Systematic Reduction of a Stochastic Signalling Cascade Model

Dong, Colin Guangqiang; Jakobowski, Luke; McMillen, David R.

doi:10.1007/s10867-006-9005-0

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…[26,21]). Such a simple model has been used successfully in a variety of applications and can generate data with the same statistical behaviour as more complicated models [27,28]. We assume that the process begins with the production of mRNA molecules (r) at rate k r .…”

Section: Resultsmentioning

confidence: 99%

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models

Komorowski

Costa

Rand

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

195

275

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We present a novel and simple method to numerically calculate Fisher information matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function that leads to an efficient computational algorithm. Our approach reduces the problem of calculating the Fisher information matrix to solving a set of ordinary differential equations. This is the first method to compute Fisher information for stochastic chemical kinetics models without the need for Monte Carlo simulations. This methodology is then used to study sensitivity, robustness, and parameter identifiability in stochastic chemical kinetics models. We show that significant differences exist between stochastic and deterministic models as well as between stochastic models with time-series and time-point measurements. We demonstrate that these discrepancies arise from the variability in molecule numbers, correlations between species, and temporal correlations and show how this approach can be used in the analysis and design of experiments probing stochastic processes at the cellular level. The algorithm has been implemented as a Matlab package and is available from the authors upon request. U nderstanding the design principles underlying complex biochemical networks cannot be grasped by intuition alone (1). Their complexity implies the need to build mathematical models and tools for their analysis. One of the powerful tools to elucidate such systems' performances is sensitivity analysis (2). Large sensitivity to a parameter suggests that the system's output can change substantially with small variation in a parameter. Similarly large changes in an insensitive parameter will have little effect on the behavior. Traditionally, the concept of sensitivity has been applied to continuous deterministic systems described by differential equations to identify which parameters a given output of the system is most sensitive to; here, sensitivities are computed via the integration of the linearization of the model parameters (2).In modeling biological processes, however, recent years have have witnessed rapidly increasing interest in stochastic models (3), as experimental and theoretical investigations have demonstrated the relevance of stochastic effects in chemical networks (4,5). Although stochastic models of biological processes are now routinely being applied to study biochemical phenomena ranging from metabolic networks to signal transduction pathways (6), tools for their analysis are in their infancy compared to the deterministic framework. In particular, sensitivity analysis in a stochastic setting is usually, if at all, performed by analysis of a system's mean behavior or using computationally intensive Monte Carlo simulations to approximate finite differences of a system's output or the Fisher information matrix with associated sensitivity measures (7,8). The Fisher information has a prominent role in statistics and information theory: It is defined as the variance of the score and therefore all...

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Section: Resultsmentioning

confidence: 99%

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models

Komorowski

Costa

Rand

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

195

275

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“…Partitioning of the EGFR signaling network into modules is not a trivial task, but it leads to a simpler model of the signaling cascade which offers clarity and computational tractability [ 25 ]. Identification of modules based on the clustering of network components and localization of signal control mechanisms is presented as an approach to attaining a simplified version of the EGFR signaling model.…”

Section: Discussionmentioning

confidence: 99%

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

et al. 2009

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BackgroundThe epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is orchestrated. One of the reasons for the complexity of this pathway is the extensive network of inter-connected components involved in the signaling. In the aim of identifying critical mechanisms controlling signal transduction we have performed extensive analysis of an executable model of the EGFR pathway using the stochastic pi-calculus as a modeling language.ResultsOur analysis, done through simulation of various perturbations, suggests that the EGFR pathway contains regions of functional redundancy in the upstream parts; in the event of low EGF stimulus or partial system failure, this redundancy helps to maintain functional robustness. Downstream parts, like the parts controlling Ras and ERK, have fewer redundancies, and more than 50% inhibition of specific reactions in those parts greatly attenuates signal response. In addition, we suggest an abstract model that captures the main control mechanisms in the pathway. Simulation of this abstract model suggests that without redundancies in the upstream modules, signal transduction through the entire pathway could be attenuated. In terms of specific control mechanisms, we have identified positive feedback loops whose role is to prolong the active state of key components (e.g., MEK-PP, Ras-GTP), and negative feedback loops that help promote signal adaptation and stabilization.ConclusionsThe insights gained from simulating this executable model facilitate the formulation of specific hypotheses regarding the control mechanisms of the EGFR signaling, and further substantiate the benefit to construct abstract executable models of large complex biological networks.

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“…Although gene expression involves numerous biochemical reactions, the current common consensus is to model it in terms of only three biochemical species (DNA, mRNA, and protein) and four reaction channels (transcription, mRNA degradation, translation, and protein degradation) (4,7,35). Such a simple model has been successfully used in a variety of applications and can generate data with the same statistical behavior as more complicated models (36,37).…”

Section: Model Of Fluorescent Gene Expressionmentioning

confidence: 99%

Using a Single Fluorescent Reporter Gene to Infer Half-Life of Extrinsic Noise and Other Parameters of Gene Expression

Komorowski

Finkenstädt

Rand

2010

Biophysical Journal

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Fluorescent and luminescent proteins are often used as reporters of transcriptional activity. Given the prevalence of noise in biochemical systems, the time-series data arising from these is of significant interest in efforts to calibrate stochastic models of gene expression and obtain information about sources of nongenetic variability. We present a statistical inference framework that can be used to estimate kinetic parameters of gene expression, as well as the strength and half-life of extrinsic noise from single fluorescent-reporter-gene time-series data. The method takes into account stochastic variability in a fluorescent signal resulting from intrinsic noise of gene expression, kinetics of fluorescent protein maturation, and extrinsic noise, which is assumed to arise at transcriptional level. We use the linear noise approximation and derive an explicit formula for the likelihood of observed fluorescent data. The method is embedded in a Bayesian paradigm, so that certain parameters can be informed from other experiments allowing portability of results across different studies. Inference is performed using Markov chain Monte Carlo. Fluorescent reporters are primary tools to observe dynamics of gene expression and the correct interpretation of fluorescent data is crucial to investigating these fundamental processes of cellular life. As both magnitude and frequency of the noise may have a dramatic effect on the cell fitness, the quantification of stochastic fluctuation is essential to the understanding of how genes are regulated. Our method provides a framework that addresses this important question.

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Systematic Reduction of a Stochastic Signalling Cascade Model

Cited by 5 publications

References 8 publications

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models

Sensitivity, robustness, and identifiability in stochastic chemical kinetics models

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

Using a Single Fluorescent Reporter Gene to Infer Half-Life of Extrinsic Noise and Other Parameters of Gene Expression

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