Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session B9: GSNP Student Speaker Award Session and Applications of Statistical and Nonlinear Physics in the Life Sciences |
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Sponsoring Units: GSNP Chair: Harvey Gould, Clark University Room: 303 |
Monday, March 16, 2009 11:15AM - 11:27AM |
B9.00001: Self-Assembly of Spherical Colloidal Particles at Low N Natalie Arkus, Vinothan Manoharan, Michael Brenner The number of rigid structures that a system of N particles can form grows exponentially with N. Stabilizing any one structure over all others is thus a challenging problem. We consider a system of N spherical colloidal particles that cannot deform or overlap, and which exhibit a short-range attractive force. We present a method, using graph theory and geometry, that solves for all possible rigid packings of N particles - the resultant set of packings is provably complete. We then present a mechanism that is capable of stabilizing any one structure over all others (in the zero temperature limit), and which is experimentally realizable - thereby, potentially allowing us to direct the self-assembly of a desired structure. We compare to preliminary experimental results. [Preview Abstract] |
Monday, March 16, 2009 11:27AM - 11:39AM |
B9.00002: Liquid to solid nucleation through onion-structure droplets Kipton Barros, William Klein We start from a Landau-Ginzburg free energy and develop a theory of crystal nucleation for metastable liquids. Saddle points of the free energy represent nucleating droplets and are obtained analytically and numerically. We find nucleating droplets with hexagonal symmetry in two dimensions and bcc and icosahedral symmetries in three dimensions. Surprisingly, we also find nucleating droplets in three dimensions with a spherically symmetric structure resembling the layers of an onion. These onion-structure objects are the preferred nucleating droplets near the spinodal. We discuss recent experiments and simulations which are consistent with our predictions. [Preview Abstract] |
Monday, March 16, 2009 11:39AM - 11:51AM |
B9.00003: Universal Scaling Relation Near Point J Thomas Haxton, Andrea Liu Recently, several studies (P. Olsson and S. Teitel. \textit{Phys. Rev. Lett.} \textbf{99}, 178001 (2007); T. Hatano. arXiv:0803.2296; L. Berthier and T. A. Witten. arXiv:0810.4405) have indicated the existence of a dynamical phase transition at or near Point J, the point at zero temperature, zero shear stress, and a critical density where repulsive amorphous sphere packings lose rigidity. However, a universal scaling relation connecting the rheology of the jammed solid to that of the viscous liquid has been lacking. We control the temperature, strain rate, and pressure in molecular dynamics simulations to show that the steady-state rheology is described by a universal scaling relation near Point J. [Preview Abstract] |
Monday, March 16, 2009 11:51AM - 12:03PM |
B9.00004: Exact results for currents in nonadiabatic stochastic pumps Jordan Horowitz Biological systems abound with examples of molecular machines: assemblies of molecules that perform specific useful mechanical tasks, such as the motor proteins kinesin and myosin. Remarkably, the first steps in developing useful artificial molecular motors have been taken with the synthesis and manipulation of molecular complexes such as catenanes and rotaxanes. These developments have spurred an interest in developing theoretical frameworks which describe these mesoscopic machines that operate in the presence of thermal noise. In this talk I will analyze a generic model of molecular machines known as stochastic pumps in which useful directed motion (or current) is produced by the variation of external parameters. The main result is an exact expression for the current in the presence of nonadiabatic pumping. This expression connects to a variety of results from the field of brownian ratchets and leads to a surprising ``no-pumping'' theorem: a set of conditions that guarantee no excess or pumped current. These predictions also agree with the observations on catenanes, interlocked ring molecules, made by Leigh et. al. [Nature, 424, 174 (2003)]. [Preview Abstract] |
Monday, March 16, 2009 12:03PM - 12:15PM |
B9.00005: A continuous time random walk description of the hopping dynamics in an aging polymer glass Mya Warren, Joerg Rottler Due to the non-equilibrium nature of the glassy state, structural relaxation becomes increasingly sluggish with the wait time $t_w$ since vitrification. As a result, dynamical correlation functions age, and often obey a simple rescaling with $t_w$: $C(t,t_w) = C_0(t) + C_{age}(t/t_w^{\mu})$. It has recently been shown that, to first order, scaling also applies to the distributions of local correlations and displacements (the van Hove function). In this study, we use molecular dynamics simulations to measure the statistics of the discontinuous hopping events that characterize structural relaxations during aging. This allows us to map the particle dynamics onto a continuous time random walk, which successfully reproduces the entire distribution of displacements. Our results bear a striking resemblance to the popular trap model of aging. We find that the hop time distribution takes the form of a power law which is independent of $t_w$, whereas the time to the first hop shifts to longer times with $t_w$. This two-timescale behavior explains not only the scaling of the distribution functions for times $t\sim t_w$, but also small deviations from perfect scaling that have been observed at longer times. [Preview Abstract] |
Monday, March 16, 2009 12:15PM - 12:27PM |
