of the present application is shown. Figure 13AA PCA score scatter plot is shown that provides observability of metabolic disorders caused by glucose consumption (as predicted by a state observer using PCA). Glucose concentrations within the circle centered at the origin represent normal operation. However, glucose values outside this range indicate a risk of decreased titer or product quality issues. Figure 13B A PCA score scatter plot is shown that provides observability of the variability of metabolic function resulting from the transition from exponential growth to the stationary phase. This graph shows an example that can provide observability of changes in metabolic activity throughout the trajectory of the feeding process. Figure 13C An example of a PCA loading plot is shown to assist in developing a process understanding of the PCA score scatter plot (as predicted by a state observer using PCA).

[0064] Figures 14A to 14C An example of the productivity and product quality predicted by the hybrid model provided by the embodiments of the present application is shown. Figure 14A The measured given productivity from experimental data and the predicted given productivity from the PLS metabolic condition model of the state observer (using PLS) are shown (such as productivity, specific consumption, metabolite). Figure 14B A PLS score scatter plot is shown that provides observability of metabolite variability related to changes in the given productivity (such as productivity, specific consumption, metabolite) from the state observer (using PLS). Figure 14C A related PLS loading plot is shown that provides a process understanding of the variables related to the variability of the given productivity (such as productivity, specific consumption, metabolite) from the state observer (using PLS).

[0065] Figure 15A and 15B Other examples of productivity and product quality provided by the embodiments of the present application are shown. Figure 15A An example of simulating growth and titer (the concentration of the target product produced by the given productivity) for given starting conditions and independent variable trajectories is shown. Measured growth and titer data are also included to compare the predicted results with the measured results. Figure 15B The given productivity (such as productivity, specific consumption, metabolite) from the state observer (using PLS) is shown.

[0066] Figure 16 An example of determining important unmeasured metabolic metrics from a monomer kinetic model provided by the embodiments of the present application is shown. In this example, according to the embodiments of the present application, the specific growth rate, specific death rate, and lysed cell concentration (all unmeasured) are predicted from the monomer kinetic model.

[0067] Figures 17A to 17CAn example of the impact of independent variable adjustment on the growth profile provided by an embodiment of the present application is shown. For each figure, the predicted curve of the growth state is shown as a solid line, and the relevant data of the measured state is included for comparison. Figure 17A An example of the measured and predicted trajectories of a batch with temperature variation (growth inhibition) is shown. Figure 17B An example of the measured and predicted trajectories of a batch with pH variation and low feed rate (glucose consumption) is shown. Figure 17C An example of the measured and predicted trajectories of a batch with pH and temperature variations is shown.

[0068] Figure 18 An example of the impact of the substrate on the growth rate as shown in Equation (6) provided by an embodiment of the present application is shown. The figure shows how the growth rate decreases when the substrate concentration is below the threshold. In the example, the growth rate multipliers for various glucose levels with a threshold of 1 (θ s，i = 1) are shown.

[0069] Figure 19 An example of the impact of the quadratic parameter on the effective growth rate described in Equation (7) provided by an embodiment of the present application is shown. When the quadratic parameter is higher or lower than a given optimal value (θ i，opt = 36.8 °C), the growth rate decreases. The rate of decrease in the growth rate is adjusted by the parameter θ q，i .

[0070] Figure 20 A schematic diagram of the system block diagram of a bioprocess reactor using a hybrid model provided by an embodiment of the present application is shown. The figure depicts a continuous stirred tank reactor 3410 (with a reaction agitator 3465) having four streams. F f refers to the feed stream 3420, which contains fresh medium, F b is the effluent stream 3430, which contains the same contents as the reactor, F h , which contains the bulk spent medium 3440 in the reactor (a large amount of fluid is separated from the cells by a separator 3460) and F r , the recycle stream 3450, which contains cells and the remaining bulk fluid in the complete recycle stream.

[0071] Figure 21 A high-level flowchart of the operation of the hybrid model provided by an embodiment of the present application is shown.

[0072] Figure 22 A high-level flowchart of the operation of configuring the hybrid model provided by an embodiment of the present application is shown. Detailed Description

[0073] In the following, a detailed description of the examples will be given with reference to the accompanying drawings. It should be understood that various modifications can be made to the examples. In particular, one or more elements of one example can be combined and used in other examples to form new examples.

[0074] Figure 1 An example of a computational environment of a hybrid model configured for observing cell metabolic states provided by an embodiment of the present application is shown. The kinetic and metabolic state observation system 5 may include a plurality of specific processing modules, including a kinetic growth model 50, a metabolic condition model 60, a state correction model 75, a process monitoring engine 80, a labeling and alert engine 85, and a consumption rate and secretion rate module 90. The metabolic condition model 60 may include additional modules, including a PCA and PLS statistical modeling engine 65 and a data-driven machine learning engine 70. Each of these components will be described in detail below.

[0075] In particular, the hybrid model includes a kinetic growth model 50 and a metabolic condition model 60. The kinetic model determines quantities such as the number of viable cells, lysed cells, live cells, and cell density. The metabolic condition model 60 provides product titer and quality control information regarding the titer and properties (such as by-products, etc.) related to the biological process. In some embodiments, the output of the metabolic condition model 60 is pushed to the kinetic growth model 50.

[0076] The hybrid model combines cell metabolism with metabolite mass balance. Generally, a metabolite is any analyte consumed or secreted / produced by a cell. Existing biological process models can be constructed to predict the trajectory of biomaterial production. However, there are uncertainties in these biological process models. Therefore, the specific consumption rate and specific secretion rate of the experimentally measured metabolites may not match the output of the biological process model. To address this uncertainty and reduce errors, a state correction model 75 can be used, which only updates the prediction of the state of the kinetic growth model 50. An error can be derived based on the difference between the measured experimental output and the predicted hybrid model output, and the parameters of the hybrid model can be adjusted based on the error signal (see also Figure 2 ) such that the error signal is zero as a function of time.

[0077] The kinetic growth model 50 is a state observer based on the monomer growth equations (see Equations 1 to 11) and metabolite mass balance equations (see Equations 12, 13). The monomer growth equations and metabolite mass balance equations are a series of differential equations that can be used to describe cell growth (such as microbial cell growth), cell density and viable cell density, total cells (such as viable cells, dead cells, and lysed cells), etc. The inputs to the kinetic growth model include temperature, feed conditions, pH, etc., and the outputs include state estimates. In some aspects, the kinetic growth model is a classical state observer. In this case, the parameters modeled internally are called states. For example, these parameters may include x v , x d , x l , m i .

