Determining noisy attractors of delayed stochastic gene regulatory networks from multiple data sources

Gene regulatory networks (GRNs) are stochastic, thus, do not have attractors, but can remain in confined regions of the state space, i.e. the 'noisy attractors', which define the cell type and phenotype.

We propose a gamma-Bernoulli mixture model clustering algorithm (GammaBMM), tailored for quantizing states from gamma and Bernoulli distributed data, to determine the noisy attractors of stochastic GRN. GammaBMM uses multiple data sources, naturally selects the number of states and can be extended to other parametric distributions according to the number and type of data sources available. We apply it to protein and RNA levels, and promoter occupancy state of a toggle switch and show that it can be bistable, tristable or monostable depending on its internal noise level. We show that these results are in agreement with the patterns of differentiation of model cells whose pathway choice is driven by the switch. We further apply GammaBMM to a model of the MeKS module of Bacillus subtilis, and the results match experimental data, demonstrating the usability of GammaBMM.

Implementation software is available upon request.