Biochemical Systems Theory Research Articles

Assessing structural uncertainty of biochemical regulatory networks in metabolic pathways under varying data quality

Ordinary differential equation (ODE) models are powerful tools for studying the dynamics of metabolic pathways. However, key challenges lie in constructing ODE models for metabolic pathways, specifically in our limited knowledge about which metabolite levels control which reaction rates. Identification of these regulatory networks is further complicated by the limited availability of relevant data. Here, we assess the conditions under which it is feasible to accurately identify regulatory networks in metabolic pathways by computationally fitting candidate network models with biochemical systems theory (BST) kinetics to data of varying quality. We use network motifs commonly found in metabolic pathways as a simplified testbed. Key features correlated with the level of difficulty in identifying the correct regulatory network were identified, highlighting the impact of sampling rate, data noise, and data incompleteness on structural uncertainty. We found that for a simple branched network motif with an equal number of metabolites and fluxes, identification of the correct regulatory network can be largely achieved and is robust to missing one of the metabolite profiles. However, with a bi-substrate bi-product reaction or more fluxes than metabolites in the network motif, the identification becomes more challenging. Stronger regulatory interactions and higher metabolite concentrations were found to be correlated with less structural uncertainty. These results could aid efforts to predict whether the true metabolic regulatory network can be computationally identified for a given stoichiometric network topology and dataset quality, thus helping to identify optimal measures to mitigate such identifiability issues in kinetic model development.

Pillars of theoretical biology: “Biochemical systems analysis, I, II and III”

Michael Savageau’s Biochemical Systems Analysis I, II, IIIpapers, published in volumes 25 and 26 of the journal,kickstarted a research programme that originated many of the core concepts and tools of Systems Biology. This article briefly summarizes these papers anddiscusses the most relevant developments in Biochemical Systems Theory since their publication.

A Review of Computational Approach for S-system-based Modeling of Gene Regulatory Network.

Inference of gene regulatory network (GRN) from time series microarray data remains as a fascinating task for computer science researchers to understand the complex biological process that occurred inside a cell. Among the different popular models to infer GRN, S-system is considered as one of the promising non-linear mathematical tools to model the dynamics of gene expressions, as well as to infer the GRN. S-system is based on biochemical system theory and power law formalism. By observing the value of kinetic parameters of S-system model, it is possible to extract the regulatory relationships among genes. In this review, several existing intelligent methods that were already proposed for inference of S-system-based GRN are explained. It is observed that finding out the most suitable and efficient optimization technique for the accurate inference of all kinds of networks, i.e., in-silico, in-vivo, etc., with less computational complexity is still an open research problem to all. This paper may help the beginners or researchers who want to continue their research in the field of computational biology and bioinformatics.

Discrete Biochemical Systems Theory.

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

Mathematical Modeling of Severe Acute Respiratory Syndrome Coronavirus 2 Infection Network with Cytokine Storm, Oxidative Stress, Thrombosis, Insulin Resistance, and Nitric Oxide Pathways.

Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is a systemic disease affecting not only the lungs but also multiple organ systems. Clinical studies implicate that SARS-CoV-2 infection causes imbalance of cellular homeostasis and immune response that trigger cytokine storm, oxidative stress, thrombosis, and insulin resistance. Mathematical modeling can offer in-depth understanding of the SARS-CoV-2 infection and illuminate how subcellular mechanisms and feedback loops underpin disease progression and multiorgan failure. We report here a mathematical model of SARS-CoV-2 infection pathway network with cytokine storm, oxidative stress, thrombosis, insulin resistance, and nitric oxide (NO) pathways. The biochemical systems theory model shows autocrine loops with positive feedback enabling excessive immune response, cytokines, transcription factors, and interferons, which can imbalance homeostasis of the system. The simulations suggest that changes in immune response led to uncontrolled release of cytokines and chemokines, including interleukin (IL)-1β, IL-6, and tumor necrosis factor α (TNFα), and affect insulin, coagulation, and NO signaling pathways. Increased production of NETs (neutrophil extracellular traps), thrombin, PAI-1 (plasminogen activator inhibitor-1), and other procoagulant factors led to thrombosis. By analyzing complex biochemical reactions, this model forecasts the key intermediates, potential biomarkers, and risk factors at different stages of COVID-19. These insights can be useful for drug discovery and development, as well as precision treatment of multiorgan implications of COVID-19 as seen in systems medicine.

Pathway analysis of new coronavirus infection disease in Japan by Biochemical systems theory

Pathway analysis of new coronavirus infection disease in Japan by Biochemical systems theory

Computational modelling of TNF\u03b1 related pathways regulated by neuroinflammation, oxidative stress and insulin resistance in neurodegeneration

Computational and mathematical modelling towards understanding the structure and dynamics of biological systems has significantly impacted on translational neuroscience to face novel approaches toward neurological disorders such as Alzheimer’s (AD) and Parkinson’s disease (PD). In this study, a computational model of AD and PD have been modelled using biochemical systems theory, and shows how Tumour Necrosis Factor alpha (TNF훼) regulated neuroinflammation, oxidative stress and insulin pathways can dysregulate its downstream signalling cascade that lead to neurodegeneration observed in AD and PD. The experimental data for initial conditions for this model and validation of the model was based on data reported in literature. In simulations, elevations in the aggregations of major proteins involved in the pathology of AD and PD including amyloid beta, alpha synuclein, tau have been modelled. Abnormal aggregation of these proteins and hyperphosphorylation of tau were observed in the model. This aggregation may lead to developing Lewy bodies, fibrils, plaques and tangles inside neurons that trigger apoptosis. An increase in the concentrations of TNF훼 and glutamate during diseased conditions was noted in the model. Accumulation of these proteins may be related to the feedback mechanism of TNF훼 that initiates its own release and the production of excess glutamate. This could lead to the prolonged activation of microglia that result in death of surrounding neurons. With the elevation in reactive oxygen species, oxidative stress also increased. Simulations suggest insulin may be an important factor identifying neurodegeneration in AD and PD, through its action along with the neuroinflammation and oxidative stress. Low insulin level was noticed in the diseased condition due to abnormal protein aggregation that leads to TNFα release. Given the role towards better design of real experiments, accumulation of oligomers of mutated proteins in AD and PD activating microglia and secreting TNFα along with other cytokines map to oxidative stress that led to cell death.

Computational modeling of convergent mechanisms in Alzheimer’s and Parkinson’s disease with insulin signaling using biochemical systems theory

Abstract Computational modeling has significantly impacted clinical assessment and treatment of diseases by improving diagnosis, prognosis, discovery of novel biomarkers and developing new drugs that assures treatment for incurable diseases. In this study, a biochemical systems theory model was developed to explore crucial pathways involved in shared mechanisms between Alzheimer’s and Parkinson’s diseases and insulin signaling involved in Parkinson’s disease (PD). Mass kinetic concentration values and rate constants were retrieved from experiments cited in literature and simulations were developed using systems of ordinary differential equations. Calcium changes were reconstructed accounting reduced levels in diseased conditions. Simulations suggest that AD and PD share some of the important cellular pathways such as α-synuclein, tau phosphorylation, calcium homeostasis, ROS and TNF-α in spite of the differences in mechanisms and symptoms. Here, modeling relates the critical role insulin signaling may have in maintaining dopamine levels in PD patients.

A computational approach to multistationarity of power-law kinetic systems

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems.

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton–Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks.

A Systems Model of Parkinson's Disease Using Biochemical Systems Theory.

Parkinson's disease (PD), a neurodegenerative disorder, affects millions of people and has gained attention because of its clinical roles affecting behaviors related to motor and nonmotor symptoms. Although studies on PD from various aspects are becoming popular, few rely on predictive systems modeling approaches. Using Biochemical Systems Theory (BST), this article attempts to model and characterize dopaminergic cell death and understand pathophysiology of progression of PD. PD pathways were modeled using stochastic differential equations incorporating law of mass action, and initial concentrations for the modeled proteins were obtained from literature. Simulations suggest that dopamine levels were reduced significantly due to an increase in dopaminergic quinones and 3,4-dihydroxyphenylacetaldehyde (DOPAL) relating to imbalances compared to control during PD progression. Associating to clinically observed PD-related cell death, simulations show abnormal parkin and reactive oxygen species levels with an increase in neurofibrillary tangles. While relating molecular mechanistic roles, the BST modeling helps predicting dopaminergic cell death processes involved in the progression of PD and provides a predictive understanding of neuronal dysfunction for translational neuroscience.

