We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy minimization occurs naturally to stabilize the system, and leads to an MMS separating the macromolecule from the solvent. For a given set of atomic constraints (as obstacles), the MMS is defined as one whose mean curvature vanishes away from the obstacles. Based on the theory of differential geometry, an iterative procedure is proposed to compute the MMS via the mean curvature minimization of molecular hypersurface functions. Extensive numerical experiments, including those with internal and open cavities, are carried out to demonstrate the proposed concept and algorithms. Comparison is given to the molecular surface. Unlike the molecular surface, the proposed MMS is typically free of singularities. The application of the MMS to the electrostatic analysis is considered for a set of twenty six proteins.

Our experimental study of the effect of ActA distribution on the motility of L. monocytogenes indicates that speed is positively correlated with both ActA intensity (amount) and polarity. The agent-based model we used to explore this behavior (from Alberts and Odell 2004) robustly demonstrates the opposite (i.e wrong) polarity relationship with speed. We initially judged this failure as an indication that model parameters, such as the those governing the ActA-actin filament bonds, were "out of tune". Extensive (though not exhaustive) searches in parameter space failed to yield solutions in agreement with experiment. We were ultimately led to the conclusion that our model was topologically incorrect --a mechanistic behavior was improperly represented, or missing altogether. The model is redeemed by inclusion of a cooperative (rather than linearly superposed) restraining force, specifically the explicit frictional drag of filaments on the bacterial surface. The redeemed model robustly captures target experimental behaviors. In light of this experience we reflect on the likely nature of complex dynamical systems in biology and our attempts to represent them in silico. Additionally, we present a one-dimensional partial-differential model (state variables: barbed-ends, actin density, speed of motion) that is instructive as a mathematical synopsis of the agent-based simulation, but fails to demonstrate sensitivity to the details that make all the difference in the complex model (and presumably in the biology).

The immersed boundary method is a modeling approach traditionally applied to macroscopic systems involving flexible elastic structures which interact with a fluid flow. To use such methods for microscopic systems requires at sufficiently small length scales that thermal fluctuations be taken into account. In this poster we discuss an extension of the immersed boundary method to incorporate thermal fluctuations of both the mechanical structures and the surrounding fluid. The formalism gives a set of stiff SPDE's for which standard numerical approaches perform poorly. We present alternative stochastic numerical methods to integrate the systems of equations. We then discuss how the methods can be used in practice and present results for simulations of a coarse grained model of a lipid bilayer membrane and a molecular motor protein.

The cluster of receptors and associated proteins at the 'front end' of the E. coli chemotaxis pathway is a paradigm for membrane complexes in cells. Like focal adhesions and synapses, it acts as a solid-state computational device that amplifies, integrates, and parses chemical signals from the environment and relays the output to the rest of the cell. Ten years ago we proposed a structure for this receptor cluster and suggested how it might provide a basis for the very high sensitivity of cells to certain attractants. In this talk I will revisit the lattice architecture in the light of recent findings and present a radically different mechanism for its amplification. The new model is more firmly based on known molecular events and gives a better understanding of how the cell responds to mixed signals.

The talk will address two aspects of the connection between nonequilibrium molecular-level processes and properties of actin related to cell motility. 1) The effects of ATP hydrolysis on force generation and polymerization dynamics. Using an extended Brownian-ratchet methodology, it is shown that hydrolysis of bound nucleotide can reduce the stall force of ensembles of actin filaments by a factor of three or more relative to the thermodynamic stall force. The force reduction occurs because the interaction with the obstacle induces hydrolysis at the tip, which converts filament tips temporarily to a depolymerizing state. It is also shown that hydrolysis can lead to overshoots in actin polymerization traces. The overshoots occur when the characteristic time of polymerization is shorter than the nucleotide exchange time on monomers. This effect may be present in cells with sufficiently high concentrations of free barbed ends. 2) The effects of network structure on the contractile stress generated by active myosin II interacting with actin filaments. Using elasticity theory combined with an effective-medium theory, it is shown that the stress generated per myosin is proportional to the average filament length. This leads to estimates of the cytokinesis tension that are much lower than existing estimates. unless the filaments are bundled into inextensible units longer than a filament. Continued contraction requires treadmilling of actin filaments, and the rate of contraction is limited by the filament treadmilling rate.

