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Studies on the role of fluctuations in signal propagation and on gene regulation in monoclonal bacterial population have been extensively pursued based on the machinery of two-component system. The bacterial two-component system shows noise utilisation through its inherent plasticity. The fluctuations propagation takes place using the phosphotransfer module and the feedback mechanism during gene regulation. To delicately observe the noisy kinetics the generic cascade needs stochastic investigation at the mRNA and protein levels. To this end, we propose a theoretical framework to investigate the noisy signal transduction in a generic two-component system. The model shows reliability in information transmission through quantification of several statistical measures. We further extend our analysis to observe the protein distribution in a population of cells. Through numerical simulation, we identify the regime of the kinetic parameter set that generates a stability switch in the steady state distribution of proteins. The results of our theoretical analysis show key features of the network. The noise permeation and information propagation in the autoregulation module is feeble. However, the phosphotransfer module compensates such weakness and plays a significant role in information transmission. The bimodality due to fluctuations pampers the emergence of persistence in an isogenic bacterial pool., Revised version 11 pages, 6 figures, 1 table

\textit{Vibrio harveyi} and \textit{Vibrio cholerae} have quorum sensing pathways with similar design and highly homologous components including multiple small RNAs (sRNAs). However, the associated luminescence phenotypes of strains with sRNA deletions differ dramatically: in \textit{V. harveyi}, the sRNAs act additively; however, in \textit{V. cholerae}, the sRNAs act redundantly. Furthermore, there are striking differences in the luminescence phenotypes for different pathway mutants in \textit{V. harveyi} and \textit{V. cholerae}. However these differences have not been connected with the observed differences for the sRNA deletion strains in these bacteria. In this work, we present a model for quorum sensing induced luminescence phenotypes focusing on the interactions of multiple sRNAs with target mRNA. Within our model, we find that one key parameter -- the fold-change in protein concentration necessary for luminescence activation -- can control whether the sRNAs appear to act additively or redundantly. For specific parameter choices, we find that differences in this key parameter can also explain hitherto unconnected luminescence phenotypes differences for various pathway mutants in \textit{V. harveyi} and \textit{V. cholerae}. The model can thus provide a unifying explanation for observed differences in luminescence phenotypes and can also be used to make testable predictions for future experiments., 10 pages, 6 figures and 1 table

Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot., Comment: RevTex4, 13 pages, 4 figures

The Fisher and Burgers' equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the traveling wavefront is dependent on the relaxation time in Fisher equation, memory effects significantly smoothen out the shock wave nature of Burgers' solution, without making any influence on the corresponding wave speed. We numerically analyze the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow travelling wave solution to exist for appreciable finite memory effect., 6 pages, 2 figures, RevTex4

We study the steady state properties of a phenomenological two-state predator model in presence of correlated Gaussian white noise. Based on the corresponding Fokker-Planck equation for probability distribution function the steady state solution of the probability distribution function and its extrema have been investigated. We show for a typical value of noise correlation there is a giant loss of bistability which in turn prevents the prey population from going into extinction., Comment: RevTex, 10 pages, 4 figures

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. Based on a relation between the dissipation of the system and the response function of the reservoir driven by external noise we derive the generalized Kramers' rate for this nonequilibrium open system., major revisions, 28 pages

We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for attainment of steady state for this nonequilibrium open system and calculate the adiabatic noise-induced rate of escape of the particle over a barrier., 6 pages, 3 figures

We consider the motion of a particle in a force field subjected to adiabatic, fluctuations of external origin. We do not put the restriction on the type of stochastic process that the noise is Gaussian. Based on a method developed earlier by us [ J. Phys. A {\bf 31} (1998) 3937, 7301] we have derived the equation of motion for probability distribution function for the particle on a coarse-grained timescale $\Delta t$ assuming that it satisfies the separation of timescales; $|\mu |^{-1} \ll \Delta t \ll \tau_c$, where $\tau_c$ is the correlation time of fluctuations. $|\mu |^{-1}$ refers to the inverse of the damping rate (or, the largest of the eigenvalues of the unperturbed system) and sets the shortest timescale in the dynamics in contrast to the conventional theory of fast fluctuations. The equation includes a third order noise term. We solve the equation for a Kramers' type potential and show that although the system is thermodynamically open, appropriate boundary conditions allow the distinct steady states. Based on the exact solution of the third order equation for the linearized potential and the condition for attainment of the steady states we calculate the adiabatic noise-induced rate of escape of a particle confined in a well. A typical variation of the escape rate as a function of dissipation which is reminiscent of Kramers' turn-over problem, has been demonstrated., Comment: 27 pages, 4 figures