[0078] Constructing state observers from differential equations is known. Thus, here, such techniques have been extended to the monomer kinetic equations and metabolite mass balance equations, which are a set of differential equations that describe cell growth and the life cycle in a biocellular culture and the amount of metabolites. Therefore, the kinetic growth model can be used to monitor the number of viable cells (and other parameters) in a bioreactor and predict the number of cells in the bioreactor at future time points. The monomer growth equation for a bioreactor system with media exchange includes the following equations:

[0079] (1) x t = x v + x d + x l , where x t is the total cell density, x v is the viable cell density, x d is the dead cell density, and x l is the lysed cell density;

[0080] (2) where dx v / dt corresponds to the change in viable cell density over time, and u eff corresponds to the effective growth rate, u d is the cell death rate, F b is the cell washout flow rate and contains the same material as the bioreactor, and V is the volume of the material in the bioreactor;

[0081] (3) u d = k d + k t x l , where k t is the mortality increment caused by the lysed cell concentration, representing the toxicity of a large amount of fluid;

[0082] (4) where k l is the conversion rate of dead cells to lysed cells, and F h is the harvest flow rate and includes a large amount of fluid (live and dead cells are separated from the liquid and recycled back to the bioreactor);

[0083] (5)

[0084] (6) u eff = u max θ sub θ quad θ inh , where the effective cell density can be determined based on u max which corresponds to the maximum growth rate, i.e., the growth rate under optimal conditions, where θ sub corresponds to the growth rate reduction caused by substrate depletion, θ quad corresponds to the growth rate reduction due to the deviation of quadratic terms (such as temperature, pH, etc.) from the target value of growth maximization, and θ inh corresponds to growth inhibition caused by an excess of biomaterials (e.g., metabolites, cell density, or independent variables);

[0085] (7) where s i is the substrate value, which can be a metabolite or sub-white energy, and θ s，i is the coefficient representing the substrate concentration below which growth is inhibited;

[0086] (8) where q i is the value of the quadratic variable, which can be a metabolite or an independent variable, θ i，opt is the coefficient representing the value of the quadratic variable for growth maximization, and θ q，i is the coefficient representing the growth inhibition sensitivity.

[0087] (9) where I i is the value of the inhibition variable, which can be a metabolite or an independent variable, and θ i，i is the coefficient representing the value of the inhibition variable above which growth is inhibited.

[0088] (10) where is the rate of change of the biomaterial in the form of a function of time, Qp is a function of the input containing the metabolite concentration m, δ m，i (t) is the specific production rate or specific consumption rate of the metabolite at the current time, u is the independent variable, and x v is the live cell density;

[0089] (11) where is the rate of change of metabolite, δ m，i (t) is the specific consumption or secretion rate of metabolite at the current time, m r，i is the concentration of metabolite in the bioreactor, m f，i is the concentration of metabolite in the feed, and F f is the feed flow rate of the fresh culture medium.

[0090] The outputs of the kinetic growth model include product titer, given productivity / specific consumption, metabolite concentration, viable cell density, and viability.

[0091] The specific consumption (or secretion) rate at a given time or cell state can be calculated from the training set (e.g., measurement data using Equations 14 and 15) and using the following equations:

[0092] (12)

[0093] (13) iVCD = (0.6x v，k + 0.4x v，k+1 )(t k+1 - t k )

[0094] These equations are defined below.

[0095] The metabolic condition model 60 classifies the internal metabolic state of the system, e.g., as an optimal or sub-optimal state or category for biomaterial production. Optionally, the inputs to the metabolic condition model can include temperature, feed conditions, etc. Generally, the metabolic condition model is independent of the kinetic growth model, and metabolic condition monitoring can be performed independently of kinetic growth.

[0096] In some aspects, the metabolic condition model can be used to enhance the kinetic growth model by providing estimates of titer and / or quality to improve titer prediction.

[0097] The metabolic condition model includes at least metabolite and VCD to calculate the specific consumption / specific production of metabolite. The metabolic condition model optionally includes additional measured parameters and / or unmeasured states to improve the prediction of product titer and / or quality. In some embodiments, the metabolic condition model includes a statistical modeling engine 65 for principal component analysis (PCA) or partial least squares (PLS) or orthogonal partial least squares (OPLS) of specific consumption / productivity (and optionally, additional parameters measured from the process or state). The model starts from Figure 9A the metabolite specific consumption / secretion rate (component 720) in and converts it to multivariate scores (T cell state, component 730).

[0098] The statistical modeling engine can include any suitable engine, including a (PCA) model, a partial least squares (PLS) model, a partial least squares discriminant analysis (PLS-DA) model, and / or an orthogonal partial least squares discriminant analysis (OPLS-DA) model.

[0099] PCA can be used to analyze the batch characteristics of a bioreactor (e.g., the overall system titer), while PLS can be used to analyze a given metabolite (e.g., glucose), e.g., to predict the output of the bioreactor. PCA is used to characterize metabolic variation in the absence of a potential environment. PLS is used to relate metabolic variation to the production of productivity (titer) or important quality metrics (product quality). Techniques for performing PLS can be found, for example, in "PLS Regression: A Basic Tool of Chemometrics, Chemometrics and Intelligent Laboratory Systems" by authors such as Wold, volume number 58 (2001) 109-130. Techniques for performing PCA can be found, for example, in "Principal Component Analysis, Second Edition of Chemometrics and Intelligent Laboratory Systems", volume number (1987) 37-52. Both PCA and PLS can be used to reduce the dimensionality of a dataset. PCA is an unsupervised dimensionality reduction technique that allows data to be summarized through linear combinations of variables without losing a large amount of information. PLS is a supervised dimensionality reduction technique that is applied based on the correlation between the dependent variable and the independent variables. These techniques are considered within the scope of those skilled in the art.

[0100] In some aspects, the output of the metabolic condition model 60 is fed into the kinetic growth model 50. The metabolic condition model 60 can also allow for the visualization of the metabolic conditions (states) of cell metabolism. Thus, the output of the metabolic condition model 60 serves both as an input to the kinetic growth model 50 and contributes to the monitoring and visualization of the metabolic conditions of cell metabolism.

[0101] The metabolic condition model can incorporate or be linked to a data-driven machine learning engine 70 and / or a principal component analysis (PCA) and partial least squares (PLS) statistical modeling engine 65. In other aspects, the metabolic condition model can incorporate the statistical modeling engine 65 and the data-driven machine learning engine 70. The machine learning engine 70 can include a neural network, a deep learning model, or other machine learning models. The machine learning engine 70 can be trained using known techniques to classify the state of a biological system / bioreactor as an optimal or suboptimal state. Additionally, the machine learning engine 70 can be trained using known techniques to classify the state of a metabolite as an optimal or suboptimal state. In some aspects, the machine learning engine 70 performs a classification equivalent to that of the statistical modeling engine 65 and, in certain cases, has higher accuracy and precision than the statistical modeling engine 65.

[0102] The state correction model 75 is based on Figure 2The state observer depicted reduces errors in the system. The difference between the output of the hybrid model and the measurement data can be determined and provided as an error signal to the state correction model 75. The role of the state correction model is to minimize the error and make the error signal zero as a function of time. In some aspects, state correction corresponds to techniques associated with an extended Kalman filter. In some aspects, the state correction model 75 can be a separate module or, optionally, can be integrated into the kinetic growth model.

[0103] Continuing to refer to Figure 1 , the process monitoring engine 80 can be connected to multiple sensors that measure one or more parameters related to the bioreactor. These parameters can include temperature, oxygen level, feed conditions, pH, or other aspects of the biological process, which can be monitored in real time or near real time. These measurements can be provided to the hybrid model to simulate the biological reaction. These measurements can also be provided to the metabolic condition module 60 to monitor cell metabolism and generate a state estimate.

[0104] The tagging and alerting engine 85 monitors process deviations in the system. If the output of the bioreactor deviates from its expected / predicted output, an alert is provided to the user. In some aspects, the biological process can be paused by the system until the process is corrected. In other aspects, the system can compensate for the deviation (e.g., adjust the feed or process conditions to reach the desired state (e.g., the optimal state)). The tagging and alerting engine 85 can also send notifications to the user about the state of the bioreactor. In other aspects, a notification can be sent to the user when the internal metabolic state is classified as a suboptimal category

[0105] The consumption rate and secretion rate module 90 determines the specific consumption rate and specific production rate of metabolites / analytes in the bioprocess reactor. The metabolic condition model 60 uses the specific consumption data. The output of the metabolic condition model 60 (e.g., an estimate of a given productivity / specific consumption) can be provided to the kinetic growth model to predict the product titer.