In recent years, there have been significant efforts to characterize the noise associated with the regulation of intracellular processes. Intrinsic fluctuations are often due to the small number of molecules that govern these processes. However, noise is not always caused by a low number of molecules; the regulatory network itself can cause large fluctuations in the number of signaling molecules. For example, systems that have an ultra-sensitive input-output relationship can be effective sources of noise because they not only amplify the input signal but also the associated noise itself. In this picture, systems that are more sensitive to intrinsic spontaneous noise also would be more sensitive to small external perturbations. In linear theory, it is common to analyze, at the equilibrium, spontaneous fluctuations (i.e. noise) in the system in order to predict the dynamical response to a small external perturbation. Here, we extend this simple mathematical framework to infer the cellular response to a small external stimulus by analyzing the noise of non-stimulated cells. We present a combination of experiments on and models of bacterial chemotaxis in E. coli that demonstrate the existence of such a relationship in living cells.

Joint work with Hye Young Kim and Robert Weaver (University of Pittsburgh, Department of Bioengineering, Pittsburgh PA 15260).

Three distinct tissues from the early frog embryo contain either cells that exhibit either no translational movement, mono-polar directed cell migration, or mediolateral cell intercalation. Interestingly, while each cell type exhibits different patterns of cell protrusions they manifest the same stereotypical periodic pattern of F-actin contractions within the pericellular cortex. Contractions form in less than a minute as cortex covering a few square micrometers appears to contract toward a focal point. As contraction progresses the F-actin network increases in density at which point the network appears to depolymerize back to the initial background state. The time-course of contraction followed by depolymerization takes less than two minutes. In order to understand the formation and disassembly of these F-actin contractions we are combining experiments to disrupt or activate the actomyosin cortex with a simple model that captures the basic dynamics of two-dimensional actomyosin networks in the cell cortex. Our model is based on a mechanical representation of myosin II mini-fibrils distributed within a network of polarized actin filaments and appears to capture the initial phase of contraction but not the later disassembly phase of F-actin contractions seen in vivo. Combined analysis of actin dynamics and modeling efforts are needed to understand the complex connections between the molecular mechanisms controlling subcellular mechanics and how these processes shape cells and tissues during development.

To move in a persistent, directed manner, motile cells must break symmetry and initiate movement that is maintained even after the stimulus is removed. In this poster, I will present a model of intracellular polarization in crawling cells that couples biochemical dynamics with spatially directed force generation. This biologically based model is able to reproduce a number of experimentally observed features including consistent responses to stimuli of varying strength and spontaneous polarization. I will discuss how polarization in other cell types will inform future directions of this model.

Joint work with Igor R. Kuznetsov and Marc Herant.

The transport of labeled G-actin from the mid-lamella region to the leading edge in a highly motile malignant rat fibroblast line has recently been studied using fluorescence localization after photo bleaching or FLAP (see Zicha et al.[Zicha2003]). The transit times recorded in these experiments were so fast, that simple diffusion was deemed an insufficient explanation. Since this conclusion has been controversial we here we re-examine the Zicha-FLAP experiments using a two-phase reactive interpenetrating flow formalism to model the cytoplasm and the transport dynamics of bleached and unbleached actin in a moving cell. This new analysis reveals a mechanism that can realistically explain the timing and the amplitude of all the observed FLAP signals in the Zicha-experiments without invoking special transport modalities. The proposed mechanism requires the existence of a small compartment at the leading edge of the lamella where actin polymerization is very fast and where this production is balanced by equally fast mechanical dilatation of F-actin caused by retrograde flow away from the leading edge. If our dilatation hypothesis is correct, the FLAP technique constitutes a novel and very sensitive probe of actin dynamics in a crucial leading edge environment which is otherwise very difficult to interrogate.

I survey our recent work on assembling the modular function and dynamics of signaling casettes that regulate actin-based motility. Arp2/3-mediated branching of actin filaments is regulated by small GTPases of the Rho family. These are modulated by phosphoinositides. Together, such signalling agents determine "front vs rear" in a stimulated cell, where new actin filament ends are nucleated or uncapped inside the cell, and where protrusion or myosin contractility will occur. I describe how we explored such biochemical dynamics in both 1D and 2D cell motility models, and how we analysed their essential features in reduced mathematical caricatures. This work is joint with AFM Maree, AT Dawes, A Jilkine, Y Mori, and V Grieneisen. It is supported by NSERC, NSF, and MITACS.

Experimental time series for trajectories of motile cells may contain so much information that a systematic analysis will yield cell-type-specific motility models. We show how here, using human keratinocytes and fibroblasts as examples. The two models that result, seem to reflect the cells' different roles in the organism, and show that a cell has a memory of past velocities. The models distinguish quantitatively between various surfaces' compatibility with the two cell types.