Piecewise synergetic systems and applications in biochemical systems theory

Abstract We study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.

Reaction networks and kinetics of biochemical systems

This paper further develops the connection between Chemical Reaction Network Theory (CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use algebraic properties of kinetic sets to study the set of complex factorizable kinetics CFK(N) on a CRN, which shares many characteristics with its subset of mass action kinetics. In particular, we extend the Theorem of Feinberg-Horn [9] on the coincidence of the kinetic and stoichiometric subsets of a mass action system to CF kinetics, using the concept of span surjectivity. We also introduce the branching type of a network, which determines the availability of kinetics on it and allows us to characterize the networks for which all kinetics are complex factorizable: A “Kinetics Landscape” provides an overview of kinetics sets, their algebraic properties and containment relationships. We then apply our results and those (of other CRNT researchers) reviewed in [1] to fifteen BST models of complex biological systems and discover novel network and kinetic properties that so far have not been widely studied in CRNT. In our view, these findings show an important benefit of connecting CRNT and BST modeling efforts.

Chemical reaction network approaches to Biochemical Systems Theory

This paper provides a framework to represent a Biochemical Systems Theory (BST) model (in either GMA or S-system form) as a chemical reaction network with power law kinetics. Using this representation, some basic properties and the application of recent results of Chemical Reaction Network Theory regarding steady states of such systems are shown. In particular, Injectivity Theory, including network concordance [36] and the Jacobian Determinant Criterion [43], a “Lifting Theorem” for steady states [26] and the comprehensive results of Müller and Regensburger [31] on complex balanced equilibria are discussed. A partial extension of a recent Emulation Theorem of Cardelli for mass action systems [3] is derived for a subclass of power law kinetic systems. However, it is also shown that the GMA and S-system models of human purine metabolism [10] do not display the reactant-determined kinetics assumed by Müller and Regensburger and hence only a subset of BST models can be handled with their approach. Moreover, since the reaction networks underlying many BST models are not weakly reversible, results for non-complex balanced equilibria are also needed.

A mathematical model of insulin resistance in Parkinson’s disease

This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson’s disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions.

A U-system approach for predicting metabolic behaviors and responses based on an alleged metabolic reaction network.

BackgroundProgress in systems biology offers sophisticated approaches toward a comprehensive understanding of biological systems. Yet, computational analyses are held back due to difficulties in determining suitable model parameter values from experimental data which naturally are subject to biological fluctuations. The data may also be corrupted by experimental uncertainties and sometimes do not contain all information regarding variables that cannot be measured for technical reasons.ResultsWe show here a streamlined approach for the construction of a coarse model that allows us to set up dynamic models with minimal input information. The approach uses a hybrid between a pure mass action system and a generalized mass action (GMA) system in the framework of biochemical systems theory (BST) with rate constants of 1, normal kinetic orders of 1, and -0.5 and 0.5 for inhibitory and activating effects, named Unity (U)-system. The U-system model does not necessarily fit all data well but is often sufficient for predicting metabolic behavior of metabolites which cannot be simultaneously measured, identifying inconsistencies between experimental data and the assumed underlying pathway structure, as well as predicting system responses to a modification of gene or enzyme. The U-system approach was validated with small, generic systems and implemented to model a large-scale metabolic reaction network of a higher plant, Arabidopsis. The dynamic behaviors obtained by predictive simulations agreed with actually available metabolomic time-series data, identified probable errors in the experimental datasets, and estimated probable behavior of unmeasurable metabolites in a qualitative manner. The model could also predict metabolic responses of Arabidopsis with altered network structures due to genetic modification.ConclusionsThe U-system approach can effectively predict metabolic behaviors and responses based on structures of an alleged metabolic reaction network. Thus, it can be a useful first-line tool of data analysis, model diagnostics and aid the design of next-step experiments.