[0106] The controller 95 can receive feedback (e.g., the output of the bioreactor) to control the bioreactor to automatically adjust the experimental process conditions to minimize the deviation from the optimal process conditions.

[0107] The database 30 contains various types of data for the kinetic and metabolic state observation system 5. The training data 32 corresponds to data that is used to identify kinetic model coefficients, calculate the specific consumption / productivity of metabolites, and / or train the metabolic condition model 60 to classify the state of the cells as optimal or suboptimal or to determine the projected production volume of biological materials such as a given productivity.

[0108] Process condition 34 corresponds to the process condition of the current biological process reaction. Process condition 34 may also include the optimal process conditions that have been determined experimentally. These conditions can be provided to the hybrid models (50, 60) to facilitate process monitoring of the current biological process operation or simulation / prediction of the bioreactor. Output 36 is the output of the kinetic and metabolic state observation system 5, which can be subtracted from the output of the experimental system to generate an error signal that is fed back into the input of the hybrid model.

[0109] The specific consumption rate and specific productivity can be calculated from experimental data measured during the biological process. In some aspects, the specific consumption and productivity can be determined using the following equations:

[0110] (12)

[0111] (13) iVCD = (0.6x v，k + 0.4x v，k+1 )(t k+1 - t k )

[0112] where δ m，i (t k ) at time (t k ) represents the specific consumption or productivity from time (t k ) to the next sampling point at time t k+1 , VCD corresponds to the viable cell density, and iVCD corresponds to the integrated VCD across the time step. To determine the iVCD for a given time step, the time step (t k+1 - t k ) is multiplied by the weighted combination of the viable cell density x v at time k and the viable cell density x v at time k + 1. To determine the specific consumption or specific productivity δ m，i (t k ), the reciprocal of iVCD is multiplied by the metabolite concentration difference over the time step (m i，k – m i，k+1 ), where m i corresponds to a specific type of metabolite. This difference is added to mAdd (i，k) , which corresponds to the rapid or continuous feed increment of metabolite i between the time intervals t = k and t = k + 1, and is divided by V k . In this example, both k and i are non-negative integers. Further, it is assumed that the measurement of metabolite i at t = k occurs before the bolus addition.

[0113] Measurements of metabolite and cell density can be obtained using process monitoring engine 80 and provided to specific consumption and secretion rate model 90 to determine the specific consumption rate or specific secretion rate of the metabolite. The specific consumption rate and the specific secretion rate can be provided as inputs to the metabolic regulation model. The specific consumption rate and the specific secretion rate allow the measured experimental data to be translated into the amount of each metabolite consumed or produced per cell. In some aspects, the specific consumption rate and the specific secretion rate can be provided to metabolic condition model 60, where PCA and PLS statistical model engine 65 and / or data-driven machine learning engine 70 classify the state of the cell to determine whether the system is in an optimal or sub-optimal condition relative to process parameters (e.g., temperature, feed concentration, pH, etc.).

[0114] Figure 2 A hybrid model in the context of state observer 240 is shown. In this example, the feed and process conditions are shown as inputs to bioreactor 210. The internal state of the bioreactor is represented as M(int). However, the internal state of the bioreactor, corresponding to the metabolism of individual cells in the bioreactor, cannot be directly measured. The closest measurements that can be performed relative to these internal states are measurements of the output of bioreactor 210. The output includes metabolite concentration, viable cell density (VCD), product titer, product quality, cell viability, product quality, temperature, pH, dissolved oxygen (DO), etc. Thus, the internal estimate determined by the hybrid model is based on indirect measurements (e.g., process conditions) related to the inputs and outputs of the bioreactor.

[0115] The output of the hybrid model (e.g., state estimate, metabolic state, etc.) is combined with the output of the bioreactor, and the difference between the measured and estimated parameters is fed back to the input of hybrid model 220 through state correction model 75. State correction model 75 attempts to modify the parameters to minimize the difference between the measured bioreactor output and the hybrid model output such that the error signal is zero as a function of time.

[0116] Typically, when the state of a system is not directly measurable, a state estimator can be used to estimate the internal state of the system. In particular, a Kalman filter can be used to determine an optimal estimate of the internal system state based on indirect measurements in a noisy environment. That is, based on process conditions and a kinetic model, a Kalman filter can be used to optimize the estimation of the internal state of the system. The Kalman filter is particularly suitable for generating an optimal estimate of the system state in a noisy system. In this example, the state correction model 75 can include a Kalman filter or an extended Kalman filter. A Kalman filter or an extended Kalman Filter (EKF) can be used to determine an optimal state value, where the error combines the uncertainty in the model state estimate, the uncertainty in the state measurement, and the covariance of the error. In some aspects, the Kalman filter is applicable to a kinetic growth model.

[0117] In this example, the state observer includes a hybrid model that includes a kinetic growth model 50 and a metabolic condition model 60. The kinetic model tracks how many cells are present, including invisible lysed cells (lysed cells typically have an incomplete cell membrane) and the amounts of different metabolites. The metabolic regulation model evaluates the functional aspects of the biological reaction (e.g., whether the cells will produce more target protein or whether the cells are outside of optimal conditions, which will lead to quality control issues in product (titer) / target production). The hybrid model allows for performing a material balance analysis (based on cells, feed, process conditions, metabolites, and titer, etc.) and monitoring / predicting the amount of product that the cells will produce.

[0118] Figure 3A A flowchart of the operation of a simplified metabolic state observer is shown. In this example, the simplified metabolic state observer is for a specific metabolite of interest, rather than a group of multiple metabolites. The simplified metabolic state observer includes a monomer growth model for tracking live cells that consume or produce the metabolite. The simplified metabolic state observer can use a look-up table to define the amount of metabolite consumed or produced by each cell at the current time point. In this example, the metabolite is a state in the growth model. The state can be estimated for time points without corresponding measurements to provide a state observer between state measurements. Unlike Figures 4A to 4B the complete state observer shown, the simplified metabolic state observer does not include the metabolic condition model 60.

[0119] In this example, the simplified metabolic state observer is configured to monitor a bioreactor process, as described with respect to Figure 1 and Figure 2 and estimate the future trajectory of the metabolite. In this example, an extended Kalman filter (EKF) can be used to account for noise in the biological process. However, any suitable estimator can be used.

[0120] At operation 305, process data is measured, including temperature, pH, feed conditions, time, metabolite concentration, etc. These variables (e.g., pH, temperature, oxygen, etc.) are treated as independent values. In some aspects, these values are measured and zero-order hold is used to estimate values over the sampling interval.

[0121] Generally, process data can be measured as a function of time. The measured process data is provided to the kinetic growth model 50.

[0122] At operation 310, the kinetic growth model initializes state values (e.g., metabolite values) from the initial measurement values, including x v , x d , x l , m i . The state observer (including the monomeric equations) is initialized at startup.

[0123] At operation 315, the kinetic growth model 50 determines parameters based on the monomeric equations, where the parameters include viable cell density (VCD), cell viability (Viab), and the total number of lysed cells, etc. During the operation, the state is updated according to the estimated values and the measured values.

[0124] At operation 320, the specific consumption / productivity of the metabolite is determined. In some aspects, a look-up table with data from previous experiments can be used, which correlates the specific consumption / productivity based on the current time. In other aspects, the specific consumption / productivity at the current time is estimated from the experimental measurements of the biological process. Thus, the metabolic state can be estimated for time points without corresponding state measurements to provide a state observer between the measurements.

