Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session W13: Applications of Statistical and Nonlinear Physics in the Life Sciences |
Hide Abstracts |
Sponsoring Units: GSNP DBP Chair: Uwe Tauber, Virginia Polytechnic Institute and State University Room: D225/226 |
Thursday, March 24, 2011 11:15AM - 11:27AM |
W13.00001: Mean-field theory of four species in cyclic competition C.H. Durney, S.O. Case, M. Pleimling, R.K.P. Zia We consider a simple model of cyclic competition of $M$ species: When a pair of individuals from species $k$ and $k+1$ interact, the latter transforms into the former. Even with no spatial structure, such systems often display interesting and counterintuitive behavior. With possible applications in both biological systems (e.g., Min proteins, E. Coli, lizards) and game theory (e.g., rock-paper-scissors), the $M=3$ case has attracted considerable recent attention. We study a $M=4$ system (with no spatial structure) and find major differences, e.g., (1) the presence of macroscopically many absorbing states, (2) coexistence of species, and (3) violation of the ``law'' of survival of the weakest - a central theme in the $M=3$ case. Like the game of Bridge, the system typically ends with ``partner pairs.'' After describing the full stochastic model and its master equation, we present the mean-field approximation. Several exact, analytic predictions will be shown. Their limitations and implications for the stochastic system will also be discussed. [Preview Abstract] |
Thursday, March 24, 2011 11:27AM - 11:39AM |
W13.00002: Stochastic evolution of four species in cyclic competition: exact and simulation results S.O. Case, C.H. Durney, M. Pleimling, R.K.P. Zia We study a stochastic system with $N$ individuals, consisting of four species competing cyclically: $A+B \longrightarrow A+A$, $\cdots$, $D+A \longrightarrow D+D$. Randomly choosing a pair and letting them react, $N$ is conserved but the fractions of each species evolve non-trivially. At late times, the system ends in a static, absorbing state $-$ typically, coexisting species $AC$ or $BD$. The master equation is shown and solved exactly for $N=4$, providing a little insight into the problem. For large $N$, we rely on simulations by Monte Carlo techniques (with a faster dynamics where a reaction occurs at every step). Generally, the results are in good agreement with predictions from mean field theory, after appropriate rescaling of Monte Carlo time. The theory fails, however, to describe extinction or predict their probabilities. Nevertheless, it can hint at many remarkable behavior associated with extinction, which we discover when studying systems with extremely disparate rates. [Preview Abstract] |
Thursday, March 24, 2011 11:39AM - 11:51AM |
W13.00003: Random inheritance in a stochastic Lotka-Volterra model Ulrich Dobramysl, Gabriel Martinez, Uwe C. T\"auber We introduce a stochastic two-species Lotka-Volterra predator-prey model that includes random inheritance features. Specifically, each individual particle takes on a predation rate value which is determined when the particle is created and is dependent on the particle's parent. Thus we arrive at a simple model for evolution due to selection pressure. We employ Monte Carlo simulations to study the time evolution of the predation rate distribution as a function of the prescribed variability. We find that this model yields a steady state with optimized rates for both predator and prey species. Contrary to, e.g., gene expression models, the rates do not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the predation rate distribution. [Preview Abstract] |
Thursday, March 24, 2011 11:51AM - 12:03PM |
W13.00004: Time-dependent mechanical response of a network model for the cytoskeleton Nasrin Afzal, Michel Pleimling Motivated by a series of experiments that study the response of the cytoskeleton in living cells to time-dependent mechanical forces, we investigate through Monte Carlo simulations a three-dimensional network subjected to time-dependent perturbations. After having prepared the system in a relaxed state, time-dependent shear or stress is applied and the response is monitored. We discuss the possible implications of our results for the time-dependent mechanical response of the cytoskeleton. [Preview Abstract] |
Thursday, March 24, 2011 12:03PM - 12:15PM |
