Abstract
Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity.
Highlights
On the single-cell level many biological processes are influenced by stochastic fluctuations [1,2,3]
We show by means of two simulation examples that using mesoscopic descriptions based on the system size expansions and moment-closure approximations can reduce this estimation error compared to inference using a macroscopic description
For the Janus family of kinases (JAK)/signal transducer and activator of transcription (STAT) pathway where experimental data is available, we show that one parameter that was not structurally identifiable when using a macroscopic description becomes structurally identifiable when using a mesoscopic description for parameter estimation
Summary
On the single-cell level many biological processes are influenced by stochastic fluctuations [1,2,3]. This stochasticity must be accounted for when constructing quantitative mechanistic models for the behavior of cells. Dynamics of stochastic biochemical processes are modeled using the Chemical Master Equation (CME) [4]. To achieve high prediction accuracy, the parameters of the CME have to be inferred from experimental data. This inference is challenging and the development of new methods to perform efficient inference is the subject of current research
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