Computational modeling of biochemical networks using COPASI

Dynamics of two feed forward genetic motifs in the presence of molecular noise

Understanding the function of common motifs in gene regulatory networks is an important goal of systems biology. Feed forward loops (FFLs) are an example of such a motif. In FFLs, a gene (X) regulates another gene (Z) both directly and via an intermediary gene (Y). Previous theoretical studies have suggested several possible functions for FFLs, based on their transient responses to changes in input signals (using deterministic models) and their fluctuations around steady state (using stochastic models). In this paper we study stochastic models of the two most common FFLs, "coherent type 1" and "incoherent type 1". We incorporate molecular noise by treating DNA binding, transcription, translation, and decay as stochastic processes. By comparing the dynamics of these loops with models of alternative networks (in which X does not regulate Y), we explore how FFLs act to process information in the presence of noise. This work highlights the importance of incorporating realistic molecular noise in studying both the transient and steady-state behavior of gene regulatory networks.

The Biology and Biochemistry of Kynurenic Acid, a Potential Nutraceutical with Multiple Biological Effects

Kynurenic acid (KYNA) is an antioxidant degradation product of tryptophan that has been shown to have a variety of cytoprotective, neuroprotective and neuronal signalling properties. However, mammalian transporters and receptors display micromolar binding constants; these are consistent with its typically micromolar tissue concentrations but far above its serum/plasma concentration (normally tens of nanomolar), suggesting large gaps in our knowledge of its transport and mechanisms of action, in that the main influx transporters characterized to date are equilibrative, not concentrative. In addition, it is a substrate of a known anion efflux pump (ABCC4), whose in vivo activity is largely unknown. Exogeneous addition of L-tryptophan or L-kynurenine leads to the production of KYNA but also to that of many other co-metabolites (including some such as 3-hydroxy-L-kynurenine and quinolinic acid that may be toxic). With the exception of chestnut honey, KYNA exists at relatively low levels in natural foodstuffs. However, its bioavailability is reasonable, and as the terminal element of an irreversible reaction of most tryptophan degradation pathways, it might be added exogenously without disturbing upstream metabolism significantly. Many examples, which we review, show that it has valuable bioactivity. Given the above, we review its potential utility as a nutraceutical, finding it significantly worthy of further study and development.

The dynamic hypoosmotic response of Vibrio cholerae relies on the mechanosensitive channel MscS

Vibrio cholerae adapts to osmotic down-shifts by releasing metabolites through two mechanosensitive (MS) channels, low-threshold MscS and high-threshold MscL. To investigate each channel's contribution to the osmotic response, we generated ΔmscS, ΔmscL, and double ΔmscL ΔmscS mutants in V. cholerae O395. We characterized their tension-dependent activation in patch-clamp, and the millisecond-scale osmolyte release kinetics using a stopped-flow light scattering technique. We additionally generated numerical models describing osmolyte and water fluxes. We illustrate the sequence of events and define the parameters that characterize discrete phases of the osmotic response. Survival is correlated to the extent of cell swelling, the rate of osmolyte release, and the completeness of post-shock membrane resealing. Not only do the two channels interact functionally, but there is also an up-regulation of MscS in the ΔmscL strain, suggesting transcriptional crosstalk. The data reveal the role of MscS in the termination of the osmotic permeability response in V. cholerae.

Microbiome modeling: a beginner's guide

Microbiomes, comprised of diverse microbial species and viruses, play pivotal roles in human health, environmental processes, and biotechnological applications and interact with each other, their environment, and hosts via ecological interactions. Our understanding of microbiomes is still limited and hampered by their complexity. A concept improving this understanding is systems biology, which focuses on the holistic description of biological systems utilizing experimental and computational methods. An important set of such experimental methods are metaomics methods which analyze microbiomes and output lists of molecular features. These lists of data are integrated, interpreted, and compiled into computational microbiome models, to predict, optimize, and control microbiome behavior. There exists a gap in understanding between microbiologists and modelers/bioinformaticians, stemming from a lack of interdisciplinary knowledge. This knowledge gap hinders the establishment of computational models in microbiome analysis. This review aims to bridge this gap and is tailored for microbiologists, researchers new to microbiome modeling, and bioinformaticians. To achieve this goal, it provides an interdisciplinary overview of microbiome modeling, starting with fundamental knowledge of microbiomes, metaomics methods, common modeling formalisms, and how models facilitate microbiome control. It concludes with guidelines and repositories for modeling. Each section provides entry-level information, example applications, and important references, serving as a valuable resource for comprehending and navigating the complex landscape of microbiome research and modeling.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

BACKGROUND

Gene regulatory network (GRN) models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such gene regulatory ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the underlying GRN governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impede either scalability, explainability, or both.

RESULTS

We developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that overcomes limitations of other methods by flexibly incorporating prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of GRN ODEs. We tested the accuracy of PHOENIX in a series of in silico experiments, benchmarking it against several currently used tools. We demonstrated PHOENIX's flexibility by modeling regulation of oscillating expression profiles obtained from synchronized yeast cells. We also assessed the scalability of PHOENIX by modeling genome-scale GRNs for breast cancer samples ordered in pseudotime and for B cells treated with Rituximab.

CONCLUSIONS

PHOENIX uses a combination of user-defined prior knowledge and functional forms from systems biology to encode biological "first principles" as soft constraints on the GRN allowing us to predict subsequent gene expression patterns in a biologically explainable manner.

ATP-free in vitro biotransformation of starch-derived maltodextrin into poly-3-hydroxybutyrate via acetyl-CoA

In vitro biotransformation (ivBT) facilitated by in vitro synthetic enzymatic biosystems (ivSEBs) has emerged as a highly promising biosynthetic platform. Several ivSEBs have been constructed to produce poly-3-hydroxybutyrate (PHB) via acetyl-coenzyme A (acetyl-CoA). However, some systems are hindered by their reliance on costly ATP, limiting their practicality. This study presents the design of an ATP-free ivSEB for one-pot PHB biosynthesis via acetyl-CoA utilizing starch-derived maltodextrin as the sole substrate. Stoichiometric analysis indicates this ivSEB can self-maintain NADP+/NADPH balance and achieve a theoretical molar yield of 133.3%. Leveraging simple one-pot reactions, our ivSEBs achieved a near-theoretical molar yield of 125.5%, the highest PHB titer (208.3 mM, approximately 17.9 g/L) and the fastest PHB production rate (9.4 mM/h, approximately 0.8 g/L/h) among all the reported ivSEBs to date, and demonstrated easy scalability. This study unveils the promising potential of ivBT for the industrial-scale production of PHB and other acetyl-CoA-derived chemicals from starch.

Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes

BACKGROUND

Factor X activation by the phospholipid-bound intrinsic tenase complex is a critical membrane-dependent reaction of blood coagulation. Its regulation mechanisms are unclear, and a number of questions regarding diffusional limitation, pathways of assembly and substrate delivery remain open.

METHODS

We develop and analyze here a detailed mechanism-driven computer model of intrinsic tenase on phospholipid surfaces. Three-dimensional reaction-diffusion-advection and stochastic simulations were used where appropriate.

RESULTS

Dynamics of the system was predominantly non-stationary under physiological conditions. In order to describe experimental data, we had to assume both membrane-dependent and solution-dependent delivery of the substrate. The former pathway dominated at low cofactor concentration, while the latter became important at low phospholipid concentration. Factor VIIIa-factor X complex formation was the major pathway of the complex assembly, and the model predicted high affinity for their lipid-dependent interaction. Although the model predicted formation of the diffusion-limited layer of substrate for some conditions, the effects of this limitation on the fXa production were small. Flow accelerated fXa production in a flow reactor model by bringing in fIXa and fVIIIa rather than fX.

CONCLUSIONS

This analysis suggests a concept of intrinsic tenase that is non-stationary, employs several pathways of substrate delivery depending on the conditions, and is not particularly limited by diffusion of the substrate.

Data integration strategies for whole-cell modeling

Data makes the world go round-and high quality data is a prerequisite for precise models, especially for whole-cell models (WCM). Data for WCM must be reusable, contain information about the exact experimental background, and should-in its entirety-cover all relevant processes in the cell. Here, we review basic requirements to data for WCM and strategies how to combine them. As a species-specific resource, we introduce the Yeast Cell Model Data Base (YCMDB) to illustrate requirements and solutions. We discuss recent standards for data as well as for computational models including the modeling process as data to be reported. We outline strategies for constructions of WCM despite their inherent complexity.

Identifying Key In Silico Knockout for Enhancement of Limonene Yield Through Dynamic Metabolic Modelling

Living cells display dynamic and complex behaviors. To understand their response and to infer novel insights not possible with traditional reductionist approaches, over the last few decades various computational modelling methodologies have been developed. In this chapter, we focus on modelling the dynamic metabolic response, using linear and nonlinear ordinary differential equations, of an engineered Escherichia coli MG1655 strain with plasmid pJBEI-6409 that produces limonene. We show the systems biology steps involved from collecting time-series data of living cells, to dynamic model creation and fitting the model with experimental responses using COPASI software.

A Fermentation State Marker Rule Design Task in Metabolic Engineering

There are several ways in which mathematical modeling is used in fermentation control, but mechanistic mathematical genome-scale models of metabolism within the cell have not been applied or implemented so far. As part of the metabolic engineering task setting, we propose that metabolite fluxes and/or biomass growth rate be used to search for a fermentation steady state marker rule. During fermentation, the bioreactor control system can automatically detect the desired steady state using a logical marker rule. The marker rule identification can be also integrated with the production growth coupling approach, as presented in this study. A design of strain with marker rule is demonstrated on genome scale metabolic model iML1515 of Escherichia coli MG1655 proposing two gene deletions enabling a measurable marker rule for succinate production using glucose as a substrate. The marker rule example at glucose consumption 10.0 is: IF (specific growth rate μ is above 0.060 h-1, AND CO2 production under 1.0, AND ethanol production above 5.5), THEN succinate production is within the range 8.2-10, where all metabolic fluxes units are mmol ∗ gDW-1 ∗ h-1. An objective function for application in metabolic engineering, including productivity features and rule detecting sensor set characterizing parameters, is proposed. Two-phase approach to implementing marker rules in the cultivation control system is presented to avoid the need for a modeler during production.

The dynamic hypoosmotic response of Vibrio cholerae relies on the mechanosensitive channel MscS

Like other intestinal bacteria, the facultative pathogen Vibrio cholerae adapts to a wide range of osmotic environments. Under drastic osmotic down-shifts, Vibrio avoids mechanical rupture by rapidly releasing excessive metabolites through mechanosensitive (MS) channels that belong to two major types, low-threshold MscS and high-threshold MscL. To investigate each channel individual contribution to V. cholerae osmotic permeability response, we generated individual ΔmscS, ∆mscL, and double ΔmscL ΔmscS mutants in V. cholerae O395 and characterized their tension-dependent activation in patch-clamp experiments, as well as their millisecond-scale osmolyte release kinetics using a stopped-flow light scattering technique. We additionally generated numerical models reflecting the kinetic competition of osmolyte release with water influx. Both mutants lacking MscS exhibited delayed osmolyte release kinetics and decreased osmotic survival rates compared to WT. The ΔmscL mutant showed comparable release kinetics to WT, but a higher osmotic survival, while ΔmscS had low survival, comparable to the double ΔmscL ΔmscS mutant. By analyzing release kinetics following rapid medium dilution, we illustrate the sequence of events and define the set of parameters that characterize discrete phases of the osmotic response. Osmotic survival rates are directly correlated to the extent and duration of cell swelling, the rate of osmolyte release and the onset time, and the completeness of the post-shock membrane resealing. Not only do the two channels interact functionally during the resealing phase, but there is also a compensatory up-regulation of MscS in the ΔmscL strain suggesting some transcriptional crosstalk. The data reveal the advantage of the low-threshold MscS channel in curbing tension surges, without which MscL becomes toxic, and the role of MscS in the proper termination of the osmotic permeability response in Vibrio.

Automatic Generation of SBML Kinetic Models from Natural Language Texts Using GPT

Kinetic modeling is an essential tool in systems biology research, enabling the quantitative analysis of biological systems and predicting their behavior. However, the development of kinetic models is a complex and time-consuming process. In this article, we propose a novel approach called KinModGPT, which generates kinetic models directly from natural language text. KinModGPT employs GPT as a natural language interpreter and Tellurium as an SBML generator. We demonstrate the effectiveness of KinModGPT in creating SBML kinetic models from complex natural language descriptions of biochemical reactions. KinModGPT successfully generates valid SBML models from a range of natural language model descriptions of metabolic pathways, protein-protein interaction networks, and heat shock response. This article demonstrates the potential of KinModGPT in kinetic modeling automation.

