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The underlying pathway structure of biochemical reaction networks

Schilling, Christophe H.; Palsson, Bernhard O.
Fonte: The National Academy of Sciences Publicador: The National Academy of Sciences
Tipo: Artigo de Revista Científica
Publicado em 14/04/1998 EN
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Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally...

Timescale analysis of rule-based biochemical reaction networks

Klinke, David J.; Finley, Stacey D.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
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The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed upon reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of Interleukin-12 (IL-12) signaling in näive CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based upon the available data. The analysis correctly predicted that reactions associated with JAK2 and TYK2 binding to their corresponding receptor exist at a pseudo-equilibrium. In contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately...

Characterizing Multistationarity Regimes in Biochemical Reaction Networks

Otero-Muras, Irene; Banga, Julio R.; Alonso, Antonio A.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Publicado em 03/07/2012 EN
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Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity...

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Flassig, R. J.; Sundmacher, K.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica
EN
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Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs).

Parameter identifiability of biochemical reaction networks in systems biology

Geffen, Dara
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado Formato: 1324816 bytes; application/pdf
EN; EN
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In systems biology, models often contain a large number of unknown or only roughly known parameters that must be estimated through the fitting of data. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. Structural or a priori identifiability of unknown parameters in biochemical reaction networks is considered. Such systems consist of continuous time, nonlinear differential equations. Several methods for analyzing identifiability of such systems exist, most of which restate the question as one of observability by expanding the state space to include parameters. However, these existing methods were not developed with biological systems in mind, so do not necessarily address the specific challenges posed by this type of problem. In this work, such methods are considered for the analysis of a representative biological system, the NF-kappaB signal transduction pathway. It is shown that existing observability-based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems that are seldom feasible. The analytical nature of the solution imposes restrictions on the size and complexity of systems that these methods can handle. This conflicts with the fact that most currently studied systems biology models are rather large networks containing many states and parameters. In this thesis...

Reconstruction of Arbitrary Biochemical Reaction Networks: A Compressive Sensing Approach

Pan, Wei; Yuan, Ye; Stan, Guy-Bart
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Reconstruction of biochemical reaction networks is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with model descriptions under the form of polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated reaction constants. To solve the network reconstruction problem, we cast it as a Compressive Sensing (CS) problem and use Bayesian Sparse Learning (BSL) algorithms as an efficient way to obtain its solution.; Comment: Submitted to IEEE Conference on Decision and Control, 2012

A scalable method for finding irreducible state-spaces for stochastic models of biochemical reaction networks

Gupta, Ankit; Khammash, Mustafa
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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695.7857%
In stochastic models of biochemical reaction networks, the dynamics is usually represented by a Markov process which describes the evolution of the copy-numbers or molecular counts of the constituent species. It is often of biological interest to determine if this Markov process has a unique stationary distribution and for this to hold, it is necessary that the state-space is irreducible in the sense that all the states are reachable from each other in a finite time, with a positive probability. Finding such irreducible state-spaces is quite challenging, because the Markovian dynamics can usually access infinitely many states and the presence of conservation relations among species can constrain the dynamics in complicated ways. The aim of this paper is to develop a computational framework for finding irreducible state-spaces for reaction networks that typically arise in Systems and Synthetic Biology. Our results can help in assessing the long-term behavior of a network and also in explicitly obtaining the stationary distributions in certain cases. The framework we present relies only on elementary linear algebra and linear programming, which makes it highly scalable and efficient, even for very large networks. We illustrate the wide applicability of our framework through several examples.; Comment: 40 pages

Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory

Pantazis, Yannis; Katsoulakis, Markos A.; Vlachos, Dionisios G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space. We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise". The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate (RER)...

Exact results for noise power spectra in linear biochemical reaction networks

Warren, Patrick B.; Tanase-Nicola, Sorin; Wolde, Pieter Rein ten
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/12/2005
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We present a simple method for determining the exact noise power spectra in linear chemical reaction networks. We apply the method to networks which are representative of biochemical processes such as gene expression and signal detection. Our results clarify how noise is transmitted by signal detection motifs, and indicate how to coarse-grain networks by the elimination of fast reactions.; Comment: 10 pages, 2 figures, RevTeX 4

A scalable computational framework for establishing long-term behavior of stochastic reaction networks

Gupta, Ankit; Briat, Corentin; Khammash, Mustafa
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs...

A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks

Arcak, Murat; Sontag, Eduardo D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/05/2007
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This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.; Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related (p)reprints

Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/10/2011
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697.25984%
The application of the quasi-steady-state approximation to the Michaelis-Menten reaction embedded in large open chemical reaction networks is a popular model reduction technique in deterministic and stochastic simulations of biochemical reactions inside cells. It is frequently assumed that the predictions of the reduced master equations obtained using the stochastic quasi-steady-state approach are in very good agreement with the predictions of the full master equations, provided the conditions for the validity of the deterministic quasi-steady-state approximation are fulfilled. We here use the linear-noise approximation to show that this assumption is not generally justified for the Michaelis-Menten reaction with substrate input, the simplest example of an open embedded enzyme reaction. The reduced master equation approach is found to considerably overestimate the size of intrinsic noise at low copy numbers of molecules. A simple formula is obtained for the relative error between the predictions of the reduced and full master equations for the variance of the substrate concentration fluctuations. The maximum error is reached when modeling moderately or highly efficient enzymes, in which case the error is approximately 30%. The theoretical predictions are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis...

