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Signal propagation in biochemical networks is characterized by the inherent randomness in gene expression and fluctuations of the environmental components, commonly known as intrinsic and extrinsic noise, respectively. We present a theoretical framework for noise propagation in a generic two-step cascade (S$\rightarrow$X$\rightarrow$Y) regarding intrinsic and extrinsic noise. We identify different channels of noise transmission that regulate the individual and the overall noise properties of each component. Our analysis shows that the intrinsic noise of S alleviates the general noise and information transmission capacity along the cascade. On the other hand, the intrinsic noise of X and Y acts as a bottleneck of information transmission. We also show a hierarchical relationship among the intrinsic noise levels of S, X, and Y, with S exhibiting the highest level of intrinsic noise, followed by X and then Y. This hierarchy is preserved within the two-step cascade, facilitating the highest information transmission from S to Y via X., Comment: Revised version. 12 pages with 4 figures

We present a stochastic framework to decipher fluctuations propagation in classes of coherent feed-forward loops. The systematic contribution of the direct (one-step) and indirect (two-step) pathways is considered to quantify fluctuations of the output node. We also consider both additive and multiplicative integration mechanisms of the two parallel pathways (one-step and two-step). Analytical expression of the output node's coefficient of variation shows contributions of intrinsic, one-step, two-step, and cross-interaction in closed form. We observe a diverse range of degeneracy and non-degeneracy in each of the decomposed fluctuations term and their contribution to the overall output fluctuations of each coherent feed-forward loop motif. Analysis of output fluctuations reveals a maximal level of fluctuations of the coherent feed-forward loop motif of type 1., Comment: 20 pages, 4 figures

We present an information-theoretic formalism to study signal transduction in four architectural variants of a model two-step cascade with increasing input population. Our results categorize these four types into two classes depending upon the effect played out by activation and repression on mutual information, net synergy, and signal-to-noise ratio. Within the Gaussian framework and using the linear noise approximation, we derive the analytic expressions for these metrics to establish their underlying relationships in terms of the biochemical parameters. We also verify our approximations through stochastic simulations., Comment: 10 pages, 4 figures

We present a theoretical formalism to study steady state information transmission in type 1 coherent feed-forward loop motif with an additive signal integration mechanism. Our construct allows a two-step cascade to be slowly transformed into a bifurcation network via a feed-forward loop which is a prominent network motif. Utilizing a Gaussian framework, we show that the feed-forward loop motif harnesses the maximum amount of Shannon mutual information fractions constructed between the input signaling species and the final gene product and also between the two downstream gene products. Our findings may explain why a feed-forward loop is naturally selected by the force of evolution as a motif in bacterial transcription control network while the two-step cascade and bifurcation network are not., Comment: Revised version, 13 pages, 8 figures

Using the formalism of information theory, we analyze the mechanism of information transduction in a simple one-step signaling cascade S$\rightarrow$X representing the gene regulatory network. Approximating the signaling channel to be Gaussian, we describe the dynamics using Langevin equations. Upon discretization, we calculate the associated second moments for linear and nonlinear regulation of the output by the input, which follows the birth-death process. While mutual information between the input and the output characterizes the channel capacity, the Fano factor of the output gives a clear idea of how internal and external fluctuations assemble at the output level. To quantify the contribution of the present state of the input to predict the future output, transfer entropy is computed. We find that higher amount of transfer entropy is accompanied by the greater magnitude of external fluctuations (quantified by the Fano factor of the output) propagation from the input to the output. We notice that low input population characterized by the number of signaling molecules S, which fluctuates in a relatively slower fashion compared to its downstream (target) species X, is maximally able to predict (as quantified by transfer entropy) the future state of the output. Our computations also reveal that with increased linear nature of the input-output interaction, all three metrics of mutual information, Fano factor and, transfer entropy achieve relatively larger magnitudes., Comment: 26 pages, 5 figures

