Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session K06: Stochasticity in Biology |
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Sponsoring Units: DBIO Chair: Steve Presse, Univ of California - San Francisco Room: LACC 153A |
Wednesday, March 7, 2018 8:00AM - 8:12AM |
K06.00001: Coarse-grained models coupling cell cycle and gene expression Jie Lin , Ariel Amir During a cell cycle, cells grow and divide. Recent single-cell experiments show that gene expression levels depend on the cell cycle. Particularly important is the proportion of the number of mRNA and protein to the cell volume. It is not clear how cells maintain a constant mRNA and protein concentration as the cells grow. Here we propose a coarse-grained gene expression model incorporating ribosomes and RNA polymerases, which captures the exponential growth of mRNA and protein number. We show that the homeostasis of mRNA and protein concentrations during the cell cycle can be achieved in a robust manner independent of cell shape. Furthermore, we show that the fluctuations in ribosome and polymerase numbers do not propagate to protein concentrations while the fluctuation in cell density does. Furthermore, our model reconciles the discrepancy between theexperimentally observed negligible correlations between mRNA and protein levels, and the predicted positive correlations from previous models |
Wednesday, March 7, 2018 8:12AM - 8:24AM |
K06.00002: Stochasticity in Mammalian Drug Resistance Daniel Charlebois , Kevin Farquhar , Dmitry Nevozhay , Gabor Balazsi Drug resistance is a global health crisis which kills 700,000 people each year, as it undermines the treatment of many infections and cancers. Despite recent advances, we still lack a complete understanding of such drug resistance processes, including the role of stochastic or “noisy” gene expression in mammalian cells. To study how stochastic gene expression affects drug resistance of mammalian cells, we combine mathematical modeling with synthetic biology. We develop a phenomenological model to explore how cellular survival depends on the interplay between the steepness of the drug’s concentration-effect curve (a fitness function) and a drug resistance gene’s expression noise. Next, we incorporate drug resistance mutations into a detailed model to predict adaptation time. Predictions from such models are tested experimentally with puromycin-treated Chinese Hamster Ovary (CHO) cells carrying synthetic negative and positive feedback gene circuits that control a puromycin antibiotic resistance gene. Overall, we show that high gene expression noise facilitates survival and evolution of resistance in high levels of drug, while the reverse is true in low levels of drug. However, we also find that these conclusions depend strongly on the steepness of the fitness function. |
Wednesday, March 7, 2018 8:24AM - 8:36AM |
K06.00003: On the Complexity of Prediction Strategies in Noisy and Changing Environments Gaia Tavoni , Joshua Gold , Vijay Balasubramanian In a noisy and dynamic world, it is important to learn from past experiences to predict future events. It is generally believed that in presence of unpredictable change-points this learning process must be adaptive to take into account the relevant past information. We show here that, for most change-point rates (h) and signal-to-noise ratios (S/N), performance of non-adaptive and adaptive strategies is comparable. When h>~0.1, adaptive models do not substantially improve over a constant learning rate delta-rule model. When S/N is very low or very high, the non-adaptive domain extends to lower h. Thus, simple strategies are widely preferable in extreme and opposite noise conditions. Increasing change-point rate beyond ~0.25 further reduces the complexity demands, such that both adaptivity and the memory of past history become largely irrelevant to make effective predictions. We characterize the optimal time scale of past data integration and unveil a phase transition at S/N = 1/Golden Ratio. In the high S/N regime, the time scale decreases with increasing h, whereas in the low S/N regime it shows a non-monotonic dependence on h and diverges at large h. Simple optimal solutions are again found for extreme and opposite (small and large h) conditions. |
Wednesday, March 7, 2018 8:36AM - 8:48AM |
K06.00004: Theoretical Investigation on Surface-mediated Search Dynamics of a Reactant Jaeoh Shin , Anatoly Kolomeisky The process of a reactant search for a target located on a surface is ubiquitous in Nature, in particular in chemical- and biological processes. We study the dynamics of a reactant search for a small target in a 2D surface from the bulk both in continuum and discrete model. We find that depending on the scanning length $\lambda$ of the reactant on the surface, which is determined by the reactant-surface interactions, the search dynamics shows different behavior: (i) for small $\lambda$, the reactant find the target via 3 dimensional bulk diffusion, (ii) for large $\lambda$, it find the target via surface diffusion, and (iii) for intermediate $\lambda$, the reactant find the target via a combination of 3D and 2D motion which can minimize the search time $T$. The search times $T$ in a continuum- and discrete model are close, but not the same even we take the parameters equivalently. We also study how the search time is dependent on the surface size and the position of the target in the discrete model. Finally, we discuss the relevance of our results with some recent experiments. |
Wednesday, March 7, 2018 8:48AM - 9:00AM |