Parameters, architecture and emergent properties of the Pseudomonas aeruginosa LasI/LasR quorum-sensing circuit

Quorum sensing is a widespread process in bacteria that controls collective behaviours in response to cell density. Populations of cells coordinate gene expression through the perception of self-produced chemical signals. Although this process is well-characterized genetically and biochemically, quantitative information about network properties, including induction dynamics and steady-state behaviour, is scarce. Here we integrate experiments with mathematical modelling to quantitatively analyse the LasI/LasR quorum sensing pathway in the opportunistic pathogen Pseudomonas aeruginosa. We determine key kinetic parameters of the pathway and, using the parametrized model, show that quorum sensing behaves as a bistable hysteretic switch, with stable on and off states. We investigate the significance of feedback architecture and find that positive feedback on signal production is critical for induction dynamics and bistability, whereas positive feedback on receptor expression and negative feedback on signal production play a minor role. Taken together, our data-based modelling approach reveals fundamental and emergent properties of a bacterial quorum sensing circuit, and provides evidence that native quorum sensing can indeed function as the gene expression switch it is commonly perceived to be.

The Reaction Mechanism of the Cu(I) Catalyzed Alkylation of Heterosubstituted Alkynes

Alkynes may be regioselectively alkylated to alkenes by organocopper reagents in a reaction known as “carbocupration”, where an alkylCu(I) binds to the alkyne and transfers its organic moiety to one of the alkyne carbon atoms. Alkynes hetero-substituted with third-row elements yield alkenes with a regiochemistry opposite to that obtained when using alkynes hetero-substituted with second-row elements. Early computational investigations of his reaction mechanism have identified the importance of the organocopper counter-cation (Li+) to the achievement of good reaction rates, but in the subsequent two decades no further progress has been reported regarding the exploration of the mechanism or the explanation of the experimental regiochemistry. In this work, density-functional theory is used to investigate the mechanism used and to describe a model that correctly explains both the reaction rates at sub-zero temperatures and the regiochemistry profiles obtained with each of the heteroalkynes. The rate-determining step is shown to vary depending on the heterosubstituent, and the alkyl transfer is consistently shown to occur, somewhat counter-intuitively, to the alkyne carbon that is complexed by Cu rather than to the “free” alkyne carbon atom, which instead interacts with the counter-cation that stabilizes the developing electronic charge distribution.

Scott W, Sheriff RSM, Suarez Diez M, Van Steen K, Westerhoff HV, Wittig U, Wolstencroft K, Zupanic A, Evelo CT, Hancock JM. Systems Biology in ELIXIR: modelling in the spotlight

In this white paper, we describe the founding of a new ELIXIR Community - the Systems Biology Community - and its proposed future contributions to both ELIXIR and the broader community of systems biologists in Europe and worldwide. The Community believes that the infrastructure aspects of systems biology - databases, (modelling) tools and standards development, as well as training and access to cloud infrastructure - are not only appropriate components of the ELIXIR infrastructure, but will prove key components of ELIXIR's future support of advanced biological applications and personalised medicine. By way of a series of meetings, the Community identified seven key areas for its future activities, reflecting both future needs and previous and current activities within ELIXIR Platforms and Communities. These are: overcoming barriers to the wider uptake of systems biology; linking new and existing data to systems biology models; interoperability of systems biology resources; further development and embedding of systems medicine; provisioning of modelling as a service; building and coordinating capacity building and training resources; and supporting industrial embedding of systems biology. A set of objectives for the Community has been identified under four main headline areas: Standardisation and Interoperability, Technology, Capacity Building and Training, and Industrial Embedding. These are grouped into short-term (3-year), mid-term (6-year) and long-term (10-year) objectives.

Scott W, Sheriff RSM, Suarez Diez M, Van Steen K, Westerhoff HV, Wittig U, Wolstencroft K, Zupanic A, Evelo CT, Hancock JM. Systems Biology in ELIXIR: modelling in the spotlight

In this white paper, we describe the founding of a new ELIXIR Community - the Systems Biology Community - and its proposed future contributions to both ELIXIR and the broader community of systems biologists in Europe and worldwide. The Community believes that the infrastructure aspects of systems biology - databases, (modelling) tools and standards development, as well as training and access to cloud infrastructure - are not only appropriate components of the ELIXIR infrastructure, but will prove key components of ELIXIR's future support of advanced biological applications and personalised medicine. By way of a series of meetings, the Community identified seven key areas for its future activities, reflecting both future needs and previous and current activities within ELIXIR Platforms and Communities. These are: overcoming barriers to the wider uptake of systems biology; linking new and existing data to systems biology models; interoperability of systems biology resources; further development and embedding of systems medicine; provisioning of modelling as a service; building and coordinating capacity building and training resources; and supporting industrial embedding of systems biology. A set of objectives for the Community has been identified under four main headline areas: Standardisation and Interoperability, Technology, Capacity Building and Training, and Industrial Embedding. These are grouped into short-term (3-year), mid-term (6-year) and long-term (10-year) objectives.

Addressing barriers in comprehensiveness, accessibility, reusability, interoperability and reproducibility of computational models in systems biology

Computational models are often employed in systems biology to study the dynamic behaviours of complex systems. With the rise in the number of computational models, finding ways to improve the reusability of these models and their ability to reproduce virtual experiments becomes critical. Correct and effective model annotation in community-supported and standardised formats is necessary for this improvement. Here, we present recent efforts toward a common framework for annotated, accessible, reproducible and interoperable computational models in biology, and discuss key challenges of the field.

