Session D27: Self-organization in Biological Cells and Tissue I

Effects of Cell Growth on Min-Protein Oscillation in \textit{E. coli}

A coarse-grained model for cell growth via elongation is implemented to study the effects of dynamic cell geometry on the spatio-temporal oscillations of the Min system of proteins in \textit{Escherichia coli}. Using a well studied reaction-diffusion model for the oscillations, numerical solutions of a system of coupled non-linear PDEs are solved with dynamic boundary conditions. The model for elongation correctly captures the behavior of wild-type cells and predicts the emergence of multi-node oscillations in filamentous mutants. Comparisons are made with results of fixed-length calculations for long filamentous cells.   

A free energy model for observed morphology of mitochondrial cristae

Electron tomograms have revealed that in normal mitochondria the inner membrane self-assembles into a complex structure that contains both tubular and flat lamellar cristae components. This structure, which contains one matrix compartment, is believed to be essential to the proper functioning of mitochondria as the powerhouse of the cell. It was indeed observed that the morphology is lost during programmed cell death - the mitochondrial inner membrane transforms into multiple vesicular matrix compartments. We have been able to construct a model in which the observed morphology can be obtained by minimizing the system's free energy. The model assumes that mechanical forces act on the membrane, which we believe to be exerted by proteins. In order to test the model, we measured the structural features of mitochondria in HeLa cells and mouse embryonic fibroblasts using 3D electron tomography. Data obtained from different mitochondria show excellent agreement. The model predicts that the crista membrane structure of healthy mitochondria is stabilized by tensile forces of the order of 10 pN, comparable to those typical of motor proteins. The model also predicts reasonable values for the pressure difference across and the surface tension of crista membranes.   

Membrane-mediated interactions drive the condensation and coalescence of FtsZ rings

The role of the coupling between the shape of membrane-bound filaments, and the membrane, is demonstrated for the dynamics of FtsZ rings on cylindrical membranes. Filaments with an arc-like spontaneous curvature, and a possible added active contractile force, are shown to spontaneously condense into tight rings, associated with a local inwards deformation of the membrane. The long-range membrane-mediated interactions are attractive at short ring-ring separations, inducing the further coarsening dynamics, whereby smaller rings merge to form larger and fewer rings, that deform the membrane more strongly. At the same time, these interactions induce a potential barrier that can suppress further ring coalescence at a separation of about $2\pi$ times the cylinder radius. These results of the model are in very good agreement with recent in-vitro experiments on the dynamics of FtsZ filaments in cylindrical liposomes. These results emphasize the important role of long-range membrane-mediated interactions in the organization of cytoskeletal elements at the membrane.   

Sculpting membranes: a mechanism of curvature generation by proteins

A wide spectrum of intracellular processes is dependent on the ability of cells to dynamically regulate membrane shape. Membrane bending by proteins is necessary for the generation of intracellular transport carriers and for the maintenance of otherwise intrinsically unstable regions of high membrane curvature in cell organelles. Understanding the mechanisms by which proteins curve membranes is therefore of primary importance. Crescent shaped N-BAR domains containing amphipathic helices can induce membrane curvature by two mechanisms: the scaffolding mechanism due to the very shape of the BAR dimer, and the hydrophobic insertion mechanism by which small shallow inclusions penetrate the membrane matrix and act as a wedge changing the local membrane curvature. We will focus on this latter mechanism, and study it from a quantitative point of view. We use an elastic model of the lipid bilayer, taking into account the internal strains and stresses generated by the presence of an inclusion. We show that large membrane curvatures found in in vitro experiments can be ascribed to this mechanism, and that shallow insertions are more powerful curvature generators than lipids.   

Calcium induced lipid domains: how to glue charge with charge

Multivalent ions such as calcium play an important role in soft and biological matter. In systems containing a fraction of highly negatively charged lipids (PIP2, an important actor in e.g. cell signaling) they can mediate an attraction between the like-charged lipids that is strong enough to promote formation of PIP2-rich domains. Such behavior is determined by charge correlations and therefore not captured by traditional mean-field (Poisson-Boltzmann) treatments. We study this effect experimentally and computationally in a mixed lipid monolayer. The simulations show that electrostatics alone can reproduce many of the trends seen in the experiments. Surprisingly, we find that electrostatic, Ca-mediated attractions between PIP2 lipids are strong enough to lead to nearly complete phase separation, so that domains of PIP2 can be found even at concentrations low enough to approach physiological conditions.   

Model of Rho-Mediated Myosin Recruitment to the Cleavage Furrow during Cytokinesis

The formation and constriction of the contractile ring during cytokinesis, the final step of cell division, depends on the recruitment of motor protein myosin to the cell's equatorial region. During cytokinesis, the myosin attached to the cell's cortex progressively disassembles at the flanking regions and concentrates in the equator [1]. This recruitment depends on myosin motor activity and activation by Rho proteins. Central spindle and astral microtubules establish a spatial pattern of differential Rho activity [2]. We propose a reaction-diffusion model for the dynamics of myosin and Rho proteins during cytokinesis. In the model, the mitotic spindle activates Rho at the equator. Active Rho promotes, in a switch-like manner, myosin assembly into cortical minifilaments. Mechanical stress by cortical myosin causes disassembly of myosin minifilaments and deactivates Rho. Our results explain both the recruitment of myosin to the cleavage furrow and the observed damped myosin oscillations in the cell's flanking regions [1]. Spatial extent, period and decay rate of myosin oscillations are calculated. Various regimes of myosin recruitment are predicted. [1] Zhou {\&} Wang, Mol. Biol. Cell \textbf{19}:318 (2008) [2] Murthy {\&} Wadsworth, J. Cell Sci. \textbf{121}:2350 (2008)   

Monodisperse domains by proteolytic control of the coarsening instability

The coarsening instability typically prevents steady-statecluster-size distributions. We show that proteolysis, or degradation coupled to the cluster size, leads to a novel fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the size distribution. We investigate how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism can lead to interesting self-organization phenomena in biology. In particular, we demonstrate how this model is consistent with the experimental phenomenology of pseudo-pilus length control in bacterial type 2 secretion systems.   

Collective motion and density fluctuations in bacterial colonies

The emergence of collective motion such as in fish schools and swarming bacteria is a ubiquitous self-organization phenomenon. Such collective behavior plays an important role in a range of phenomenon, such as formation and migration of animal or fish groups. To understand the collective motion, tracking of large numbers of individuals is needed, but such measurements have been lacking. Here we examine a microscopic system, where we are able to measure simultaneously the positions, velocities, and orientations of up to a thousand bacteria in a colony. The motile bacteria form closely-packed dynamic clusters within which they move cooperatively. The number of bacteria in a cluster exhibits a power-law distribution truncated by an exponential tail, and the probability of finding large clusters grows markedly as bacterial density increases. Mobile clusters exhibit anomalous fluctuations in bacterial density: the standard deviation ($\Delta N$) grows with the mean ($N$) of the number of bacteria as $\Delta N\sim N^{3/4}$ rather than $\Delta N\sim N^{1/2}$, as in thermal equilibrium systems.   

Fluctuations and Pattern Formation in collective dynamics of bacteria

We consider a coarse-grained description of a bacterial system modeled as rod like self-propelled particles. The dynamics is given by hydrodynamic equations for a density and an orientation field that corresponds to the velocity of the bacteria. We find that the ordered swarming state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of individual units. In this unstable regime, the system goes into an inhomogeneous state that is characterized by well-defined robust propagating stripes of swarming particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous swarming state is stable, the system is characterized by large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize these two phases of the swarming state.   

Controlling Collective Behaviors of Dictyostelium

We study the collective dynamics of a population of Dictyostelium cells, focusing on how single cell dynamics influence, and give rise to, the behavior of the aggregate. Through analysis of quantitative single cell experiments, we develop a simple model of the single cell response to time-dependent pulses of the extracellular signaling molecule cAMP, characterized by a particular type of excitable system. We then use this model to study collective multicellular dynamics mediated by diffusion coupling. We first consider the mean-field case where we find an intriguing ``dynamical quorum sensing'' transition in which all cells simultaneously transition from quiescent to oscillating across the phase boundary. Then we include spatial dynamics and study pattern formation, both with and without the cells capable of chemotactic response to signal gradients. Finally, we highlight how modification of single cells can alter the collective dynamics.   

Cell speeds, persistence, and information transmission during signal relay and collective migration in Dictyostelium discoideum

Upon nutrient deprivation, the social amoebae Dictyostelium discoideum enter a developmental program causing them to aggregate into multicellular organisms. During this process cells sense and secrete chemical signals, often moving in a head-to-tail fashion called a `stream' as they assemble into larger entities. We compare key metrics of motion -- speed, persistence in direction, and directionality toward a chemical signal - in streaming cells versus mutants unable to stream, and we find that speed and directional persistence on short timescales remain unchanged under all conditions tested. These results point to the presence of an intrinsic motility machinery with inherent persistence and speed that is unaffected by the complicated external signaling environment. However, chemoattractants steer cells on longer timescales. We find that signal relay allows cells to move toward a point source of chemoattractant with equal accuracy independent of distance to the source and strength of the source.   

Variation in the excitability of developed D. discoideum cells as a function of agar concentration in the substrate

In the absence of nutrients, Dictyostelium discoideum cells enter a developmental cycle--they signal each other, aggregate, and ultimately form fruiting bodies. During the signaling stage, the cells relay waves of cyclic adenosine 3',5' monophosphate (cAMP). We observed a transition from spiral to circular patterns in the signaling wave, depending on the agar concentration of the substrate. In this talk we will present the changes in the times for the onset of signaling and synchronization versus agar concentration, as measured by spectral entropy. We also will discuss the origin of these effects.