Moment estimation for chemically reacting systems by extended Kalman filtering

Ruess, Jakob; Milias-Argeitis, Andreas; Summers, Sean; Lygeros, John

doi:10.1063/1.3654135

Cited by 39 publications

(41 citation statements)

References 17 publications

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“…Alternative methods set out to reduce the computational burden by tracking only low-order moments instead of the whole probability distribution. A standard scheme in this class is moment closure, which provides a means to capture the stochasticity of reactions while leveraging the scalability of ordinary differential equation models (18)(19)(20).Here we introduce a moment-based inference scheme for calibrating stochastic models with heterogeneous single-cell measurements. We show how by extending the method of moment closure by conditional moment equations one can properly account for extrinsic factors.…”

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confidence: 99%

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Moment-based inference predicts bimodality in transient gene expression

Zechner¹,

Ruess²,

Krenn³

et al. 2012

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

208

295

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Recent computational studies indicate that the molecular noise of a cellular process may be a rich source of information about process dynamics and parameters. However, accessing this source requires stochastic models that are usually difficult to analyze. Therefore, parameter estimation for stochastic systems using distribution measurements, as provided for instance by flow cytometry, currently remains limited to very small and simple systems. Here we propose a new method that makes use of low-order moments of the measured distribution and thereby keeps the essential parts of the provided information, while still staying applicable to systems of realistic size. We demonstrate how cell-to-cell variability can be incorporated into the analysis obviating the need for the ubiquitous assumption that the measurements stem from a homogeneous cell population. We demonstrate the method for a simple example of gene expression using synthetic data generated by stochastic simulation. Subsequently, we use time-lapsed flow cytometry data for the osmo-stress induced transcriptional response in budding yeast to calibrate a stochastic model, which is then used as a basis for predictions. Our results show that measurements of the mean and the variance can be enough to determine the model parameters, even if the measured distributions are not well-characterized by low-order moments only-e.g., if they are bimodal.extrinsic variability | high-osmolarity glycerol pathway | moment dynamics | parameter inference | stochastic kinetic models B uilding predictive computational models of intracellular reaction kinetics is still a dauntingly ill-posed task (1), characterized by low-dimensional experimental readouts of the hypothesized high-dimensional process. Single-cell technologies hold promise to partly alleviate this ill-posedness by exploiting the observed variability for the calibration of stochastic kinetic models (2, 3). The same technologies, however, also reveal that isogenic cells in a single population exhibit large cell-to-cell variability (4, 5). The variation can be shown to be a convolution of two sources, namely the intrinsic molecular noise and extrinsic factors that render single cells different even in the absence of molecular noise; in many cases, the latter was reported to dominate the former (4, 5). Extrinsic factors comprise difference in cell size, cell-cycle stage, expression capacity, local growth conditionsto name but a few (6, 7). Thus, although single-cell technology offers a way out of the predicament of ill-posedness, it requires new methods to deal properly with intrinsic and extrinsic variability. The effect of extrinsic variability on the dynamics of stochastic models is studied in refs. 7 and 8, whereas first attempts have been made to address the inverse problem of quantifying the extrinsic (9) and any additional intrinsic (10) components from measurements. Because the latter is based on path sampling, its applicability remains limited to small systems. Naturally, extrinsic variability is bypassed when...

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confidence: 99%

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confidence: 99%

Moment-based inference predicts bimodality in transient gene expression

Zechner¹,

Ruess²,

Krenn³

et al. 2012

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

208

295

View full text Add to dashboard Cite

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“…(34) and (35)] with estimated values derived from available data or from sampling the master equation using Monte Carlo (Chevalier and El-Samad, 2011;Ruess et al, 2011). A technique proposed by Ruess et al (2011) employs a small number of Monte Carlo samples to obtain crude estimates of the higher-order moments. The resulting estimates are interpreted as noisy measurements of the true moment values and an extended Kalman filtering approach is then used to obtain more accurate estimates of these values.…”

Section: Moment Approximationmentioning

confidence: 99%

Markovian dynamics on complex reaction networks

2013

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Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.

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“…Specifically, in these applications interacting molecules play the role of interacting individuals (Balazsi et al, 2011;Goutsias and Jenkinson, 2013;Neuert et al, 2013). These developments have stimulated research on new methods for analyzing IBMs (see, e.g., Munsky and Khammash, 2006;Wolf et al, 2010;Ruess et al, 2011, which opened the path for using larger and more complicated models that are more suitable to represent the complex systems encountered in applications. As a consequence of these new modeling capabilities, problems that were for a long time solvable only using PLMs can now be analyzed (and hence receive renewed interest) in the context of IBMs.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for stochastic individual-based models of ecological systems: a pest control simulation study

Parise

Lygeros

Ruess

2015

Front. Environ. Sci.

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Mathematical models are of fundamental importance in the understanding of complex population dynamics. For instance, they can be used to predict the population evolution starting from different initial conditions or to test how a system responds to external perturbations. For this analysis to be meaningful in real applications, however, it is of paramount importance to choose an appropriate model structure and to infer the model parameters from measured data. While many parameter inference methods are available for models based on deterministic ordinary differential equations, the same does not hold for more detailed individual-based models. Here we consider, in particular, stochastic models in which the time evolution of the species abundances is described by a continuous-time Markov chain. These models are governed by a master equation that is typically difficult to solve. Consequently, traditional inference methods that rely on iterative evaluation of parameter likelihoods are computationally intractable. The aim of this paper is to present recent advances in parameter inference for continuous-time Markov chain models, based on a moment closure approximation of the parameter likelihood, and to investigate how these results can help in understanding, and ultimately controlling, complex systems in ecology. Specifically, we illustrate through an agricultural pest case study how parameters of a stochastic individual-based model can be identified from measured data and how the resulting model can be used to solve an optimal control problem in a stochastic setting. In particular, we show how the matter of determining the optimal combination of two different pest control methods can be formulated as a chance constrained optimization problem where the control action is modeled as a state reset, leading to a hybrid system formulation.

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Moment estimation for chemically reacting systems by extended Kalman filtering

Cited by 39 publications

References 17 publications

Moment-based inference predicts bimodality in transient gene expression

Moment-based inference predicts bimodality in transient gene expression

Markovian dynamics on complex reaction networks

Bayesian inference for stochastic individual-based models of ecological systems: a pest control simulation study

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