Metabolic engineering with multi-objective optimization of kinetic models

Deep Neural Networks for Predicting Single-Cell Responses and Probability Landscapes

Engineering biology relies on the accurate prediction of cell responses. However, making these predictions is challenging for a variety of reasons, including the stochasticity of biochemical reactions, variability between cells, and incomplete information about underlying biological processes. Machine learning methods, which can model diverse input-output relationships without requiring a priori mechanistic knowledge, are an ideal tool for this task. For example, such approaches can be used to predict gene expression dynamics given time-series data of past expression history. To explore this application, we computationally simulated single-cell responses, incorporating different sources of noise and alternative genetic circuit designs. We showed that deep neural networks trained on these simulated data were able to correctly infer the underlying dynamics of a cell response even in the presence of measurement noise and stochasticity in the biochemical reactions. The training set size and the amount of past data provided as inputs both affected prediction quality, with cascaded genetic circuits that introduce delays requiring more past data. We also tested prediction performance on a bistable auto-activation circuit, finding that our initial method for predicting a single trajectory was fundamentally ill-suited for multimodal dynamics. To address this, we updated the network architecture to predict the entire distribution of future states, showing it could accurately predict bimodal expression distributions. Overall, these methods can be readily applied to the diverse prediction tasks necessary to predict and control a variety of biological circuits, a key aspect of many synthetic biology applications.

Kinetic-model-based pathway optimization with application to reverse glycolysis in mammalian cells

Over the last two decades, model-based metabolic pathway optimization tools have been developed for the design of microorganisms to produce desired metabolites. However, few have considered more complex cellular systems such as mammalian cells, which requires the use of nonlinear kinetic models to capture the effects of concentration changes and cross-regulatory interactions. In this study, we develop a new two-stage pathway optimization framework based on kinetic models that incorporate detailed kinetics and regulation information. In Stage 1, a set of optimization problems are solved to identify and rank the enzymes that contribute the most to achieving the metabolic objective. Stage 2 then determines the optimal enzyme interventions for specified desired numbers of enzyme adjustments. It also incorporates multi-scenario optimization, which allows the simultaneous consideration of multiple physiological conditions. We apply the proposed framework to find enzyme adjustments that enable a reverse glucose flow in cultured mammalian cells, thereby eliminating the need for glucose feed in the late culture stage and enhancing process robustness. The computational results demonstrate the efficacy of the proposed approach; it not only captures the important regulations and key enzymes for reverse glycolysis but also identifies differences and commonalities in the metabolic requirements for different carbon sources.

Limited Mechanistic Link Between the Monod Equation and Methanogen Growth: a Perspective from Metabolic Modeling

The Monod equation has been widely applied as the general rate law of microbial growth, but its applications are not always successful. By drawing on the frameworks of kinetic and stoichiometric metabolic models and metabolic control analysis, the modeling reported here simulated the growth kinetics of a methanogenic microorganism and illustrated that different enzymes and metabolites control growth rate to various extents and that their controls peak at either very low, intermediate, or very high substrate concentrations. In comparison, with a single term and two parameters, the Monod equation only approximately accounts for the controls of rate-determining enzymes and metabolites at very high and very low substrate concentrations, but neglects the enzymes and metabolites whose controls are most notable at intermediate concentrations. These findings support a limited link between the Monod equation and methanogen growth, and unify the competing views regarding enzyme roles in shaping growth kinetics. The results also preclude a mechanistic derivation of the Monod equation from methanogen metabolic networks and highlight a fundamental challenge in microbiology: single-term expressions may not be sufficient for accurate prediction of microbial growth. IMPORTANCE The Monod equation has been widely applied to predict the rate of microbial growth, but its application is not always successful. Using a novel metabolic modeling approach, we simulated the growth of a methanogen and uncovered a limited mechanistic link between the Monod equation and the methanogen's metabolic network. Specifically, the equation provides an approximation to the controls by rate-determining metabolites and enzymes at very low and very high substrate concentrations, but it is missing the remaining enzymes and metabolites whose controls are most notable at intermediate concentrations. These results support the Monod equation as a useful approximation of growth rates and highlight a fundamental challenge in microbial kinetics: single-term rate expressions may not be sufficient for accurate prediction of microbial growth.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges

This review is a part of the SI 'Genome-Scale Modeling of Microorganisms in the Real World'. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review focuses on the dynamic phenotype; prediction of the real-life behaviors of microorganisms, such as cell proliferation, dormancy, and mortality; balanced and unbalanced growth; steady-state and transient processes; primary and secondary metabolism; stress responses; etc. Constraint-based metabolic reconstructions were successfully started two decades ago as FBA, followed by more advanced models, but this review starts from the earlier nongenomic predecessors to show that some GEMs inherited the outdated biokinetic frameworks compromising their performances. The most essential deficiencies are: (i) an inadequate account of environmental conditions, such as various degrees of nutrients limitation and other factors shaping phenotypes; (ii) a failure to simulate the adaptive changes of MMCC (MacroMolecular Cell Composition) in response to the fluctuating environment; (iii) the misinterpretation of the SGR (Specific Growth Rate) as either a fixed constant parameter of the model or independent factor affecting the conditional expression of macromolecules; (iv) neglecting stress resistance as an important objective function; and (v) inefficient experimental verification of GEM against simple growth (constant MMCC and SGR) data. Finally, we propose several ways to improve GEMs, such as replacing the outdated Monod equation with the SCM (Synthetic Chemostat Model) that establishes the quantitative relationships between primary and secondary metabolism, growth rate and stress resistance, process kinetics, and cell composition.

Comparison of Optimization-Modelling Methods for Metabolites Production in Escherichia coli

The metabolic network is the reconstruction of the metabolic pathway of an organism that is used to represent the interaction between enzymes and metabolites in genome level. Meanwhile, metabolic engineering is a process that modifies the metabolic network of a cell to increase the production of metabolites. However, the metabolic networks are too complex that cause problem in identifying near-optimal knockout genes/reactions for maximizing the metabolite’s production. Therefore, through constraint-based modelling, various metaheuristic algorithms have been improvised to optimize the desired phenotypes. In this paper, PSOMOMA was compared with CSMOMA and ABCMOMA for maximizing the production of succinic acid in E. coli. Furthermore, the results obtained from PSOMOMA were validated with results from the wet lab experiment.

MOMO - multi-objective metabolic mixed integer optimization: application to yeast strain engineering

BACKGROUND

In this paper, we explore the concept of multi-objective optimization in the field of metabolic engineering when both continuous and integer decision variables are involved in the model. In particular, we propose a multi-objective model that may be used to suggest reaction deletions that maximize and/or minimize several functions simultaneously. The applications may include, among others, the concurrent maximization of a bioproduct and of biomass, or maximization of a bioproduct while minimizing the formation of a given by-product, two common requirements in microbial metabolic engineering.

RESULTS

Production of ethanol by the widely used cell factory Saccharomyces cerevisiae was adopted as a case study to demonstrate the usefulness of the proposed approach in identifying genetic manipulations that improve productivity and yield of this economically highly relevant bioproduct. We did an in vivo validation and we could show that some of the predicted deletions exhibit increased ethanol levels in comparison with the wild-type strain.

CONCLUSIONS

The multi-objective programming framework we developed, called MOMO, is open-source and uses POLYSCIP (Available at http://polyscip.zib.de/). as underlying multi-objective solver. MOMO is available at http://momo-sysbio.gforge.inria.fr.