The whole-cell kinetic metabolic model of the pH regulation mechanisms in human erythrocytes

Mathematical modeling in recent years helped to obtain answers to questions that were difficult or even impossible to answer experimentally, to predict several unexpected connections in cell metabolism and to understand and importance of certain biochemical reactions. Due to the complexity and variety of processes underlying the mechanisms of intracellular pH (pHi) regulation, mathematical modeling and metabolome analysis are powerful tools for their analysis. In this regard, a mathematical metabolic model for human erythrocytes was created, which combines cellular metabolism with acid-base processes and gas exchange. The model consists of the main metabolic pathways, such as glycolysis, the pentose phosphate pathway, some membrane transport systems, and interactions between hemoglobin and metabolites. The Jacobs-Stewart cycle, which is fundamental in gas exchange and pH regulation, was included to these pathways. The model was created in the COPASI environment, consisted of 85 reactions, the rate of which is based on accurate kinetic equations. The time dependences of reaction flows and metabolite concentrations, as an outcome of calculations, allowed us to reproduce the behaviour of the metabolic system after its disturbance in vitro and to establish the recovery mechanisms or approximation to stationary states. The COPASI simulation environment provides model flexibility by reproducing any experimental design by optimizing direct quantitative comparisons between measured and predicted results. Thus, the procedure of parameters optimization (Parameter Estimation) followed by the solution of the model’s differential equations (Time Course procedure) was used to predict the behaviour of all measured and unmeasured variables over time. The initial intracellular concentrations of CO2, HCO3– in human erythrocytes used for incubation in a phosphate buffer medium were calculated. Changes in CO2, HCO3– content over time were shown. It was established that the regulation of pH in erythrocytes placed in a buffer medium takes place with the participation of two types of processes – fast (takes place in 1.3 s) and slow. It is shown that fast processes are aimed at restoring the intracellular balance between CO2 and HCO3–, slow processes are aimed at establishing the balance of H+ between the cell and the extracellular environment. The role of carbonic anhydrase (CA) and hemoglobin in the processes of pH stabilization is shown and analyzed. The physiological role of the metabolon between band 3 protein (AE1), CA, aquaporin and hemoglobin in maintaining pH homeostasis in the conditions of in vitro experiments are discussed.

From Seeing to Simulating: A Survey of Imaging Techniques and Spatially-Resolved Data for Developing Multiscale Computational Models of Liver Regeneration

Liver regeneration, which leads to the re-establishment of organ mass, follows a specifically organized set of biological processes acting on various time and length scales. Computational models of liver regeneration largely focused on incorporating molecular and signaling detail have been developed by multiple research groups in the recent years. These modeling efforts have supported a synthesis of disparate experimental results at the molecular scale. Incorporation of tissue and organ scale data using noninvasive imaging methods can extend these computational models towards a comprehensive accounting of multiscale dynamics of liver regeneration. For instance, microscopy-based imaging methods provide detailed histological information at the tissue and cellular scales. Noninvasive imaging methods such as ultrasound, computed tomography and magnetic resonance imaging provide morphological and physiological features including volumetric measures over time. In this review, we discuss multiple imaging modalities capable of informing computational models of liver regeneration at the organ-, tissue- and cellular level. Additionally, we discuss available software and algorithms, which aid in the analysis and integration of imaging data into computational models. Such models can be generated or tuned for an individual patient with liver disease. Progress towards integrated multiscale models of liver regeneration can aid in prognostic tool development for treating liver disease.

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.

Kinetic and Stoichiometric Modeling-Based Analysis of Docosahexaenoic Acid (DHA) Production Potential by C. cohnii from Glycerol, Glucose and Ethanol

Docosahexaenoic acid (DHA) is one of the most important long-chain polyunsaturated fatty acids (LC-PUFAs), with numerous health benefits. Crypthecodinium cohnii, a marine heterotrophic dinoflagellate, is successfully used for the industrial production of DHA because it can accumulate DHA at high concentrations within the cells. Glycerol is an interesting renewable substrate for DHA production since it is a by-product of biodiesel production and other industries, and is globally generated in large quantities. The DHA production potential from glycerol, ethanol and glucose is compared by combining fermentation experiments with the pathway-scale kinetic modeling and constraint-based stoichiometric modeling of C. cohnii metabolism. Glycerol has the slowest biomass growth rate among the tested substrates. This is partially compensated by the highest PUFAs fraction, where DHA is dominant. Mathematical modeling reveals that glycerol has the best experimentally observed carbon transformation rate into biomass, reaching the closest values to the theoretical upper limit. In addition to our observations, the published experimental evidence indicates that crude glycerol is readily consumed by C. cohnii, making glycerol an attractive substrate for DHA production.

Mini-batch optimization enables training of ODE models on large-scale datasets

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

Relationship Between Dimensionality and Convergence of Optimization Algorithms: A Comparison Between Data-Driven Normalization and Scaling Factor-Based Methods Using PEPSSBI

Ordinary differential equation models are used to represent intracellular signaling pathways in silico, aiding and guiding biological experiments to elucidate intracellular regulation. To construct such quantitative and predictive models of intracellular interactions, unknown parameters need to be estimated. Most of biological data are expressed in relative or arbitrary units, raising the question of how to compare model simulations with data. It has recently been shown that for models with large number of unknown parameters, fitting algorithms using a data-driven normalization of the simulations (DNS) performs best in terms of the convergence time and parameter identifiability. DNS approach compares model simulations and corresponding data both normalized by the same normalization procedure, without requiring additional parameters to be estimated, as necessary for widely used scaling factor-based methods. However, currently there is no parameter estimation software that directly supports DNS. In this chapter, we show how to apply DNS to dynamic models of systems and synthetic biology using PEPSSBI (Parameter Estimation Pipeline for Systems and Synthetic Biology). PEPSSBI is the first software that supports DNS, through algorithmically supported data normalization and objective function construction. PEPSSBI also supports model import using SBML and repeated parameter estimation runs executed in parallel either on a personal computer or a multi-CPU cluster.

IMFLer: A Web Application for Interactive Metabolic Flux Analysis and Visualization

Increasing genome-wide data in biological sciences and medicine has contributed to the development of a variety of visualization tools. Several automatic, semiautomatic, and manual visualization tools have already been developed. Some even have integrated flux balance analysis (FBA), but in most cases, it depends on separately installed third party software that is proprietary and does not allow customization of its functionality and has many restrictions for easy data distribution and analysis. In this study, we present an interactive metabolic flux analyzer and visualizer (IMFLer)-a static single-page web application that enables the reading and management of metabolic model layout maps, as well as immediate visualization of results from both FBA and flux variability analysis (FVA). IMFLer uses the Escher Builder tool to load, show, edit, and save metabolic pathway maps. This makes IMFLer an attractive and easily applicable tool with a user-friendly interface. Moreover, it allows to faster interpret results from FBA and FVA and improves data interoperability by using a standardized file format for the genome-scale metabolic model. IMFLer is a fully open-source tool that enables the rapid visualization and interpretation of the results of FBA and FVA with no time setup and no programming skills required, available at https://lv-csbg.github.io/IMFLer/.