W13.00005: Hopf Bifurcations in a Model for Circadian Rhythms in Arabidopsis Thaliana Orrin Shindell, Randall Tagg Arabidopsis thaliana is a plant used for many fundamental studies, including circadian rhythms. Numerically integrating the 7-equation kinetic model of Locke et al. [J. Theor. Bio. 234 (2005) 383], we have mapped regions of parameter space where circadian expression of key mRNA and proteins undergoes limit cycle oscillation. We seek to relate this to the work of Fukuda et al. [Phys. Rev. Lett. 99 (2007) 098102], where a coupled system of cells individually described by Stuart-Landau equations is used phenomenologically to describe experimentally observed spatio-temporal patterns in the plant leaves. To that end we have done a weakly nonlinear analysis of the system of kinetic equations. We also comment on possible experimental directions to further connect the kinetic models to dynamics in this multi-cellular system. [Preview Abstract] |
Thursday, March 24, 2011 12:15PM - 12:27PM |
W13.00006: Translation with secondary structure: Dynamic blockages in totally asymmetric simple exclusion process Leah Shaw The totally asymmetric simple exclusion process (TASEP) is often used as a model for protein synthesis, with the lattice and particles representing the mRNA and ribosomes, respectively. Here we model the effect of secondary structure (folding) of the mRNA by introducing a dynamic blockage region in the lattice. If the region is unoccupied by particles, the blockage can close and prevent upstream particles from moving into it, representing the folding of that section of mRNA. Reopening of the blockage, allowing particles to pass, represents unfolding. We study the effects of the blockage size, closing/opening probabilities, and TASEP parameters on the particle current and blockage switching rates. [Preview Abstract] |
Thursday, March 24, 2011 12:27PM - 12:39PM |
W13.00007: Rescue Interventions in Biological and Physical Networks Sean Cornelius Gene knockout experiments on single cells have established that expression of most genes is not needed for optimal growth. Yet, environmental and genetic perturbations to these organisms are known to be accompanied by the transient activation of a large number of latent metabolic pathways, suggesting that the temporarily activated reactions increase growth in the presence of perturbations. We have tested this hypothesis computationally and found, surprisingly, that the availability of latent pathways tends in fact to inhibit growth after genetic perturbations. This adverse effect indicates that latent pathway activation is derivative of a suboptimal response and that consequently, growth can actually be improved by removing these pathways from the network. In this talk, I will relate this counterintuitive effect to very recent research showing that a loss in network performance inflicted by an external perturbation can be mitigated by the application of additional perturbations. The challenge is to identify such ``rescues'' under constraints that limit the type of perturbations that can be made. I will present an approach to identify such eligible rescues for general networks modeled as dynamical systems, and present computational examples for biological and physical networks. [Preview Abstract] |
Thursday, March 24, 2011 12:39PM - 12:51PM |
W13.00008: Feedback control for stabilizing chaotic spiral waves during cardiac ventricular fibrillation Ilija Uzelac, John Wikswo, Richard Gray The cardiac arrhythmias that lead to ventricular fibrillation (VF) arise from electrical spiral waves (SW) rotating within the heart with a characteristic period $\tau$. A single drifting SW can degenerate into a chaotic system of multiple SWs and VF. Hence early SW detection and termination is crucial to prevent VF. Time-delayed feedback control (TDFC) is well known approach for stabilizing unstable periodic orbits embedded in chaotic attractors. We hypothesize that cardiac SWs can be stabilized by TDFC with a time-delay of $\tau$. Implementing this approach will require precise, closed-loop control of the charge delivered to the heart during the defibrillation process. To do this, we have developed a 2 kW arbitrary-waveform voltage-to-current converter (V2CC) with a 1 kHz bandwidth that can deliver up to 5 A at 400 V for 500 ms, and a photodiode system for recording in real time an optical electrocardiogram, OECG(t). The feedback signal driving the V2CC will be the time-difference (OECG(t) - OECG(t-T), where we hypothesize that T is $\tau$, the period of the SW. This may dramatically decrease defibrillation voltages by using a defibrillation waveform customized to the VF event, unlike commercial capacitor defibrillators. [Preview Abstract] |
Thursday, March 24, 2011 12:51PM - 1:03PM |
W13.00009: Experimental and theoretical evidence for fluctuation driven activations in an excitable chemical system Harold Hastings, Sabrina Sobel, Richard Field, Scott Minchenberg, Nicole Spinelli, Keith Zauderer An excitable medium is a system in which small perturbations die out, but sufficiently large perturbations generate large ``excitations.'' Biological examples include neurons and the heart; the latter supports waves of excitation normally generated by the sinus node, but occasionally generated by other mechanisms. The ferroin-catalyzed Belousov-Zhabotinsky reaction is the prototype chemical excitable medium. We present experimental and theoretical evidence for that random fluctuations can generate excitations in the Belousov-Zhabothinsky reaction. Although the heart is significantly different, there are some scaling analogies. [Preview Abstract] |
Thursday, March 24, 2011 1:03PM - 1:15PM |
W13.00010: The statistical physics of decision-making in insect colonies Patrick M. Hogan, Thomas Schlegel, Nigel R. Franks, James A.R. Marshall We apply the stochastic methods of statistical physics to analyse collective-decision making in social insect colonies, allowing us to derive the colony-level behaviour from an individual-level model. This contrasts with the traditional approach where a differential equation model, with or without arbitrary noise terms, is assumed. Social insect colonies vary in size from on the order 100 to 10,000,000 individuals, and such a statistical physics approach allows us explicitly to derive equations for both the average behaviour and the noise in the system, across this entire scale. We develop such a framework by building upon an existing stochastic model of opinion formation to model the decision-making processes in emigrating ant colonies. This new model is both driven by and evaluated against results from experiments with rock ants. This allows us to elucidate rigorously the role played by the individual-level phenomena of direct switching in the colony-level decision-making process, which optimality theory has predicted to be of crucial importance, and which we compare with our experimental results. This illustrates the power of the stochastic methods of statistical physics for understanding social insect colonies as complex systems. [Preview Abstract] |
Thursday, March 24, 2011 1:15PM - 1:27PM |
W13.00011: Thermodynamic efficiency out of equilibrium David Sivak, Gavin Crooks Molecular-scale machines typically operate far from thermodynamic equilibrium, limiting the applicability of equilibrium statistical mechanics to understand their efficiency. Thermodynamic length analysis relates a non-equilibrium property (dissipation) to equilibrium properties (equilibrium fluctuations and their relaxation time). Herein we demonstrate that the thermodynamic length framework follows directly from the assumptions of linear response theory. Uniting these two frameworks provides thermodynamic length analysis a firmer statistical mechanical grounding, and equips linear response theory with a metric structure to facilitate the prediction and discovery of optimal (minimum dissipation) paths in complicated free energy landscapes. To explore the applicability of this theoretical framework, we examine its accuracy for simple bistable systems, parametrized to model single-molecule force-extension experiments. Through analytic derivation of the equilibrium fluctuations and numerical calculation of the dissipation and relaxation time, we verify that thermodynamic length analysis (though derived in a near-equilibrium limit) provides a strikingly good approximation even far from equilibrium, and thus provides a useful framework for understanding molecular motor efficiency. [Preview Abstract] |
Thursday, March 24, 2011 1:27PM - 1:39PM |
W13.00012: A simple model for the transmission of malaria Adriana Dickman We study a simple lattice model describing the transmission of malaria. The transmission of the disease to humans occurs through contact with an infected mosquito, while a healthy mosquito can become infected through contact with an infected human. Recovered individuals are susceptible to re-infection. The mosquitoes diffuse through the lattice, spreading the disease. We show preliminary results for the model obtained via site approximation (mean-field theory). [Preview Abstract] |
Thursday, March 24, 2011 1:39PM - 1:51PM |
W13.00013: Genearlized force-extension relation for DNA confined in sub-100nm nanoslits Yeng-Long Chen, Po-Keng Lin, Chia-Fu Chou We generalize the force-extension relation of DNA molecules confined in persistence length scale nanoslits. In strong confinement with slit geometry, the segmental correlation length of DNA molecules have two components -- in the confined and unconfined dimensions. In the confined dimension, the segmental correlation length is controlled by the slit height. In the unconfined dimension, the segmental correlation length increases as the slit height decreases. We characterize this effect, and generalize how this affects the entropic elasticity of confined DNA molecules. In addition, we investigate the structure of dense strongly confined semi-flexible polymers. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700