A Bayesian approach to characterize fold change detection in Dictyostelium Discoideum

Abstract

The survivability of Dictyostelium cells is highly dependent on how cells sense and response to cyclic-AMP chemoattractant. A key factor in the sense-response mechanism is a feature called 'fold change detection' (FCD), where cells response to the fold changes in stimulus as opposed to its absolute values. Studies have proposed models of the signalling pathway for the sense-response mechanism and skeletal network motifs that exhibit FCD. However, FCD properties in models of sense-response mechanism compatible with experiments that exhibit FCD are poorly understood. In this thesis, we characterize the properties of FCD of Dictyostelium cells by using a mathematical model of experiments that incorporates biochemical variables of the signalling pathway. We created a population of virtual cells by estimating posterior distributions of the model parameters using a Bayesian method. We studied the responses of the virtual cells to various fold changes in stimulus and found that the population of cells is more consistent in sensing lower fold changes. By computing the overlapping areas of distribution of responses we found that the population of cells can distinguish lower fold changes better than higher fold changes. We propose a hyperbolic equation to describe the stimulus-response relation with a logarithmic relation to characterize the uncertainties of the stimulus. We inferred the posterior probability of detecting fold changes using Bayes' theorem and introduce a novel model of prior probability of fold changes. We found that the chances of detecting lower fold changes is higher and posteriors are biased strongly by the conditional probability. To derive the population of cells' perception of fold change, a Bayesian Observer model is constructed and evaluated. It is found that the population of cells perceive uncertainties of lower fold changes better than higher fold changes. There is also a stark difference between perceptions derived from priors modelled from chemotaxis experiment and priors from known families of distribution. We quantified the biases in the perceptions and discovered that biases are more prominent in higher fold changes. The fold distinguishability threshold is also evaluated and its relation with the perceptual bias examined. Our work shows that the characterization of FCD in models of sense-response mechanism can derive theoretical insights not seen in experiments and impose constraints for model selection.

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