K06.00005: Microscopic Langevin model for the modified Fürth equation Mendeli Vainstein , Gilberto Thomas , Rita de Almeida Recent experimental research on the mobility of living cells indicate that their diffusion is not completely described by Fürth's equation since they display a normal diffusive regime before the onset of the ballistic motion. Moreover, results from a cellular Potts model simulation for the motion of cells in two dimensions present the same type of behavior and a modification of Fürth's equation has been proposed to fit the mean squared displacements (MSD) found both experimentally and computationally (Fortuna et al., submitted). Here, we propose a microscopic Langevin model to explain this anomaly in the MSD: we show that a polarization direction for the persistent motion as well as at least two time scales are needed. The model reproduces well the MSD obtained from the modified Fürth equation and is robust to changes in the microscopic dynamics of the polarization as a function of cell migration speed, which is in agreement with experimental data which suggests that persistence of trajectories is coupled to cell migration speed mediated by actin flows (Maiuri et al., 2015). |
Wednesday, March 7, 2018 9:00AM - 9:12AM |
K06.00006: Extracting dynamical laws from targeted biological processes Nicolas Lenner , Stephan Eule , Fred Wolf Time dependent biological processes progressing towards irreversible target points, such as the dynamics of cytokinetic ring constriction, can often be characterized with one or a small set of phenomenological relevant dynamical variables. While the onset of these dynamics is typically affected by strong uncertainties, e.g., due to overlapping consecutive dynamical laws, we expect the dynamics close to completion to show its purest and most informative form. This observation motivates to align measured sample paths of such a stochastic dynamic to their irreversible target point. The resulting set of aligned sample paths can then be treated as a realization of an ensemble evolving in reverse time. Interestingly, this seemingly harmless data analysis operation of terminal alignment creates an ensemble which can not be analyzed with conventional notions of stochastic differential equations. We expose the origin of this problem and derive a general formalism which allows to recover a phenomenological description of the forward process based on the analysis of the time reversed and terminal aligned ensemble. We demonstrate the applicability of this approach on mock data of cytokinetic ring constriction. |
Wednesday, March 7, 2018 9:12AM - 9:24AM |
K06.00007: Role of noise and parameter variation in gene circuit dynamics Vivek Kohar , Mingyang Lu Stochasticity in gene expression influences the functions and dynamics of gene regulatory circuits. Intrinsic noises, such as those caused by transcriptional bursting and low copy number of molecules, are typically studied by stochastic analysis using Gillespie algorithm and Langevin simulations. Yet, the role of other extrinsic factors, such as the heterogeneity in the microenvironment and cell-to-cell variability, is still elusive. To identify the effects of both intrinsic and extrinsic noises, we integrate stochastic analysis with our newly developed algorithm, named random circuit perturbation (RACIPE). Unlike conventional methods, RACIPE generates and analyzes an ensemble of random models with distinct kinetic parameters. We have shown previously that the expression profiles of stable steady states from random models form robust clusters. Here, we further propose using a constant-noise-based method to capture the basins of attraction and an annealing-based method to identify the most stable states. From the tests on several gene circuits, we found that high intrinsic noises, but not high parameter variations, merge states together. Our study sheds light on a novel mechanism of noise-induced hybrid states. |
Wednesday, March 7, 2018 9:24AM - 9:36AM |
K06.00008: Statistical physics of multicellular systems Yiteng Dang , Hyun Youk How does a system of communicating cells generate spatial organization in their gene expression levels? Various studies have addressed collective effects arising from a population of secrete-and-sense cells, which communicate by secreting and sensing the same signalling molecule. Yet a general theoretical framework for describing this collective behaviour remains lacking. We constructed a lattice model in which cells can have either a high or a low expression level. Each cell updates its state according to the concentration of signalling molecule it senses. The macroscopic behaviour can be described by two variables, the mean expression level and a “spatial order parameter”, together with a monotonically decreasing “Hamiltonian” that is a function of these variables. An effective Langevin equation based on the gradient of this Hamiltonian describes the macroscopic dynamics. We extend the framework to cells with a graded response and show that the main qualitative features are conserved. Moreover, the system exhibits a transition between an autonomous phase – where each cell determines its own fate - and a collective phase in which spatial organisation can arise. Further extensions of the model include addition of noise, multiple cell types and spatial inhomogeneity. |
Wednesday, March 7, 2018 9:36AM - 9:48AM |
K06.00009: Does biochemical noise help bacteria find its food faster? - A theoretical and computational study Ushasi Roy , Manoj Gopalakrishnan How intrinsic noise affects the output of biochemical circuits, and hence the functioning of organisms is a problem of tremendous current interest in the physics of biological systems. We propose a minimal, but realistic mathematical model of signal transduction in the bacterium E. coli, which incorporates intrinsic noise in a rigorous manner, and analyze how these fluctuations affect the statistics of flagellar motor switching. We derive a differential equation for the survival probability of a motor in the counter-clockwise (CCW) state (roughly corresponding to straight runs of the bacterium). The equation incorporates the switching dynamics of the motor as well as the internal dynamics of the upstream signaling cascade. By solving the equation, we obtain analytical expressions for the distribution of the CCW intervals, which turns out to be non-exponential, a manifestation of the inherently noisy nature of the underlying network. Our theoretical results, in tandem with numerical simulations, resembles experimental observations by Park et al. (Nature 2010 and Biophys J. 2011). Further extensions of our analysis suggest that methylation noise has a beneficial effect on chemotactic drift in some parameter regimes. |
