MASSpy: Building, simulating, and visualizing dynamic biological models in Python using mass action kinetics

Biological and genetic determinants of glycolysis: Phosphofructokinase isoforms boost energy status of stored red blood cells and transfusion outcomes

Mature red blood cells (RBCs) lack mitochondria and thus exclusively rely on glycolysis to generate adenosine triphosphate (ATP) during aging in vivo or storage in blood banks. Here, we leveraged 13,029 volunteers from the Recipient Epidemiology and Donor Evaluation Study to identify associations between end-of-storage levels of glycolytic metabolites and donor age, sex, and ancestry-specific genetic polymorphisms in regions encoding phosphofructokinase 1, platelet (detected in mature RBCs); hexokinase 1 (HK1); and ADP-ribosyl cyclase 1 and 2 (CD38/BST1). Gene-metabolite associations were validated in fresh and stored RBCs from 525 Diversity Outbred mice and via multi-omics characterization of 1,929 samples from 643 human RBC units during storage. ATP and hypoxanthine (HYPX) levels-and the genetic traits linked to them-were associated with hemolysis in vitro and in vivo, both in healthy autologous transfusion recipients and in 5,816 critically ill patients receiving heterologous transfusions, suggesting their potential as markers to improve transfusion outcomes.

Generative machine learning produces kinetic models that accurately characterize intracellular metabolic states

Generating large omics datasets has become routine for gaining insights into cellular processes, yet deciphering these datasets to determine metabolic states remains challenging. Kinetic models can help integrate omics data by explicitly linking metabolite concentrations, metabolic fluxes and enzyme levels. Nevertheless, determining the kinetic parameters that underlie cellular physiology poses notable obstacles to the widespread use of these mathematical representations of metabolism. Here we present RENAISSANCE, a generative machine learning framework for efficiently parameterizing large-scale kinetic models with dynamic properties matching experimental observations. Through seamless integration of diverse omics data and other relevant information, including extracellular medium composition, physicochemical data and expertise of domain specialists, RENAISSANCE accurately characterizes intracellular metabolic states in Escherichia coli. It also estimates missing kinetic parameters and reconciles them with sparse experimental data, substantially reducing parameter uncertainty and improving accuracy. This framework will be valuable for researchers studying metabolic variations involving changes in metabolite and enzyme levels and enzyme activity in health and biotechnology.

Learning metabolic dynamics from irregular observations by Bidirectional Time-Series State Transfer Network

Modeling microbial metabolic dynamics is important for the rational optimization of both biosynthetic systems and industrial processes to facilitate green and efficient biomanufacturing. Classical approaches utilize explicit equation systems to represent metabolic networks, enabling the quantification of pathway fluxes to identify metabolic bottlenecks. However, these white-box models, despite their diverse applications, have limitations in simulating metabolic dynamics and are intrinsically inaccurate for industrial strains that lack information on network structures and kinetic parameters. On the other hand, black-box models do not rely on prior mechanistic knowledge of strains but are built upon observed time-series trajectories of biosynthetic systems in action. In practice, these observations are typically irregular, with discontinuously observed time points across multiple independent batches, each time point potentially containing missing measurements. Learning from such irregular data remains challenging for existing approaches. To address this issue, we present the Bidirectional Time-Series State Transfer Network (BTSTN) for modeling metabolic dynamics directly from irregular observations. Using evaluation data sets derived from both ideal dynamic systems and a real-world fermentation process, we demonstrate that BTSTN accurately reconstructs dynamic behaviors and predicts future trajectories. This approach exhibits enhanced robustness against missing measurements and noise, as compared to the state-of-the-art methods.IMPORTANCEIndustrial biosynthetic systems often involve strains with unclear genetic backgrounds, posing challenges in modeling their distinct metabolic dynamics. In such scenarios, white-box models, which commonly rely on inferred networks, are thereby of limited applicability and accuracy. In contrast, black-box models, such as statistical models and neural networks, are directly fitted or learned from observed time-series trajectories of biosynthetic systems in action. These methods typically assume regular observations without missing time points or measurements. If the observations are irregular, a pre-processing step becomes necessary to obtain a fully filled data set for subsequent model training, which, at the same time, inevitably introduces errors into the resulting models. BTSTN is a novel approach that natively learns from irregular observations. This distinctive feature makes it a unique addition to the current arsenal of technologies modeling metabolic dynamics.