WinBEST-KIT: Biochemical Reaction Simulator for Analyzing Multi-Layered Metabolic Pathways

We previously developed the biochemical reaction simulator WinBEST-KIT. In recent years, research interest has shifted from analysis of individual biochemical reactions to analysis of metabolic pathways as systems. These large-scale and complicated metabolic pathways can be considered as characteristic multi-layered structures, which, for convenience, are separated from whole biological systems according to their specific roles. These pathways include reactants having the same name but with unique stoichiometric coefficients arranged across many different places and connected between arbitrary layers. Accordingly, in this study, we have developed a new version of WinBEST-KIT that allows users (1) to utilize shortcut symbols that can be arranged with multiple reactants having the same name but with unique stoichiometric coefficients, thereby providing a layout that is similar to metabolic pathways depicted in biochemical textbooks; (2) to create layers that divide large-scale and complicated metabolic pathways according to their specific roles; (3) to connect the layers by using shortcut symbols; and (4) to analyze the interactions between these layers. These new and existing features allow users to create and analyze such multi-layered metabolic pathways efficiently. Furthermore, WinBEST-KIT supports SBML, making it possible for users to utilize these new and existing features to create and publish SBML models.

Ten steps to investigate a cellular system with mathematical modeling

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.

Physiologically based metformin pharmacokinetics model of mice and scale-up to humans for the estimation of concentrations in various tissues

Metformin is the primary drug for type 2 diabetes treatment and a promising candidate for other disease treatment. It has significant deviations between individuals in therapy efficiency and pharmacokinetics, leading to the administration of an unnecessary overdose or an insufficient dose. There is a lack of data regarding the concentration-time profiles in various human tissues that limits the understanding of pharmacokinetics and hinders the development of precision therapies for individual patients. The physiologically based pharmacokinetic (PBPK) model developed in this study is based on humans’ known physiological parameters (blood flow, tissue volume, and others). The missing tissue-specific pharmacokinetics parameters are estimated by developing a PBPK model of metformin in mice where the concentration time series in various tissues have been measured. Some parameters are adapted from human intestine cell culture experiments. The resulting PBPK model for metformin in humans includes 21 tissues and body fluids compartments and can simulate metformin concentration in the stomach, small intestine, liver, kidney, heart, skeletal muscle adipose, and brain depending on the body weight, dose, and administration regimen. Simulations for humans with a bodyweight of 70kg have been analyzed for doses in the range of 500-1500mg. Most tissues have a half-life (T_1/2) similar to plasma (3.7h) except for the liver and intestine with shorter T_1/2 and muscle, kidney, and red blood cells that have longer T_1/2. The highest maximal concentrations (C_max) turned out to be in the intestine (absorption process) and kidney (excretion process), followed by the liver. The developed metformin PBPK model for mice does not have a compartment for red blood cells and consists of 20 compartments. The developed human model can be personalized by adapting measurable values (tissue volumes, blood flow) and measuring metformin concentration time-course in blood and urine after a single dose of metformin. The personalized model can be used as a decision support tool for precision therapy development for individuals.

Stochastic models for single-cell data: Current challenges and the way forward

Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

Introduction to In Silico Modeling to Study ROS Dynamics

This book chapter is drafted for biologists with experimental experiences in ROS biology but being newcomers in the field of modeling. We start with a general introduction about computational modeling in biology and an overview of software tools suitable for beginners. This chapter encompasses an introduction to computational models with special focus on simulation of ROS dynamics. A step-by-step tutorial follows providing guidance for all relevant model development processes. This course of action gives a comprehensible way to understand the benefits of computational models and to gain the necessary knowledge to build own small equation-based models. Small models can be created without any special programming expertise or in-depth technical and mathematical knowledge. Afterward in the final section, a short overview of pitfalls, challenges, and limitations is provided, combined with suggestions for further reading to improve and expand modeling skills of biologists.

Response to "Molecular-level understanding of biological energy coupling and transduction: Response to "Chemiosmotic misunderstandings""

The most recent contribution by Sunil Nath in these pages is, mostly, a repetition of his previous claims regarding failures of the chemiosmotic hypotheses, supplemented with some fresh misunderstandings of the points I had sought to clarify in my previous critique⁠. Considerable portions rehash 50-60 years-old controversies, with no apparent understanding that the current chemiosmotic hypothesis, while birthed by Mitchell, differs from Mitchell's details in many respects. As such, Nath has devoted much time dealing with a few errors (or wrong hypotheses) by Mitchell (in a few places I would almost venture to say "typographical mistakes in typesetting") and presents the ensuing conclusions as "refutations" of the chemiosmotic paradigm, completely neglecting that such details (such as the precise H⁺/ATP or H⁺:O ratios) are completely irrelevant to the reality (or not) of an electron-transport chain that uses the free energy liberated by electron-transfer to remove H⁺ from a compartment, to which it returns through and ATP synthase which uses the energy in that spontaneous return to drive ATP synthesis. The thermodynamical mistakes and misunderstandings of the relevant literature present in Nath's new contribution are so numerous, though, that I feel forced to call the attention of the readers of "Biophysical Chemistry" to them.

WinBEST-KIT: Biochemical reaction simulator that can define and customize algebraic equations and events as GUI components

We previously developed Windows-based Biochemical Engineering System analyzing Tool-KIT (WinBEST-KIT), a biochemical reaction simulator for analyzing large-scale and complicated biochemical reaction networks. One particularly notable feature is the ability for users to define original mathematical equations for representing unknown kinetic mechanisms and customize them as GUI components for representing reaction steps. Many simulators support System Biology Markup Language SBML; however, since the definition of the algebraic equations (AssignmentRule) and the events are made through an interface that is distinct from the definition of the reaction steps, there are tough works to define them. Accordingly, we have developed a new version of WinBEST-KIT that allows users to define the algebraic equations and the events through the same interface as those used in the definition of the reaction steps and customize them as GUI components appearing in the symbol selection area. The customized algebraic equations and events can thus be visually arranged at any time and any place. It also allows users to easily understand the roles of the algebraic equations and the events. We have also implemented other useful features, including importing/exporting of SBML format files, exporting to MATLAB, and merging the existing models into the model currently being created. The current version of WinBEST-KIT is freely available at http://winbest-kit.org/.

