Mathematical models of haploinsufficiency

We study simple mathematical models of gene expression to explore the possible origins of haploinsufficiency (HI). In a diploid organism, each gene exists in two copies and when one of these is mutated, the amount of proteins synthesized is reduced and may fall below a threshold level for the onset of some desired activity. This can give rise to HI, a manifestation of which is in the form of a disease. We consider both deterministic and stochastic models of gene expression and suggest possible scenarios for the occurrence of HI in the two cases. In the stochastic case, random fluctuations around the mean protein level give rise to a finite probability that the protein level falls below a threshold. Increased gene copy number and faster gene expression kinetics reduce the variance around the mean protein level. The difference between slow and fast gene expression kinetics, as regards response to a signaling gradient, is further pointed out. The majority of results reported in the paper are derived analytically.