The formalism of partial information decomposition provides independent or non-overlapping components constituting total information content provided by a set of source variables about the target variable. These components are recognised as unique information, synergistic information and, redundant information. The metric of net synergy, conceived as the difference between synergistic and redundant information, is capable of detecting synergy, redundancy and, information independence among stochastic variables. And it can be quantified, as it is done here, using appropriate combinations of different Shannon mutual information terms. Utilisation of such a metric in network motifs with the nodes representing different biochemical species, involved in information sharing, uncovers rich store for interesting results. In the current study, we make use of this formalism to obtain a comprehensive understanding of the relative information processing mechanism in a diamond motif and two of its sub-motifs namely bifurcation and integration motif embedded within the diamond motif. The emerging patterns of synergy and redundancy and their effective contribution towards ensuring high fidelity information transmission are duly compared in the sub-motifs and independent motifs (bifurcation and integration). In this context, the crucial roles played by various time scales and activation coefficients in the network topologies are especially emphasised. We show that the origin of synergy and redundancy in information transmission can be physically justified by decomposing diamond motif into bifurcation and integration motif., Comment: Revised version, 23 pages, 8 figures

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., Comment: Revised version 11 pages, 6 figures, 1 table

We present a stochastic framework to study signal transmission in a generic two-step cascade $\text{S} \rightarrow \text{X} \rightarrow \text{Y}$. Starting from a set of Langevin equations obeying Gaussian noise processes we calculate the variance and covariance while considering both linear and nonlinear production terms for different biochemical species of the cascade. These quantities are then used to calculate the net synergy within the purview of partial information decomposition. We show that redundancy in information transmission is essentially an important consequence of Markovian property of the two-step cascade motif. We also show that redundancy increases fidelity of the signalling pathway., Comment: Revised version, 7 pages, 2 figures

Biochemical networks related to similar functional pathways are often correlated due to cross-talk among the homologous proteins in the different networks. Using a stochastic framework, we address the functional significance of the cross-talk between two pathways. Our theoretical analysis on generic MAPK pathways reveals cross-talk is responsible for developing coordinated fluctuations between the pathways. The extent of correlation evaluated in terms of the information theoretic measure provides directionality to net information propagation. Stochastic time series and scattered plot suggest that the cross-talk generates synchronization within a cell as well as in a cellular population. Depending on the number of input and output, we identify signal integration and signal bifurcation motif that arise due to inter-pathway connectivity in the composite network. Analysis using partial information decomposition quantifies the net synergy in the information propagation through these branched pathways., Comment: Revised version, 17 pages, 5 figures

Intracellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and quantify Fano factor and mutual information. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components are shown to act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions., Comment: 14 pages, 6 figures

We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters are estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the fourteen model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction $\epsilon_{hb}(\mathtt{AT})$ for an $\mathtt{AT}$ base pair and the ring factor $\xi$ turn out to be the most sensitive parameters. In addition, the stacking interaction $\epsilon_{st}(\mathtt{TA}-\mathtt{TA})$ for an $\mathtt{TA}-\mathtt{TA}$ nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization., Comment: 10 pages, 3 figures, 4 tables

To address the dynamics of a Brownian particle on a periodic symmetric substrate under high-frequency periodic forcing with a vanishing time average, we construct an effective Langevin dynamics by invoking Kapitza-Landau time window. Our result is then exploited to simulate the mobility both for original and effective dynamics which are in good agreement with theoretical predictions. This close agreement and the enhancement of mobility are very robust against the tailoring of amplitude-to-frequency ratio which substantiates the correctness of our calculation. Present results may be illuminating for understanding the dynamics of cold atoms in electromagnetic fields., Comment: This paper has been withdrawn by the author due to text overlap with arXiv:nlin/0301033 by other authors

We present a stochastic formalism for signal transduction processes in bacterial two-component system. Using elementary mass action kinetics, the proposed model takes care of signal transduction in terms of phosphotransfer mechanism between the cognate partners of a two-component system, viz, the sensor kinase and the response regulator. Based on the difference in functionality of the sensor kinase, the noisy phosphotransfer mechanism has been studied for monofunctional and bifunctional two component system using the formalism of linear noise approximation. Steady state analysis of both models quantifies different physically realizable quantities, e.g., variance, coefficient of variation, mutual information. The resultant data reveals that both systems reliably transfer information of extra-cellular environment under low external stimulus and at high kinase and phosphatase regime. We extend our analysis further by studying the role of two-component system in downstream gene regulation., Comment: Revised version, 11 pages, 7 figures