A multi-inverse approach for a holistic understanding of applied animal science systems

Technological and mathematical advances have provided opportunities to investigate new approaches for the holistic quantification of complex biological systems. One objective of these approaches, including the multi-inverse deterministic approach proposed in this paper, is to deepen the understanding of biological systems through the structural development of a useful, best-fitted inverse mechanistic model. The objective of the present work was to evaluate the capacity of a deterministic approach, that is, the multi-inverse approach (MIA), to yield meaningful quantitative nutritional information. To this end, a case study addressing the effect of diet composition on sheep weight was performed using data from a previous experiment on saccharina (a sugarcane byproduct), and an inverse deterministic model (named Paracoa) was developed. The MIA successfully revealed an increase in the final weight of sheep with an increase in the percentage of corn in the diet. Although the soluble fraction also increased with increasing corn percentage, the effective nonsoluble degradation increased fourfold, indicating that the increased weight gain resulted from the nonsoluble substrate. A profile likelihood analysis showed that the potential best-fitted model had identifiable parameters, and that the parameter relationships were affected by the type of data, number of parameters and model structure. It is necessary to apply the MIA to larger and/or more complex datasets to obtain a clearer understanding of its potential.

Estradiol and progesterone affect enzymes but not glucose consumption in a mink uterine cell line (GMMe)

Cells lining the uterus are responsible for storage and secretion of carbohydrates to support early embryonic development. Histotrophic secretions contain glycogen and glycolytic products such as lactate and pyruvate. Insufficient carbohydrate storage as glycogen has been correlated with infertility in women. While it is clear that changes in estrogen (17-β-estradiol (E2)) and progesterone (P4) in vivo affect the distribution of glucose in the uterine cells and secretions, the biochemical mechanism(s) by which they affect this crucial allocation is not well understood. Furthermore, in cultured uterine cells, neither E2 nor P4 affect glycogen storage without insulin present. We hypothesized that P4 and E2 alone affect the activity of glycolytic enzymes, glucose and glycolytic flux to increase glycogen storage (E2) and catabolism (P4) and increase pyruvate and lactate levels in culture. We measured the rate of glucose uptake and glycolysis in a mink immortalized epithelial cell line (GMMe) after 24-h exposure to 10 μM P4 and 10 nM E2 (pharmacologic levels) at 5 mM glucose and determined the kinetic parameters (Vmax, Km) of all enzymes. While the activities of many glycolytic enzymes in GMMe cells were shown to be decreased by E2 treatment, in contrast, glucose uptake, glycolytic flux and metabolites levels were not affected by the treatments. The cellular rationale for P4- and E2-induced decreases in the activity of enzymes may be to prime the system for other regulators such as insulin. In vivo, E2 and P4 may be necessary but not sufficient signals for uterine cycle carbohydrate allocation.

Human and Mouse TRPA1 Are Heat and Cold Sensors Differentially Tuned by Voltage

Transient receptor potential ankyrin 1 channel (TRPA1) serves as a key sensor for reactive electrophilic compounds across all species. Its sensitivity to temperature, however, differs among species, a variability that has been attributed to an evolutionary divergence. Mouse TRPA1 was implicated in noxious cold detection but was later also identified as one of the prime noxious heat sensors. Moreover, human TRPA1, originally considered to be temperature-insensitive, turned out to act as an intrinsic bidirectional thermosensor that is capable of sensing both cold and heat. Using electrophysiology and modeling, we compare the properties of human and mouse TRPA1, and we demonstrate that both orthologues are activated by heat, and their kinetically distinct components of voltage-dependent gating are differentially modulated by heat and cold. Furthermore, we show that both orthologues can be strongly activated by cold after the concurrent application of voltage and heat. We propose an allosteric mechanism that could account for the variability in TRPA1 temperature responsiveness.

Protons in small spaces: Discrete simulations of vesicle acidification

The lumenal pH of an organelle is one of its defining characteristics and central to its biological function. Experiments have elucidated many of the key pH regulatory elements and how they vary from compartment-to-compartment, and continuum mathematical models have played an important role in understanding how these elements (proton pumps, counter-ion fluxes, membrane potential, buffering capacity, etc.) work together to achieve specific pH setpoints. While continuum models have proven successful in describing ion regulation at the cellular length scale, it is unknown if they are valid at the subcellular level where volumes are small, ion numbers may fluctuate wildly, and biochemical heterogeneity is large. Here, we create a discrete, stochastic (DS) model of vesicular acidification to answer this question. We used this simplified model to analyze pH measurements of isolated vesicles containing single proton pumps and compared these results to solutions from a continuum, ordinary differential equations (ODE)-based model. Both models predict similar parameter estimates for the mean proton pumping rate, membrane permeability, etc., but, as expected, the ODE model fails to report on the fluctuations in the system. The stochastic model predicts that pH fluctuations decrease during acidification, but noise analysis of single-vesicle data confirms our finding that the experimental noise is dominated by the fluorescent dye, and it reveals no insight into the true noise in the proton fluctuations. Finally, we again use the reduced DS model explore the acidification of large, lysosome-like vesicles to determine how stochastic elements, such as variations in proton-pump copy number and cycling between on and off states, impact the pH setpoint and fluctuations around this setpoint.

Organelles harbor specific ion channels, transporters, and other molecular components that allow them to achieve specific intracellular ionic conditions required for their proper function. How all of these components work together to regulate these concentrations, such as maintaining a specific pH value, is complex, and continuum mathematical models have been helpful for evaluating different mechanisms and making quantitative predictions that can be tested experimentally. Nonetheless, organelles can be quite small and some contain only a handful of free protons—can continuum models accurately describe systems with so few molecules? We tested this by creating a discrete, stochastic (DS) model of vesicle acidification that tracks how all of these individual molecules in the vesicle change their state in time. When fitting experimental data, the DS model provides the same parameter estimates as a corresponding continuum model, indicating that both models are equally valid. However, the DS model additionally informs on the noise in the vesicle. When compared to the experimental noise in pH, we show that there is no agreement, because experimental fluctuations do not report on the true pH fluctuations, but rather they report on the fluctuations in reporter molecule protonation. Given experimental limitations, our result highlights the importance of DS models in predicting noise in organelles.

