Estimation and Discrimination of Stochastic Biochemical Circuits from Time-Lapse Microscopy Data

David Thorsley,Eric Klavins

doi:10.1371/journal.pone.0047151

Abstract

The ability of systems and synthetic biologists to observe the dynamics of cellular behavior is hampered by the limitations of the sensors, such as fluorescent proteins, available for use in time-lapse microscopy. In this paper, we propose a generalized solution to the problem of estimating the state of a stochastic chemical reaction network from limited sensor information generated by microscopy. We mathematically derive an observer structure for cells growing under time-lapse microscopy and incorporates the effects of cell division in order to estimate the dynamically-changing state of each cell in the colony. Furthermore, the observer can be used to discrimate between models by treating model indices as states whose values do not change with time. We derive necessary and sufficient conditions that specify when stochastic chemical reaction network models, interpreted as continuous-time Markov chains, can be distinguished from each other under both continual and periodic observation. We validate the performance of the observer on the Thattai-van Oudenaarden model of transcription and translation. The observer structure is most effective when the system model is well-parameterized, suggesting potential applications in synthetic biology where standardized biological parts are available. However, further research is necessary to develop computationally tractable approximations to the exact generalized solution presented here.

Highlights

Developing an understanding of biological phenomena through modeling requires the notion of a state that captures the essential components of the system and a model that describes its essential functions
Consider a reaction network in a chamber that satisfies the standard assumptions of stochastic chemical kinetics [8] and contains a set of n species S~fS1,S2, . . . Sng that interact along a set of m reaction channels R~fR1,R2, . . . Rmg
A fundamental issue limiting our understanding of the dynamics of cellular networks is that of sensing

Summary

Introduction

Developing an understanding of biological phenomena through modeling requires the notion of a state that captures the essential components of the system and a model that describes its essential functions. When a collection of cells is considered in aggregate, measurement noise is usually primarily responsible for complicating the problem of identifying state and model parameters in genetic networks. At the single-cell level, the presence of cellular variability in experimental data [1] introduces systemic noise that further complicates this problem. Noise can be used as a tool in the identification process. Munsky et al [2] demonstrate the power of using both transient and steady-state noise statistics in parameter identification, as using both types of statistics yields more information about cellular parameters than steady-state noise alone. Dunlop et al [3] use the averages of correlations in expression level to identify regulatory elements in Escherichia coli

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