[0125] At operation 325, the parameters from the kinetic growth model are used to estimate the current state, including the current metabolite value. In certain aspects, given the measured values of the process parameters, the current state is estimated by integrating a set of kinetic equations (e.g., equations 1 to 11) from the start time of the reaction to the current time.

[0126] At operation 330, the predicted / estimated state from the state observer is compared with the measured experimental conditions. At operation 340, the optimal state estimate (metabolite) is determined. In some aspects, the embodiment of operation 340 is an extended Kalman filter. These values are fed back to operation 325. Thus, the state estimate can be updated as a function of time from the feedback loop.

[0127] The output 345 of the kinetic growth model 50 can include product titer, metabolite concentration, viable cell density, and viability. Based on this, at operation 335, a simple metabolic state observer can estimate the future value (e.g., trajectory) of the metabolite of interest (m est ).

[0128] The kinetic growth model does not reflect the internal state of the cells in the bioreactor. If the cells experience fluctuations or deviations under process conditions (e.g., temperature changes, metabolite increases or decreases, feed condition changes, etc.), the cells may enter a sub-optimal state, and the output (e.g., the titer of the biologic material in production) may be sub-optimal. Thus, operations 325 to 335 provide a method for estimating the internal state of the cells and correlating the output production with environmental variables to optimize production. Additionally, if the system deviates from the optimal range, the user may receive a notification prompting the user to correct the bioprocess to return the reaction to the optimal conditions. In some embodiments, the system can automatically correct the feed or environmental conditions to return the system to the optimal conditions. For example, by providing feedback to the controller that controls the bioreactor, the experimental process conditions can be automatically adjusted to minimize the deviation from the optimal process conditions.

[0129] In this example, note that the kinetic parameters do not change over time. However, in other embodiments, the specific consumption and production can change over time and thus can be updated.

[0130] Figure 3B A high-level flowchart of a simplified metabolic state observer is shown, where the input 350 is processed by a simplified metabolic state sensor 355 (see Figure 3A ) to produce an output (optimal estimate) 365.

[0131] FIG. 4 shows a flowchart of the operation of a complete metabolic state observer. In this example, the complete metabolic state observer is directed to a set of multiple metabolites.

[0132] In this example, the complete metabolic state observer is configured to monitor the bioreactor process as described with respect to Figure 1 and Figure 2 and estimate the future trajectories of one or more metabolites. Similar to Figure 3A , the output of the kinetic growth model and / or the complete metabolic state observer can be used to estimate future states. In this example, an extended Kalman filter (EKF) can be used to account for the noise in the bioprocess. However, any suitable estimator can be used. Compared to the simplified metabolic state observer, in this example, there is a metabolic condition model 60 and the state is extended to more than a single metabolite.

[0133] At operation 405, process data is measured, including temperature, pH, feed conditions, time, metabolite concentrations, etc. Generally, the process data can be measured as a function of time. The measured process data is provided to the kinetic growth model 50 and the metabolite condition model. In other respects, the measured process data can optionally be provided to the metabolite condition model. At operation 410, the kinetic growth model initializes the state values (e.g., metabolite values), including xv , x d , x l , m i . The state observer is initialized when it starts. During operation, the state is updated based on the estimated value and the measured value, as described below. At operation 415, the coefficients of the kinetic growth model 50 for the monomer equation are initialized, where the coefficients include u max , k d , k t , θ s , θ iopt , θ q and θ i .

[0134] The output of the kinetic growth model 50 ( Figure 4B which is part of the complete metabolite state observer 470) can include product titer, metabolite concentration, viable cell density, lysed cells, and viability. Based on this, the complete metabolite state observer can estimate (e.g., the trajectory) the future values of titer, biomaterial, viable cell density, viability, lysed cells, metabolites, and the cell state of interest (m est ) (see Figure 4B ).

[0135] The kinetic growth model does not reflect the internal state of the cells in the bioreactor. If the cells experience fluctuations or deviations under process conditions (e.g., temperature changes, metabolite increases or decreases, feed condition changes, etc.), the cells may enter a sub-optimal state, and the output (e.g., the titer of the biomaterial in production) may be sub-optimal. In a multi-dimensional system with a large number of states, including some interrelated states, it is challenging to determine which process conditions to adjust. Therefore, the state of the metabolic condition model 60 and operations 425 to 440 provide a method for estimating the internal state of the cells and correlating the output yield with environmental conditions (variables) to optimize the titer yield. Additionally, if the system deviates from the optimal range, the user may receive a notification prompting the user to correct the biological process to restore the biological reaction to the optimal conditions. In other embodiments, the system can automatically correct the feed or environmental conditions to automatically return the system to the optimal conditions. This ability is described in more detail below and throughout the specification. For example, an optimization routine can be used to determine process adjustments, as described below.

[0136] At operation 420, the specific consumption / productivity of the metabolite at a given time is determined. In some aspects, a look-up table calibrated from experimental data can be used, which correlates the specific consumption / productivity based on the current time. Thus, the metabolic state can be estimated for time points without corresponding state measurements to provide a state observer between the measurements. In other aspects, Equations 12 and 13 can be used to provide the consumption and productivity.

[0137] At operation 425, monomer equations from the kinetic growth model are used to estimate the current state including current metabolite values. In some aspects, given measured values of process parameters, the current state is estimated by integrating kinetic equations (e.g., monomer equations) from the start time of the reaction to the current time. In other aspects, saturation kinetic equations may be used.

[0138] At operation 430, the predicted / estimated state from the state observer is compared with the measured experimental conditions. At operation 440, an optimal state estimate (metabolite) is determined. This can be performed using an extended Kalman filter. At operation 425, these values are fed back into the system. Thus, the state estimate can be updated as a function of time from the feedback loop. Operations 425 to 440 correspond to Figure 2 the feedback path shown, from the output of the hybrid model through the state correction model back to the hybrid model.

[0139] Unlike the simple state observer, the complete metabolic state observer includes additional operations, including operations 445 to 460, which monitor the metabolic state of a multivariable system. At operation 445, the specific consumption / productivity of metabolites in the current measurement data δ m，i (t k ) is calculated. This can be performed based on measured process data. At operation 450, the metabolic state is determined according to the metabolic condition model and based on the specific consumption and productivity. At operation 455, the specific productivity or specific production of a quality attribute may optionally be calculated. The given productivity (yield of the target protein) can be used in the kinetic growth model to estimate the product titer. At operation 460, the current metabolic state for process monitoring is classified according to data-driven methods (e.g., data-driven classification, PLS, deep learning, etc.). Due to the complexity of a multivariable system with a large number of states, including relevant states, it is difficult to determine which process conditions to adjust. The data-driven methods provided in this application (e.g., PCA and PLS statistical modeling engines 65 and data-driven machine learning engine 70) can be used to reduce the dimensionality of the system and allow the identification of conditions affecting the titer. In other words, suboptimal conditions can be identified and adjusted to restore the system to optimal productivity. This application provides an improvement over the prior art because these improvements provide fine-grained and specific control of the bioreactor by identifying process variables outside the optimal determination range. In this context, optimal refers to the range of process or feed conditions corresponding to optimized titer production.

[0140] For this example, note that the kinetic parameters do not change over time. However, the specific consumption and production may change over time and thus may be updated.

[0141] Figure 4BShows a high level of the complete metabolic state observer, displaying various outputs and inputs of the complete metabolic state observer. Specifically, process data is collected in operation 405 and provided to the complete metabolic state observer 470. The complete metabolic state observer monitors cell metabolism, titer, and quality in operation 460 using a hybrid model as described in this application and predicts the given productivity and product quality of the biomaterial in operation 455. The titer and quality of the biomaterial can be predicted in operation 535.

[0142] As Figure 5 shown, the hybrid model can be used for other applications. For example, the hybrid model can be used as part of a digital twin simulation to digitally replicate the behavior of a living system.

[0143] Optimization involves searching for various input variables to find a set that maximizes the titer, quality, or other desired outcomes using an optimization package. The input variables typically include nutrient additions and independent process parameters such as temperature and pH. The optimized parameters can be provided as input variables to operation 610.

[0144] In operation 610, trajectories are specified for the input variables (u i )) and nutrient additions. In operation 615, the state values are initialized from the initial measurement data (x v , x d , x l , m i ). In operation 620, the specified trajectories from operation 610 and the initialized state values from operation 615 are received as inputs. The monomer growth equation for determining the growth and metabolite trajectories is integrated within a suitable parameter range.

[0145] In operation 625, cell metabolism is classified using data-driven classification (e.g., PLS, deep learning, etc.). In operation 630, the hybrid model is used to predict the given productivity and product quality, including the kinetic growth module 50 and the metabolic condition module 60. In operation 635, the titer and quality of the biomaterial are predicted. In this example, the hybrid model is configured to mirror or replicate the output produced by the bioreactor.

[0146] Figure 6 Shows an example of the calibration of the kinetic growth model 50. In operation 705, a training set of historical measurement process data is generated.

[0147] In operation 715, the specific consumption / productivity of metabolites is calculated for each observation in the training set from the historical measurement process data. In operation 720, the representative specific consumption / production function (δ m，i (t k))。In this example, a lookup table is used to perform this function. In some aspects, each metabolite has a separate function (lookup table). In general, any suitable method can be used to estimate the specific consumption / production at a given time.

[0148] Figure 7 An example of a calibration method for the metabolic condition model 60 is shown. At operation 810, a training set of historical measurement process data is generated. Optionally, the measured process variable 811 can be added to the metabolic condition model. At operation 815, the specific consumption / production rate of the metabolite is calculated for each observation in the training set from the historical measurement process data.

[0149] At operation 820, the specific consumption / production rate of the metabolite is calculated for a selected response variable. The response variables include titer (output) and quality metrics. This operation is optional.

[0150] At operation 825, PCA (or PLS if there are response variables) is applied to the specific consumption / production rate data. In addition to the specific consumption / production rate data, the metabolic regulation model can also include measured process parameters.

[0151] Figure 8 is a flowchart of operations for hybrid model calibration (decoupled system identification), including a kinetic model and a metabolic regulation model. Operations 910, 915, and 920 correspond to the kinetic growth model. Operation 925 corresponds to the metabolic condition model.

[0152] At operation 905, a training data set is obtained. At operation 910, the specific growth rate is identified under optimal conditions. At operation 915, the inhibition kinetic coefficient is identified. At operation 920, the death kinetic coefficient is identified. At operation 925, the specific consumption trajectory of the metabolite is calculated. At operation 930, these values can be provided to the kinetic growth model to determine various parameters (e.g., VCD, live cells, total cells, lysed cells, etc.). At operation 935, data-driven techniques are used to classify cell metabolism, using the metabolite condition model 60. At operation 940, the cell metabolism condition model can be used to predict the given production rate and product quality.

[0153] Figure 9A is an example of the data flow through the hybrid model. The data section 705 corresponds to the process measurements of the bioreactor (m, u). The experimental data is provided to the kinetic growth model to generate the estimated growth state 715 (x t , x d , x l , )), where is the state estimate and is provided to the metabolic regulation model 60 to generate the calculated parameter 720 (δ meas) and the metabolic cell state 730. The upper part of the figure corresponds to the kinetic growth model, while the lower part of the figure corresponds to the metabolic regulation model. Although not shown in the figure for simplicity, data from the lower path can be provided to the upper path, as described in this application.

[0154] The cell state 730 is generated based on the calculated parameters 720. From these data sets (715 and 730), the calculated parameters of the product titer 740 Qp and the biomaterial 750 are determined.

[0155] These examples are not intended to limit the data flow through the hybrid model, as additional data flow paths can be described in the application. Other paths of the data flow may be applicable to the hybrid model.

[0156] Figure 9B The data flow path of the PCA / PLS of the metabolic condition model is shown. Optionally, the variable 760 is used to determine a given productivity or quality metric 765. The variable 760 and the productivity / metric 765 are used for PCA or PLS analysis to generate the principal component scores (T) and / or to generate the predicted given productivity or quality metric 775.

[0157] Figure 10 is a table showing various bioreactor runs and the conditions used for each run. It can be seen from this chart that the process conditions (e.g., pH, temperature, feed, etc.) are varied to find the optimal conditions for producing an optimized titer. The process conditions can be adjusted based on an optimization method to determine the configuration of the process conditions for the optimized prediction trajectory, product quantity (titer), and / or product quality.

[0158] Finding the optimal adjustment or setting of the process can be defined as finding a set of manipulated variables (u or independent variables, in this case the process conditions and feed) that minimize the mathematical objective function j.

[0159] (14)

[0160] For example, at a future time point t| [t+k] The objective function for maximizing the titer can take the following form:

[0161] (15) where where

[0162] is the predicted titer at the future time point;

[0163] x| [t] is the current value of the state, and

[0164] u| [t] is a set of manipulated variables implemented between the present [t] and the future time point [t + k].

[0165] There may be multiple objectives to be optimized simultaneously. This can be performed by weighting the objectives based on their importance. For example, to maximize the titer and maintain the objective quality metric, the objective function can take the following form:

[0166] (16) where

[0167] θ is the relative weight of each parameter to be optimized, and

[0168] q sp is the target or set point for the quality parameter q.

[0169] A function (f q ) similar to the function of IgG can predict the future quality variable at future time points.

[0170] Typically, there are constraints added to the function. For example, the optimization objective of maximizing the titer while keeping the quality within the operating specifications can be controlled by the following equation:

[0171] (17)

[0172] Subject to:

[0173] (18)

[0174] To prevent the optimization algorithm from selecting an infeasible new set of inputs, restrictions are also imposed on u. The aggressiveness of the control action is adjusted by imposing a penalty on the change in u from the recipe or current settings. This can prevent the controller from making unstable or large changes to the process conditions, thus providing minimal improvement to the target parameters. Then the complete objective function is described as finding the set of optimal feasible u that maximizes the titer (IgG) and maintains the quality within the target and specified ranges. This can be controlled by the following formula:

[0175] (19)

[0176] Subject to:

[0177] (20)

[0178] (21)u min ≤u| [t] ≤u max where

[0179] θ u is the penalty weight for u (note that there may be more than one u), and

[0180] u spis the target value of u, which is typically a set value or a current value.

[0181] Example

[0182] Figure 11 Shows example trajectories of VDC and glucose. This data can be used to determine the center points of these corresponding parameters.

[0183] Figures 12A to 12B Shows an example of metabolite state estimation, e.g., for glucose.

[0184] The following process can be used to construct a state observer for metabolites.

[0185] 1. Calculate the specific consumption / secretion rate based on the collected data.

[0186] Note that δ at time (t) m，i (t) represents the consumption rate from (t) to the next BEM sampling point. The following equation can be used:

[0187] (12)

[0188] (13)

[0189] where mAdd i，k is the bolus addition amount of the metabolite at t = k. It is assumed that the measurement of the metabolite at t = k is made before the bolus addition.