B9.00006: On the Mass Distribution of Animal Species Sidney Redner, Aaron Clauset, David Schwab We develop a simple diffusion-reaction model to account for the broad and asymmetric distribution of adult body masses for species within related taxonomic groups. The model assumes three basic evolutionary features that control body mass: (i) a fixed lower limit that is set by metabolic constraints, (ii) a species extinction risk that is a weakly increasing function of body mass, and (iii) cladogenetic diffusion, in which daughter species have a slight tendency toward larger mass. The steady-state solution for the distribution of species masses in this model can be expressed in terms of the Airy function. This solution gives mass distributions that are in good agreement with data on 4002 terrestrial mammal species from the late Quaternary and 8617 extant bird species. [Preview Abstract] |
Monday, March 16, 2009 12:27PM - 12:39PM |
B9.00007: Epidemic spread in coupled populations with seasonally varying migration rates Adam Muzyczyn, Leah B. Shaw The H5N1 strain of avian influenza has spread worldwide, and this spread may be due to seasonal migration of birds and mixing of birds from different regions in the wintering grounds. We studied a multipatch model for avian influenza with seasonally varying migration rates. The bird population was divided into two spatially distinct patches, or subpopulations. Within each patch, the disease followed the SIR (susceptible-infected-recovered) model for epidemic spread. Migration rates were varied periodically, with a net flux toward the breeding grounds during the spring and towards the wintering grounds during the fall. The case of two symmetric patches reduced to single-patch SIR dynamics. However, asymmetry in the birth and contact rates in the breeding grounds and wintering grounds led to bifurcations to longer period orbits and chaotic dynamics. We studied the bifurcation structure of the model and the phase relationships between outbreaks in the two patches. [Preview Abstract] |
Monday, March 16, 2009 12:39PM - 12:51PM |
B9.00008: Blasting and Zipping: Sequence Alignment and Mutual Information Orion Penner, Peter Grassberger, Maya Paczuski Alignment of biological sequences such as DNA, RNA or proteins is one of the most widely used tools in computational bioscience. While the accomplishments of sequence alignment algorithms are undeniable the fact remains that these algorithms are based upon heuristic scoring schemes. Therefore, these algorithms do not provide model independent and objective measures for how similar two (or more) sequences actually are. Although information theory provides such a similarity measure - the mutual information (MI) - numerous previous attempts to connect sequence alignment and information have not produced realistic estimates for the MI from a given alignment. We report on a simple and flexible approach to get robust estimates of MI from global alignments. The presented results may help establish MI as a reliable tool for evaluating the quality of global alignments, judging the relative merits of different alignment algorithms, and estimating the significance of specific alignments. [Preview Abstract] |
Monday, March 16, 2009 12:51PM - 1:03PM |
B9.00009: Competition For Resources in a Model for Protein Synthesis Larry Cook, Royce Zia The Totally Asymmetric Simple Exclusion Process (TASEP) is often used to explore translation during protein synthesis. The particles represent ribosomes that move along mRNA, which is represented by the one-dimensional lattice. Unlike ordinary TASEP where the supply of particles is unlimited, there is a finite number of ribosome in a cell. In addition, there are many genes which compete for this pool of ribosomes. Thus, we are motivated to consider the effects of multiple TASEPs (of varying lengths) coupled to a single, finite reservoir of particles. In particular, the total occupation numbers, the density profiles and the particle currents of individual TASEPs are studied, as the overall reservoir of particles is varied. Both Monte Carlo simulation results and analytic considerations will be presented. [Preview Abstract] |
Monday, March 16, 2009 1:03PM - 1:15PM |
B9.00010: Estimating currents in totally asymmetric simple exclusion process with extended particles and inhomogeneous hopping rates. R.K.P. Zia, Jiajia Dong, B. Schmittmann Motivated by translation in protein synthesis, we study the totally asymmetric simple exclusion process with extended particles transported along a 1-D lattice with (quenched) inhomogeneous hopping rates. The particles model ribosomes, the lattice models sequences of codons, and the hopping rates reflect the aa-tRNA concentrations. Taking the latter from data for real \textit{E.Coli} genes, Monte Carlo simulations allow us to find the steady state currents, associated with protein production rates. An application would be to predict the effects of ``silent mutations'' in biological systems. In such mutations, one or more codons are replaced by others which code for the \textit{same} amino-acid, so that the \textit{same} protein (amino-acid chain) is synthesized by a different sequence of codons. However, the rate of production (the overall current), which depends on the details of sequence, will differ. We aim to predict the changes in these currents for all possible silent mutations. Beyond this application, this study of ``quenched distribution of distributions'' is expected to have far reaching implications in other areas of physics. [Preview Abstract] |
Monday, March 16, 2009 1:15PM - 1:27PM |
