Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session L47: Focus Session: Stochastic Model Inference |
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Sponsoring Units: DBIO Chair: Steve Presse, Indiana University - Purdue University Indianapolis Room: 217B |
Wednesday, March 4, 2015 8:00AM - 8:36AM |
L47.00001: Integrating discrete stochastic models and single-cell experiments to infer predictive models of MAPK-induced transcription dynamics Invited Speaker: Brian Munsky MAPK signal-activated transcription plays central roles in myriad biological processes including stress adaptation responses and cell fate decisions. Recent single-cell and single-molecule experiments have advanced our ability to quantify the spatial, temporal, and stochastic fluctuations for such signals and their downstream effects on transcription regulation. This talk explores how integrating such experiments with discrete stochastic computational analyses can yield quantitative and predictive understanding of transcription regulation in both space and time. We use single-molecule mRNA fluorescence in situ hybridization (smFISH) experiments to reveal locations and numbers of multiple endogenous mRNA species in 100,000's of individual cells, at different times and under different genetic and environmental perturbations. We use finite state projection methods to precisely and efficiently compute the full joint probability distributions of these mRNA, which capture measured spatial, temporal and correlative fluctuations. By combining these experimental and computational tools with uncertainty quantification, we systematically compare models of varying complexity and select those which give optimally precise and accurate predictions in new situations. We use these tools to explore two MAPK-activated gene regulation pathways. In yeast adaptation to osmotic shock, we analyze Hog1 kinase activation of transcription for three different genes STL1 (osmotic stress), CTT1 (oxidative stress) and HSP12 (heat shock). In human osteosarcoma cells under serum induction, we analyze ERK activation of c-Fos transcription. [Preview Abstract] |
Wednesday, March 4, 2015 8:36AM - 8:48AM |
L47.00002: Motor Switching Rates in Caulobacter Crescentus Follow First Passage Time Distribution Jay Tang, Michael Morse, Jordan Bell, Guanglai Li The flagellar motor of uni-flagellated bacterium Caulobacter crescentus switches stochastically between clockwise (CW) and counterclockwise (CCW) rotation. We performed measurements of the time intervals between switches in order to gain insight on motor dynamics and regulation. Our measurements were performed both on free swimming cells and tethered cells with their flagella attached to a glass slide. A peak time of approximately one second was observed in both motor directions with counterclockwise intervals more sharply peaked. The distributions of switching times can be fitted using biased first passage time statistics. We present a model of motor switching dynamics, which is controlled by the binding of CheY-P to motor subunits FliM. A lower threshold number of FliM with CheY-P bound triggers a switch in motor rotation from CW to CCW, whereas a higher threshold triggers an opposing switch from CCW to CW. The time intervals between alternating switches may be increased or decreased by regulating CheY-P concentration, resulting in biased directional motion in the cells swimming trajectory over many motor cycles under external spatial or temporal gradients. [Preview Abstract] |
Wednesday, March 4, 2015 8:48AM - 9:00AM |
L47.00003: Consequences of Irreversibility in Fundamental Models of Transcription Stuart Sevier, Herbert Levine The ability to watch biochemical events play out at the single-molecule level has led to the discovery that transcription occurs in a noisy, ``bursty'' manner. Recently, as the single-molecule lens is placed over a larger number of organisms and genes, relationships between mean expression and noise beyond the ``bursty'' paradigm have emerged. Through a master-equation formulation of transcription we have found that many powerful physical principles relating to irreversibility seem to play a central role in the newly uncovered trends. Specifically, the relationships between mean expression and noise appears to be a direct consequence of network currents. We discuss how emphasizing the underlying principles in the models can explain recent experimental data and lead to a generalized view of transcription. [Preview Abstract] |
Wednesday, March 4, 2015 9:00AM - 9:12AM |
L47.00004: Variability and Reliabiltiy in Axon Growth Cone Navigation Decision Making Marta Garnelo, S\'ebastien G. Ricoult, David Juncker, Timothy E. Kennedy, Aldo A. Faisal The nervous system's wiring is a result of axon growth cones navigating through specific molecular environments during development. In order to reach their target, growth cones need to make decisions under uncertainty as they are faced with stochastic sensory information and probabilistic movements. The overall system therefore exhibits features of whole organisms (perception, decision making, action) in the subset of a single cell. We aim to characterise growth cone navigation in defined nano-dot guidance cue environments, by using the tools of computational neuroscience to conduct ``molecular psychophysics.'' We start with a generative model of growth cone behaviour and we 1. characterise sensory and internal sources of noise contributing to behavioural variables, by combining knowledge of the underlying stochastic dynamics in cue sensing and the growth of the cytoskeleton. This enables us to 2. produce bottom-up lower limit estimates of behavioural response reliability and visualise it as probability distributions over axon growth trajectories. Given this information we can match our in silico model's ``psychometric'' decision curves with empirical data. Finally we use a Monte-Carlo approach to predict response distributions of axon trajectories from our model. [Preview Abstract] |
