scholarly journals A structural property for reduction of biochemical networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Anika Küken ◽  
Philipp Wendering ◽  
Damoun Langary ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Model Reduction ◽  
Structural Property ◽  
Large Scale ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Reduced Models ◽  
Metabolic Phenotypes ◽  
Genome Scale

AbstractLarge-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

scholarly journals A structural property for reduction of biochemical networks

2021 ◽  
Author(s):  
Anika Kueken ◽  
Philipp Wendering ◽  
Damoun Langary ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Model Reduction ◽  
Structural Property ◽  
Large Scale ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Reduced Models ◽  
Metabolic Phenotypes ◽  
Genome Scale

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that growth predictions from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

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

2020 ◽  
Author(s):  
Zachary B. Haiman ◽  
Daniel C. Zielinski ◽  
Yuko Koike ◽  
James T. Yurkovich ◽  
Bernhard O. Palsson
Keyword(s):  
Steady State ◽  
Dynamic Modeling ◽  
Metabolic Networks ◽  
Dynamic Models ◽  
Mass Action ◽  
System Level ◽  
Modeling Tools ◽  
Mass Action Kinetics ◽  
Simulation Engine ◽  
Genome Scale

AbstractMathematical models of metabolic networks utilize simulation to study system-level mechanisms and functions. Various approaches have been used to model the steady state behavior of metabolic networks using genome-scale reconstructions, but formulating dynamic models from such reconstructions continues to be a key challenge. Here, we present the Mass Action Stoichiometric Simulation Python (MASSpy) package, an open-source computational framework for dynamic modeling of metabolism. MASSpy utilizes mass action kinetics and detailed chemical mechanisms to build dynamic models of complex biological processes. MASSpy adds dynamic modeling tools to the COnstraint-Based Reconstruction and Analysis Python (COBRApy) package to provide an unified framework for constraint-based and kinetic modeling of metabolic networks. MASSpy supports high-performance dynamic simulation through its implementation of libRoadRunner; the Systems Biology Markup Language (SBML) simulation engine. Three case studies demonstrate how to use MASSpy: 1) to simulate dynamics of detailed mechanisms of enzyme regulation; 2) to generate an ensemble of kinetic models using Monte Carlo sampling to approximate missing numerical values of parameters and to quantify uncertainty, and 3) to overcome issues that arise when integrating experimental data with the computation of functional states of detailed biological mechanisms. MASSpy represents a powerful tool to address challenge that arise in dynamic modeling of metabolic networks, both at a small and large scale.Author SummaryGenome-scale reconstructions of metabolism appeared shortly after the first genome sequences became available. Constraint-based models are widely used to compute steady state properties of such reconstructions, but the attainment of dynamic models has remained elusive. We thus developed the MASSpy software package, a framework that enables the construction, simulation, and visualization of dynamic metabolic models. MASSpy is based on the mass action kinetics for each elementary step in an enzymatic reaction mechanism. MASSpy seamlessly unites existing software packages within its framework to provide the user with various modeling tools in one package. MASSpy integrates community standards to facilitate the exchange of models, giving modelers the freedom to use the software for different aspects of their own modeling workflows. Furthermore, MASSpy contains methods for generating and simulating ensembles of models, and for explicitly accounting for biological uncertainty. MASSpy has already demonstrated success in a classroom setting. We anticipate that the suite of modeling tools incorporated into MASSpy will enhance the ability of the modeling community to construct and interrogate complex dynamic models of metabolism.

scholarly journals The unraveling of balanced complexes in metabolic networks

2021 ◽  
Author(s):  
Damoun Langary ◽  
Anika Kueken ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Metabolic Networks ◽  
Network Models ◽  
Steady States ◽  
Biochemical Networks ◽  
Computational Approaches ◽  
Metabolic Models ◽  
Large Scale Networks ◽  
General Conditions

Balanced complexes in biochemical networks are at core of several theoretical and computational approaches that make statements about the properties of the steady states supported by the network. Recent computational approaches have employed balanced complexes to reduce metabolic networks, while ensuring preservation of particular steady-state properties; however, the underlying factors leading to the formation of balanced complexes have not been studied, yet. Here, we present a number of factorizations providing insights in mechanisms that lead to the origins of the corresponding balanced complexes. The proposed factorizations enable us to categorize balanced complexes into four distinct classes, each with specific origins and characteristics. They also provide the means to efficiently determine if a balanced complex in large-scale networks belongs to a particular class from the categorization. The results are obtained under very general conditions and irrespective of the network kinetics, rendering them broadly applicable across variety of network models. Application of the categorization shows that all classes of balanced complexes are present in large-scale metabolic models across all kingdoms of life, therefore paving the way to study their relevance with respect to different properties of steady states supported by these networks.