Multi-Objective Optimization of an ABE Fermentation System for Butanol Production as Biofuel

In this work, a previously reported unstructured kinetic model of Clostridium acetobutylicum ATCC 824, validated with experimental data under different culture conditions, was used to determine the optimal process conditions from an ABE fermentation system for biofuel production. The goal of this work was to simultaneously maximize two conflicting objectives: volumetric productivity and final concentration of butanol considering both Fed-Batch and single-stage CSTR operation regimes using either a free or immobilized cell reactor. The result of the after mentioned strategy was the construction of the Pareto Fronts and optimal trajectories for the inlet solution feeding rate and concentration using a Sequential Quadratic Programming methodology.

The obtained results suggest that the maximum concentration and productivity of butanol are achieved in a semi-continuous system operating with immobilized cells, obtaining values of 19.1454 kg m-3 and 0.3655 kg m-3 h-1, respectively, representing an increase of 48 % and 104 % compared to the most recent industrial process reported to date.

System-level analysis of metabolic trade-offs during anaerobic photoheterotrophic growth in Rhodopseudomonas palustris

BACKGROUND

Living organisms need to allocate their limited resources in a manner that optimizes their overall fitness by simultaneously achieving several different biological objectives. Examination of these biological trade-offs can provide invaluable information regarding the biophysical and biochemical bases behind observed cellular phenotypes. A quantitative knowledge of a cell system's critical objectives is also needed for engineering of cellular metabolism, where there is interest in mitigating the fitness costs that may result from human manipulation.

RESULTS

To study metabolism in photoheterotrophs, we developed and validated a genome-scale model of metabolism in Rhodopseudomonas palustris, a metabolically versatile gram-negative purple non-sulfur bacterium capable of growing phototrophically on various carbon sources, including inorganic carbon and aromatic compounds. To quantitatively assess trade-offs among a set of important biological objectives during different metabolic growth modes, we used our new model to conduct an 8-dimensional multi-objective flux analysis of metabolism in R. palustris. Our results revealed that phototrophic metabolism in R. palustris is light-limited under anaerobic conditions, regardless of the available carbon source. Under photoheterotrophic conditions, R. palustris prioritizes the optimization of carbon efficiency, followed by ATP production and biomass production rate, in a Pareto-optimal manner. To achieve maximum carbon fixation, cells appear to divert limited energy resources away from growth and toward CO2 fixation, even in the presence of excess reduced carbon. We also found that to achieve the theoretical maximum rate of biomass production, anaerobic metabolism requires import of additional compounds (such as protons) to serve as electron acceptors. Finally, we found that production of hydrogen gas, of potential interest as a candidate biofuel, lowers the cellular growth rates under all circumstances.

CONCLUSIONS

Photoheterotrophic metabolism of R. palustris is primarily regulated by the amount of light it can absorb and not the availability of carbon. However, despite carbon's secondary role as a regulating factor, R. palustris' metabolism strives for maximum carbon efficiency, even when this increased efficiency leads to slightly lower growth rates.

Risk-Based Bioengineering Strategies for Reliable Bacterial Vaccine Production

Design of a reliable process for bacterial antigen production requires understanding of and control over critical process parameters. Current methods for process design use extensive screening experiments for determining ranges of critical process parameters yet fail to give clear insights into how they influence antigen potency. To address this gap, we propose to apply constraint-based, genome-scale metabolic models to reduce the need of experimental screening for strain selection and to optimize strains based on model driven iterative Design-Build-Test-Learn (DBTL) cycles. Application of these systematic methods has not only increased the understanding of how metabolic network properties influence antigen potency, but also allows identification of novel critical process parameters that need to be controlled to achieve high process reliability.