Wednesday, March 4, 2015 9:12AM - 9:24AM |
L47.00005: Stability of a Random Walk Model for Fruiting Body Aggregation in M. xanthus G.C. McKenzie-Smith, H.B. Sch\"{u}ttler, C. Cotter, L. Shimkets Myxococcus xanthus exhibits the social starvation behavior of aggregation into a fruiting body containing myxospores able to survive harsh conditions. During fruiting body aggregation, individual bacteria follow random walk paths determined by randomly selected runtimes, turning angles, and speeds. We have simulated this behavior in terms of a continuous-time random walk (CTRW) model, re-formulated as a system of integral equations, describing the angle-resolved cell density, R(r, t, $\theta$), at position r and cell orientation angle $\theta$ at time t, and angle-integrated ambient cell density $\rho$(r, t). By way of a linear stability analysis, we investigated whether a uniform cell density R$_{0}$ will be unstable for a small non-uniform density perturbation $\delta$R(r, t, $\theta$). Such instability indicates aggregate formation, whereas stability indicates absence of aggregation. We show that a broadening of CTRW distributions of the random speed and/or random runtimes strongly favors aggregation. We also show that, in the limit of slowly-varying (long-wavelength) density perturbations, the time-dependent linear density response can be approximated by a drift-diffusion model for which we calculate diffusion and drift coefficients as functions of the CTRW model parameters. [Preview Abstract] |
Wednesday, March 4, 2015 9:24AM - 9:36AM |
L47.00006: Single-cell analysis of transcription kinetics across the cell cycle Samuel Skinner, Heng Xu, Sonal Jaiswal, Pablo Freire, Thomas Zwaka, Ido Golding Transcription is a highly stochastic process. A common way of inferring transcription kinetics is to measure mRNA abundance in individual cells and compare the observed copy-number statistics to the prediction of a theoretical stochastic model. However, the reliability of this procedure is hampered by the fact that the measured mRNA numbers represent integration over the finite lifetime of mRNA, over multiple copies of the same gene, and the mixing of cells from different phases of the cell cycle. Here we address these limitations by simultaneously quantifying nascent and mature mRNA in individual cells, and incorporating gene-copy and cell-cycle effects in the analysis of mRNA statistics. We demonstrate this approach on \textit{Oct4} and \textit{Nanog}, two key players in the mouse pluripotency network. We find that both genes are well described by a two-state stochastic model for transcription initiation. The difference in their expression characteristics is attributed to a 2.6-fold difference in the probability of switching to an active transcriptional state. Early in the cell cycle, the two copies of each gene exhibit independent activity. However, after gene replication, the probability of each gene copy to be active diminishes, resulting in dosage compensation. [Preview Abstract] |
Wednesday, March 4, 2015 9:36AM - 10:12AM |
L47.00007: Inference of protein diffusion probed via fluorescence correlation spectroscopy Invited Speaker: Konstantinos Tsekouras Fluctuations are an inherent part of single molecule or few particle biophysical data sets. Traditionally, ``noise'' fluctuations have been viewed as a nuisance, to be eliminated or minimized. Here we look on how statistical inference methods -- that take explicit advantage of fluctuations -- have allowed us to draw an unexpected picture of single molecule diffusional dynamics. Our focus is on the diffusion of proteins probed using fluorescence correlation spectroscopy (FCS). First, we discuss how -- in collaboration with the Bustamante and Marqusee labs at UC Berkeley -- we determined using FCS data that individual enzymes are perturbed by self-generated catalytic heat (Riedel et al, Nature, 2014). Using the tools of inference, we found how distributions of enzyme diffusion coefficients shift in the presence of substrate revealing that enzymes performing highly exothermic reactions dissipate heat by transiently accelerating their center of mass following a catalytic reaction. Next, when molecules diffuse in the cell nucleus they often appear to diffuse anomalously. We analyze FCS data -- in collaboration with Rich Day at the IU Med School -- to propose a simple model for transcription factor binding-unbinding in the nucleus to show that it may give rise to apparent anomalous diffusion. Here inference methods extract entire binding affinity distributions for the diffusing transcription factors, allowing us to precisely characterize their interactions with different components of the nuclear environment. From this analysis, we draw key mechanistic insight that goes beyond what is possible by simply fitting data to ``anomalous diffusion'' models. [Preview Abstract] |
Wednesday, March 4, 2015 10:12AM - 10:24AM |
