Recently, several theoretical and experimental studies have been undertaken to probe the effect of stochasticity on gene expression (GE). In experiments, the GE response to an inducing signal in a cell, measured by the amount of mRNAs/proteins synthesized, is found to be either graded or binary. The latter type of response gives rise to a bimodal distribution in protein levels in an ensemble of cells. One possible origin of binary response is cellular bistability achieved through positive feedback or autoregulation. In this paper, we study a simple, stochastic model of GE and show that the origin of binary response lies exclusively in stochasticity. The transitions between the active and inactive states of the gene are random in nature. Graded and binary responses occur in the model depending on the relative stability of the activated and deactivated gene states with respect to that of mRNAs/proteins. The theoretical results on binary response provide a good description of the 'all-or-none' phenomenon observed in an eukaryotic system.

A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e., patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z. The protein product x of X controls the synthesis of protein product y of Y. Proteins x and y jointly regulate the synthesis of z proteins from the gene Z. The FFLs, depending on the nature of the regulating interactions, can be of eight different types which can again be classified into two categories: coherent and incoherent. In this paper, we study the noise characteristics of FFLs using the Langevin formalism and the Monte Carlo simulation technique based on the Gillespie algorithm. We calculate the variances around the mean protein levels in the steady states of the FFLs and find that, in the case of coherent FFLs, the most abundant FFL, namely, the type-1 coherent FFL, is the least noisy. This is shown to be true for all parameter values when the FFLs operate above their thresholds of activation/repression. In the case of incoherent FFLs, no such general conclusion can be shown. The results suggest possible relationships between noise, functionality and abundance.

A single gene, regulating its own expression via a positive feedback loop, constitutes a common motif in gene regulatory networks and signalling cascades. Recent experiments on the development of competence in the bacterial population B. subtilis show that the autoregulatory genetic module by itself can give rise to two types of cellular states. The states correspond to the low and high expression states of the master regulator ComK. The high expression state is attained when the ComK protein level exceeds a threshold value leading to a full activation of the autostimulatory loop. Stochasticity in gene expression drives the transitions between the two stable states. In this paper, we explain the appearance of bimodal protein distributions in B. subtilis cell population in the framework of three possible scenarios. In two of the cases, bistability provides the basis for binary gene expression. In the third case, the system is monostable in a deterministic description and stochasticity in gene expression is solely responsible for the appearance of the two expression states.

Appropriate regulation of gene expression is essential to ensure that protein synthesis occurs in a selective manner. The control of transcription is the most dominant type of regulation mediated by a complex of molecules such as transcription factors. In general, regulatory molecules are of two types: activator and repressor. Activators promote the initiation of transcription whereas repressors inhibit transcription. In many cases, they regulate the gene transcription on binding the promoter mutually exclusively and the observed gene expression response is either graded or binary. In experiments, the gene expression response is quantified by the amount of proteins produced on varying the concentration of an external inducer molecules in the cell. In this paper, we study a gene regulatory network where activators and repressors both bind the same promoter mutually exclusively. The network is modeled by assuming that the gene can be in three possible states: repressed, unregulated, and active. An exact analytical expression for the steady-state probability distribution of protein levels is then derived. The exact result helps to explain the experimental observations that in the presence of activator molecules the response is graded at all inducer levels, whereas in the presence of both activator and repressor molecules, the response is graded at low and high inducer levels and binary at an intermediate inducer level.

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes, gene A and gene B, which synthesize the TFs and the target gene proteins, respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with the knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx 3.1, are explained with the help of the stochastic model of TF-regulated gene expression.