### Session P39: Self-Organization in Biological Cells and Tissues I

 Wednesday, March 18, 2009 8:00AM - 8:12AM P39.00001: Statistical analysis and modeling of collective cell motion and pattern formation Andras Czirok , Andras Szabo Cell motility and its guidance through cell-cell contacts is instrumental in vasculogenesis and in several other morphogenic processes as well. During vasculogenesis multicellular sprouts invade rapidly into avascular areas, eventually creating an interconnected network pattern. Epithelial cell sheets migrate during organogenesis or wound healing. These phenomena were studied with time-lapse microscopy both in vivo and in vitro. Statistical analysis of cell trajectories reveals that motile confluent cultures may behave either as vortical fluids or as deforming elastic sheets. The observed flow fields and pattern formation can be explained by our generalized cellular Potts model -- representing cell polarization and self-propulsion, links between the cytoskeleton of adjacent cells as well as an asymmetric preferential attraction to the surface of adjacent cells. Wednesday, March 18, 2009 8:12AM - 8:24AM P39.00002: Self-organization in Systems ofTreadmilling Filaments. Konstantin Doubrovinski , Karsten Kruse The cytoskeleton is an active intracellular network of polar filaments responsible for maintenance of cell shape, cell division, and cell locomotion. A broad variety of cellular processes depend critically on the ability of cyoskeletal filaments to treadmill, i.e. to move by growing at one end while simultaneously shrinking at the other end. In particular, treadmilling is indispensable for cell crawling as well as for generation of various cellular appendages including stereocilia, microvilli, and filipodia. Quantitative modeling of systems involving treadmilling filaments is challenging since it requires describing long-range interactions of particles with many degrees of freedom. We introduce a novel framework for describing systems of treadilling filaments. Within our framework, we identify a class of systems that admit exact solution of the underlying dynamic equations. We compare the corresponding solutions to those obtained by coarse-graining, an approximation which is valid on large length-scales. We apply our new framework to treat two biological systems: cytoskeletal dynamics in fish melanophores and locomotion of human neutrophil cells. In both cases our theory faithfully accounts for the qualitative and semi-quantitative properties of the intracellular structures observed in the corresponding experiments. Wednesday, March 18, 2009 8:24AM - 8:36AM P39.00003: Self-assembly of the yeast actomyosin contractile ring as an aggregation process: kinetics of formation and instability regimes Nikola Ojkic , Dimitrios Vavylonis Fission yeast cells assemble an equatorial contractile ring for cytokinesis, the last step of mitosis. The ring assembles from $\sim$ 65 membrane-bound nodes''' containing myosin motors and other proteins. Actin filaments that grow out from the nodes establish transient connections among the nodes and aid in pulling them together in a process that appears as pair-wise attraction (Vavylonis et al. Science 97:319, 2008). We used scaling arguments, coarse grained stability analysis of homogeneous states, and Monte Carlo simulations of simple models, to explore the conditions that yield fast and efficient ring formation, as opposed to formation of isolated clumps. We described our results as a function of: number of nodes, rate of establishing connections, range of node interaction, distance traveled per node interaction and broad band width, $w$. Uniform cortical 2d distributions of nodes are stable over short times due to randomness of connections among nodes, but become unstable over long times due to fluctuations in the initial node distribution. Successful condensation of nodes into a ring requires sufficiently small $w$ such that lateral contraction occurs faster then clump formation. Wednesday, March 18, 2009 8:36AM - 8:48AM P39.00004: Discrete and continuous models of protein sorting in the Golgi Haijun Gong , Russell Schwartz The Golgi apparatus plays an important role in processing and sorting proteins and lipids. Golgi compartments constantly exchange material with each other and with other cellular components, allowing them to maintain and reform distinct identities despite dramatic changes in structure and size during cell division, development and osmotic stress. We have developed two minimal models of membrane and protein exchange in the Golgi --- a discrete, stochastic model [1] and a continuous ordinary differential equation (ODE) model --- both based on two fundamental mechanisms: vesicle-coat-mediated selective concentration of soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins during vesicle formation and SNARE-mediated selective fusion of vesicles. Both show similar ability to establish and maintain distinct identities over broad parameter ranges, but they diverge in extreme conditions where Golgi collapse and reassembly may be observed. By exploring where the models differ, we hope to better identify those features essential to minimal models of various Golgi behaviors. [1] H. Gong, D. Sengupta, A. D. Linstedt, R. Schwartz. Biophys J. 95: 1674-1688, 2008. Wednesday, March 18, 2009 8:48AM - 9:00AM P39.00005: ABSTRACT WITHDRAWN Wednesday, March 18, 2009 9:00AM - 9:12AM P39.00006: Studying the Transition to Multicellular Life by Altering a Chemical Signaling Channel Carl Franck , Kayvon Daie The starvation response of the eukaryotic microbial system Dictyostelium discoideum has continued to provide opportunities to explore the transition from solitary to collective life. Specifically, one observes a change of behavior from random to synchronized cellular motion reflecting successful long-ranged chemical signaling that leads to aggregation. In the typical experimental universe life goes on upon a flat substrate underneath an ocean of liquid media through which these chemical signals pass. In our observations of starvation development we have uniquely exploited the possibilities afforded by varying the depth of this signaling channel over an interesting range: from essentially infinitely thick (mm's of depth) to an extremely thin wetting layer (below 1 micron). We also examine the development system over a wide range of surface density: from almost a full monolayer to a few percent areal coverage. Our key observation is a striking reduction of the time from the beginning of starvation to the onset of synchronized movement when we reduce the aqueous overlayer thickness to the thinnest values. We provide an interpretation for our observations by combining an exact solution to the diffusive transport problem with a rough dynamical theory for multiagent synchronization. This work was supported by the NIH (P01 GM078586). Wednesday, March 18, 2009 9:12AM - 9:24AM P39.00007: Simulation of cellular shapes on micro-patterned substrate using the Cellular Potts Model Benoit Vianay , Herve Guillou Cell adhesion and motility are processes involved in fundamental biological phenomena using biological structures as anchorage points and cytoskeleton filaments which are very dynamical and at non-equilibrium. We study cell adhesion on micro-patterned substrate where an introduction of a finite distance between anchorage points of the cell modifies drastically the organization of the cytoskeleton and the anchorage point's distribution. Some of statistically most used shapes represent stationary states of the system which should minimize the energy dissipation. We verified this hypothesis reproducing morphologies by simulation of Monte Carlo using the Cellular Potts Model (Graner and Glazier, PRL69 p2013 (1992)). Shapes obtained by simulation depend of four phenomenological parameters as interaction between cell and ECM and are in excellent qualitative agreement with experimental shapes. The aim of this presented work is to link model parameters to physico-chemical properties of cells and to establish phenomenological relations between interesting parameters controlling the cytoskeleton organization. Collaborations : J. Kafer {\&} F. Graner : Laboratoire de spectrometrie Physique -- Grenoble; E. Plannus {\&} M. Block~: Institut Albert Bonniot -- Grenoble. Wednesday, March 18, 2009 9:24AM - 9:36AM P39.00008: Turing instabilities on curved surfaces with applications to postsynaptic domain formation Christoph Haselwandter , Martin M. M\"uller , Jemal Guven , Mehran Kardar , Roya Zandi Postsynaptic receptor molecules are one of the key regulators of signal transmission across synapses. Receptors mostly populate postsynaptic domains, which also comprise stabilizing scaffold molecules. The formation of receptor-scaffold domains can be understood as a Turing instability arising from the interactions between receptors and scaffolds. The curvature of the membrane modifies the developing patterns which will be explored using analytical and numerical methods. Wednesday, March 18, 2009 9:36AM - 9:48AM P39.00009: Perturbing Streaming in \textit{Dictyostelium discoidium} Aggregation Erin Rericha , Gene Garcia , Carole Parent , Wolfgang Losert The ability of cells to move towards environmental cues is a critical process allowing the destruction of intruders by the immune system, the formation of the vascular system and the whole scale remodeling of tissues during embryo development. We examine the initial transition from single cell to group migration in the social amoeba \textit{Dictyostelium discoidium}. Upon starvation, \textit{D. discoidium} cells enter into a developmental program that triggers solitary cells to aggregate into a multicellular structure. The aggregation is mediated by the small molecule, cyclic-AMP, that cells sense, synthesize, secrete and migrate towards often in a head-to-tail fashion called a stream. Using experiment and numerical simulation, we study the sensitivity of streams to perturbations in the cyclic-AMP concentration field. We find the stability of the streams requires cells to shape the cyclic-AMP field through localized secretion and degradation. In addition, we find the streaming phenotype is sensitive to changes in the substrate properties, with slicker surfaces leading to longer more branched streams that yield large initial aggregates. Wednesday, March 18, 2009 9:48AM - 10:00AM P39.00010: Matrix Production