Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session T9: Focus Session: Stochastic Processes in Biological Systems I |
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Sponsoring Units: GSNP Chair: Uwe C. Tauber, Virginia Polytechnic Institute and State University Room: 303 |
Wednesday, March 18, 2009 2:30PM - 3:06PM |
T9.00001: Stochastic models of viral infection Invited Speaker: Tom Chou We develop biophysical models of viral infections from a stochastic process perspective. The entry of enveloped viruses is treated as a stochastic multiple receptor and coreceptor engagement process that can lead to membrane fusion or endocytosis. The probabilities of entry via fusion and endocytosis are computed as functions of the receptor/coreceptor engagement rates. Since membrane fusion and endocytosis entry pathways can lead to very different infection outcomes, we delineate the parameter regimes conducive to each entry pathway. After entry, viral material is biochemically processed and degraded as it is transported towards the nucleus. Productive infections occur only when the material reaches the nucleus in the proper biochemical state. Thus, entry into the nucleus in an infectious state requires the proper timing of the cytoplasmic transport process. We compute the productive infection probability and show its nonmonotonic dependence on both transport speeds and biochemical transformation rates. Our results carry subtle consequences on the dosage and efficacy of antivirals such as reverse transcription inhibitors. [Preview Abstract] |
Wednesday, March 18, 2009 3:06PM - 3:18PM |
T9.00002: Stochastic modeling of gene regulation by small RNAs Vlad Elgart, Tao Jia, Andrew Fenley, Rahul Kulkarni Recent research has uncovered several examples wherein post-transcriptional regulation by small RNAs plays an important role in critical cellular processes. We considered a stochastic model for regulation of target mRNAs by small RNAs. While the corresponding master equation is analytically intractable, application of the bursty synthesis approximation yields results for the steady-state protein probability distribution and the first moments. We compare our analytical results to stochastic simulation results using the Gillespie algorithm and to the results of linear noise approximation approach. The effects of transcriptional pulsing on protein steady-state expression are also explored within the same formalism. [Preview Abstract] |
Wednesday, March 18, 2009 3:18PM - 3:30PM |
T9.00003: Stochastic modeling of protein-based post-transcriptional regulation Tao Jia, Rahul Kulkarni Recent experiments have enabled monitoring gene expression in living cells at the level of single proteins. Data from such experiments for protein burst-size distribution and burst frequency can be used to obtain analytical expressions for the steady-state protein distribution across a population. We extend this analysis to the case of modulation of gene expression by binding/unbinding of a post-transcriptional regulatory protein. Closed-form analytical expressions and results from stochastic simulations will be presented. In the case that regulator binding results in complete repression of protein expression, the steady-state protein distribution has the same functional form as the unregulated case, once the mRNA degradation rate is appropriately renormalized. For the general case, wherein binding can result in partial repression or even activation of protein expression, we derive an analytical expression for the steady-state distribution which generalizes the result for the unregulated case. [Preview Abstract] |
Wednesday, March 18, 2009 3:30PM - 3:42PM |
T9.00004: Accurate fluctuation prediction in epidemics using stochastic model reduction Eric Forgoston, Ira Schwartz We consider a large-scale dynamical system with stochastic forcing and outline a general theory to reduce the dimension of the stochastic system. The general procedure employs a stochastic normal form coordinate transform and allows one to analytically derive both the stochastic center manifold and the reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. We have applied the theory to a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. When compared with the original model, the reduced dynamical system accurately predicts fluctuations of disease outbreaks both in amplitude and phase. [Preview Abstract] |
Wednesday, March 18, 2009 3:42PM - 3:54PM |
T9.00005: Stochastic disease extinction in multistrain diseases with interacting strains Simone Bianco, Leah Shaw, Ira Schwartz The study of multistrain diseases, diseases with several coexisting strains, is a major challenge for mathematical biology. Examples of such diseases are influenza, HIV, dengue and ebola. In this work we present an agent-based model for multistrain diseases with strain interactions mediated by antibody-dependent enhancement. An individual infected with a strain develops antibodies which will protect him/her against all the strains. When the level of protection wanes, the presence of antibodies will enhance the infectiousness of the individual when an infection with a different strain occurs. This mechanism is called antibody-dependent enhancement (ADE). We use this model to investigate the role that fluctuations due to system size have on disease extinction paths and discuss how interactions mediated by ADE affect rates of disease fade-out. Finally, we discuss the effect that varying the number of strains has on disease extinction. [Preview Abstract] |