The Determination of Multiple Steady States in Two Families of Biological Systems

2004 ◽  
Vol 59 (3) ◽  
pp. 136-146
Author(s):  
Guo-Syong Chuang ◽  
Pang-Yen Ho ◽  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Transport Model ◽  
Biological Systems ◽  
Linear Equations ◽  
Steady States ◽  
Metabolic Energy ◽  
Mass Action ◽  
Multiple Steady States ◽  
Mass Action Kinetics ◽  
Subnetwork Analysis

The capacity of computational multiple steady states in two biological systems are determined by the Deficiency One Algorithm and the Subnetwork Analysis. One is a bacterial glycolysis model involving the generation of ATP, and the other one is an active membrane transport model, which is performed by pump proteins coupled to a source of metabolic energy. Mass action kinetics, is assumed and both models consist of eight coupled non-linear equations. A set of rate constants and two corresponding steady states are computed. The phenomena of bistability and hysteresis are discussed. The bifurcation of multiple steady states is also displayed. A signature of multiplicity is derived, which can be applied to mechanism identifications if steady state concentrations for some species are measured. The capacity of steady state multiplicity is extended to their families of reaction networks.

scholarly journals Model Reduction Tools For Phenomenological Modeling of Input-Controlled Biological Circuits

2020 ◽  
Author(s):  
Ayush Pandey ◽  
Richard M. Murray
Keyword(s):  
Phenomenological Models ◽  
Model Reduction ◽  
Chemical Reaction ◽  
Species Abundance ◽  
Reaction Model ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Time Scale Separation ◽  
Effective Relationships ◽  
Biological Circuits

AbstractWe present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits that guide the design using chemical reaction-level descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species’ abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure.

scholarly journals Noise control for molecular computing

2018 ◽  
Vol 15 (144) ◽  
pp. 20180199 ◽  
Author(s):  
Tomislav Plesa ◽  
Konstantinos C. Zygalakis ◽  
David F. Anderson ◽  
Radek Erban
Keyword(s):  
Stochastic Dynamics ◽  
Noise Control ◽  
Reaction System ◽  
Reaction Network ◽  
Intrinsic Noise ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Interdisciplinary Field ◽  
Biochemical Systems

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production–decay reaction system, and on an exotic system displaying bistability. For the production–decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

scholarly journals The effects of model complexity and size on metabolic flux distribution and control. Case study inE. coli

2019 ◽  
Author(s):  
Tuure Hameri ◽  
Georgios Fengos ◽  
Vassily Hatzimanikatis
Keyword(s):  
Metabolic Engineering ◽  
Kinetic Models ◽  
Large Scale ◽  
Ad Hoc ◽  
Scaling Up ◽  
Steady States ◽  
Model Complexity ◽  
Reduced Models ◽  
Genome Scale ◽  
Stoichiometric Models