Biological and Genetic Determinants of Glycolysis: Phosphofructokinase Isoforms Boost Energy Status of Stored Red Blood Cells and Transfusion Outcomes

Mature red blood cells (RBCs) lack mitochondria, and thus exclusively rely on glycolysis to generate adenosine triphosphate (ATP) during aging in vivo or storage in the blood bank. Here we leveraged 13,029 volunteers from the Recipient Epidemiology and Donor Evaluation Study to identify an association between end-of-storage levels of glycolytic metabolites and donor age, sex, and ancestry-specific genetic polymorphisms in regions encoding phosphofructokinase 1, platelet (detected in mature RBCs), hexokinase 1, ADP-ribosyl cyclase 1 and 2 (CD38/BST1). Gene-metabolite associations were validated in fresh and stored RBCs from 525 Diversity Outbred mice, and via multi-omics characterization of 1,929 samples from 643 human RBC units during storage. ATP and hypoxanthine levels - and the genetic traits linked to them - were associated with hemolysis in vitro and in vivo, both in healthy autologous transfusion recipients and in 5,816 critically ill patients receiving heterologous transfusions, suggesting their potential as markers to improve transfusion outcomes.

eTOC and Highlights

Highlights

Blood donor age and sex affect glycolysis in stored RBCs from 13,029 volunteers;Ancestry, genetic polymorphisms in PFKP, HK1, CD38/BST1 influence RBC glycolysis;Modeled PFKP effects relate to preventing loss of the total AXP pool in stored RBCs;ATP and hypoxanthine are biomarkers of hemolysis in vitro and in vivo.

Bottom-up parameterization of enzyme rate constants: Reconciling inconsistent data

Kinetic models of metabolism are promising platforms for studying complex metabolic systems and designing production strains. Given the availability of enzyme kinetic data from historical experiments and machine learning estimation tools, a straightforward modeling approach is to assemble kinetic data enzyme by enzyme until a desired scale is reached. However, this type of 'bottom up' parameterization of kinetic models has been difficult due to a number of issues including gaps in kinetic parameters, the complexity of enzyme mechanisms, inconsistencies between parameters obtained from different sources, and in vitro-in vivo differences. Here, we present a computational workflow for the robust estimation of kinetic parameters for detailed mass action enzyme models while taking into account parameter uncertainty. The resulting software package, termed MASSef (the Mass Action Stoichiometry Simulation Enzyme Fitting package), can handle standard 'macroscopic' kinetic parameters, including Km, kcat, Ki, Keq, and nh, as well as diverse reaction mechanisms defined in terms of mass action reactions and 'microscopic' rate constants. We provide three enzyme case studies demonstrating that this approach can identify and reconcile inconsistent data either within in vitro experiments or between in vitro and in vivo enzyme function. We further demonstrate how parameterized enzyme modules can be used to assemble pathway-scale kinetic models consistent with in vivo behavior. This work builds on the legacy of knowledge on kinetic behavior of enzymes by enabling robust parameterization of enzyme kinetic models at scale utilizing the abundance of historical literature data and machine learning parameter estimates.

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

Rational strain design with minimal phenotype perturbation

Devising genetic interventions for desired cellular phenotypes remains challenging regarding time and resources. Kinetic models can accelerate this task by simulating metabolic responses to genetic perturbations. However, exhaustive design evaluations with kinetic models are computationally impractical, especially when targeting multiple enzymes. Here, we introduce a framework for efficiently scouting the design space while respecting cellular physiological requirements. The framework employs mixed-integer linear programming and nonlinear simulations with large-scale nonlinear kinetic models to devise genetic interventions while accounting for the network effects of these perturbations. Importantly, it ensures the engineered strain's robustness by maintaining its phenotype close to that of the reference strain. The framework, applied to improve the anthranilate production in E. coli, devises designs for experimental implementation, including eight previously experimentally validated targets. We expect this framework to play a crucial role in future design-build-test-learn cycles, significantly expediting the strain design compared to exhaustive design enumeration.

neo4jsbml: import systems biology markup language data into the graph database Neo4j

