Oleg Lenive | bioRxiv Science

bioRxiv2015

Inferring extrinsic noise from single-cell gene expression data using Approximate Bayesian Computation.

BackgroundGene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed \"intrinsic noise\", does not account for all the variability between genetically identical cells growing in a homogeneous environment. Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly. In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point.\n\nResultsTo make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules. We employ this algorithm, approximate Bayesian computation, and published gene expression data for Escherichia coli to simultaneously infer the models rate parameters and parameters describing extrinsic noise for 86 genes.

Systems Biology↗

bioRxiv2015

Information Processing by Simple Molecular Motifs and Susceptibility to Noise

Biological organisms rely on their ability to sense and respond appropriately to their environment. The molecular mechanisms that facilitate these essential processes are however subject to a range of random effects and stochastic processes, which jointly affect the reliability of information transmission between receptors and e.g. the physiological downstream response. Information is mathematically defined in terms of the entropy; and the extent of information flowing across an information channel or signalling system is typically measured by the \"mutual information\", or the reduction in the uncertainty about the output once the input signal is known. Here we quantify how extrinsic and intrinsic noise affect the transmission of simple signals along simple motifs of molecular interaction networks. Even for very simple systems the effects of the different sources of variability alone and in combination can give rise to bewildering complexity. In particular extrinsic variability is apt to generate \"apparent\" information that can in extreme cases mask the actual information that for a single system would flow between the different molecular components making up cellular signalling pathways. We show how this artificial inflation in apparent information arises and how the effects of different types of noise alone and in combination can be understood.

Systems Biology↗