The ability of cells to spatially and temporally regulate traction forces on their extracellular matrix is fundamental to tissue morphogenesis and directed cell migration. Forces generated in the actin filament (F-actin) cytoskeleton are transmitted through the cell plasma membrane to the extracellular matrix via mechano-sensitive focal adhesions1. In migrating cells, F-actin and focal adhesions exhibit stereotypical patterns of assembly, disassembly and motion2-8. It is well appreciated that an intact F-actin cytoskeleton is required for cellular force generation; however, the role of F-actin motion dynamics in force generation is unknown. We show here that F-actin motion spatially correlates with traction stresses on the extracellular matrix. Near the cell edge, traction stress and F-actin speed are inversely correlated, suggesting that focal adhesions strengthen by slowing F-actin and engaging it to the stationary extracellular matrix. However, instead of observing maximal traction stress when F-actin motion is minimized, we find that an intermediate speed of F-actin motion marks a switch to focal adhesion weakening. The switch from focal adhesion strengthening to weakening is not correlated with focal adhesion protein density, age, stress magnitude, assembly/disassembly status or subcellular position. In contrast, the F-actin speed associated with maximal traction stress and the transition to adhesion weakening is strikingly robust. Thus, we identify F-actin motion dynamics as an important regulator of focal adhesion-mediated traction forces at the leading edge of migrating cells.

Joint work with Henry T. Schek², Alan J. Hunt², and David J. Odde¹.

Microtubule ends are intrinsically unstable, and although this property is critical for establishing cellular morphology and motility, the molecular basis of assembly remains unclear. Our 3D mechanochemical model for microtubule dynamic instability predicts that a spatially extended GTP cap allows for highly variable growth dynamics, and specifically that substantial nanoscale shortening of the microtubule tip could occur during a microtubule growth phase. Here we use optical tweezers to track microtubule polymerization against microfabricated barriers, permitting unprecedented spatial resolution. We find that microtubules exhibit extensive nanometer-scale variability in growth rate, and often undergo shortening excursions, in some cases exceeding 5 tubulin layers, during periods of overall net growth. This result indicates that the GTP cap does not exist as a single layer as previously proposed. Rather, simulations that rely on an exponentially distributed GTP-Cap qualitatively reproduce the experimentally observed variability in microtubule growth.

¹Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN ²Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI

The outer membrane of a living cell is very different from an inert lipid bilayer or a vesicle. Most notably, there exists a strong coupling between the membrane and the underlying cytoskeletal network of the cell. The cytoskeleton is a dynamic formation of proteins that is continuously reshaping itself, and in the process applies forces to the membrane. The membrane of a living cell is therefore constantly deformed by the forces of the underlying cytoskeleton. The energy produced by the cell's metabolism, in the form of ATP, drives the motion of the cytoskeleton and membrane through the polymerization of cytoskeletal filaments (actin and microtubules), the action of cytoskeleton-bound molecular motors and membrane-bound ions pumps. The cytoskeleton modifies the physical properties, such as the tension, fluctuation amplitude and effective bending modulus of the lipid membrane. In turn, the cytoskeletal organization can be influenced by the membrane shape (curvature) and tension. We describe several theoretical models of the physics of an active cytoskeleton and membrane and their coupling with the cell metabolism. The cytoskeleton-membrane coupling can lead to dynamic instabilities which are manifested as shape transitions of the membrane from the uniform flat configuration to one with finger-like protrusions. These transitions are coupled with composition phase separation inside the membrane, and are triggered by the active forces of the cytoskeleton. A similar instability is proposed as a model for the initiation of the contractile ring in dividing cells. Furthermore, traveling (propagating) waves can also arise when there are opposing forces of protrusion and contraction, or due to the effect of calcium ion influx. We compare these results to the observed behavior of living cell membranes, which exhibit a variety of dynamic behaviors.

Cell migration is essential in many physiological and pathological processes. To understand this complex behavior, researchers have turned to quantitative, in vitro, image-based measurements to dissect the steps of cellular motility. With the rise of automated microscopy, the bottleneck in these approaches is no longer data acquisition, but data analysis Using time-lapse microscopy and computer-assisted image analysis, we have developed a novel mid-throughput, quantitative assay that extracts a multivariate profile for cellular motility. This technique measures three dynamic parameters per single cell: speed, surface area, and an index of cell expansion/contraction activity (DECCA). Our assay can be used in combination with a variety of extracellular matrix components, or other soluble agents, to analyze the effects of the microenvironment on migration cellular dynamics in vitro. Our application was developed and tested using A431 and HT1080 cell lines plated on laminin-332 or fibronectin substrates. Our results indicate that HT1080 cells migrate faster, have a greater surface area, and have a higher DECCA index than A431 cells on both matrices (for all parameters p