Systems Biology Markup Language (SBML) has emerged as a standard for representing biological models, facilitating model sharing and interoperability. It stores many types of data and complex relationships, complicating data management and analysis. Traditional database management systems struggle to effectively capture these complex networks of interactions within biological systems. Graph-oriented databases perform well in managing interactions between different entities. We present neo4jsbml, a new solution that bridges the gap between the Systems Biology Markup Language data and the Neo4j database, for storing, querying and analyzing data. The Systems Biology Markup Language organizes biological entities in a hierarchical structure, reflecting their interdependencies. The inherent graphical structure represents these hierarchical relationships, offering a natural and efficient means of navigating and exploring the model's components. Neo4j is an excellent solution for handling this type of data. By representing entities as nodes and their relationships as edges, Cypher, Neo4j's query language, efficiently traverses this type of graph representing complex biological networks. We have developed neo4jsbml, a Python library for importing Systems Biology Markup Language data into a Neo4j database using a user-defined schema. By leveraging Neo4j's graphical database technology, exploration of complex biological networks becomes intuitive and information retrieval efficient. Neo4jsbml is a tool designed to import Systems Biology Markup Language data into a Neo4j database. Only the desired data is loaded into the Neo4j database. neo4jsbml is user-friendly and can become a useful new companion for visualizing and analyzing metabolic models through the Neo4j graphical database. neo4jsbml is open source software and available at https://github.com/brsynth/neo4jsbml.

VSCode-Antimony: a source editor for building, analyzing, and translating antimony models

MOTIVATION

Developing biochemical models in systems biology is a complex, knowledge-intensive activity. Some modelers (especially novices) benefit from model development tools with a graphical user interface. However, as with the development of complex software, text-based representations of models provide many benefits for advanced model development. At present, the tools for text-based model development are limited, typically just a textual editor that provides features such as copy, paste, find, and replace. Since these tools are not "model aware," they do not provide features for: (i) model building such as autocompletion of species names; (ii) model analysis such as hover messages that provide information about chemical species; and (iii) model translation to convert between model representations. We refer to these as BAT features.

RESULTS

We present VSCode-Antimony, a tool for building, analyzing, and translating models written in the Antimony modeling language, a human readable representation of Systems Biology Markup Language (SBML) models. VSCode-Antimony is a source editor, a tool with language-aware features. For example, there is autocompletion of variable names to assist with model building, hover messages that aid in model analysis, and translation between XML and Antimony representations of SBML models. These features result from making VSCode-Antimony model-aware by incorporating several sophisticated capabilities: analysis of the Antimony grammar (e.g. to identify model symbols and their types); a query system for accessing knowledge sources for chemical species and reactions; and automatic conversion between different model representations (e.g. between Antimony and SBML).

AVAILABILITY AND IMPLEMENTATION

VSCode-Antimony is available as an open source extension in the VSCode Marketplace https://marketplace.visualstudio.com/items?itemName=stevem.vscode-antimony. Source code can be found at https://github.com/sys-bio/vscode-antimony.

Modeling Red Blood Cell Metabolism in the Omics Era

Red blood cells (RBCs) are abundant (more than 80% of the total cells in the human body), yet relatively simple, as they lack nuclei and organelles, including mitochondria. Since the earliest days of biochemistry, the accessibility of blood and RBCs made them an ideal matrix for the characterization of metabolism. Because of this, investigations into RBC metabolism are of extreme relevance for research and diagnostic purposes in scientific and clinical endeavors. The relative simplicity of RBCs has made them an eligible model for the development of reconstruction maps of eukaryotic cell metabolism since the early days of systems biology. Computational models hold the potential to deepen knowledge of RBC metabolism, but also and foremost to predict in silico RBC metabolic behaviors in response to environmental stimuli. Here, we review now classic concepts on RBC metabolism, prior work in systems biology of unicellular organisms, and how this work paved the way for the development of reconstruction models of RBC metabolism. Translationally, we discuss how the fields of metabolomics and systems biology have generated evidence to advance our understanding of the RBC storage lesion, a process of decline in storage quality that impacts over a hundred million blood units transfused every year.

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications.

Optimal enzyme utilization suggests that concentrations and thermodynamics determine binding mechanisms and enzyme saturations

Deciphering the metabolic functions of organisms requires understanding the dynamic responses of living cells upon genetic and environmental perturbations, which in turn can be inferred from enzymatic activity. In this work, we investigate the optimal modes of operation for enzymes in terms of the evolutionary pressure driving them toward increased catalytic efficiency. We develop a framework using a mixed-integer formulation to assess the distribution of thermodynamic forces and enzyme states, providing detailed insights into the enzymatic mode of operation. We use this framework to explore Michaelis-Menten and random-ordered multi-substrate mechanisms. We show that optimal enzyme utilization is achieved by unique or alternative operating modes dependent on reactant concentrations. We find that in a bimolecular enzyme reaction, the random mechanism is optimal over any other ordered mechanism under physiological conditions. Our framework can investigate the optimal catalytic properties of complex enzyme mechanisms. It can further guide the directed evolution of enzymes and fill in the knowledge gaps in enzyme kinetics.

libRoadRunner 2.0: a high performance SBML simulation and analysis library

MOTIVATION

This article presents libRoadRunner 2.0, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using the systems biology markup language (SBML).