Wednesday, March 18, 2009 3:54PM - 4:06PM |
T9.00006: Controlling rare events: optimizing disease extinction with limited vaccine M. Khasin, M.I. Dykman In rare events such as switching between stable states or disease extinction the system has to overcome an effective barrier. The barrier height can be changed by applying a control field. The change is determined by the effective work of the field along the most probable trajectory followed in a rare event. In turn, the barrier change results in an exponentially strong change of the event rate. We study the optimal temporal shape of the control field with a constraint that the time- average field value and the sign of the field are fixed. An example is vaccination with a limited vaccine production rate or control by light intensity with a limited laser power. For a comparatively weak field, for a broad class of rare events, optimal control is accomplished by periodically applying $\delta$-like pulses. We show that the barrier change may display resonant dependence on the pulse period and is linear in the pulse area. For a stronger field, the dependence of the barrier change on the field amplitude becomes system-dependent. The results are applied to simple models of population dynamics. [Preview Abstract] |
Wednesday, March 18, 2009 4:06PM - 4:18PM |
T9.00007: Extinction Time Distribution in Stochastic Lotka-Volterra System Matthew Parker, Alex Kamenev The Lotka-Volterra model is one of the most basic problems in population dynamics. The mean-field solution to this problem predicts oscillatory evolution of two competing populations. However, an account of the discrete nature of agents inevitably results in the extinction of one or both species. We studied the distribution function of times required for such an extinction event to take place. We employed a combination of Monte-Carlo simulations and analytic techniques. As a result we achieved a complete understanding of the distribution function in the limiting cases of long and short extinction times. The long time tail is perfectly described by the lowest eigenvalue of the corresponding Fokker-Planck operator. Moreover, due to time scale separation, one may reduce the initial 2D operator to an effective 1D radial one. Remarkably, in the short time limit the Fokker-Planck approach fails, and one has to resort to the WKB treatment of the full evolution operator of the corresponding discrete stochastic problem. [Preview Abstract] |
Wednesday, March 18, 2009 4:18PM - 4:30PM |
T9.00008: Refined mean-field approaches to ``edge-effects'' in open TASEP's Jiajia Dong, Royce K.P. Zia, Beate Schmittmann We study the totally asymmetric simple exclusion process (TASEP) with a defect site, hopping rate $q <$ 1, at the edge of the system and particles occupying $\ell$ lattice sites. Using two different mean-field approximations, we analyze the behavior of the steady state current $J$ in the presence of the defect as a function of entry rate $\alpha $ and $q.$ In good agreement with Monte Carlo simulations, these two methods bring insight to understanding the significance of having one or a cluster of slow codons (unit of messenger RNA, template of protein synthesis) immediately after initiation during protein synthesis. Related work is published in Journal of Physics A, vol. 41 (2008). [Preview Abstract] |
Wednesday, March 18, 2009 4:30PM - 4:42PM |
T9.00009: Parallel Coupling of Symmetric and Asymmetric Exclusion Processes Konstantinos Tsekouras, Anatoly Kolomeisky A system consisting of a simple symmetric exclusion process (SSEP) and a totally asymmetric exclusion process (TASEP) coupled to each other at every site is constructed as a simplified model of a microtubule and the surrounding medium within the context of intracellular particle transport. Transitions between the channels are allowed at every site of both lattices. A cluster-based mean-field theory allows calculation of stationary phase diagrams, particle currents and densities for symmetric/asymmetric transition rates between the channels. It is shown that in general there are three stationary phases, similar to the case of a single-channel totally asymmetric exclusion process.Density profiles are identical in both channels if transition rates are symmetric, not so if they are asymmetric.At certain limiting values of the transition rates our theory provides exact solutions, so that the system can be described as a partially asymmetric exclusion process (PASEP). Extensive Monte Carlo simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation. Dynamic properties and phase diagrams are discussed by analyzing symmetry requirements and constraints on the particle currents, as are possible implications for the problem of intracellular particle transport. [Preview Abstract] |
Wednesday, March 18, 2009 4:42PM - 4:54PM |