Mechanical properties are a key feature in a wide rage of animal cell functions, including growth, motility, and gene expression. On the poster, we outline different mathematical and computational tools for theoretical investigations of the mechanobiology of cells. Modelling mechanics of cytoskeletal networks often discrete microscopic models in terms of energy functionals are employed. However macroscopic continuum models are usually preferable form a computational point of view. But finding such macroscopic descriptions is often a non-trivial task. Considering microscopic models given in terms of free energies Gamma-convergence is the ideal framework for rigorously bridging the gap between discrete microscopic and continuous macroscopic models. On this poster mechanics of red blood cells are considered to show how such a multiscale framework can be employed to derive appropriate constitutive laws. The second focus of this poster are computational tools for studying the mechanobiology of cells. We outline two approaches: a Lagrangian approach, which represents evolving domains via transformations of a fixed grid, and an Eulerian approach, which characterises evolving domains implicitly using levelset methods. Both approaches are capable of coupling surface and bulk mechanics, as well as chemical and mechanical processes within one implicit time-stepping scheme.

Joint work with Colin K. Choi ^1,2, Miguel Vicente-Manzanares², Jessica Zareno², Leanna A. Whitmore², and Alex Mogilner³.

We have developed a new model for the assembly and maturation of nascent adhesions. Using dual label imaging and high resolution TIRF microscopy, we show that nascent adhesions assemble and are stable only within the lamellipodium. The assembly is myosin II-independent and requires actin polymerization. A computational model has been developed that accommodates the quantitative data on the dynamics of the nascent adhesions and the linkage of their assembly to actin polymerization. As the back of the lamellipodium moves past the nascent adhesions, they either disassemble as the protrusion continues to advance or begin to grow and elongate and mature as the protrusion pauses. Rescue of a myosin IIA knockdown with a motor-inhibited mutant of myosin IIA shows that the cross-linking function of myosin II is sufficient to promote adhesion maturation. Using an RNAi knockdown of ?-actinin, we demonstrate that a-actinin-actin filaments serve as a template that guides the centripetal elongation of the nascent adhesion. Measurements of paxillin dynamics and clustering using correlation microscopy show that adhesions tend to assemble by addition of monomers or small aggregates while they disassemble as large aggregates. From these studies, a new model emerges for adhesion assembly and maturation that clarifies the relative contributions of actin polymerization, stabilization and myosin II motor activity to adhesion dynamics.

¹ Department of Biomedical Engineering and ² Cell Biology, University of Virginia, Charlottesville, Virginia 22908; ³Department of Neurobiology, Physiology and Behavior and Department of Mathematics, University of California, Davis, California 95618.

In this talk I will discuss our group's efforts at elucidating the mechanisms underlying chemotaxis. Using known biochemical data, we have developed mathematical models that can account for many of the observed chemotactic behavior of the model organism Dictyostelium. I will discuss experiments used to test these models. Finally, I will describe how information-theoretic methods can be used to evaluate the optimality of the gradient sensing mechanisms.

We are currently attempting to understand how the basic processes of contractility, protrusion and adhesion are integrated to produce cell migration. This is an intellectually challenging problem that requires new approaches. The overall plan is to test an in silico model developed by A. Mogilner and colleagues for migration and check this model by perturbing these basic processes locally using photomanipulative techniques to see if the experimentally determined changes in migration can be accounted for by the model. The feasibility of two types of perturbations has now been demonstrated. Caged actin binding proteins and peptides derived from Focal Adhesion Kinase (FAK) can be uncaged and produce dramatic phenotypes. A complementary loss of function technique, EGFP-chromophore-assisted laser inactivation (EGFP-CALI), has been applied locally to several actin binding proteins including EGFP-a-actinin, EGFP-Mena and EGFP-capping protein, again with strong phenotypes. Photochemical mechanisms mediating CALI will be discussed.

I will also describe a graph theoretic approach to modeling motile phenomena that has been developed in collaboration with Gabriel Weinreb, Maryna Kapustina and Tim Elston. The causal map (CMAP) is a course-grained biological network tool that permits description of causal interactions between the elements of the network which leads to overall system dynamics. On one hand, the CM CMAP is an intermediate between experiments and physical modeling, describing major requisite elements, their interactions and paths of causality propagation. On the other hand, the CMAP is an in independent tool to explore the hierarchical organization of cell and the role of uncertainties in the system. It appears to be a promising easy-to-use technique for cell biologists to systematically probe v verbally formulated, qualitative hypotheses. We apply the CMAP to study the phenomenon of contractility oscillations in spreading cells in which microtubules have been depolymerized.

