Robustness of Cellular Functions

Stelling, Jörg; Sauer, Uwe; Szállási, Zoltán; Doyle, Francis J.; Doyle, John C.

doi:10.1016/j.cell.2004.09.008

Cited by 963 publications

(763 citation statements)

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“…Finally, we also show that certain characteristics of biological networks, such as widespread coupling of nonlinear and irreversible reaction mechanisms, make them particularly amenable to nonclassical effects. These characteristics are common throughout many biotechnologically and biomedically relevant systems, such as transcription/translation and Michaelian enzyme processes, because the nonlinearities they introduce are frequently required to effect the complex dynamics and robust regulation observed 13,[23][24][25][26] .…”

Section: Discussionmentioning

confidence: 99%

Deviant effects in molecular reaction pathways

2006

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In biological networks, any manifestations of behaviors substantially 'deviant' from the predictions of continuousdeterministic classical chemical kinetics (CCK) are typically ascribed to systems with complex dynamics and/or a small number of molecules. Here we show that in certain cases such restrictions are not obligatory for CCK to be largely incorrect. By systematically identifying properties that may cause significant divergences between CCK and the more accurate discrete-stochastic chemical master equation (CME) system descriptions, we comprehensively characterize potential CCK failure patterns in biological settings, including consequences of the assertion that CCK is closer to the 'mode' rather than the 'average' of stochastic reaction dynamics, as generally perceived. We demonstrate that mechanisms underlying such nonclassical effects can be very simple, are common in cellular networks and result in often unintuitive system behaviors. This highlights the importance of deviant effects in biotechnologically or biomedically relevant applications, and suggests some approaches to diagnosing them in situ.Although the temporal evolution of a spatially homogeneous molecular system subject to a set of (bio)chemical reactions is often described macroscopically via the classical chemical kinetics (CCK) formalism through a set of deterministic differential equations (ODEs) 1 -otherwise referred to as 'reaction rate equations' or 'mass action kinetics'-this approach does not substantially reflect the fundamentally random and discrete nature of individual molecular interactions. The latter is well described by the chemical master equation (CME) 2-4 . Although this makes CME an intrinsically much more accurate description of biological or chemical molecular system dynamics, CCK is significantly more efficient computationally and could be viewed as derived from CME via a set of limiting approximations 5 .The conditions under which these approximations hold are often considered to be broadly valid for biological and/or simple chemical systems. However, as shown here, neither is guaranteed to be the case. Breakdowns in the limiting approximations can occur in some of the most basic processes owing to mechanisms that are particularly common in biological systems. These breakdowns then manifest themselves as various 'deviant nonclassical effects'-distinctive behaviors not accounted for by the classical molecular kinetic description-whereby the discrete and/or stochastic nature of reaction events conspires to drive the characteristic behavior of the system substantially away from that predicted by classical kinetics.Notably, we demonstrate that although deviant effects may be stochastic in origin, this is by no means a requirement. The behavior of the system might be accurately characterized by a deterministic formalism, albeit not by CCK. In particular, although CCK dynamics is at times casually interpreted as describing the evolution of CME averages-this is only strictly accurate for purely linear (unimolecular and consta...

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Section: Discussionmentioning

confidence: 99%

Deviant effects in molecular reaction pathways

2006

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“…The spatiotemporal evolution of chemical or electrochemical signals is at the origin of many biological phenomena related with cell growth and distribution as well as with cell communication -see (Murray, 2002b;Stelling et al, 2004;Jin et al, 2005)-. At the level of tissues and organs, neurological activity or cardiac cycles are among the best known examples of relevant biological phenomena also induced by spatiotemporal changes in ion concentrations.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of inhomogeneous patterns in a diffusion–reaction system under structural and parametric uncertainties

Vilas¹,

García²,

Banga³

et al. 2006

Journal of Theoretical Biology

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Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHughNagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feed-back controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feed-back logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.

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Section: Introductionmentioning

confidence: 99%

“…In other cases, parameters can have a weak influence on the system behaviour. In fact, various biological systems seem to have evolved robustness, that is, low sensitivity and thus low variability, against a typical amount of parameter variation (see [7] and references therein) [8 -10].If the parameter variability is fairly small, the width of variable distributions can be computed by expansion of the variables around the mean parameter values. This expansion has been applied [11,12] to study the uncertainty of control coefficients due to errors in reaction elasticities.…”

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confidence: 99%

Biochemical networks with uncertain parameters

Liebermeister

Klipp

2005

IEE Proc. Syst. Biol.

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The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the 'dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients. IntroductionCell simulations aspired to in systems biology [1] require knowledge of enzyme kinetic parameters. However, owing to a lack of measurements, measurement errors and biological variability, most of these parameters are still unknown or uncertain, which turns out to be a major obstacle in large-scale cell modelling. In this situation, a probabilistic description of the parameters can be helpful: to assess the effects of measurement errors, to find out which model results persist for a wide range of parameters, and to derive probabilities for different model outcomes. Besides this, parameter distributions can also be employed to study the natural variability and robustness of biological systems. The effects of temporal random fluctuations in gene expression [2,3] and metabolism [4,5] have been studied. Here, we focus on models with static yet uncertain parameters: the parameters are described by a probability distribution, and the standard deviation of the resulting variable distributions (their variability) reflects how strongly the variables respond to parameter variations. (In this paper, we use the term 'variable' quite generally for quantitative model results, such as concentrations or fluxes in steady state or as functions of time, or functions of them, such as signal amplitudes or durations [6].) Of course, this influence depends on the system, on the variable of interest and on the parameter: at bifurcation points, a small parameter change can even change the qualitative dynamic behaviour. In other cases, parameters can have a weak influence on the system behaviour. In fact, various biological systems seem to have evolved robustness, that is, low sensitivity and thus low variability, against a typical amount of parameter variation (see [7] and references therein) [8 -10].If the parameter v...

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Robustness of Cellular Functions

Cited by 963 publications

References 100 publications

Deviant effects in molecular reaction pathways

Deviant effects in molecular reaction pathways

Stabilization of inhomogeneous patterns in a diffusion–reaction system under structural and parametric uncertainties

Biochemical networks with uncertain parameters

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