T9.00010: Anomalous diffusion and scaling in the dynamics of coupled stochastic processes. Golan Bel, Ilya Nemenman Stochastic processes are ubiquitous in nature, and multiple dynamical variables in the same physical system can be stochastic simultaneously. Common mathematical treatement of such cases limit the interactions among multiple stochastic variables to simple correlations. However, more complicated couplings are possible as well. For example, for many biochemical reactions, the rate (stochastic) of creation of one substance may depend on the presence of another one, itself stochastic variable. Here we present a theoretical study of one class of such coupled stochastic processes. We observe that, contrary to traditional modeling frameworks, even very weak coupling yields anomalous diffusion. Interestingly, the diffusion exponent cannot be predicted by simple scaling arguments, and anomalous scaling appears as well. Further, we show that even weak inhibitive coupling between the two processes may result in dynamics equivalent to that of the celebrated comb model, where the coupling between the two stochastic variables is so strong that one is able to diffuse only when the other is within a certain range. We compare the model to various mechanisms for generating anomalous diffusion and show that coarse-graining yields behavior equivalent to that of the non-ergodic continuous time random walk. We end with brief discussion of applications of the developed theory to biochemical systems. [Preview Abstract] |
Wednesday, March 18, 2009 4:54PM - 5:06PM |
T9.00011: Subdiffusion in the Internal Dynamics of Peptides Thomas Neusius, Jeremy C. Smith The internal dynamics of biopolymers is a topic of intense current research, both in experiment and theory. Recent experimental results have demonstrated the presence of internal subdiffusion in biopolymers at equilibrium. Molecular dynamics simulation of oligopeptide chains reveals configurational subdiffusion at equilibrium extending from 10$^{-12}$ to 10$^{-8}$~s. We examine the possible origins of the subdiffusion and demonstrate that it arises from the fractal-like structure of the accessible configurational space [PRL \textbf{100}, 188103 (2008)]. [Preview Abstract] |
Wednesday, March 18, 2009 5:06PM - 5:18PM |
T9.00012: Stochastic waiting times of complex biochemical reactions may exhibit universal behavior B. Munsky, G. Bel, N. Sinitsyn, I. Nemenman To model cell regulatory pathways, one must understand completion times of complex, multistep, often reversible biochemical reactions. As transient properties, these completion (first passage) times are typically unobtainable from stationary behavior, and their distributions are known only for simple homogeneous network topologies. Here, we derive explicit formulas for first passage time distributions of various biological models, such as multi-site phosphorylation, kinetic proofreading, and discrete walks along an inhomogeneous line, and others. In many cases, as system size grows, the system behavior frequently becomes simpler, approaching an unexpected universality. Under many conditions, this limiting behavior is deterministic, under others it is a memoryless Markovian dynamics, and the two results are separated by a phase transition. For example, below a critical parameter, the time to complete a given complex multistep reaction obeys a narrow gamma distribution, and above this threshold, waiting times are exponentially distributed. These findings suggest first that possibilities to coarse-grain cellular networks are immense, and second that the common practice of arbitrarily replacing unknown dynamics with ballistic motion or exponential waiting times may be justified in a wide array of circumstances. [Preview Abstract] |
Wednesday, March 18, 2009 5:18PM - 5:30PM |
T9.00013: Mechanisms of large length fluctuations during actin filament growth Matthew B. Smith, Dimitrios Vavylonis Prior TIRF microscopy experiments monitoring the growth of single actin filaments have indicated that the magnitude of growth rate fluctuations, characterized by a ``length diffusion coefficient'' $D$, is much larger than the value expected from a simple monomer-by-monomer polymerization process. Several theoretical studies have explored mini-catastrophes or oligomeric annealing and fragmentation as sources of enhanced fluctuations. We used numerical simulations and analytical theory to examine additional mechanisms that contribute to length fluctuations. Fluctuations caused by cooperative kinetics, in which the rate of monomer addition and/or subtraction depends on the type of nucleotide bound to neighboring actin subunits exhibit qualitatively distinct dependence on actin monomer concentration and on concentration of phosphate than those caused by ``short pauses.'' By comparing to analysis of experimental data, we show that the experimentally measured $D$ values can be distinguished from random noise. Further we propose experiments that will distinguish these sources of fluctuations. We relate our findings to other one-dimensional directed processes, such as in molecular motor walks. [Preview Abstract] |
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