Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session Y9: Stochastic Processes in Biological Systems II |
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Sponsoring Units: GSNP Chair: Leah Shaw, The College of William and Mary Room: 303 |
Friday, March 20, 2009 8:00AM - 8:12AM |
Y9.00001: A Stochastic Single-Molecule Event Triggers Phenotype Switching of a Bacterial Cell Sunney Xie, Paul Choi, Long Cai By monitoring fluorescently labeled lactose permease with single-molecule sensitivity, we investigated the molecular mechanism of how an Escherichia coli cell with the lac operon switches from one phenotype to another. At intermediate inducer concentrations, a population of genetically identical cells exhibits two phenotypes: induced cells with highly fluorescent membranes and uninduced cells with a small number of membrane-bound permeases. We found that this basal-level expression results from partial dissociation of the tetrameric lactose repressor from one of its operators on looped DNA. In contrast, infrequent events of complete dissociation of the repressor from DNA result in large bursts of permease expression that trigger induction of the lac operon. Hence, a stochastic single-molecule event determines a cell's phenotype. [Preview Abstract] |
Friday, March 20, 2009 8:12AM - 8:24AM |
Y9.00002: The role of time scales in extrinsic noise propagation Srividya Iyer-Biswas, Juan Manuel Pedraza, C. Jayaprakash Cell-to cell variability in the number of proteins has been studied extensively experimentally. There are many sources of this stochastic variability or noise that can be classified as intrinsic, due to the stochasticity of chemical reactions and extrinsic, due to environmental differences. The different stages in the production of proteins in response to a stimulus, the signaling cascade before transcription, transcription, and translation are characterized by different time scales. We analyze how these time scales determine the effect of the reactions at each stage on different sources of noise. For example, even if intrinsic noise dominates the fluctuations in mRNA number, for typical degradation rates, extrinsic noise can dominate corresponding protein number fluctuations. Such results are important in determining the importance of intrinsic noise at earlier stages of a genetic network on the products of subsequent stages. We examine cases in which the dynamics of the extrinsic noise can lead to differences from cases in which extrinsic noise arises from static (in time) cell-to-cell variations. We will interpret the experiments of Pedraza et al*. in the light of these results. *J. M. Pedraza et al, Science 25 March 2005:Vol. 307. no. 5717, pp. 1965 - 1969. [Preview Abstract] |
Friday, March 20, 2009 8:24AM - 8:36AM |
Y9.00003: Determination of the equilibrium free energy for pulled single molecules from nonequilibrium work measurements Liao Chen The Jarzynski equality (JE) is widely accepted for extracting equilibrium free energy from non-equilibrium work measured in single-molecule pulling experiments, even though questions remain on its validity and applicability. In this talk, I will show that the JE is actually inapplicable outside the near-equilibrium regime. I will also present a new fluctuation-dissipation theorem (FDT) that is derived within the context of Brownian dynamics. The new FDT agrees with the JE in the near equilibrium regime but it is valid in far nonequilibrium regime where the JE does not stand. \textit{In silico} experiments of unfolding polypeptides show that the new FDT is indeed accurate for far non-equilibrium processes. [Preview Abstract] |
Friday, March 20, 2009 8:36AM - 8:48AM |
Y9.00004: Efficient stochastic sampling of first passage times for multi-scale simulations Navodit Misra, Russell Schwartz Monte Carlo methods have become increasingly popular for simulating stochastic dynamics in biological systems. However, the standard Stochastic Simulation Algorithm (SSA) can become highly inefficient for multi-timescale problems, where important events occur in parallel and at a much slower rate than other relatively unimportant events. We present two new algorithms based on the spectral analysis of Continuous Time Markov Model (CTMM) graphs to accelerate sampling of rare events in SSA models. These methods are well suited for simulating a broad class of ``stiff'' reaction networks such as models of bond networks and nucleation-limited self-assembly in biological systems. [Preview Abstract] |
Friday, March 20, 2009 8:48AM - 9:00AM |
