Consequences of resource constraint on stochastic gene regulation

In this contribution, we systematically investigate how intracellular constraints on resources impact stochastic gene expression and regulation. We first consider a model of a single gene with discrete integer-valued mRNA and protein copy numbers that evolved stochastically based on probability occurrences of biochemical reactions. The resource constraints are imposed by considering a finite number of ribosomes binding to mRNAs to form a translation complex, and the complex dissociates to give back a free ribosome and a protein molecule. Analytical analysis reveals that ribosomal constraints reduce the magnitude of stochastic fluctuations in protein copy numbers, and also lead to lower statistical single-cell concordance between mRNA and protein levels of the same gene. We also identify parameter regimes where copy-number fluctuations become sub-Poisson - less variation than expected from a Poisson distribution. Considering fast ribosomal binding/unbinding to mRNAs, we also develop a reduced stochastic model that faithfully captures the statistical fluctuation of the system. Finally, we extend the model to consider an incoherent feedforward loop, and our results show noise minimization by resource constraints in gene regulation.