Supported by the NIH Cell Migration Consortium, IK54GM64346.

The complex system of actin filaments spanning the volume of a moving cell can be subdivided into distinct zones differing in their dynamic behaviour, structure and function and ordered in space sequentially beginning from the cell leading edge towards the cell interior. The first two zones are the lamellipodium, which underlies the cell membrane at the leading edge, and the lamellum adjacent to the lamellipodium and propagating further into the cell volume.

The lamellipodium and lamellar actin networks do not overlap; they are separated by a distinct interface marked by an abrupt change of the velocity of the retrograde actin flow, and by a sharp change of the actin network density and structure. Revealing the physical forces responsible for the generation and dynamics of the lamellipodium-lamellum interface is of a primary importance for understanding the factors which govern organization of actin at the cell front into the spatially segregated and essentially distinct sub-systems.

The goal of the present work is to propose a physical mechanism for this phenomenon. Based on the existing knowledge on the mechanical properties of actin gels, we consider the lamellipodium actin network as a two-dimensional elastic medium, which slides towards the cell centre over a row of focal adhesions and exerts a friction-like interaction with the latter.

We show that the friction-like interaction between the actin gel and the focal adhesions results in formation of a lamellipodium boundary passing through the row of the FAs and having a shape similar to that observed within cells. This boundary is suggested to represent the lamellipodium-lamellum interface. We further consider advancing of the lamellipodium-lamellum interface to a new row of focal adhesions.

A mathematical modeling and simulation for concentration-dependent contraction of cell is shown in an illustrative way. The cell is supposed to have actomyosin fibers parallelly in cytoplasm. Those fibers are sensitive to local calcium concentration regarding elastic stiffness and resting length by Hill-type curves. Initially the calcium is low in intracellular domain, and high in extracellular domain. With the membrane permeable to calcium, actomyosin network gets activated and contracted by increased calcium inside. By the water semi-permeability of the membrane and the osmotic effect, the volume change is available in the course of contraction. Membrane and fibers being moving in a viscous fluid, the spatio-temporal dynamics of ion concentration are possible by the computational framework of the immersed boundary method with advection-electrodiffusion.

Intracellular protein concentration gradients are generally thought to be unsustainable at steady-state due to diffusion. Here we show how protein concentration gradients can theoretically be sustained indefinitely through a relatively simple mechanism that couples diffusion to a spatially segregated kinase–phosphatase system. Although it is appreciated that such systems can theoretically give rise to phosphostate gradients, it has been assumed that they do not give rise to gradients in the total protein concentration. Here we show that this assumption does not hold if the two forms of protein have different diffusion coefficients. If, for example, the phosphorylated state binds selectively to a second larger protein or protein complex, then a steady-state gradient in total protein concentration will be created. We illustrate the principle with an analytical solution to the diffusion-reaction problem and by stochastic individual-based simulations using the Smoldyn program. Looking at the example of bacterial chemotaxis, our model accounts for gradients of total CheY and CheZ, which were observed, but not explained, previously. We argue that protein gradients created in this way need to be considered in experiments using fluorescent probes and could in principle encode spatial information in the cytoplasm.

Joint work with Steven S. Andrews (The Molecular Sciences Institute, Berkeley, MA).

Smoldyn is a computer program for performing detailed simulations of cell biology. Proteins and other molecules of interest are represented by individual point-like particles that diffuse within a continuous (non-lattice) space. Smoldyn accurately and efficiently simulates diffusion, first and second order chemical reactions, allostery, and a wide variety of molecule-membrane interactions. As in the eponymous Smoluchowski theory, simulated bimolecular reactions occur when reactants diffuse closer together than a so-called binding radius. Smoldyn was written on OS X in C and OpenGL. It is open source, multi-platform, and easy to use, running on any machine from laptop to computer cluster. Smoldyn is freely available, designed for both the research and teaching communities. We present the algorithm and its speed performance, and its application in modelling various aspects of the bacterial chemotaxis system.

Joint work with C.P. McCann^1,2, P.W. Kriebel¹, E.C. Rericha², C.A. Parent¹.

