The different cell types in a living organism acquire their identity through the process of cell differentiation in which multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role played by a two-gene motif in cell differentiation in a number of cell systems. The two genes express transcription factors which repress each other's expression and autoactivate their own production. A number of theoretical models have recently been proposed based on the two-gene motif to provide a physical understanding of how cell differentiation occurs. In this paper, we study a simple model of cell differentiation which assumes no cooperativity in the regulation of gene expression by the transcription factors. The latter repress each other's activity directly through DNA binding and indirectly through the formation of heterodimers. We specifically investigate how deterministic processes combined with stochasticity contribute in bringing about cell differentiation. The deterministic dynamics of our model give rise to a supercritical pitchfork bifurcation from an undifferentiated stable steady state to two differentiated stable steady states. The stochastic dynamics of our model are studied using the approaches based on the Langevin equations and the linear noise approximation. The simulation results provide a new physical understanding of recent experimental observations. We further propose experimental measurements of quantities like the variance and the lag-1 autocorrelation function in protein fluctuations as the early signatures of an approaching bifurcation point in the cell differentiation process.

Recently, a large number of studies have been carried out on the early signatures of sudden regime shifts in systems as diverse as ecosystems, financial markets, population biology and complex diseases. Signatures of regime shifts in gene expression dynamics are less systematically investigated. In this paper, we consider sudden regime shifts in the gene expression dynamics described by a foldbifurcation model involving bistability and hysteresis. We consider two alternative models, Models 1 and 2, of competence development in the bacterial population B.subtilis and determine some early signatures of the regime shifts between competence and vegetative state. We use both deterministic and stochastic formalisms for the purpose of our study. The early signatures studied include the critical slowing down as a transition point is approached, rising variance and the lag-1 autocorrelation function, skewness and a ratio of two mean first passage times. Some of the signatures could provide the experimental basis for distinguishing between bistability and excitability as the correct mechanism for the development of competence.

Cell differentiation is an important process in living organisms. Differentiation is mostly based on binary decisions with the progenitor cells choosing between two specific lineages. The differentiation dynamics have both deterministic and stochastic components. Several theoretical studies suggest that cell differentiation is a bifurcation phenomenon, well-known in dynamical systems theory. The bifurcation point has the character of a critical point with the system dynamics exhibiting specific features in its vicinity. These include the critical slowing down, rising variance and lag-1 autocorrelation function, strong correlations between the fluctuations of key variables and non-Gaussianity in the distribution of fluctuations. Recent experimental studies provide considerable support to the idea of criticality in cell differentiation and in other biological processes like the development of the fruit fly embryo. In this review, an elementary introduction is given to the concept of criticality in cell differentiation. The correspondence between the signatures of criticality and experimental observations on blood cell differentiation in mice is further highlighted.

Transcriptional regulation by transcription factors and post-transcriptional regulation by microRNAs constitute two major modes of regulation of gene expression. While gene expression motifs incorporating solely transcriptional regulation are well investigated, the dynamics of motifs with dual strategies of regulation, i.e., both transcriptional and posttranscriptional regulation, have not been studied as extensively. In this paper, we probe the dynamics of a four-gene motif with dual strategies of regulation of gene expression. Some of the functional characteristics are compared with those of a two-gene motif, the genetic toggle, employing only transcriptional regulation. Both the motifs define positive feedback loops with the potential for bistability and hysteresis. The four-gene motif, contrary to the genetic toggle, is found to exhibit bistability even in the absence of cooperativity in the regulation of gene expression. The four-gene motif further exhibits a novel dynamical feature in which two regions of monostability with linear threshold response are separated by a region of bistability with digital response. Using the linear noise approximation (LNA), we further show that the coefficient of variation (a measure of noise), associated with the protein levels in the steady state, has a lower magnitude in the case of the four-gene motif as compared to the case of the genetic toggle. We next compare transcriptional with post-transcriptional regulation from an information theoretic perspective. We focus on two gene expression motifs, Motif 1 with transcriptional regulation and Motif 2 with post-transcriptional regulation. We show that amongst the two motifs, Motif 2 has a greater capacity for information transmission for an extended range of parameter values. * sghosh@kol.amity.edu † indrani@jcbose.ac.in

In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this paper, we study a reaction-diffusion (RD) model of popoulation growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortatility rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at the bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations .