Designing experiments to understand the variability in biochemical reaction networks

Abstract

Exploiting the information provided by the molecular noise of a biological process has proved to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single-cell measurements. However, quantifying this additional information a priori, to decide whether a single-cell experiment might be beneficial, is currently only possible in systems where either the chemical master equation is computationally tractable or a Gaussian approximation is appropriate. Here, we provide formulae for computing the information provided by measured means and variances from the first four moments and the parameter derivatives of the first two moments of the underlying process. For stochastic kinetic models for which these moments can be either computed exactly or approximated efficiently, the derived formulae can be used to approximate the information provided by single-cell distribution experiments. Based on this result, we propose an optimal experimental design framework which we employ to compare the utility of dual-reporter and perturbation experiments for quantifying the different noise sources in a simple model of gene expression. Subsequently, we compare the information content of a set of experiments which have been performed in an engineered light-switch gene expression system in yeast and show that well-chosen gene induction patterns may allow one to identify features of the system which remain hidden in unplanned experiments.

Variability among individuals is generated at the gene expression level

“…In addition, efforts to develop predictive systems biology models using both experimental and theoretical network approaches are revealing the complexity of factors that influence biochemical pathways, even at the single cell level, producing measureable intracellular fluctuations that lead to higher-level effects (Elowitz et al 2002, Rosenfeld et al 2005. For example biochemical parameters that can be accurately described in vitro using MichaelisMenten parameters are not well described in vivo, but have been shown to be affected by microscale intracellular states such as metabolic fluxes, concentration control coefficients, and cell history (Klipp et al 2004, Ruess et al 2013. These all potentially add layers where variation may be affected.…”

Identification and Control of Cell Populations

“…The aim here is to determine a priori which perturbation signals and which measurements will maximize the information on the underlying chemical process that can be extracted from experimental data, Encyclopedia of Systems and Control DOI 10.1007/978-1-4471-5102-9_92-1 © Springer-Verlag London 2014 reducing the risk of conducting expensive but uninformative experiments. One can show that, given a tentative model for the biochemical process, the moments of the stochastic process X.t/ (and cross X.t/-parameter moments in the presence of extrinsic variability) can be used to approximate the Fischer information matrix and hence characterize the information that particular experiments contain about the model parameters; an approximation of the Fischer information based on the first two moments was derived in Komorowski et al (2011) and an improved estimate using correction terms based on moments up to order 4 was derived in Ruess et al (2013). Once an estimate of the Fischer information matrix is available, one can design experiments to maximize the information gained about the parameters of the model.…”

Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space

“…For higher orders, the solution of the minimal moment equations was on average up to 80%-90% faster. Specifically for applications where moments have to be computed iteratively, such as for parameter inference 21 or experiment design, 19,27 this is extremely important and may determine whether algorithms that are typically used in such applications require hours or days of running time. …”