Upon nutrient deprivation, the social amoeba Dictyostelium discoideum enter a developmental program allowing them to aggregate and differentiate into a multicellular organism made of spores atop a stalk of vacuolated cells. During the aggregation process individual cells sense and migrate up a chemoattractant gradient of cyclic adenosine monophosphate (cAMP), relaying the signal by synthesizing and releasing additional cAMP. This process leads to a characteristic chain migration where cells align in a head-to-tail fashion and migrate in streams. We have quantitatively analyzed time-lapse images of cells as they migrate in streams. We find that the average cell migration speed and the formation of streams are sensitive to cell plating density. At a density of 7x104 cells/cm2 cells stream with an average speed of ~10 micron/min outside steams, while at 2x104 cells/cm2 cells do not stream and move with an average speed of ~5 micron/min. In addition, for a given plating density, the volume of fluid above the cells has a strong influence on the formation of streams, suggesting that excess extracelluar fluid effectively dilutes cell-to-cell signals. We are currently performing cell mixing experiments with fluorescently labeled cells to assess the speed of cells both inside and outside streams. Our findings provide insights into the requirements for signal relay during chemotaxis and highlight the importance of environmental conditions for cell migration.

¹Laboratory of Molecular and Cellular Biology, CCR, NCI, NIH, Bethesda, MD; ²Dept. of Physics, University of Maryland, College Park, MD

In normal development and tumor metastasis, epithelial cells can acquire migratory and invasive properties. Border cells in the Drosophila ovary provide a genetic model for such behaviors. Earlier work has shown that JAK/STAT signaling is critical to specify the migratory population and sustain their motility. In a genetic screen for new mutations that affect border cell motility, we identified the gene apontic. Apontic, a nuclear protein, converts an initially graded pattern of STAT activity into an all-or-nothing response. This defines and limits the invasive border cell population. Apt functions as a feedback inhibitor of STAT, providing a molecular mechanism to explain a classic problem in embryology: how a graded signal can generate discrete cellular responses. This work, which includes a mathematical model, elucidates one mechanism to limit cell invasion in vivo.

Motile bacteria seek optimal living habitats by following gradients of attractant and repellent chemicals in their environment. The signaling machinery for these chemotactic behaviors, although assembled from just a few protein components, has extraordinary information-processing capabilities. Escherichia coli, the best-studied model, employs a networked cluster of transmembrane receptors to detect minute chemical stimuli, to integrate multiple and conþicting inputs, and to generate an ampliÞed output signal that controls the cell's þagellar motors. Signal gain arises through cooperative action of chemoreceptors of different types. The signaling teams within a receptor cluster may be built from trimers of receptor dimers that communicate through shared connections to their partner signaling proteins.

Coauthors: Junhwan Jeon ^[1], Alissa M. Weaver ^[2] and Peter T. Cummings ^[1,3].

We have implemented the cellular dynamics simulation methodology (originally developed for bacterial migration) to describe the random migration of MCF-10A pbabe, neuN and neuT cells using the experimental parameters extracted for each cell type, by the application of bimodal analysis technique developed by us. The Bimodal framework inspired from the bacterial run-tumble scheme segregates mammalian cell tracks into alternating directional and re-orientation modes. We find from simulations that the HER-2 transformed neuT cells have higher random motility coefficient compared to the control pbabes.

^[1]Department of Chemical Engineering, Vanderbilt University, Nashville TN ^[2]Department of Cancer Biology, Vanderbilt University Medical Center, Nashville, TN ^[3]Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN

The social amoebae Dictyostelium and human leukocytes possess the ability to polarize and move in a directed fashion in response to chemical signals. We are interested in understanding how cells transduce shallow external chemotactic signals into highly polarized cellular responses, which are required for directed cell migration. By tagging various signaling proteins with the green fluorescent protein (GFP) we have been able to visualize in live cells where and when various cascades are activated. This has led us to propose a novel mechanism that explains how chemotactic gradients are amplified by signal relay. Our research projects are designed to provide insight on the role of various signaling cascades in chemotaxis and have direct bearing on the understanding of clinically important processes as such leukocyte migration to sites of inflammation as well as cancer metastasis.

Recently, a computational model addressing cell biomechanics has been introduced, called the Subcellular Element Model (SEM). The model is primarily designed to represent deformable cells in multi-cellular systems, but can also be used to represent a single cell in more detail. Within the model framework, a cell is represented by a collection of elastically coupled elements, interacting with one another via short-range potentials, and dynamically updated using over-damped Langevin dynamics. We have tested whether the model yields viscoelastic properties consistent with those measured on single living cells and reconstituted cytoskeletal networks. Employing methods of microrheology we find that weak power law rheology emerges. With further phenomenology of treating the cytoskeleton as a viscoelastic network, we show here a novel one-dimensional model, which as well displays intermediate time regime/weak power law rheology.

The lamellipodium is the movement organ of several types of crawling cells. Motility is driven by the dynamics of the actin cytoskeleton, a flat network of polymers. The dynamics is influenced by actin (de)polymerization, by crosslinking of polymers, by their stiffness, by adhesion of the network to the substrate through transmembrane proteins, by active contraction of the network by motor proteins, and by the mechanical properties of the cell membrane. In a recent modelling effort, these effects are modelled on a microscopic scale, where the elastic response of individual filaments and the stochastic properties of protein reactions are taken into account. Then, by a homogenization procedure, continuum models for the cytoplasm in a lamellipodium are derived. The derivation of this new class of models, their mathematical properties, as well as results of numerical simulations will be presented.

Joint work with Michael Halter¹, Kurt J. Langenbach², Alex Tona³, Anne L. Plant¹, John T. Elliott¹

Tenascin-C expression is frequently upregulated during wound healing, inflammation, and tumorigenesis. Using live cell automated microscopy, we quantified the fluorescence intensity from individual NIH-3T3 fibroblasts stably transfected with a tenascin-C promoter driving a destabilized eGFP reporter. Hundreds of individual cells were followed throughout the cell cycle during live cell imaging experiments lasting 62 hours. We will describe techniques used to track these cells as they migrate. We observed that the GFP production in individual cells increased as they approached mitosis. On average the increase began when cells were approximately 60% through the cell cycle, suggesting that the tenascin-C promoter is more active at the end of the cell cycle. We conclude that the increase in GFP within individual cells was unlikely due to a systematic change in the degradation of GFP because we found no correlation between the GFP degradation kinetics and GFP fluorescence intensity when measured across a large number of individual cells. This work illustrates the application of quantitative, live cell microscopy using a promoter-driven GFP reporter cell line to measure the dynamics of single cell gene expression activity. A large number of signaling pathways have been implicated in the activation of tenascin-C gene transcription. Our results suggest that tenascin-C expression is, at least in part, directly coupled to proliferation and cell cycle progression.

¹ National Institute of Standards and Technology, Gaithersburg MD ²ATCC, Manassas, VA ³SAIC, Arlington, VA

Joint work with S.L. Porter², P.K. Maini^1,3, J.P. Armitage^2,3.

The role that spatial protein localisation plays in altering the expression of flagellar motor driving proteins in bacterial chemotaxis has to date largely been ignored. The work presented here focuses on a mathematical spatiotemporal reaction-diffusion model of signal transduction developed to describe phosphotransfer in Rhodobacter sphaeroides. The mathematical model is used to understand the role that spatial protein localisation has on affecting the motor protein expression and the connection between the cytoplasmic and receptor clusters in describing the overall bacterial response.

¹ Centre for Mathematical Biology, Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB. ²Department of Biochemistry, Microbiology Unit, University of Oxford, South Parks Road, Oxford, OX1 3QU. ³Oxford Centre for Integrative Systems Biology, Department of Biochemistry, University of Oxford, South Parks Road, Oxford, OX1 3QU.

In this talk, I will present our recent work in trying to understand bacterial chemotaxis (bacteria’s ability to sense and track chemical gradient) by using a quantitative modeling approach. Based on molecular level knowledge of the E. coli chemotaxis pathway, we propose a simple model for bacterial chemotaxis and use it to address several interesting, important system-level questions: 1) What kind of computation does a E. coli cell perform in response to complex time-varying stimuli? 2) What kind of memory does E. coli have? How long does it take the cell to forget? 3) How does the cell use its memory and computation capability to sense and respond to a minute chemical gradient (food or poison) among a wide range of background.

Joint work with Mahesh S. Tirumkudulu and K.V. Venkatesh

We describe a technique to create stable glucose gradients without requiring any fluid flow. The gradients are measured in both, space and time, using fluorescent glucose. We quantify the chemotaxis of E. coli by measuring the diffusivity and drift velocity of individual bacteria at varying glucose gradients.

We have applied new experimental and computational approaches to understand the mechanical events of adherent cells. While the extensive use of flexible substrates has lead to excellent understanding of traction forces, introduction of long polymers into the cytoplasm has started to shed light on weak gradients of forces generated by the cortex. In addition, a top-down mathematical model has been developed to simulate the control circuit that coordinates protrusions and retractions. The model is capable of generating experimentally measurable parameters, which in turn allows the use of optimization algorithms to match the model with observations, and to provide insights into how a unified feedback mechanism might generate a wide range of behaviors.