[0190] 2. Calculate the average trajectory from the training set.

[0191] Using the SIMCA average BEM trajectory is a simple way to determine δ m，i (t).

[0192] 3. For simulation and state observation, calculate the parameter δ using zero-order hold of the BEM values m，i (t).

[0193] Figures 13A to 13C Shows an example of cell state classification using a data-driven method. In this method, the specific consumption rate is calculated based on the measured data, e.g., using the method described in this application to calculate δ m，i (t k ). This set of δ m，i (t k ) values can be used to construct a data-driven model to classify the cell state (e.g., metabolite).

[0194] In some aspects, a metabolic condition model is used to classify cell states to estimate specific consumption rates or specific production rates of metabolites. In some aspects, machine learning processes can be used to classify cell states. In other aspects, statistical models can be used to classify cell states. For example, PCA can be used for high-level classification of a system, e.g., to determine whether cell culture growth is operating within an optimal range (see Figure 13B ). PLS can be used to classify individual metabolites, e.g., to predict titer and / or product quality and to determine whether individual parameters are operating within an optimal range (see Figure 13A , for glucose). Figure 13C Shows predictions of state observations of various parameters (e.g., growth, viability, by-products such as ammonia, amino acids, feeds, etc.).

[0195] Figures 14A to 14B Shows the identification of parameters related to production rate. The related (not necessarily causal) relationships can provide valuable references for managing bioprocess reactions. Figure 14C Shows that ammonia decreases the production rate, while all other metabolites increase the production rate. The consumption of nutrients (e.g., glucose, glutamine, etc.) is related to high production rate. Lower consumption (or production) of other metabolites, such as lactate and ammonia, is related to low production rate. Changes in pH value and temperature can also be studied. Generally, decreasing the pH value increases the production rate, while decreasing the temperature decreases the production rate.

[0196] Figures 15A to 15B Shows that cell density inhibits the growth rate. For example, a cell density of approximately 12 times 10 to the 5th power begins to inhibit the growth rate. The hybrid model allows separate analysis of the effects of cell density and lysed cells. The growth inhibition can be explained by ammonia, which increases with increasing cell density. However, lysed dead cells release toxins into the bulk fluid and further increase cell death rate. Perfusion data analysis can be used to distinguish these effects, because perfusion can remove toxic metabolites, and removing toxins can prevent the increase in cell death rate. Therefore, these results indicate that cell death rate is largely affected by lysed cells.

[0197] Figure 16 Shows a graph of predicted VCD, growth rate, and death rate. The graph shows growth inhibition (e.g., with increasing cell density, metabolite accumulation, nutrient consumption, temperature change). The death rate increases with increasing lysed cell density, ammonia formation, and pH value change (less affected). Bolus feed addition is associated with very short-term nutrient consumption. Growth inhibition is related to cell density.

[0198] Figures 17A to 17CShows the effects of various parameter changes. The predicted behavior of the mixed growth model is compared with the measured experimental behavior. As shown in these figures, changes in temperature are confirmed to inhibit growth. Changes in pH value seem to slightly increase cell death rate but do not seem to inhibit the growth rate. These cells seem to be able to well adapt to and recover from the consumption of glucose and glutamine. Therefore, no significant changes are observed in growth because the cells may metabolize other carbon sources.

[0199] The following procedure can be used to obtain the growth curves under various experimental conditions:

[0200] 1. Initialize the model (observer).

[0201] Obtain the starting conditions (e.g., VCD, viability, metabolites (glucose, glutamine, glutamate, lactate, ammonia, etc.), input parameters (temperature, pH, etc.)).

[0202] 2. Integrate the kinetic model over the time interval.

[0203] (22)

[0204] 3. Update the metabolites and input parameters.

[0205] Update the state estimate of the metabolites according to the mismatch between the measured and estimated values. Update the input parameters to the current measured values and use zero-order hold over the sampling interval.

[0206] 4. Continue with step 2.

[0207] The growth curves are affected by the input variables and metabolite trajectories. Unless otherwise stated, the estimates of the growth curves (e.g., VCD, Viab, etc.) are not adjusted by the measurement data. These results show good agreement between the measured and predicted growth curves (e.g., VCD, Viab), indicating that the mixed model accurately reflects the behavior of cells in the bioreactor. It is worth noting that the mixed model takes into account the predicted dead and lysed cells, which enables the mixed model to accurately track the bioreactor over a longer time scale than other models. The mixed model allows exploration of various parameters on the bioreactor system to determine how individual parameter changes affect the biological process.

[0208] Figure 18 Shows another example of parameter change. In this example, when the substrate such as glucose is limited, the growth is limited. This effect can be modeled by incorporating the following equation into the kinetic growth model.

[0209] (25)u eff = u max θ sub θ quadθ inh

[0210] (26)

[0211] where s glu :1

[0212] Figure 19 shows experimental data demonstrating the effect of the quadratic term on the growth rate. When the quadratic term deviates from its optimal value, the growth rate is inhibited. The quadratic term includes temperature, pH, or other factors. This effect can be modeled by incorporating the following equation into the kinetic growth model.

[0213] (27)u eff = u max θ sub θ quad θ corr

[0214] (28)

[0215] where θ q，temp : 20, and

[0216] θ etemp，opt : 36.8

[0217] Figure 21 is an operating flowchart of the hybrid system model. In operation 2110, the process conditions and metabolite concentrations of the biological system are measured as a function of time. In operation 2120, the metabolic rate of the biological system is determined, including the specific consumption rate of metabolites and the specific production rate of metabolites. In operation 2130, the process conditions and metabolic rate are provided to a hybrid system model configured to predict the production of biological materials, the hybrid system model including a kinetic growth model configured to estimate cell growth in the form of a function of time, and a metabolic condition model that selects process conditions based on the specific consumption rate or secretion rate of metabolites. Wherein the metabolic condition model is configured to classify the biological system into a metabolic state. In operation 2140, the amount of biological material is predicted based on the hybrid system model.

[0218] Figure 22It is a flowchart of operations for configuring a hybrid system model. In operation 2210, experimental data is obtained, including one or more process conditions, one or more metabolite concentrations, and cell counts for multiple bioreactor batches. Each batch is associated with a particular process condition configuration. In operation 2220, based on the experimental data, using the kinetic model of the hybrid system model, the growth rate is determined under optimal conditions. In operation 2230, based on the growth rate under the optimal conditions and the growth rate from the experimental data, the cell lysis parameters are determined using the kinetic model. In operation 2240, the specific productivity or specific consumption rate of the metabolite is determined. In operation 2250, the kinetic parameters of the growth inhibitory factor are determined to minimize the difference between the growth rate under the optimal conditions and the growth rate from the experimental data. In operation 2260, the determined kinetic parameters, cell lysis parameters, growth rate, and the specific productivity or specific consumption rate of the metabolite are provided to the metabolic condition model of the hybrid system model for classifying the biological system into a metabolic state associated with a given productivity of the biomaterial produced by the biological system, based on the measured specific consumption rate or measured secretion rate of the metabolite.

[0219] Based on the hybrid model, the parameters of the bioreactor can be adjusted to optimize the titer. These techniques are compatible with simulation, optimization, and process monitoring (state observation).

[0220] The techniques provided in this application provide a model that accurately simulates cell behavior in a bioreactor. As shown by the experimental data, the predicted VCD and viability curves match the measured experimental values for various feed, pH, and temperature curves.