Y9.00005: Dynamics of segregation of polymers in a confined geometry Ya Liu, Bulbul Chakraborty Chromosomes are enormous DNA molecules living in the crowded, confined environment of a cell. They carry important genetic information and are stably propagated to new generations through replication. During the replication, two identical DNA molecules are generated and segregate rapidly into opposite pole of the cell. We have used numerical simulation to investigate the effects of confinement on the segregation of two identical self-avoiding chains. Simulation shows the existence of a transition from a mixing state to a demixing state with changes in the confining geometry. Using the blob picture, we construct a free energy function that depends on the distance between the two chains. We describe the dynamics of segregation as a stochastic process driven by this energy function. We will present comparisons of our theoretical results with numerical simulations. [Preview Abstract] |
Friday, March 20, 2009 9:00AM - 9:12AM |
Y9.00006: Modeling DNA unhooking from a single post as a translocation process Nabil Laachi, Jaeseol Cho, Kevin Dorfman We will present theoretical results on the stochastic unhooking of a long DNA chain from an isolated, stationary micropillar obtained by mapping the unhooking process to the translocation of a long chain through a nanopore. We show how stochastic methods, developed for DNA translocation, can thus be utilized to study chain-post unhooking. In particular, implementing such methods leads to the full probability distribution of the unhooking time and the ensuing moments in a fast and efficient manner for a wide range of chain and field parameters. The results thus obtained compare favorably to more realistic (and computationally intense) Brownian Dynamics simulation data, indicating that the finite size of the insulating micropillar and the elasticity of the DNA make at most a small contribution to the dynamics. We will also address the relevant electric fields and time scales for this process, making a connection between the theoretical data obtained here and experimental separations. [Preview Abstract] |
Friday, March 20, 2009 9:12AM - 9:24AM |
Y9.00007: Evolutionary advantage of a mixed strategy for the competence phenotype in bacteria Christopher Wylie, Herbert Levine, David Kessler Under certain stressful conditions, bacterial species such as \textit{B. subtilis} undergo a differentiation process in which a \textit{finite subpopulation} transiently and stochastically enters the ``competent'' state. This state is defined by the ability to import and homologously incorporate extracellular DNA fragments into the genome. This ability is accompanied by a reduced growth rate that tends to slow adaptive evolution. On the other hand, the increased genetic diversity generated by recombination tends to speed evolution. Using stochastic simulation and analytic methods, we show that this tradeoff implies that a ``mixed strategy'' optimizes the rate at which populations acquire beneficial mutations. [Preview Abstract] |
Friday, March 20, 2009 9:24AM - 9:36AM |
Y9.00008: Physical limits on computation by assemblies of allosteric proteins John Robinson Assemblies of allosteric proteins are the principle information processing devices in biology. Using the Ca$^{2+}$-sensitive cardiac regulatory assembly as a paradigm for Brownian computation, we examine how system complexity and system resetting impose physical limits on computation. Nearest-neighbor-limited interactions among assembly components constrains the topology of the system's macrostate free energy landscape and produces degenerate transition probabilities. As a result, signaling fidelity and deactivation kinetics can not be simultaneously optimized. This imposes an upper limit on the rate of information processing by assemblies of allosteric proteins that couple to a single ligand type. [Preview Abstract] |
Friday, March 20, 2009 9:36AM - 9:48AM |
Y9.00009: Calcium waves in the the maturing oocyte Aman Ullah, Ghanim Ullah, Peter Jung, Khaled Machaca Calcium waves in oocytes are sustained by release of Ca2+ from the endoplasmic reticulum (ER) through clustered release channels. As the oocytes matures, a) the calcium waves slow down by about a factor of two, b) the overall duration of Ca2+ elevation grows substantially, and c) the cell is more susceptible to wave initiation. At the same time, the kinetics of release of Ca2+ from a single cluster is changed only insignificantly. Based on a computational model that accurately reproduces elemental Ca2+ release kinetics from channel clusters, we propose that the changing spatial organization of signaling effectors is a common underlying cause for all the above described observations as the Ca2+ signaling machinery matures. [Preview Abstract] |
Friday, March 20, 2009 9:48AM - 10:00AM |
Y9.00010: Calcium puffs: From microdomain to a channel. Divya Swaminathan, Peter Jung Calcium puffs describe the release of calcium ($Ca^{2+}$) ions from internal stores into the cytosol through clusters of up to tens of ion channels. It is believed that during the release process, when the channels open, steep $Ca^{2+}$ concentration gradients are established around the cluster. These large local concentrations are consequential as they determine the opening and closing rates of the ion channel and therefore control receptor kinetics. We present a computational study, wherein we simulate the release and diffusion of $Ca^{2+}$ and its interaction with buffers and indicator dyes around one channel cluster. Our goal is to relate local steep $Ca^{2+}$ gradients with experimentally observable microdomain-averaged $Ca^{2+}$ concentrations thereby putting the high concentration hypothesis to test. [Preview Abstract] |