Invadopodia are subcellular protrusive structures associated with sites of extracellular matrix (ECM) degradation. Little is known about the regulation of invadopodia functions by ECM properties. I will discuss a joint experimental-computational study in which we have modeled and tested the regulation of invadopodia formation and function by crosslinked gelatin and collagen substrates. We find that crosslinking inhibits degradation and penetration of invadopodia in dense substrates, such as gelatin, but not in loose collagen matrices. These results provide a framework for consideration of diverse types of matrices that invasive cells may experience in vivo.

We investigate the molecular mechanisms by which cells produce and detect chemotactic signals and translate this information in directed coordinated movement up or down chemical gradients in the social amoebae Dictyostelium discoideum, and during gastrulation in the chick embryo.

In Dictyostelium starvation for food induces the aggregation of up to hundreds of thousands of individual amoebae into a multi-cellular aggregate. During aggregation the cells differentiate into several distinct celltypes, which sort out to form a migrating slug, which after a variable period of migration transforms into a fruiting body consisting of a stalk supporting a mass of spores. Experiments show that chemotactic cell migration in all stages of development is controlled by propagating waves of the chemo-attractant cAMP. At present we concentrate on investigation of the mechanisms that drive chemotactic cell sorting which results in slug formation. We use quantitative imaging techniques to investigate cell type specific differences in signal transduction dynamics, polarised activation of the actin-myosin cytoskeleton and force generation that drive cell sorting.

Gastrulation in the chick embryo starts with the occurring of extensive cell flows that result in the formation of the primitive streak, a structure through which the mesoderm and endoderm precursor cells ingress to take up their correct positions in the embryo. We are tracking the in-vivo migration of these cells during streak formation and after their ingression through the primitive streak to gain insight in the mechanisms that drive these cell movements. Our current hypothesis is that formation of the primitive streak as well as the movement of the mesoderm cells after their ingression through the streak is controlled by a combination of attractive and repulsive guidance cues, delivered at least in part by members of the FGF, VEGF, PDGF and Wnt families of signalling molecules.

The ability of a cell to change shape is crucial for the proper function of many cellular processes, such as chemotaxis. Traditionally, cell motility has been characterized by a number of different parameters, determined either by the position of the cell's centroid as it migrates, or by limited aspects of the cell shape such as perimeter, area roundness and body orientation. These parameters primarily provide global information about chemotaxis and chemoattractant-induced cell shape changes. They are insufficient to distinguish cell strains based on local morphological information, such as pseudopodial protrusions, that typify amoeboid motility. When the activity of pseudopods has been described, the protrusions and retractions have been identified and outlined mostly manually. In addition to being highly time consuming, these manual methods have the drawback that they are based on subjective judgments. Here we describe a series of automated methods used to characterize amoeboid locomotion based on the skeleton of a planar shape. We demonstrate that the skeleton can be used to identify pseudopods in microscopic images of moving cells. Moreover, the time-varying evolution of the skeleton can be used to capture the dynamic nature of the pseudopodial protrusions and retractions

Joint work with Trachette Jackson (Mathematics Department, University of Michigan).

A new multiscale mathematical model of angiogenesis is developed to quantify the relative roles of cell quiescence, proliferation and migration. Migration is assumed to be the primary event of sprouting, and the governing equation is derived based on cellular mechanics. The extension of the vessel, however, is restricted by the supply of endothelial cells, which is dominated by the proliferation. Although all cells are capable of proliferating, experimental observations often conclude that the proliferative activity is concentrated in the region proximal to the leading edge. In order to capture this phenomenon, we introduce the concept of maturation level, which is modulated by angiopoietins, to describe a quiescent phenotype of endothelial cells. All of these features are combined into a multiscale model of vessel extension in angiogenesis, including vessel anastomosis and branching. Relations between extension and proliferation are investigated, and comparisons to rat cornea experiments are made.

The presentation deals with the modelling approach on the Actin-cytoskeleton presented too in the talk of C. Schmeiser. In the first part of the talk we derive the model in a step by step way starting form the curve straightening flow of planar open curves generated by the Kirchhoff bending energy. We show numerical simulations and present a local in time existence result of solutions and regularity results. In the second part we go back to the curve straightening flow and formulate the governing equations in terms of the indicatrix and a scalar Lagrange multiplier function. We prove existence and (improved) regularity of solutions. We compute the energy dissipation, prove its coercivity and conclude the exponential decay of the energy.