An Efficient and Very Accurate Method for Calculating Steady-State Sensitivities in Metabolic Reaction Systems.

Stability and sensitivity analyses of biological systems require the ad hocwriting of computer code, which is highly dependent on the particular model and burdensome for large systems. We propose a very accurate strategy to overcome this challenge. Its core concept is the conversion of the model into the format of biochemical systems theory (BST), which greatly facilitates the computation of sensitivities. First, the steady state of interest is determined by integrating the model equations toward the steady state and then using a Newton-Raphson method to fine-tune the result. The second step of conversion into the BST format requires several instances of numerical differentiation. The accuracy of this task is ensured by the use of a complex-variable Taylor scheme for all differentiation steps. The proposed strategy is implemented in a new software program, COSMOS, which automates the stability and sensitivity analysis of essentially arbitrary ODE models in a quick, yet highly accurate manner. The methods underlying the process are theoretically analyzed and illustrated with four representative examples: a simple metabolic reaction model; a model of aspartate-derived amino acid biosynthesis; a TCA-cycle model; and a modified TCA-cycle model. COSMOS has been deposited to https://github.com/BioprocessdesignLab/COSMOS.

Simulation of the Denitrification Process of Waste Water with a Biochemical Systems Model: A Non-Conventional Approach

Abstract Matching experimental and theoretical approaches have often been fruitful in the investigation of complex biological processes. Here we develop a novel non-conventional model for the denitrification of waste water. Earlier models of the denitrification process were compiled by the International Association on Water Quality group. The Activated Sludge Models 1–3, which are the most frequently used all over the world, are presently not adapted towards the integration of both nitrous and nitric oxide emissions during the denitrification process. In the present work, a Generalized Mass Action model, based on Biochemical Systems Theory, was designed to simulate the nitrate reduction observed in specific experimental conditions. The model was implemented and analysed with the software package PLAS. Data from a representative experiment were chosen (T=10°C, pH=7, C/N=3, with acetate as carbon source) to simulate greenhouse NO and N2O gas emissions, in order to test hypotheses about the corresponding bacterial metabolic pathways. The results show that the reduction of nitrate and nitrite is kinetically limiting and that nitrate reduction is limited by diffusion and support that distinct microbial subpopulations are involved in the denitrification pathway, which has consequences for NO emissions.

Building Simulations from the Ground Up: Modeling and Theory in Systems Biology

In this article, we provide a case study examining how integrative systems biologists build simulation models in the absence of a theoretical base. Lacking theoretical starting points, integrative systems biology researchers rely cognitively on the model-building process to disentangle and understand complex biochemical systems. They build simulations from the ground up in a nest-like fashion, by pulling together information and techniques from a variety of possible sources and experimenting with different structures in order to discover a stable, robust result. Finally, we analyze the alternative role and meaning theory has in systems biology expressed as canonical template theories like Biochemical Systems Theory.

The Neurochemical Mobile with Non-Linear Interaction Matrix: An Exploratory Computational Model

Several years ago, the "neurochemical mobile" was introduced as a visual tool for explaining the different balances between neurotransmitters in the brain and their role in mental disorders. Here we complement this concept with a non-linear computational systems model representing the direct and indirect interactions between neurotransmitters, as they have been described in the "neurochemical interaction matrix." The model is constructed within the framework of biochemical systems theory, which facilitates the mapping of numerically ill-characterized systems into a mathematical and computational construct that permits a variety of analyses. Simulations show how short- and long-term perturbations in any of the neurotransmitters migrate through the entire system, thereby affecting the balances within the mobile. In cases of short-term alterations, transients are of particular interest, whereas long-term changes shed light on persistently altered, allostatic states, which in mental diseases and sleep disorders could be due to a combination of unfavorable factors, resulting from a specific genetic predisposition, epigenetic effects, disease, or the repeated use of drugs, such as opioids and amphetamines.