Mobile Ad Hoc Network (MANET) is a dynamic multihop wireless network which is established by a set of mobile nodes on a shared wireless channel. One of the major issues in MANET is routing due to the mobility of the nodes. Routing means the act of moving information across an internet work from a source to a destination. When it comes to MANET, the complexity increases due to various characteristics like dynamic topology, time varying QoS requirements, limited resources and energy etc. QoS routing plays an important role for providing QoS in wireless ad hoc networks. The most complex issue in this kind of networks is to find a path between the communication end points satisfying QoS requirement for the user. Nature-inspired algorithms (swarm intelligence) such as ant colony optimization ACO)algorithms have shown to be a good technique for developing routing algorithms for MANETs. In this paper, a new QoS algorithm for mobile ad hoc network has been proposed. The proposed algorithm combines the idea of Ant Colony Optimization (ACO) with Optimized Link State Routing (OLSR) protocol to identify multiple stable paths between source and destination nodes., Comment: This paper has been withdrawn by the author due to a crucial sign error in equation 1

We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end we study a dimerization kinetics of protein as a model system. We follow the dimerization kinetics using a stochastic simulation algorithm and combine it with three different optimization techniques (Genetic Algorithm, Simulated Annealing and Parallel Tempering) to obtain the rate constants involved in each reaction step. We find good convergence of the numerical scheme to the rate constants of the process. We also perform a sensitivity test on the reaction kinetic parameters to see the relative effects of the parameters for the associated profile of the monomer/dimer distribution., Comment: 19 pages, 6 figures

The DevRS two component system of Mycobacterium tuberculosis is responsible for its dormancy in host and becomes operative under hypoxic condition. It is experimentally known that phosphorylated DevR controls the expression of several downstream genes in a complex manner. In the present work we propose a theoretical model to show role of binding sites in DevR mediated gene expression. Individual and collective role of binding sites in regulating DevR mediated gene expression has been shown via modeling. Objective of the present work is two fold. First, to describe qualitatively the temporal dynamics of wild type genes and their known mutants. Based on these results we propose that DevR controlled gene expression follows a specific pattern which is efficient in describing other DevR mediated gene expression. Second, to analyze behavior of the system from information theoretical point of view. Using the tools of information theory we have calculated molecular efficiency of the system and have shown that it is close to the maximum limit of isothermal efficiency., Comment: Title changed in this submission. 33 pages, 16 figures, 2 tables

We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, role of fluctuations of the network output in the regulation of a promoter with random activation/deactivation dynamics has been analyzed., Comment: Revised version, 7 pages, 5 figures

A system-reservoir nonlinear coupling model has been proposed for a situation where the reservoir is nonlinearly driven by an external Gaussian stationary noise which exposes the system particles to a nonequilibrium environment. Apart from the internal thermal noise, the thermodynamically open system encounters two other noises that are multiplicative in nature. Langevin equation derived from the resulting composite system contains the essential features of the interplay between these noise processes. Based on the numerical simulation of the full model potential, we show that one can recover the turnover features of the Kramers dynamics even when the reservoir is modulated nonlinearly by an external noise., Comment: 7 pages, 2 figures

We suggest that the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles). On the basis of the reconstructed bubble size distribution, this is achieved through stochastic optimization of the free energies in terms of Simulated Annealing. In particular, it is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy. This method will be useful to obtain the DNA stacking and hydrogen bonding free energies from single bubble breathing assays rather than equilibrium data., Comment: 6 pages, 4 figures