A Review of Dynamic Modeling Approaches and Their Application in Computational Strain Optimization for Metabolic Engineering

Mathematical modeling is a key process to describe the behavior of biological networks. One of the most difficult challenges is to build models that allow quantitative predictions of the cells' states along time. Recently, this issue started to be tackled through novel in silico approaches, such as the reconstruction of dynamic models, the use of phenotype prediction methods, and pathway design via efficient strain optimization algorithms. The use of dynamic models, which include detailed kinetic information of the biological systems, potentially increases the scope of the applications and the accuracy of the phenotype predictions. New efforts in metabolic engineering aim at bridging the gap between this approach and other different paradigms of mathematical modeling, as constraint-based approaches. These strategies take advantage of the best features of each method, and deal with the most remarkable limitation—the lack of available experimental information—which affects the accuracy and feasibility of solutions. Parameter estimation helps to solve this problem, but adding more computational cost to the overall process. Moreover, the existing approaches include limitations such as their scalability, flexibility, convergence time of the simulations, among others. The aim is to establish a trade-off between the size of the model and the level of accuracy of the solutions. In this work, we review the state of the art of dynamic modeling and related methods used for metabolic engineering applications, including approaches based on hybrid modeling. We describe approaches developed to undertake issues regarding the mathematical formulation and the underlying optimization algorithms, and that address the phenotype prediction by including available kinetic rate laws of metabolic processes. Then, we discuss how these have been used and combined as the basis to build computational strain optimization methods for metabolic engineering purposes, how they lead to bi-level schemes that can be used in the industry, including a consideration of their limitations.

Model-based metabolism design: constraints for kinetic and stoichiometric models

The implementation of model-based designs in metabolic engineering and synthetic biology may fail. One of the reasons for this failure is that only a part of the real-world complexity is included in models. Still, some knowledge can be simplified and taken into account in the form of optimization constraints to improve the feasibility of model-based designs of metabolic pathways in organisms. Some constraints (mass balance, energy balance, and steady-state assumption) serve as a basis for many modelling approaches. There are others (total enzyme activity constraint and homeostatic constraint) proposed decades ago, but which are frequently ignored in design development. Several new approaches of cellular analysis have made possible the application of constraints like cell size, surface, and resource balance. Constraints for kinetic and stoichiometric models are grouped according to their applicability preconditions in (1) general constraints, (2) organism-level constraints, and (3) experiment-level constraints. General constraints are universal and are applicable for any system. Organism-level constraints are applicable for biological systems and usually are organism-specific, but these constraints can be applied without information about experimental conditions. To apply experimental-level constraints, peculiarities of the organism and the experimental set-up have to be taken into account to calculate the values of constraints. The limitations of applicability of particular constraints for kinetic and stoichiometric models are addressed.

OPP Labeling Enables Total Protein Synthesis Quantification in CHO Production Cell Lines at the Single-Cell Level

Accurate measurement of global and specific protein synthesis rates is becoming increasingly important, especially in the context of biotechnological applications such as process modeling or selection of production cell clones. While quantification of total protein translation across whole cell populations is easily achieved, methods that are capable of tracking population dynamics at the single-cell level are still lacking. To address this need, we apply O-propargyl-puromycin (OPP) labeling to assess total protein synthesis in single recombinant Chinese hamster ovary (CHO) cells by flow cytometry. Thereby we demonstrate that global protein translation rates slightly increase with progression through the cell cycle during exponential growth. Stable CHO cell lines producing recombinant protein display similar levels of total protein synthesis as their parental CHO host cell line. Global protein translation does not correlate with intracellular product content of three model proteins, but the host cell line with high transient productivity has a higher OPP signal. This indicates that production cell lines with increased overall protein synthesis capacity can be identified by our method at the single-cell level. In conclusion, OPP-labeling allows rapid and reproducible assessment of global protein synthesis in single CHO cells, and can be multiplexed with DNA staining or any type of immunolabeling of specific proteins or markers for organelles.