L47.00008: Simple models do not explain early dynamics of {\em H.~influenzae} bacteremia Xinxian Shao, Bruce Levin, Ilya Nemenman There is an abundance of largely qualitative information about the physiological and molecular mechanisms of bacterial pathogenesis. However, little is known about population dynamic processes by which bacteria colonize hosts and invade cells and tissues and thereby cause disease. Classic experiment of Moxon and Murphy\footnote{ Moxon E R,Murphy P A (1978). Haemophilus influenzae bacteremia and meningitis resulting from survival of a single organism. PNAS, 75(3), 1534-1536.} observed that, when inoculated intranasally with a mixture of equally virulent strains of Haemophilus influenzae type b(Hib), neonatal rats develop a bacteremic infection that often is dominated by only one random competing strain. A common qualitative explanation for this phenomenon is that the bacteria must switch stochastically into a rapidly growing phenotype to start the full-fledged invasion. Then the first bacterium to switch activates the host immune response, which in turn ’shuts the door’ in front of the second strain. We implemented this model computationally and analytically, and we conclude that this model cannot explain the data, specifically, the observed dependence of the rate of infections on the inoculum size. New experiments are needed to identify mechanisms underlying the dependence. [Preview Abstract] |
Wednesday, March 4, 2015 10:24AM - 10:36AM |
L47.00009: The Dynamics in Epithelial Cell Intercalation in Drosophila Morphogenesis Fred Wolf, Lars Reichl, Deqing Kong, Yujun Zhang, Stephan Eule, Jakob Metzger, J\"org Gro{\ss}hans Epithelial cell rearrangement is important for many processes in morphogenesis. During germband extension in early gastrulation of Drosophila embryos, exchange of neighbors is achieved by junction remodeling that follows a topological T1 process. Its first step is the constriction of dorsal-ventral junctions and fusion of two 3x vertices into a 4x vertex a process believed to be junction autonomous. We established a high throughput imaging pipeline, by which we recorded, segmented and analysed more than 1000 neighbor exchanges in drosophila embryos. Characterizing the dynamics of junction lengths we find that the constriction of cell contacts follows intriguingly simple quantitative laws. (1) The mean contact length decreases approximately as a square root of time to collapse. (2) The time dependent variance of contact lengths is proportional to the square of the mean. (3) The time dependent probability density of the contact lengths remains close to Gaussian during the entire process. These observations are sufficient to derive a stochastic differential equation for contact length that captures the non-equilibrium statistical mechanics of contact collapse. [Preview Abstract] |
Wednesday, March 4, 2015 10:36AM - 10:48AM |
L47.00010: Stochastic Terminal Dynamics in Epithelial Cell Intercalation Stephan Eule, Jakob Metzger, Lars Reichl, Deqing Kong, Yujun Zhang, Joerg Grosshans, Fred Wolf We found that the constriction of epithelial cell contacts during intercalation in germ band extension in Drosophila embryos follows intriguingly simple quantitative laws. The mean contact length $\langle L \rangle$ follows $\langle L \rangle(t)\sim (T-t)^\alpha$ , where $T$ is the finite collapse time; the time dependent variance of contact length is proportional to the square of the mean; finally the time dependent probability density of the contact lengths remains close to Gaussian during the entire process. These observations suggest that the dynamics of contact collapse can be captured by a stochastic differential equation analytically tractable in small noise approximation. Here, we present such a model, providing an effective description of the non-equilibrium statistical mechanics of contact collapse. All model parameters are fixed by measurements of time dependent mean and variance of contact lengths. The model predicts the contact length covariance function that we obtain in closed form. The contact length covariance function closely matches experimental observations suggesting that the model well captures the dynamics of contact collapse. [Preview Abstract] |
Wednesday, March 4, 2015 10:48AM - 11:00AM |
L47.00011: Methods for reconstructing sets of ordinary differential equations from time series data Manuel Mai, Corey O'Hern, Mark D. Shattuck We propose a novel method for reconstructing the underlying nonlinear ordinary differential equations (ODE) for a physical system from time series data. Common methods for ODE reconstruction generate suitable candidate equations for the system and then fit the ODE parameters to the time series data. Candidate sets of ODEs are evolved using genetic programming methods and candidates that poorly fit the data are discarded. Such schemes are computationally expensive. We develop an alternative more efficient approach to ODE reconstruction. In the first step, we identify key features of the set of ODEs (such as the number and stability of fixed points) from the data. In the second step, we develop functional forms for the right-hand sides of the ODEs that interpolate between fixed points and saddles. We will show a number of examples where we can reconstruct nonlinear ordinary differential equations that capture the equivalent dynamics as that found in the original time series data. [Preview Abstract] |
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