Wednesday, March 7, 2018 9:48AM - 10:00AM |
K06.00010: Optimizng the Success of Multi-Agent Foraging Farnaz Golnaraghi , Ajay Gopinathan Many animals such as the albatross, gray seal, and deer are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a particular heavy tailed distribution (a power law) known as a Levy distribution. Previous studies have shown that, under conditions of sparse resources, this search process is optimized with respect to the efficiency, defined as the ratio of total number of targets found to the total distance travelled, when the power-law has an exponent equal to 2. Although single agent Levy search processes have been studied well in the literature, little is known about multi-agent search processes. In many natural settings, there are typically multiple foragers who can interact with each other in different ways including either cooperating or competing with each other. We develop a stochastic agent-based simulation to study the effect of the number of agents, and various types of interactions between them on the search efficiency, and present our results for the optimum search strategy for cases in which foragers try to avoid encountering each other in different ways. |
Wednesday, March 7, 2018 10:00AM - 10:12AM |
K06.00011: Hard Bounds on Molecular Fluctuations in Stochastic Reaction Systems Jiawei Yan , Andreas Hilfinger , Glenn Vinnicombe , Johan Paulsson The probabilistic nature of single chemical events spontaneously creates fluctuations in molecule concentrations in cells. A major challenge to analyze such intracellular noise is that most dynamical phenomena in biology do not depend on the expression pattern of any single gene on its own, but on the interactions between proteins, mRNA, DNA, and other components in the cells. In principle, fluctuations in each component may propagate to other components and to the whole genetic regulatory network. I will present fundamental limits on suppressing such molecular fluctuations in a general stochastic reaction systems which allow arbitrary regulatory topologies and control functions. The results, briefly, indicate that to reduce the fluctuation in one component will inevitably increase fluctuations of other components. I will also discuss how such trade-off of noise suppression relates to information theory. |
Wednesday, March 7, 2018 10:12AM - 10:24AM |
K06.00012: Behavior of stochastic reaction network towards the thermodynamic limit Michail Vlysidis , Yiannis Kaznessis An important concept for describing chemical reaction networks is the thermodynamic limit, where the number of molecules and the size of the system are asymptotically large. Systems in the thermodynamic (macroscopic) limit can be modeled with a deterministic modeling formalism; away from it, at the microscopic limit, a stochastic approach is more suitable . However, due to numerical and computational difficulties, little is known for the behavior of networks in the mesoscopic area, where the system is sizable yet still under the influence of thermal noise. |
Wednesday, March 7, 2018 10:24AM - 10:36AM |
K06.00013: A Path Integral Method for Analytically Tractable Inference of Evolutionary Dynamics John Barton , Raymond Louie , Matthew McKay , Muhammad Sohail Understanding the forces that shape genetic evolution is a subject of fundamental importance in biology and one with numerous practical applications. Modern experimental techniques give insight into these questions, but inferring evolutionary parameters from sequence data, such as how an organism’s genotype affects its fitness, remains challenging. Here we present a method to infer selection from genetic time-series data using a path integral approach based in statistical physics. Through extensive numerical tests we find that our method exceeds the current state of the art in the successful classification of mutations as beneficial or deleterious in a variety of scenarios, while also yielding orders of magnitude improvements in run time. Our approach can also be extended to jointly infer other evolutionary parameters such as the effective population size and mutation rates. |
Wednesday, March 7, 2018 10:36AM - 10:48AM |
K06.00014: Automated force-field parametrization guided by multisystem ensemble averages Andrea Cesari , Sandro Bottaro , Giovanni Bussi RNA structure and dynamics play a fundamental role in many cellular processes. Molecular dynamics (MD) is a computational tool that can be used to investigate RNA structure and dynamics. However, its capability to predict and explain experimental data is limited by the accuracy of the employed potential energy functions, known as force fields. Recent works have shown that state-of-the-art force fields could predict unphysical RNA conformations that are not in agreement with experiments. The emerging strategy to overcome these limitations is to complement MD with experimental data included as restraints. We recently suggested a maximum entropy based method to enforce solution experiments in MD simulations by simultaneously adapting force-field corrections to multiple systems. We here push this idea further and develop a general scheme to fit arbitrary force-field parameters given a set of ensemble averages ranging from NMR data to native state populations. The key feature is the possibility to concurrently combine ensemble averages from multiple systems into a unique error function to be minimized, drastically enhancing corrections’ transferability. The method is applied to maximize native state populations of GAGA and UUCG tetraloops by refining torsional potentials alone. |
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