Mobile Ad-hoc Network (MANET) is the self organizing collection of mobile nodes. The communication in MANET is done via a wireless media. Ad hoc wireless networks have massive commercial and military potential because of their mobility support. Due to demanding real time multimedia applications, Quality of Services (QoS) support in such infrastructure less networks have become essential. QoS routing in mobile Ad-Hoc networks is challenging due to rapid change in network topology. Consequently, the available state information for routing is inherently imprecise. QoS routing may suffer badly due to several factors including radio interference on available bandwidth, and inefficient flooding of information to the adjacent nodes. As a result the performance of the network degrades substantially. This paper aims at the solution for energy efficient QoS routing by best utilization of network resources such as energy and bandwidth. A comparative study shows that despite the overhead due to QoS management, this solution performs better than classical OLSR protocol in terms of QoS and efficient utilization of energy., Comment: 4 Pages, 3 Figures

Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in Bordetella pertussis. The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the bvg locus. To understand the system behavior under elevated temperature, the developed model has been studied in two different ways. First, a quasi-steady state analysis has been carried out for the two component system, comprising of sensor BvgS and response regulator BvgA. The quasi-steady state analysis reveals temperature induced sharp molecular switch, leading to amplification in the output of BvgA. Accumulation of a large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin. Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed in vivo. Furthermore, the developed model has been utilized to study mutants that are impaired in their ability to phosphorylate the transcription factor, BvgA, of the signaling network., Comment: Final version, 15 pages, 11 figures, 2 tables

\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., Comment: 10 pages, 6 figures and 1 table

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes., Comment: 5 pages

We present a framework for analyzing luminescence regulation during quorum sensing in the bioluminescent bacterium \emph{Vibrio harveyi}. Using a simplified model for signal transduction in the quorum sensing pathway, we identify key dimensionless parameters that control the system's response. These parameters are estimated using experimental data on luminescence phenotypes for different mutant strains. The corresponding model predictions are consistent with results from other experiments which did not serve as inputs for determining model parameters. Furthermore, the proposed framework leads to novel testable predictions for luminescence phenotypes and for responses of the network to different perturbations., Comment: 18 pages, 5 figures, IOP style files included

We demonstrate how the stochastic global optimization scheme of Simulated Annealing can be used to evaluate optimum parameters in the problem of DNA breathing dynamics. The breathing dynamics is followed in accordance with the stochastic Gillespie scheme with the denaturation zones in double stranded DNA studied as a single molecule time series. Simulated Annealing is used to find the optimum value of the activation energy for which the equilibrium bubble size distribution matches with a given value. It is demonstrated that the method overcomes even large noise in the input surrogate data., Comment: 9 pages, 4 figures, iop article package included

A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result., Comment: 10 pages, 2 figures, RevTex4, minor corrections

Based on a microscopic system reservoir model,where the associated bath is not in thermal equilibrium, we simulate the nonstationary Langevin dynamics and obtained the generalized nonstationary fluctuation dissipation relation (FDR) which asymptotically reduces to the traditional form. Our Langevin dynamics incorporates non-Markovian process also, the origin of which lies on the decaying term of the nonstationary FDR. We then follow the stochastic dynamics of the Langevin particle based on the Fokker-Planck-Smoluchowski description, in ratchet potential to obtain the steady and time dependent current in an analytic form. We also examine the influence of initial excitation and subsequent relaxation of bath modes on the transport of the Langevin particle to show that the nonequilibrium nature of the bath leads to both strong non-exponential dynamics as well as nonstationary current., Comment: 10 pages, RevTex4, references updated, final version to appear in Journal of Mathematical Physics

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers' theory for activated rate processes in a nonequilibrium open system (one-dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations., Comment: 9 pages, 1 figures, RevTex 4

We present a microscopic Hamiltonian framework to develop Maxwell demon like engine. Our model consists of a equilibrium thermal bath and a non-equilibrium bath; latter generated by driving with an external stationary, Gaussian noise. The engine we develop, can be considered as a device to extract work by modifying internal fluctuations. Our theoretical analysis focusses on finding the essential ingredients necessary for generating fluctuation induced transport under non-equilibrium condition. An important outcome of our model is that the net motion occurs when the non-linear bath is modulated by the external noise, creating the non-zero effective temperature even when the temperature of both the baths are same., Comment: 6 pages, RevTex4

Based on the system heat bath approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation we construct a Langevin equation with multiplicative noise and space dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase induced current as a consequence of state dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise., Comment: 10 pages, 2 figures, iopart.cls included

