Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session F44: Focus Session: Stochasticity in Cellular Networks |
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Sponsoring Units: DBIO Chair: Ilya Nemenman, Emory University Room: Hilton Baltimore Holiday Ballroom 1 |
Tuesday, March 19, 2013 8:00AM - 8:12AM |
F44.00001: Positive feedback produces broad distributions in maximum activation attained within a narrow time window in stochastic biochemical reactions Jayajit Das Stochastic fluctuations in biochemical reactions can regulate single cell decision processes. Using exact solutions and semi-analytical methods we calculate distributions of the maximum value ($N$) of species concentrations ($P_{max}(N)$) and the time ($t$) taken to reach the maximum value ($P_{max}(t)$) in minimal models of stochastic chemical reactions commonly found in cell signaling systems. We find, the presence of positive feedback interactions make $P_{max}(N)$ more spread out with a higher ``peakedness'' in $P_{max}(t)$. Thus positive feedback interactions may help single cells to respond sensitively to a stimulus when cell decision processes require upregulation of activated forms of key proteins to a threshold number within a time window. Moreover, unlike other models of strongly correlated random variables such as Brownian walks or fluctuating interfaces, the extreme value distributions for the chemical reactions display multiscaling behavior emphasizing the presence of many time scales in cell signaling kinetics. [Preview Abstract] |
Tuesday, March 19, 2013 8:12AM - 8:24AM |
F44.00002: The effect of extrinsic noise on cellular decision making Elijah Roberts, Michael Assaf, Zaida Luthey-Schulten, Nigel Goldenfeld Many cellular processes are not deterministic, i.e., genetically identical cells can display different phenotypic behavior even in identical environments. Such processes involve cellular decision making, in which individual cells randomly make choices determining their fate. One view is that the stochastic nature of cellular decision making is due to noise present in the biomolecular interaction networks. Most previous work has focused on the role of intrinsic noise of these networks. Yet, especially in the high copy-number regime, extrinsic noise may be much more significant, likely governing the overall dynamics. Here we develop a theoretical framework describing the combined effect of intrinsic and extrinsic noise on the stochastic dynamics of genetic switches responsible for cellular decision making. We do so by devising a semi-classical theory accounting for extrinsic noise as an effective species. Our theory, corroborated by extensive Monte-Carlo simulations, is tested on a simple bistable self-regulating gene model, and is then generalized to gain insight on the behavior of the lac genetic switch under extrinsic noise. We show that extrinsic noise not only significantly lowers the escape time from a phenotypic state, but can fundamentally change the actual escape process. [Preview Abstract] |
Tuesday, March 19, 2013 8:24AM - 8:36AM |
F44.00003: Temporally Resolved Axonal Growth Rates: A Stochastic Study Daniel Rizzo, Ross Beighley, Matt Wiens, James White, Timothy Atherton, Cristian Staii Description of neuron growth behavior is essential in elucidating the environmental factors that prompt the formation of neural networks. However, the staggering number of physical and chemical guidance cues that influence axonal growth prohibits understanding of growth behavior from a purely mechanistic perspective. Using a phenomenological approach, we record the distribution of growth speeds in neurons at several time points, under well-controlled conditions. Using these distributions in combination with a 1-dimensional Fokker-Planck equation, we solve for the velocity potential of axonal growth for our system as a function of time. In so doing, we aim to resolve time-sensitive growth events that are otherwise overlooked in post-growth studies. [Preview Abstract] |
Tuesday, March 19, 2013 8:36AM - 9:12AM |
F44.00004: Coarse-graining stochastic biochemical networks Invited Speaker: Ilya Nemenman Biochemical processes typically involve huge numbers of individual reversible or irreversible steps, each with its own dynamical rate constants. Does the structural complexity of these biochemical networks necessarily result in complex dynamics? I will discuss a few examples where simple, nearly universal stochastic dynamical behaviors emerge from this complexity, and sometimes precisely because of this complexity. [Preview Abstract] |
Tuesday, March 19, 2013 9:12AM - 9:24AM |
F44.00005: The addition of a coarse-grained looping state enhances bistability in a gene expression model of lac Tyler Earnest, Elijah Roberts, Michael Assaf, Karin Dahmen, Zaida Luthey-Schulten Bistability of the \textit{lac} genetic switch in \textit{Escherichia coli} is known to depend on its ability to form DNA loops with the \textit{lac} repressor. Here we present a stochastic gene--mRNA--protein model of the \textit{lac} switch that includes a third transcriptional state describing the DNA loop. We introduce a novel geometric burst extension to the finite state projection method, which allows us to eliminate mRNA as an independent species and rapidly search the parameter space of the model. We evaluate how the addition of the third state changes the model's bistability properties and find a region of parameter space where the system behaves in a way consistent to that seen experimentally for \textit{lac}. Induction in the looping model is preceded by a rare complete dissociation of the loop followed by an immediate burst of mRNA rather than a slower build up of mRNA as in the two-state model. The overall effect of the looped state is to allow for faster switching times while at the same time further separating the uninduced and induced phenotypes from each other. These properties of loop regulatory elements give them intriguing implications for use in synthetic biology. [Preview Abstract] |
Tuesday, March 19, 2013 9:24AM - 9:36AM |
F44.00006: Large number of receptors may reduce cellular response time variation Xiang Cheng, Lina Merchan, Martin Tchernookov, Ilya Nemenman Cells often have tens of thousands of receptors, even though only a few activated receptors can trigger full cellular responses. Reasons for the overabundance of receptors remain unclear. We suggest that the large number of receptors results in a competition among receptors to be the first to activate the cell. The competition decreases the variability of the time to cellular activation, and hence results in a more synchronous activation of cells. We argue that, in simple models, this variability reduction does not necessarily interfere with the receptor specificity to ligands achieved by the kinetic proofreading mechanism. Thus cells can be activated accurately in time and specifically to certain signals or ligands. We predict the minimum number of receptors needed to reduce the coefficient of variation for the time to activation following binding of a specific ligand. Further, we predict the maximum number of receptors so that the kinetic proofreading mechanism still can improve the specificity of the activation. These predictions fall in line with experimentally reported receptor numbers for multiple systems. [Preview Abstract] |