Computational Approaches on Stoichiometric and Kinetic Modeling for Efficient Strain Design

Engineering biological systems that are capable of overproducing products of interest is the ultimate goal of any biotechnology application. To this end, stoichiometric (or steady state) and kinetic models are increasingly becoming available for a variety of organisms including prokaryotes, eukaryotes, and microbial communities. This ever-accelerating pace of such model reconstructions has also spurred the development of optimization-based strain design techniques. This chapter highlights a number of such frameworks developed in recent years in order to generate testable hypotheses (in terms of genetic interventions), thus addressing the challenges in metabolic engineering. In particular, three major methods are covered in detail including two methods for designing strains (i.e., one stoichiometric model-based and the other by integrating kinetic information into a stoichiometric model) and one method for analyzing microbial communities.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

Total enzyme activity constraint and homeostatic constraint impact on the optimization potential of a kinetic model

The application of biologically and biochemically relevant constraints during the optimization of kinetic models reduces the impact of suggested changes in processes not included in the scope of the model. This increases the probability that the design suggested by model optimization can be carried out by an organism after implementation of design in vivo. A case study was carried out to determine the impact of total enzyme activity and homeostatic constraints on the objective function values and the following ranking of adjustable parameter combinations. The application of constraints on the model of sugar cane metabolism revealed that a homeostatic constraint caused heavier limitations of the objective function than a total enzyme activity constraint. Both constraints changed the ranking of adjustable parameter combinations: no "universal" constraint-independent top-ranked combinations were found. Therefore, when searching for the best subset of adjustable parameters, a full scan of their combinations is suggested for a small number of adjustable parameters, and evolutionary search strategies are suggested for a large number. Simultaneous application of both constraints is suggested.

Engineering biological systems using automated biofoundries

Engineered biological systems such as genetic circuits and microbial cell factories have promised to solve many challenges in the modern society. However, the artisanal processes of research and development are slow, expensive, and inconsistent, representing a major obstacle in biotechnology and bioengineering. In recent years, biological foundries or biofoundries have been developed to automate design-build-test engineering cycles in an effort to accelerate these processes. This review summarizes the enabling technologies for such biofoundries as well as their early successes and remaining challenges.

First principle-based models in plant suspension cell cultures: a review

In this work, the development and application of published models for describing the behavior of plant cell cultures is reviewed. The structure of each type of model is analyzed and the new tendencies for the modeling of biotechnological processes that can be applied in plant cell cultures are presented. This review is a tool for clarifying the main features that characterize each type of model in the field of plant cell cultures and can be used as a support on the selection of the more suitable model type, taking into account the purpose of specific research.

Model-guided combinatorial optimization of complex synthetic gene networks

Constructing gene circuits that satisfy quantitative performance criteria has been a long-standing challenge in synthetic biology. Here, we show a strategy for optimizing a complex three-gene circuit, a novel proportional miRNA biosensor, using predictive modeling to initiate a search in the phase space of sensor genetic composition. We generate a library of sensor circuits using diverse genetic building blocks in order to access favorable parameter combinations and uncover specific genetic compositions with greatly improved dynamic range. The combination of high-throughput screening data and the data obtained from detailed mechanistic interrogation of a small number of sensors was used to validate the model. The validated model facilitated further experimentation, including biosensor reprogramming and biosensor integration into larger networks, enabling in principle arbitrary logic with miRNA inputs using normal form circuits. The study reveals how model-guided generation of genetic diversity followed by screening and model validation can be successfully applied to optimize performance of complex gene networks without extensive prior knowledge.

AMIGO2, a toolbox for dynamic modeling, optimization and control in systems biology

Motivation: Many problems of interest in dynamic modeling and control of biological systems can be posed as non-linear optimization problems subject to algebraic and dynamic constraints. In the context of modeling, this is the case of, e.g. parameter estimation, optimal experimental design and dynamic flux balance analysis. In the context of control, model-based metabolic engineering or drug dose optimization problems can be formulated as (multi-objective) optimal control problems. Finding a solution to those problems is a very challenging task which requires advanced numerical methods.

Results: This work presents the AMIGO2 toolbox: the first multiplatform software tool that automatizes the solution of all those problems, offering a suite of state-of-the-art (multi-objective) global optimizers and advanced simulation approaches.

Availability and Implementation: The toolbox and its documentation are available at: sites.google.com/site/amigo2toolbox.

Contact:ebalsa@iim.csic.es

Supplementary information:Supplementary data are available at Bioinformatics online.