We propose generalization of escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate to large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength., Comment: 9 pages, 1 figure

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space dependent diffusion coefficient to study the escape rate from a metastable state in the moderate to large damping regime. By considering the dynamics in a model cubic potential we analyze the result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise., Comment: 13 pages, 5 figures, Revtex4. To appear in Physical Review E

While the statistical mechanical description of DNA has a long tradition, renewed interest in DNA melting from a physics perspective is nourished by measurements of the fluctuation dynamics of local denaturation bubbles by single molecule spectroscopy. The dynamical opening of DNA bubbles (DNA breathing) is supposedly crucial for biological functioning during, for instance, transcription initiation and DNA's interaction with selectively single-stranded DNA binding proteins. Motivated by this, we consider the bubble breathing dynamics in a heteropolymer DNA based on a (2+1)-variable master equation and complementary stochastic Gillespie simulations, providing the bubble size and the position of the bubble along the sequence as a function of time. We utilize new experimental data that independently obtain stacking and hydrogen bonding contributions to DNA stability. We calculate the spectrum of relaxation times and the experimentally measurable autocorrelation function of a fluorophore-quencher tagged base-pair, and demonstrate good agreement with fluorescence correlation experiments. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a promoter sequence of the T7 phage. The strong dependence on sequence, temperature and salt concentration for the breathing dynamics of DNA found here points at a good potential for nanosensing applications by utilizing short fluorophore-quencher dressed DNA constructs., Comment: 11 pages, 8 figures

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement., Comment: 12 pages, 8 figures

We study the fluctuation dynamics of localized denaturation bubbles in heteropolymer DNA with a master equation and complementary stochastic simulation based on novel DNA stability data. A significant dependence of opening probability and waiting time between bubble events on the local DNA sequence is revealed and quantified for a biological sequence of the T7 bacteriophage. Quantitative agreement with data from fluorescence correlation spectroscopy (FCS) is demonstrated., Comment: 4 pages, 5 figures, to appear in Physical Review Letters

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well known turnover feature can be restored from our model., Comment: 11 pages, 2 figures

We propose a stochastic Gillespie scheme to describe the temporal fluctuations of local denaturation zones in double-stranded DNA as a single molecule time series. It is demonstrated that the model recovers the equilibrium properties. We also study measurable dynamical quantities such as the bubble size autocorrelation function. This efficient computational approach will be useful to analyse in detail recent single molecule experiments on clamped homopolymer breathing domains, to probe the parameter values of the underlying Poland-Scheraga model, as well as to design experimental conditions for similar setups., Comment: 7 pages, 6 figures, epl.cls

On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002); {\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time dependent quantum transmission coefficient - a quantum analogue of classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for intermediate to strong damping regime with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low temperature regime., Comment: 20 pages, 10 figures, RevTex4

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

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers' equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers' equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders., Comment: 26 pages, RevTex

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure., Comment: 10 pages, To appear in the Proceedings of Statphys - Kolkata IV

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models., Comment: RevTex, 13 pages, 5 figures. To appear in Physical Review E

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit)., Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision)

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., Comment: 6 pages, 2 figures, RevTex4

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\it true probability distribution functions} and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermal activated processes and tunneling., Comment: RevTex, 18 pages, 2 figures; Minor corrections; To appear in Phys. Rev. E

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

Based on a Fokker-Planck description of external Ornstein-Uhlenbeck noise and cross-correlated noise processes driving a dynamical system we examine the interplay of the properties of noise processes and the dissipative characteristic of the dynamical system in the steady state entropy production and flux. Our analysis is illustrated with appropriate examples., Comment: RevTex, 1 figure, To appear in Phys. Rev. E

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 numerically examine the model using a full bistable potential to show that one can recover the turn-over features of the usual Kramers' dynamics when the external noise modulates the reservoir rather than the system directly. We derive the generalized Kramers' rate for this nonequilibrium open system. The theoretical results are verified by numerical simulation., Comment: Revtex, 25 pages, 5 figures. To appear in Phys. Rev. E