Tuesday, March 19, 2013 9:36AM - 9:48AM |
F44.00007: Information flow through calcium binding proteins Ji Hyun Bak, William Bialek Calcium signaling is a ubiquitous mode of biological communication, which regulates a great variety of vital processes in living systems. Such a signal typically begins with an elementary event, in which calcium ions bind to a protein, inducing a change in the protein's structure. Information can only be lost, from what was conveyed through this initial event, as the signal is further transduced through the downstream networks. In the present work we analyze and optimize the information flow in the calcium binding process. We explicitly calculate the mutual information between the calcium concentration and the states of the protein, using a simple model for allosteric regulation in a dimeric protein. The optimal solution depends on the dynamic range of the input as well as on the timescale of signal integration. According to our result, the optimizing strategy involves allowing the calcium-binding protein to be ``activated'' by a partial occupation of its sites, and tuning independently the strengths of cooperative interactions in the binding and unbinding processes. [Preview Abstract] |
Tuesday, March 19, 2013 9:48AM - 10:24AM |
F44.00008: Noise and fidelity of information transmission through the Tumor Necrosis Factor signaling circuit Invited Speaker: Andre Levchenko Molecular noise restricts the ability of an individual cell to resolve input signals of different strengths and gather information about the external environment. We developed an integrative theoretical and experimental framework, based on the formalism of information theory, to quantitatively predict and measure the amount of information transduced by molecular and cellular networks. Analyzing tumor necrosis factor (TNF) signaling revealed that individual TNF signaling pathways transduce information sufficient for accurate binary decisions, and an upstream bottleneck limits the information gained via multiple integrated pathways. Negative feedback to this bottleneck could both alleviate and enhance its limiting effect, despite decreasing noise. Bottlenecks likewise constrain information attained by networks signaling through multiple genes or cells. We further use this new analysis formalism to ``map'' the noise amplitude across different parts of the network. Finally, we show that the redundancy in signaling due to the existence of parallel pathways is not absolute, and that parallel pathways can transmit different types of information about the input, i.e., the duration vs. amplitude. [Preview Abstract] |
Tuesday, March 19, 2013 10:24AM - 10:36AM |
F44.00009: Morphogenesis at criticality? Dmitry Krotov, Julien Dubuis, Eric Wieschaus, Thomas Gregor, William Bialek Embryonic development of many multicellular organisms begins with the generation of spatially varying patterns of morphogens that encode the body plan of the future organism. We study the spatial pattern formed by the gap gene proteins in the early fruit fly embryo, which is anchored by ``crossing points'' between expression levels of different genes; these are thought to result from mutual repression. We explore a broad class of models for such interacting genes and show that the parameters implied implied by recent quantitative measurements are non-generic, but rather tuned to certain values, so that the entire gap gene network operates close to the critical surface in its phase diagram. We develop a mean field description of this system as well as derive signatures of critical behavior in the structure of expression noise. One such signature is that fluctuations are dominated by a single ``massless'' mode, so that fluctuations of expression levels of different genes are highly correlated/anticorrelated. We find a surprisingly high degree of anticorrelation in the real experimental data. These results suggest an interesting possibility that the network of genes responsible for development is operating near criticality. [Preview Abstract] |
Tuesday, March 19, 2013 10:36AM - 10:48AM |
F44.00010: Modeling the Dynamics of Bivalent Histone Modifications in Embryonic Stem Cells Wai Lim Ku, Guo Cheng Yuan, Francesco Sorrentino, Michelle Girvan, Edward Ott Epigenetic modifications to histones may either promote the activation or repression of the transcription of nearby genes. Recent experiments have discovered bivalent domains of nucleosomes in which the domain as a whole contains both active and repressive marks. These domains occur in the promoters of most lineage-control genes in embryonic stem cells. It is generally agreed that bivalent domains play an important role in stem cell differentiation, but the mechanisms remain unclear. Here we propose and study a dynamical model of histone modification which, unlike previous models, captures the general features of the bivalent domains observed in experiments. A key feature of our model is the existence of ``A/R states,'' by which we mean states in which there are a significant number of nucleosomes \textit{each} of which \textit{individually} has both active and repressive marks. We use our model to investigate the formation and decay of A/R states, the localization of A/R nucleosomes, and the effect of DNA replication on the stability of A/R states. The goals of our model are to help understand the underlying principles and mechanisms of bivalent domain dynamics and to suggest directions for future experiments. [Preview Abstract] |
Tuesday, March 19, 2013 10:48AM - 11:00AM |
F44.00011: Using entropy to cut complex time series David Mertens, Julia Poncela Casasnovas, Bonnie Spring, L.A.N. Amaral Using techniques from statistical physics, physicists have modeled and analyzed human phenomena varying from academic citation rates to disease spreading to vehicular traffic jams. The last decade's explosion of digital information and the growing ubiquity of smartphones has led to a wealth of human self-reported data. This wealth of data comes at a cost, including non-uniform sampling and statistically significant but physically insignificant correlations. In this talk I present our work using entropy to identify stationary sub-sequences of self-reported human weight from a weight management web site. Our entropic approach--inspired by the infomap network community detection algorithm--is far less biased by rare fluctuations than more traditional time series segmentation techniques. [Preview Abstract] |
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