B9.00011: An information geometric approach to least squares minimization Mark Transtrum, Benjamin Machta, James Sethna Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the origin. The standard algorithm for minimizing sums of squares, the Levenberg-Marquardt algorithm, also has geometric meaning. When the standard algorithm fails to efficiently find accurate fits to the data, geometric considerations suggest improvements. Problems involving large numbers of parameters, such as often arise in biological contexts, are notoriously difficult. We suggest an algorithm based on geodesic motion that may offer improvements over the standard algorithm for a certain class of problems. \newline [Preview Abstract] |
Monday, March 16, 2009 1:27PM - 1:39PM |
B9.00012: Large-Scale Organization of Glycosylation Networks Pan-Jun Kim, Dong-Yup Lee, Hawoong Jeong Glycosylation is a highly complex process to produce a diverse repertoire of cellular glycans that are frequently attached to proteins and lipids. Glycans participate in fundamental biological processes including molecular trafficking and clearance, cell proliferation and apoptosis, developmental biology, immune response, and pathogenesis. N-linked glycans found on proteins are formed by sequential attachments of monosaccharides with the help of a relatively small number of enzymes. Many of these enzymes can accept multiple N-linked glycans as substrates, thus generating a large number of glycan intermediates and their intermingled pathways. Motivated by the quantitative methods developed in complex network research, we investigate the large-scale organization of such N-glycosylation pathways in a mammalian cell. The uncovered results give the experimentally-testable predictions for glycosylation process, and can be applied to the engineering of therapeutic glycoproteins. [Preview Abstract] |
Monday, March 16, 2009 1:39PM - 1:51PM |
B9.00013: Network dynamics mediated by heterogeneous topology as related to hippocampal memory management Jane Wang, Gina Poe, Michal Zochowski Hippocampal-cortical network interactions, including reactivation of recently acquired memories in the hippocampus during sleep, are key to the consolidation of memory traces to long-term storage sites in the neocortex. Network heterogeneities, in the form of regional changes in the connectivity densities of excitatory synapses, support this process in simulated hippocampal-cortical networks by regulating intrinsic network dynamics and thus mediating stimulus familiarity detection as well as selective memory consolidation. We characterize this network model by investigating dynamics due to distributed and overlapping memory structures and examine the ability of regional heterogeneities to both selectively activate in the presence of controlled stimuli and reactivate in the absence of stimuli, the former being indicative of active exploration and the latter of memory replay during sleep. [Preview Abstract] |
Monday, March 16, 2009 1:51PM - 2:03PM |
B9.00014: The topological structure of a network formed during simulations of a reversible polymeric gel M. Wilson, J. Billen, A. Baljon, A. Rabinovitch We investigate the topologies of the ensemble of telechelic polymers for which we previously studied the sol/gel transition [1]. The polymers serve as ``links'' between ``nodes,'' which consist of aggregates of their associating endgroups. The number of associations and hence the topology depends on the employed temperature. Our analysis shows that the degree distribution of the systems is bimodal and consists of two Poisson distributions with different average degrees $<$k$>$. Nodes in the distribution with the higher $<$k$>$ we call ``superpeers,'' those in the other distribution ``peers.'' With decreasing temperature, the fraction of superpeer nodes increases. This increase is steepest at the ``jamming'' transition. The eigenvalue spectra of the networks reveal that in the jammed state peers are only connected to superpeers, a topology known to be very robust. By contrast, at high temperatures peers are connected to each other as well. Due to the finite size of the polymers, our telechelic networks differ from random Erdos-Renyi (ER) bimodal networks. As in many real-world networks, spatial effects play a role. After rewiring the networks obtained in the simulations, we reach the ER limit, that is, the clustering coefficients are equal to those obtained for random ER networks. \\[0pt] [1] JCP 126, 044907(2007) [Preview Abstract] |
Monday, March 16, 2009 2:03PM - 2:15PM |
B9.00015: Generalized fractional Fokker-Planck equation for anomalous diffusion Alex Veksler, Rony Granek The problem of anomalous diffusion is important for a variety of systems, such as fluids, glasses, polymers, proteins etc. It is characterized by a mean square displacement evolving in time as a power-law $\langle x^2\rangle = 2 D_0 t^{\alpha}$. However, a Fokker-Planck-like equation which could describe a stationary Gaussian process with anomalous-diffusion behavior, such as the one described by the Generalized Langevin equation, is still missing. We propose a generalization for constant force to the fractional Fokker-Planck equation (fFP) [Metzler, R. and Klafter, J., Phys. Rep. \textbf{339} (2000), 1-77], based on a series expansion in spatial and fractional time derivatives and powers of the Fokker-Planck operator. The proposed equation, GfFP, recovers the generalized Einstein relation and leads to Gaussian distribution, in particular, for free particle diffusion. We apply GfFP to 1-D first passage time problem. The long-time asymptote of the probability distribution behaves like $\exp(-t^\alpha)$. This contrasts with the power-law behavior of the corresponding solutions of the fFP. We further propose to generalize GfFP for treating other outstanding problems, such as the anomalous diffusion under an harmonic potential and the Kramers` escape problem. [Preview Abstract] |
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