Computational Modeling Reveals Frequency Modulation of Calcium-cAMP/PKA Pathway in Dendritic Spines

Dendritic spines are the primary excitatory postsynaptic sites that act as subcompartments of signaling. Ca²⁺ is often the first and most rapid signal in spines. Downstream of calcium, the cyclic adenosine monophosphate (cAMP)/protein kinase A (PKA) pathway plays a critical role in the regulation of spine formation, morphological modifications, and ultimately, learning and memory. Although the dynamics of calcium are reasonably well-studied, calcium-induced cAMP/PKA dynamics, particularly with respect to frequency modulation, are not fully explored. In this study, we present a well-mixed model for the dynamics of calcium-induced cAMP/PKA dynamics in dendritic spines. The model is constrained using experimental observations in the literature. Further, we measured the calcium oscillation frequency in dendritic spines of cultured hippocampal CA1 neurons and used these dynamics as model inputs. Our model predicts that the various steps in this pathway act as frequency modulators for calcium, and the high frequency of calcium input is filtered by adenylyl cyclase 1 and phosphodiesterases in this pathway such that cAMP/PKA only responds to lower frequencies. This prediction has important implications for noise filtering and long-timescale signal transduction in dendritic spines. A companion manuscript presents a three-dimensional spatial model for the same pathway.

Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths

Collective behaviour is of fundamental importance in the life sciences, where it appears at levels of biological complexity from single cells to superorganisms, in demography and the social sciences, where it describes the behaviour of populations, and in the physical and engineering sciences, where it describes physical phenomena and can be used to design distributed systems. Reasoning about collective behaviour is inherently difficult, as the non-linear interactions between individuals give rise to complex emergent dynamics. Mathematical techniques have been developed to analyse systematically collective behaviour in such systems, yet these frequently require extensive formal training and technical ability to apply. Even for those with the requisite training and ability, analysis using these techniques can be laborious, time-consuming and error-prone. Together these difficulties raise a barrier-to-entry for practitioners wishing to analyse models of collective behaviour. However, rigorous modelling of collective behaviour is required to make progress in understanding and applying it. Here we present an accessible tool which aims to automate the process of modelling and analysing collective behaviour, as far as possible. We focus our attention on the general class of systems described by reaction kinetics, involving interactions between components that change state as a result, as these are easily understood and extracted from data by natural, physical and social scientists, and correspond to algorithms for component-level controllers in engineering applications. By providing simple automated access to advanced mathematical techniques from statistical physics, nonlinear dynamical systems analysis, and computational simulation, we hope to advance standards in modelling collective behaviour. At the same time, by providing expert users with access to the results of automated analyses, sophisticated investigations that could take significant effort are substantially facilitated. Our tool can be accessed online without installing software, uses a simple programmatic interface, and provides interactive graphical plots for users to develop understanding of their models.

Kinetic modeling of Stickland reactions-coupled methanogenesis for a methanogenic culture

Studying amino acid catabolism-coupled methanogenesis is the important standpoints to decipher the metabolic behavior of a methanogenic culture. l-Glycine and l-alanine are acted as sole carbon and nitrogen sources for acidogenic bacteria. One amino acid is oxidized and another one is reduced for acetate production via pyruvate by oxidative deamination process in the Stickland reactions. Herein, we have developed a kinetic model for the Stickland reactions-coupled methanogenesis (SRCM) and simulated objectively to maximize the rate of methane production. We collected the metabolic information from enzyme kinetic parameters for amino acid catabolism of Clostridium acetobutylicum ATCC 824 and methanogenesis of Methanosarcina acetivorans C2A. The SRCM model of this study consisted of 18 reactions and 61 metabolites with enzyme kinetic parameters derived experimental data. The internal or external metabolic flux rate of this system found to control the acidogenesis and methanogenesis in a methanogenic culture. Using the SRCM model, flux distributions were calculated for each reaction and metabolite in order to maximize the methane production rate from the glycine–alanine pair. Results of this study, we demonstrated the metabolic behavior, metabolite pairing while mutually interact, and advantages of syntrophic metabolism of amino acid-directed methane production in a methanogenic starter culture.

Putative interaction site for membrane phospholipids controls activation of TRPA1 channel at physiological membrane potentials

The transient receptor potential ankyrin 1 (TRPA1) channel is a polymodal sensor of environmental irritant compounds, endogenous proalgesic agents, and cold. Upon activation, TRPA1 channels increase cellular calcium levels via direct permeation and trigger signaling pathways that hydrolyze phosphatidylinositol-4,5-bisphosphate (PIP₂ ) in the inner membrane leaflet. Our objective was to determine the extent to which a putative PIP₂ -interaction site (Y1006-Q1031) is involved in TRPA1 regulation. The interactions of two specific peptides (L992-N1008 and T1003-P1034) with model lipid membranes were characterized by biophysical approaches to obtain information about affinity, peptide secondary structure, and peptide effect in the lipid organization. The results indicate that the two peptides interact with lipid membranes only if PIP₂ is present and their affinities depend on the presence of calcium. Using whole-cell electrophysiology, we demonstrate that mutation at F1020 produced channels with faster activation kinetics and with a rightward shifted voltage-dependent activation curve by altering the allosteric constant that couples voltage sensing to pore opening. We assert that the presence of PIP₂ is essential for the interaction of the two peptide sequences with the lipid membrane. The putative phosphoinositide-interacting domain comprising the highly conserved F1020 contributes to the stabilization of the TRPA1 channel gate.

A predictive computational model reveals that GIV/girdin serves as a tunable valve for EGFR-stimulated cyclic AMP signals

Cellular levels of the versatile second messenger cyclic (c)AMP are regulated by the antagonistic actions of the canonical G protein → adenylyl cyclase pathway that is initiated by G-protein–coupled receptors (GPCRs) and attenuated by phosphodiesterases (PDEs). Dysregulated cAMP signaling drives many diseases; for example, its low levels facilitate numerous sinister properties of cancer cells. Recently, an alternative paradigm for cAMP signaling has emerged in which growth factor–receptor tyrosine kinases (RTKs; e.g., EGFR) access and modulate G proteins via a cytosolic guanine-nucleotide exchange modulator (GEM), GIV/girdin; dysregulation of this pathway is frequently encountered in cancers. In this study, we present a network-based compartmental model for the paradigm of GEM-facilitated cross-talk between RTKs and G proteins and how that impacts cellular cAMP. Our model predicts that cross-talk between GIV, Gα_s, and Gα_i proteins dampens ligand-stimulated cAMP dynamics. This prediction was experimentally verified by measuring cAMP levels in cells under different conditions. We further predict that the direct proportionality of cAMP concentration as a function of receptor number and the inverse proportionality of cAMP concentration as a function of PDE concentration are both altered by GIV levels. Taking these results together, our model reveals that GIV acts as a tunable control valve that regulates cAMP flux after growth factor stimulation. For a given stimulus, when GIV levels are high, cAMP levels are low, and vice versa. In doing so, GIV modulates cAMP via mechanisms distinct from the two most often targeted classes of cAMP modulators, GPCRs and PDEs.