[0221] In addition, the hybrid model effectively acts as a soft sensor for cell metabolism and metabolites, allowing for the monitoring and characterization of the specific consumption and production of metabolites, as well as the monitoring and characterization of changes in cell state and metabolic activity.

[0222] Unlike other models that do not estimate or otherwise account for lysed cells, the hybrid model takes into account the number of lysed cells that affect the toxicity of the bulk fluid. This approach allows the hybrid model to be more accurate than other models that do not consider this feature, and over a longer time scale than other models.

[0223] Other advantages of the hybrid model include increased understanding of cell metabolism and the factors driving cell growth, cell death, viability, titer, and product quality. The hybrid model also provides the ability to simulate the performance of new process conditions (e.g., feed, temperature, pH curves, etc.) to maximize productivity and observe cell states (e.g., metabolic activity, etc.) or their changes. In other aspects, perfusion performance can be predicted from fed-batch operations.

[0224] These techniques provide improved predictions, improved titer predictions, and product quality, based on monitoring and prediction. This technology is applicable to a wide range of application areas, including simple univariate metabolite state predictors, comprehensive multivariate metabolite state predictors, real-time systems (e.g., digital twin simulations), etc. Thus, this technology provides improvements in the field of bioreactor control and biologic manufacturing.

[0225] Continuing to refer Figure 1 , an exemplary hardware configuration of a computing system that can be used to implement at least a portion of system 100 as described herein is provided. Server system 10 includes a central processing unit (CPU) 16, a system memory 17, a network interface 18, and a user interface 19. These components of the computer are coupled to each other, for example, via a system bus (not shown). The CPU 16 can perform arithmetic, logical, and / or control operations by accessing the system memory 17. The CPU 16 can include multiple processors (e.g., cores) that can perform parallel processing, which can result in higher performance of the computing system 100. The CPU 16 can implement Figure 1 and Figure 2 the processors, engines, and modules of the exemplary devices and / or systems described in and other figures. The system memory 17 can store information and / or instructions for use in conjunction with the CPU 16. The system memory 17 can include volatile and non-volatile memory, such as random access memory (RAM) and read only memory (ROM). A basic input / output system (BIOS) containing basic routines that transfer information between elements within the server system 10 during startup, for example, can be stored in the memory 17 (e.g., ROM). The system bus can be any of a variety of bus structures, including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The computer can include a network interface 18 for communicating with other computers (e.g., client system 20) and / or devices via a network (e.g., network 45).

[0226] In addition, the computer may include a hard disk drive (HDD) for reading from and writing to a hard disk (not shown), and an external disk drive (not shown) for reading from or writing to a removable disk (not shown). The removable disk may be a magnetic disk for a disk drive or an optical disk such as a CD ROM for an optical disk drive. The HDD and the external disk drive are connected to the system bus via an HDD interface and an external disk drive interface, respectively. The drives and their associated computer-readable media provide non-volatile storage of computer-readable instructions, data structures, program modules, and other data for a general-purpose or special-purpose computer. The data structures may include associated data for implementing the exemplary methods and their variations as described herein. The associated data may be organized in a database, such as a relational database or an object database.

[0227] Although the exemplary environment described herein employs a hard disk (not shown) and an external disk (not shown), those skilled in the art will appreciate that other types of computer-readable media that can store computer-accessible data may also be used in the exemplary operating environment, such as magnetic tape cartridges, flash memory cards, digital video disks, random access memory, read-only memory, and the like.

[0228] Many program modules may be stored on the hard disk, external disk, ROM, or RAM, including an operating system (not shown), one or more application programs, other program modules (not shown), and custom software (such as the kinetic growth model 50, the metabolic condition model 60, the state correction module 75, the process monitoring engine 80, the tagging and alerting engine 85, the consumption rate and secretion rate module 90, etc.). The application programs may include at least a portion of the above functions.

[0229] As a supplement or alternative to the implementation of the server system 10 as shown in Figure 1 part or all of the functions of the exemplary embodiments described herein may be implemented as one or more hardware circuits. Examples of such hardware circuits may include, but are not limited to: Large Scale Integration (LSI), Reduced Instruction Set Circuits (RISC), Application Specific Integrated Circuits (ASIC), and Field Programmable Gate Arrays (FPGA).

[0230] The database 30 can store various information for the technologies provided herein, such as training data 32, process conditions 34, and output data 36, or any other data generated by the kinetic and metabolic state observation system in a test or real environment. The database system 30 can be local or remote to the server system 10 and the client system 20, and can communicate via any suitable communication medium, such as a local area network (LAN), a wide area network (WAN), the Internet, an intranet, hardwiring, a wireless link, etc.

[0231] The client system 20 can be implemented by any suitable computer system, which is preferably equipped with a display or monitor, at least one hardware processor (e.g., a microprocessor, a controller, a central processing unit (CPU), a GPU, etc.), one or more memories, and / or an internal or external network interface or communication device (e.g., a modem, a network card, etc.). The system can also include optional input devices, such as a keyboard, a mouse, or other input devices, as well as any commercially available and customized software. For example, as Figure 1 shown, the client includes at least one CPU / processor 22, one or more memories 24, and / or an internal or external network interface or communication device 26, such as a modem or a network card, as well as a user interface 28, etc. Optional input devices may include a keyboard, a mouse, or other input devices. The client system 20 can request information from the user to provide to the server system 10. The client system can present a graphical user interface, such as a GUI, etc., or other interfaces, such as a command line prompt, a menu screen, etc., to obtain information from the user to operate the biological process reaction and monitor the biological process reaction using the kinetic and metabolic state observation system.

[0232] The embodiments of the present application can be generally applicable to provide support in any context and are not limited to any specific application fields, such as bioreactor manufacturing, health, etc.

[0233] The description provided in this application is presented for purposes of illustration and description and is not intended to be exhaustive or limited to the examples disclosed herein. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the technology provided herein. The selected examples are chosen to best explain the working principles of the device and its components, enabling those of ordinary skill in the art to understand the various embodiments envisioned herein.

[0234] Aspects of the kinetic and metabolic state observation system are described herein with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products. Each block of the flowchart and / or block diagram, as well as combinations of blocks in the flowchart and / or block diagram, can be implemented by computer-readable program instructions. Each block or combination of blocks illustrated by the block diagram and / or flowchart can be implemented by a system based on dedicated software that performs specific functions to execute combinations of dedicated computer instructions disclosed herein.

[0235] Glossary

[0236] F b : Flow rate of cell loss

[0237] F f : Feed flow rate of fresh culture medium

[0238] F h : Harvest flow rate

[0239] k d : Mortality rate of non-lysed cells

[0240] k l : Conversion rate of dead cells to lysed cells

[0241] k t : Increase in mortality rate caused by lysed cell concentration

[0242] IgG: Biomaterial, which is an immunoglobulin here

[0243] Rate of change of biomaterial in the form of a function of time

[0244] I i : Numerical value of the inhibitory variable, which can be a metabolite or an independent variable

[0245] Rapid or continuous feed increment of metabolite i between time intervals t = k and t = k + 1

[0246] Rate of change of metabolite

[0247] m r，i : Concentration of metabolite in the bioreactor

[0248] m f，i : Concentration of metabolite in the feed

[0249] m i : Given metabolite

[0250] Qp: Input contains a function of metabolite concentration m

[0251] q i: Value of the quadratic variable, which may be a metabolite or an independent variable

[0252] s i : Substrate value, which may be a metabolite or an independent variable

[0253] u d : Cell death rate

[0254] u: Independent variable

[0255] u max : Maximum growth rate (under optimal conditions)

[0256] VCD: Viable cell density

[0257] iVCD: Integrated VCD across time steps

[0258] V: Volume of material in the bioreactor

[0259] Change in viable cell density over time

[0260] Change in lysed cell density over time

[0261] Change in dead cell density over time

[0262] x t : Total cell density

[0263] x v : Viable cell density

[0264] x d : Dead cell density

[0265] x l : Lysed cell density

[0266] θ i : Coefficient related to growth rate inhibition under optimal conditions

[0267] θ i，i : Coefficient representing the value of the inhibitory variable above which growth is inhibited

[0268] θ i，opt : Coefficient representing the value of the quadratic variable that maximizes growth

[0269] θ inh : Growth inhibition caused by excess biological material

[0270] θ q，i : Coefficient representing growth inhibition sensitivity

[0271] θ quad: Growth rate reduction caused by secondary terms (such as temperature, pH, etc.)