RESULTS

libRoadRunner is a self-contained library, able to run either as a component inside other tools via its C++, C and Python APIs, or interactively through its Python or Julia interface. libRoadRunner uses a custom just-in-time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a large variety of processors, making it fast enough to simulate extremely large models or repeated runs in reasonable timeframes. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) as well as several SBML extensions such as hierarchical composition and probability distributions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, sensitivity, stability and structural analyses.

AVAILABILITY AND IMPLEMENTATION

libRoadRunner binary distributions for Windows, Mac OS and Linux, Julia and Python bindings, source code and documentation are all available at https://github.com/sys-bio/roadrunner, and Python bindings are also available via pip. The source code can be compiled for the supported systems as well as in principle any system supported by LLVM-13, such as ARM-based computers like the Raspberry Pi. The library is licensed under the Apache License Version 2.0.

Digital models in biotechnology: Towards multi-scale integration and implementation

Industrial biotechnology encompasses a large area of multi-scale and multi-disciplinary research activities. With the recent megatrend of digitalization sweeping across all industries, there is an increased focus in the biotechnology industry on developing, integrating and applying digital models to improve all aspects of industrial biotechnology. Given the rapid development of this field, we systematically classify the state-of-art modelling concepts applied at different scales in industrial biotechnology and critically discuss their current usage, advantages and limitations. Further, we critically analyzed current strategies to couple cell models with computational fluid dynamics to study the performance of industrial microorganisms in large-scale bioprocesses, which is of crucial importance for the bio-based production industries. One of the most challenging aspects in this context is gathering intracellular data under industrially relevant conditions. Towards comprehensive models, we discuss how different scale-down concepts combined with appropriate analytical tools can capture intracellular states of single cells. We finally illustrated how the efforts could be used to develop digitals models suitable for both cell factory design and process optimization at industrial scales in the future.

Construction of Multiscale Genome-Scale Metabolic Models: Frameworks and Challenges

Genome-scale metabolic models (GEMs) are effective tools for metabolic engineering and have been widely used to guide cell metabolic regulation. However, the single gene–protein-reaction data type in GEMs limits the understanding of biological complexity. As a result, multiscale models that add constraints or integrate omics data based on GEMs have been developed to more accurately predict phenotype from genotype. This review summarized the recent advances in the development of multiscale GEMs, including multiconstraint, multiomic, and whole-cell models, and outlined machine learning applications in GEM construction. This review focused on the frameworks, toolkits, and algorithms for constructing multiscale GEMs. The challenges and perspectives of multiscale GEM development are also discussed.

Programmatic modeling for biological systems

Computational modeling has become an established technique to encode mathematical representations of cellular processes and gain mechanistic insights that drive testable predictions. These models are often constructed using graphical user interfaces or domain-specific languages, with community standards used for interchange. Models undergo steady state or dynamic analysis, which can include simulation and calibration within a single application, or transfer across various tools. Here, we describe a novel programmatic modeling paradigm, whereby modeling is augmented with software engineering best practices. We focus on Python - a popular programming language with a large scientific package ecosystem. Models can be encoded as programs, adding benefits such as modularity, testing, and automated documentation generators, while still being extensible and exportable to standardized formats for use with external tools if desired. Programmatic modeling is a key technology to enable collaborative model development and enhance dissemination, transparency, and reproducibility.

Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Enhancing in silico strain design predictions through next generation metabolic modeling approaches

The reconstruction and analysis of metabolic models has garnered increasing attention due to the multitude of applications in which these have proven to be practical. The growing number of generated metabolic models has been accompanied by an exponentially expanding arsenal of tools used to analyze them. In this work, we discussed the biological relevance of a number of promising modeling frameworks, focusing on the questions and hypotheses each method is equipped to address. To this end, we critically analyzed the steady-state modeling approaches focusing on resource allocation and incorporation of thermodynamic considerations which produce promising results and aid in the generation and experimental validation of numerous predictions. For smaller networks involving more complex regulation, we addressed kinetic modeling techniques which show encouraging results in addressing questions outside the scope of steady-state modeling. Finally, we discussed the potential application of the discussed frameworks within the field of strain design. Adoption of such methodologies is believed to significantly enhance the accuracy of in silico predictions and hence decrease the number of design-build-test cycles required.