Friday, March 20, 2009 10:00AM - 10:12AM |
Y9.00011: Dynamical Phase Transitions In Periodically Driven Model Neurons Jan R. Engelbrecht$^1$, Renato Mirollo$^2$ Transitions between dynamical states in integrate-and-fire (IF) neuron models with periodic stimuli result from tangent or discontinuous bifurcations of a return map. We study their characteristic scaling laws and show that discontinuous bifurcations exhibit a new kind of phase transition intermediate between continuous and first order. We then consider a much more complicated Hodgkin-Huxley type of model and show that in the presence of periodic stimuli an attracting 2D invariant subspace develops in the 7D state space. A Poincare section on this subspace yields a 1D return map, remarkably similar to the IF case. This reduction to 1D map dynamics should extend to real neurons in a periodic current clamp setting. [Preview Abstract] |
Friday, March 20, 2009 10:12AM - 10:24AM |
Y9.00012: Stochastic and Deterministic Flagellar Dynamics Provide a Mechanism for Eukaryotic Swimming Reorientation Marco Polin, Idan Tuval, Knut Drescher, Raymond Goldstein The biflagellated alga \textit{Chlamydomonas reinhardtii} is a good model organism to study the origin of flagellar synchronization. Here we employ high-speed imaging to study the beating of the two flagella of \textit{Chlamydomonas}, and show that a single cell can alternate between two distinct dynamical regimes: asynchronous and synchronous. The asynchronous state is characterized by a large interflagellar frequency difference. In the synchronous state, the flagella beat in phase for lengthy periods, interrupted episodically by an extra beat of either flagellum. The statistics of these events are consistent with a model of hydrodynamically coupled noisy oscillators. Previous observations have suggested that the two flagella have well separated intrinsic beat frequencies, and are synchronized by their mutual coupling. Our analysis shows instead that the synchronized state is incompatible with coupling-induced synchronization of flagella with those intrinsic frequencies. This suggests that the beat frequencies themselves are under the control of the cell. Moreover, high-resolution three-dimensional tracking of swimming cells provides strong evidence that these dynamical states are related to non-phototactic reorientation events in the trajectories, yielding a eukaryotic equivalent of the ``run and tumble'' motion of peritrichously flagellated bacteria. [Preview Abstract] |
Friday, March 20, 2009 10:24AM - 10:36AM |
Y9.00013: Active stochastic oscillations and amplification of mechanical stimuli in a hair cell model Lijuan Han, Alexander Neiman We study signal transduction in spontaneously oscillating hair bundles of an auditory hair cell using a computational model. The effects of intrinsic noise from the Brownian motion of hair bundles and from stochastic fluctuations of transduction ion channels as well as periodic fluctuations of the receptor potential are taken into account. The model shows the explosion of a canard trajectory near the Hopf bifurcation. We have found that the system's gain of weak mechanical stimuli can be greatly enhanced when the system operates slightly beyond the Hopf bifurcation, i.e. in the canard region. The gain can also be optimized by tuning the noise intensity. [Preview Abstract] |
Friday, March 20, 2009 10:36AM - 10:48AM |
Y9.00014: The co-existence of spirals with multiple rates of rotation Joseph Tranquillo Two findings in homogeneous reaction-diffusion media are that a single spiral may break into multiple spirals and that rapidly rotating spirals push slowly rotating spirals to domain boundaries. These two findings together fail to explain how cardiac tissue can support multiple stable spirals with different periods of rotation. Numerical simulations are presented in which a thin inhomogeneous region forms a functionally protective barrier between spirals rotating at different rates. The only requirement of the insulating region is that it partially block alternating wavefronts from the fast spiral. Parameters of both reaction and diffusion can result in functional insulation and multiple insulating regions can result in the broad frequency spectrum characteristic of cardiac fibrillation. The results suggest that the healthy ventricle, although containing intrinsic inhomogeneities, is functionally connected, while disease may create functionally disconnected regions. This simple mechanism may shed light on why defibrillation and pacing are not always successful, and why some patients are more susceptible to a transition from tachycardia to fibrillation. [Preview Abstract] |
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