in Response to Nutrient Depletion in Bacillus Subtilis Biofilms Thomas Angelini , Michael Brenner , David Weitz Encasing the cells that comprise a bacterial biofilm, the extracellular polysaccharide (EPS) matrix may serve several purposes in biofilm development and survival. One class of examples involves adhesion; the EPS can contribute to cell-cell adhesion and cell substrate adhesion. In contrast to biofilm expansion by proliferation, which produces more nutrient consumers, EPS production could be an alternative, more efficient method of biofilm expansion. The recent work of Vlamakis, et al (2008) demonstrated a transition in the rate of EPS production during biofilm growth. At early stages of development, when the biofilm is thin, a low level of matrix is expressed. At later stages, when the biofilm has thickened, EPS production is dramatically increased. This transition could be a response to nutrient depletion, as there must be a critical biofilm thickness, above which nutrients cannot diffuse into the center of the biofilm before being consumed by cells at the edge. Here we quantify biofilm size and shape during the early stages of Bacillus Subtilis biofilm growth, simultaneously monitoring matrix expression levels. We show that the critical biofilm size scales with nutrient concentration as expected by a simple nutrient depletion model. Wednesday, March 18, 2009 10:00AM - 10:12AM P39.00011: Degenerate polygonal tilings in simple animal tissues Primoz Ziherl , Ana Hocevar We study 2D polygonal tilings as models of the en-face structure of single-layer biological tissues. Using numerical simulations, we explore the phase diagram of equilibrium tilings of equal-area, equal-perimeter convex polygons whose energy is independent of their shape. We identify 3 distinct phases, which are all observed in simple epithelial tissues: The disordered phase of polygons with 4-9 sides, the hexatic phase, and the hexagonal phase with perfect 6-fold coordination. We quantify their structure using Edwards' statistical mechanics of cellular systems. Wednesday, March 18, 2009 10:12AM - 10:24AM P39.00012: Non-equilibrium self-assembly of a filament coupled to ATP hydrolysis Padinhateeri Ranjith We study the stochastic dynamics of growth and shrinkage of single actin filaments or microtubules taking into account insertion, removal, and ATP/GTP hydrolysis of subunits. The resulting phase diagram contains three different phases: two phases of unbounded growth : a rapidly growing phase and an intermediate phase, and one bounded growth phase. We analyze all these phases, with an emphasis on the bounded growth phase. We also discuss how hydrolysis affects force-velocity curves. The bounded growth phase shows features of dynamic instability, which we characterize in terms of the time needed for the ATP/GTP cap to disappear as well as the time needed for the filament to reach a length of zero ({\it i.e.} to collapse) for the first time. We obtain exact expressions for all these quantities, which we test using Monte Carlo simulations. Wednesday, March 18, 2009 10:24AM - 10:36AM P39.00013: Chemotaxis of catalytically-driven nanorods Young-Moo Byun , Paul Lammert , Vincent Crespi , Yiying Hong , Ayusman Sen Chemotaxis, a kind of taxis, is the directed motion of nanoscale organisms such as bacteria along the gradient of chemical concentration. Chemists have created non-biological nanorods, made of gold at one end and platinum at the other, which move autonomously through a solution of hydrogen peroxide due to a catalytic reaction,1 and showed that those metallic nanorods mimic chemotaxis by moving towards regions in a solution with a high concentration of hydrogen peroxide.2 In this talk, we present a theoretical model for chemotaxis and a way of how to analyze the motion of nanorods, and then compare our theory to the experimental data. 1. Paxton et al, J. Am. Chem. Soc., 126, 13424-13431 (2004) 2. Hong et al, Phys. Rev. Lett. 99, 178103 (2007) Wednesday, March 18, 2009 10:36AM - 10:48AM P39.00014: Self-organization of the MinE ring in subcellular Min oscillations Julien Derr , Jason T. Hopper , Anirban Sain , Andrew D. Rutenberg In the bacterium {\it Escherichia coli}, the mid-cell positioning of division is achieved by the sub-cellular oscillation of Min proteins. MinD interacts with the membrane and polymerizes into filaments. MinE binds to membrane bound MinD leading to the depolymerization of the MinD filaments. It has been observed experimentally that MinE forms a ring, known as the E-ring, near the end of the MinD polymers. We model and solve the self-organization of the E-ring. Rebinding of MinE to depolymerizing MinD filament tips controls MinE ring formation. We find two types of E-ring profiles near the filament tip: a strong plateau-like E-ring as seen {\it in vivo}, controlled by 1D diffusion along the bacterial length, or a weak cusp-like E-ring controlled by 3D diffusion near the filament tip. We discuss the initial instability that leads to MinD filament depolymerization and the formation of the E-ring. We also discuss the duration of transients leading towards strong or weak E-rings. We compare with experiment both in {\it vivo} and {\it in vitro}.