AbstractSignificant efforts have been made in building large-scale kinetic models of cellular metabolism in the past two decades. However, most kinetic models published to date, remain focused around central carbon pathways or are built aroundad hocreduced models without clear justification on their derivation and usage. Systematic algorithms exist for reducing genome-scale metabolic reconstructions to build thermodynamically feasible and consistently reduced stoichiometric models. It has not been studied previously how network complexity affects the Metabolic Sensitivity Coefficients (MSCs) of large-scale kinetic models build around consistently reduced models. We reduced the iJO1366Escherichia Coligenome-scale metabolic reconstruction (GEM) systematically to build three stoichiometric models of variable size. Since the reduced models are expansions around the core subsystems for which the reduction was performed, the models are modular. We propose a method for scaling up the flux profile and the concentration vector reference steady-states from the smallest model to the larger ones, whilst preserving maximum equivalency. Populations of non-linear kinetic models, preserving similarity in kinetic parameters, were built around the reference steady-states and their MSCs were computed. The analysis of the populations of MSCs for the reduced models evidences that metabolic engineering strategies - independent of network complexity - can be designed using our proposed workflow. These findings suggest that we can successfully construct reduced kinetic models from a GEM, without losing information relevant to the scope of the study. Our proposed workflow can serve as an approach for testing the suitability of a model for answering certain study-specific questions.Author SummaryKinetic models of metabolism are very useful tools for metabolic engineering. However, they are generatedad hocbecause, to our knowledge, there exists no standardized procedure for constructing kinetic models of metabolism. We sought to investigate systematically the effect of model complexity and size on sensitivity characteristics. Hence, we used the redGEM and the lumpGEM algorithms to build the backbone of three consistently and modularly reduced stoichiometric models from the iJO1366 genome-scale model for aerobically grownE.coli. These three models were of increasing complexity in terms of network topology and served as basis for building populations of kinetic models. We proposed for the first time a way for scaling up steady-states of the metabolic fluxes and the metabolite concentrations from one kinetic model to another and developed a workflow for fixing kinetic parameters between the models in order to preserve equivalency. We performed metabolic control analysis (MCA) around the populations of kinetic models and used their MCA control coefficients as measurable outputs to compare the three models. We demonstrated that we can systematically reduce genome-scale models to construct kinetic models of different complexity levels for a phenotype that, independent of network complexity, lead to mostly consistent MCA-based metabolic engineering conclusions.

scholarly journals Dynamical modelling of the heat shock response inChlamydomonas reinhardtii

2016 ◽  
Author(s):  
Stefano Magni ◽  
Antonella Succurro ◽  
Alexander Skupin ◽  
Oliver Ebenhöh
Keyword(s):  
Steady State ◽  
Heat Shock ◽  
Heat Shock Response ◽  
Model Organism ◽  
Mass Action ◽  
Large Temperature ◽  
System Response ◽  
Yield Reduction ◽  
Mass Action Kinetics ◽  
Shock Response

AbstractGlobal warming is exposing plants to more frequent heat stress, with consequent crop yield reduction. Organisms exposed to large temperature increases protect themselves typically with a heat shock response (HSR). To study the HSR in photosynthetic organisms we present here a data driven mathematical model describing the dynamics of the HSR in the model organismChlamydomonas reinhartii. Temperature variations are sensed by the accumulation of unfolded proteins, which activates the synthesis of heat shock proteins (HSP) mediated by the heat shock transcription factor HSF1. Our dynamical model employs a system of ordinary differential equations mostly based on mass-action kinetics to study the time evolution of the involved species. The signalling network is inferred from data in the literature, and the multiple experimental data-sets available are used to calibrate the model, which allows to reproduce their qualitative behaviour. With this model we show the ability of the system to adapt to temperatures higher than usual during heat shocks longer than three hours by shifting to a new steady state. We study how the steady state concentrations depend on the temperature at which the steady state is reached. We systematically investigate how the accumulation of HSPs depends on the combination of temperature and duration of the heat shock. We finally investigate the system response to a smooth variation in temperature simulating a hot day.

scholarly journals Enzyme-sharing as a cause of multi-stationarity in signalling systems

2011 ◽  
Vol 9 (71) ◽  
pp. 1224-1232 ◽  
Author(s):  
Elisenda Feliu ◽  
Carsten Wiuf
Keyword(s):  
Steady State ◽  
Chemical Species ◽  
Steady States ◽  
Mass Action ◽  
Signalling Pathways ◽  
Necessary Condition ◽  
Full Generality ◽  
Mass Action Kinetics ◽  
Cellular Decision Making ◽  
The Stability

Multi-stationarity in biological systems is a mechanism of cellular decision-making. In particular, signalling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multi-stationarity are of particular interest to determine, as well as the stability, properties of the steady states. In this paper, we determine conditions for the emergence of multi-stationarity in small motifs without feedback that repeatedly occur in signalling pathways. We derive an explicit mathematical relationship φ between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that φ determines the number of steady states and provides a necessary condition for a steady state to be stable—that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead to multi-stationarity, and extend the view that multi-stationarity in signalling pathways arises from multi-site phosphorylation. Our approach relies on mass-action kinetics, and the conclusions are drawn in full generality without resorting to simulations or random generation of parameters. The approach is extensible to other systems.

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