Modelling the role of redox-related mechanisms in musculoskeletal ageing

The decline in the musculoskeletal system with age is driven at the cellular level by random molecular damage. Cells possess mechanisms to repair or remove damage and many of the pathways involved in this response are regulated by redox signals. However, with ageing there is an increase in oxidative stress which can lead to chronic inflammation and disruption of redox signalling pathways. The complexity of the processes involved has led to the use of computational modelling to help increase our understanding of the system, test hypotheses and make testable predictions. This paper will give a brief background of the biological systems that have been modelled, an introduction to computational modelling, a review of models that involve redox-related mechanisms that are applicable to musculoskeletal ageing, and finally a discussion of the future potential for modelling in this field.

Carbon Acidity in Enzyme Active Sites

The pK_a values for substrates acting as carbon acids (i.e., C-H deprotonation reactions) in several enzyme active sites are presented. The information needed to calculate them includes the pK_a of the active site acid/base catalyst and the equilibrium constant for the deprotonation step. Carbon acidity is obtained from the relation pK_eq = pKar–pKap = ΔpK_a for a proton transfer reaction. Five enzymatic free energy profiles (FEPs) were calculated to obtain the equilibrium constants for proton transfer from carbon in the active site, and six additional proton transfer equilibrium constants were extracted from data available in the literature, allowing substrate C-H pK_as to be calculated for 11 enzymes. Active site-bound substrate C-H pK_a values range from 5.6 for ketosteroid isomerase to 16 for proline racemase. Compared to values in water, enzymes lower substrate C-H pK_as by up to 23 units, corresponding to 31 kcal/mol of carbanion stabilization energy. Calculation of Marcus intrinsic barriers (ΔG0‡) for pairs of non-enzymatic/enzymatic reactions shows significant reductions in ΔG0‡ for cofactor-independent enzymes, while pyridoxal phosphate dependent enzymes appear to increase ΔG0‡ to a small extent as a consequence of carbanion resonance stabilization. The large increases in carbon acidity found here are central to the large rate enhancements observed in enzymes that catalyze carbon deprotonation.

Using Systems Biology and Mathematical Modeling Approaches in the Discovery of Therapeutic Targets for Spinal Muscular Atrophy

Systems biology uses a combination of experimental and mathematical approaches to investigate the complex and dynamic interactions with a given system or biological process. Systems biology integrates genetics, signal transduction, biochemistry and cell biology with mathematical modeling. It can be used to identify novel pathways implicated in diseases as well as to understand the mechanisms by which a specific gene is regulated. This review describes the development of mathematical models for the regulation of an endogenous modifier gene, SMN2, in spinal muscular atrophy-an early-onset motor neuron disease that is a leading genetic cause of infant mortality worldwide-by cAMP signaling. These mathematical models not only can aid in understanding how SMN2 expression is regulated but they can also be used to examine the best ways to manipulate cAMP signaling to maximally increase SMN2 expression. These models will lead to the development of therapeutic strategies for treating SMA. This systems biology approach can also be applied to other neurological diseases, particularly those in which a disease-causing gene or a modifier gene has been identified.

Tellurium notebooks-An environment for reproducible dynamical modeling in systems biology

The considerable difficulty encountered in reproducing the results of published dynamical models limits validation, exploration and reuse of this increasingly large biomedical research resource. To address this problem, we have developed Tellurium Notebook, a software system for model authoring, simulation, and teaching that facilitates building reproducible dynamical models and reusing models by 1) providing a notebook environment which allows models, Python code, and narrative to be intermixed, 2) supporting the COMBINE archive format during model development for capturing model information in an exchangeable format and 3) enabling users to easily simulate and edit public COMBINE-compliant models from public repositories to facilitate studying model dynamics, variants and test cases. Tellurium Notebook, a Python–based Jupyter–like environment, is designed to seamlessly inter-operate with these community standards by automating conversion between COMBINE standards formulations and corresponding in–line, human–readable representations. Thus, Tellurium brings to systems biology the strategy used by other literate notebook systems such as Mathematica. These capabilities allow users to edit every aspect of the standards–compliant models and simulations, run the simulations in–line, and re–export to standard formats. We provide several use cases illustrating the advantages of our approach and how it allows development and reuse of models without requiring technical knowledge of standards. Adoption of Tellurium should accelerate model development, reproducibility and reuse.

There is considerable value to systems and synthetic biology in creating reproducible models. An essential element of reproducibility is the use of community standards, an often challenging undertaking for modelers. This article describes Tellurium Notebook, a tool for developing dynamical models that provides an intuitive approach to building and reusing models built with community standards. Tellurium automates embedding human–readable representations of COMBINE archives in literate coding notebooks, bringing to systems biology this strategy central to other literate notebook systems such as Mathematica. We show that the ability to easily edit this human–readable representation enables users to test models under a variety of conditions, thereby providing a way to create, reuse, and modify standard–encoded models and simulations, regardless of the user’s level of technical knowledge of said standards.

Inhibition of C298S mutant of human aldose reductase for antidiabetic applications: Evidence from in silico elementary mode analysis of biological network model

Human aldose reductase (hAR) is the key enzyme in sorbitol pathway of glucose utilization and is implicated in the etiology of secondary complications of diabetes, such as, cardiovascular complications, neuropathy, nephropathy, retinopathy, and cataract genesis. It reduces glucose to sorbitol in the presence of NADPH and the major cause of diabetes complications could be the change in the osmotic pressure due to the accumulation of sorbitol. An activated form of hAR (activated hAR or ahAR) poses a potential obstacle in the development of diabetes drugs as hAR-inhibitors are ineffective against ahAR. The therapeutic efficacy of such drugs is compromised when a large fraction of the enzyme (hAR) undergoes conversion to the activated ahAR form as has been observed in the diabetic tissues. In the present study, attempts have been made to employ systems biology strategies to identify the elementary nodes of human polyol metabolic pathway, responsible for normal metabolic states, followed by the identification of natural potent inhibitors of the activated form of hAR represented by the mutant C298S for possible antidiabetic applications. Quantum Mechanical Molecular Mechanical docking strategy was used to determine the probable inhibitors of ahAR. Rosmarinic acid was found as the most potent natural ahAR inhibitor and warrants for experimental validation in the near future.