Design principles of noise-induced oscillation in biochemical reaction networks: II. coupled positive and negative feedback loops

Joo, Jaewook; Chauhan, Sanjeev
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/08/2014
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812.80375%
According to the chemical reaction network theory, the topology of a certain class of chemical reaction networks, regardless of the kinetic details, sets a limit on the dynamical properties that a particular network can potentially admit; the structure of a network predetermines the dynamic capacity of the network. We note that stochastic fluctuations can possibly confer a new dynamical capability to a network. Thus, it is of tremendous value to understand and be able to control the landscape of stochastic dynamical behaviors of a biochemical reaction network as a function of network architecture. Here we investigate such a case where stochastic fluctuations can give rise to the new capability of noise-induced oscillation in a subset of biochemical reaction networks, the networks with only three biochemical species whose reactions are governed by mass action kinetics and with the coupling of positive and negative feedback loops. We model the networks with the master equations and approximate them, using the linear noise approximation. For each network, we read the signal-to-noise ratio value, an indicator of amplified and coherent noise-induced oscillation, off from the analytically derived power spectra. We classify the networks into three performance groups based on the average values of the signal-to-noise ratio and the robustness. We identify the common network architecture among the networks belonging to the same performance group...

Multiscale Analysis of Reaction Networks

Sbano, L.; Kirkilionis, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/02/2008
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698.11805%
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological activity. There are essentially two types of processes related to biochemical reaction networks, the interactions among molecules and interactions involving their conformational changes, so in a sense, their internal state. The first type of processes can be conveniently approximated by the so-called mass-action kinetics, but this is not necessarily so for the second kind where molecular states do not define any kind of density or concentration. In this paper we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space-time scales and the number of particles. The continuum limit procedure naturally creates equations of Fokker-Planck type where the evolution of the concentration occurs on a slower time scale when compared to the evolution of the conformational changes...

Reduction of dynamical biochemical reaction networks in computational biology

Radulescu, Ovidiu; Gorban, Alexander N.; Zinovyev, Andrei; Noel, Vincent
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/05/2012
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Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques.

SABRE: A Tool for Stochastic Analysis of Biochemical Reaction Networks

Didier, Frederic; Henzinger, Thomas A.; Mateescu, Maria; Wolf, Verena
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/05/2010
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The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction networks. SABRE implements fast adaptive uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks. Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain. SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains. Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study. We illustrate the different functionalities of SABRE by means of biological case studies.

Quantifying Stochastic Effects in Biochemical Reaction Networks using Partitioned Leaping

Harris, Leonard A.; Piccirilli, Aaron M.; Majusiak, Emily R.; Clancy, Paulette
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice.; Comment: v3: Final accepted version. 15 pages...

Identifying Biochemical Reaction Networks From Heterogeneous Datasets

Pan, Wei; Yuan, Ye; Ljung, Lennart; Goncalves, Jorge; Stan, Guy-Bart
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/09/2015
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In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed on a biological system; (b) data measured from a biochemical network subjected to different experimental conditions, for example, changes/perturbations in biological inductions, temperature, gene knock-out, gene over-expression, etc. Simultaneous integration of various datasets to perform system identification has the potential to avoid non-identifiability issues typically arising when only single datasets are used.

Global Sensitivity Analysis of Biochemical Reaction Networks via Semidefinite Programming

Waldherr, Steffen; Findeisen, Rolf; Allgöwer, Frank
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/04/2009
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We study the problem of computing outer bounds for the region of steady states of biochemical reaction networks modelled by ordinary differential equations, with respect to parameters that are allowed to vary within a predefined region. Using a relaxed version of the corresponding feasibility problem and its Lagrangian dual, we show how to compute certificates for regions in state space not containing any steady states. Based on these results, we develop an algorithm to compute outer bounds for the region of all feasible steady states. We apply our algorithm to the sensitivity analysis of a Goldbeter--Koshland enzymatic cycle, which is a frequent motif in reaction networks for regulation of metabolism and signal transduction.; Comment: Proceedings of the 17th IFAC World Congress, Seoul, Korea, 2008

Time-Scaled Stochastic Input to Biochemical Reaction Networks

Thomas, Rachel Lee
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação Formato: 1902416 bytes; application/pdf
Publicado em //2010 EN_US
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Biochemical reaction networks with a sufficiently large number of molecules may be represented as systems of differential equations. Many networks receive inputs that fluctuate continuously in time. These networks may never settle down to a static equilibrium and are of great interest both mathematically and biologically. Biological systems receive inputs that vary on multiple time scales. Hormonal and neural inputs vary on a scale of seconds or minutes; inputs from meals and circadian rhythms vary on a scale of hours or days; and long term environmental changes (such as diet, disease, and pollution) vary on a scale of years. In this thesis, we consider the limiting behavior of networks in which the input is on a different time scale compared to the reaction kinetics within the network.

We prove analytic results of how the variance of reaction rates within a system compares to the variance of the input when the input is on a different time scale than the reaction kinetics within the network. We consider the behavior of simple chains, single species complex networks, reversible chains, and certain classes of non-linear systems with time-scaled stochastic input, as the input speeds up and slows down. In all cases...