[0272] θ s，i : Coefficient representing the substrate concentration below which growth is inhibited

[0273] θ sub : Growth rate reduction caused by substrate depletion

[0274] θ inh : Population density

[0275] μ eff : Effective growth rate

[0276] δ m，i (t): Specific consumption rate or secretion rate of metabolites at the current moment

Claims

1. A method for predicting the amount of at least one biomaterial produced or consumed by a biological system in a bioreactor, characterized in that, the method comprises: measuring the process conditions of the biological system and the change of metabolite concentration over time; determining the metabolic rate of the biological system, including the specific consumption rate of metabolites and the specific production rate of metabolites; providing the process conditions and the metabolic rate to a hybrid system model configured to predict the production of the biomaterial, wherein the hybrid system model comprises: a kinetic growth model configured to predict cell growth in the form of a function of time, and a metabolic condition model configured to select process conditions based on the specific consumption rate or secretion rate of metabolites, wherein the metabolic condition model is further configured to classify the biological system into a metabolic state; and predicting the amount of biomaterial based on the hybrid system model.

2. The method according to claim 1, characterized in that, the kinetic growth model is further configured to predict cell viability.

3. The method according to claim 1, characterized in that, the kinetic growth model is further configured to refer to lysed cells.

4. The method according to claim 1, characterized in that, the method further comprises: constructing a metabolic state observer for metabolites to provide a prediction result of the internal metabolic state of the biological system.

5. The method according to claim 4, characterized in that, the method further comprises: obtaining the current measurement result of the metabolite; using the metabolic state observer to determine the consumption rate of the metabolite; and using the metabolic state observer and the current measurement result to predict the future concentration of the metabolite.

6. The method according to claim 4, characterized in that, the method further comprises: using the metabolic state observer to perform cell state classification to predict the specific consumption rate or specific production rate of the metabolite.

7. The method according to claim 6, characterized in that, the predicted specific consumption rate or the predicted specific production rate is determined using training data.

8. The method according to claim 4, characterized in that, the method further comprises: classifying the internal metabolic state into an optimal or sub-optimal category for biomaterial production; and when the internal metabolic state is classified as the sub-optimal category, sending a notification to the user.

9. The method according to claim 1, characterized in that, the kinetic growth model comprises a monomer kinetic model or a saturation kinetic model.

10. The method according to claim 1, characterized in that, the method further comprises: measuring the cell density or cell viability in the form of a function of time for the biological system.

11. The method according to claim 1, characterized in that, the kinetic growth model is further configured to predict the growth of microbial cells in the form of a function of time.

12. The method according to claim 1, characterized in that, The metabolic condition model includes one or more of the following: machine learning model, deep learning model, principal component analysis (PCA) model, partial least squares (PLS) model, partial least squares discriminant analysis (PLS-DA) model, and orthogonal partial least squares discriminant analysis (OPLS-DA) model.

13. The method according to claim 1, wherein, the method further includes: obtaining a test sample from the bioreactor; and determining whether the amount of the biological material in the test sample is within the range predicted by the hybrid system model.

14. The method according to claim 1, wherein, the method further includes: updating the parameters of the hybrid system model when the hybrid system model is running, wherein the parameters include the metabolic rate and coefficients associated with the hybrid system model.

15. The method according to claim 1, wherein, the process conditions include one or more of the following: pH, temperature, dissolved oxygen, osmotic pressure, process flow leaving the bioreactor, growth medium, by-products, amino acids, metabolites, oxygen flow rate, nitrogen flow rate, carbon dioxide flow rate, air flow rate, and agitation speed.

16. The method according to claim 15, wherein, the growth medium includes nutrients having amino acids, sugars, or organic acids.

17. The method according to claim 15, wherein, the by-products include amino acids, sugars, organic acids, or ammonia.

18. The method according to claim 1, wherein, the method further includes at least one of the following: determining optimal process conditions for the bioreactor based on the hybrid system model; measuring the experimental process conditions in the form of a function of time of the bioreactor using one or more sensors; monitoring the measured experimental process conditions to detect deviations from the optimal process conditions; and when a deviation is detected, sending a notification to the user.

19. The method according to claim 1, wherein, the method further includes at least one of the following: determining optimal process conditions for the bioreactor based on the hybrid system model; measuring the experimental process conditions in the form of a function of time of the bioreactor using one or more sensors; monitoring the measured experimental process conditions to detect deviations from the optimal process conditions; and providing feedback to a controller controlling the bioreactor to automatically adjust the experimental process conditions to minimize deviations from the optimal process conditions.

20. The method according to claim 1, wherein, providing the process conditions and metabolic rate to a hybrid system model configured to predict the production of biological materials includes: initializing the hybrid system model according to the process conditions; simulating a predicted amount of at least one biological material using the hybrid system model initialized according to the process conditions; and determining one or more states of the biological system based on the results of the simulation.

21. The method according to claim 20, wherein, The simulation further includes: a configuration for adjusting the process conditions based on an optimization method to determine process conditions for optimizing a predicted trajectory, product quantity, and / or product quality.

22. A method for calibrating a hybrid system model for predicting biomaterials produced by a biological system in a bioreactor Characterized in that the method includes: obtaining experimental data including measurements of one or more process conditions, one or more metabolite concentrations, and cell numbers for a plurality of bioreactor batches, wherein each batch is associated with a given configuration of process conditions; using a kinetic model of the hybrid system model to determine a growth rate under optimal conditions based on the experimental data; using the kinetic model to determine cell lysis parameters based on the growth rate under the optimal conditions and the growth rate from the experimental data; determining a metabolite specific productivity or specific consumption rate; determining kinetic parameters of a growth inhibitory factor to minimize the gap between the growth rate under the optimal conditions and the growth rate from the experimental data; and providing the determined kinetic parameters, the cell lysis parameters, the growth rate, and the metabolite specific productivity or specific consumption rate to a metabolic condition model of the hybrid system model, wherein the metabolic condition model is configured to classify the biological system into a metabolic state associated with a given productivity of the biomaterials produced by the biological system based on the measured metabolite specific consumption rate or the measured productivity.

23. The method according to claim 22, Characterized in that the method further includes: providing a parameter configuration to an optimization module, wherein the parameter configuration includes the growth rate under the optimal conditions, the metabolite specific consumption rate and specific productivity, and new process conditions, to determine process conditions for optimizing the production of the biomaterials.

24. The method according to claim 22, Characterized in that the method further includes: monitoring batch properties of the bioreactor using principal component analysis (PCA).

25. The method according to claim 22, Characterized in that the method further includes: predicting an output of the bioreactor using partial least squares (PLS).

26. The method according to claim 25, Characterized in that the output is the quantity of the biomaterials.

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