Session U35: Focus Session: Cytoskeletal Dynamics and Cell Migration II

Modelling cell motility and pathways that signal to the actin cytoskeleton

Gradient sensing, polarization, and motility of rapidly moving cells such as neutrophils involves the actin cytoskeleton, and regulatory modules such as membrane bound phosphoinositides (PIs), kinases/phosphatases, and proteins of the Rho family (Rho GTPases). I describe recent work in my group in which we have modeled components of these modules, their interconversions, interactions, and action in the context of protrusive cell motility. By connecting three modules, we find that Rho GTPases work as a spatial switch, and that PIs filter noise, and define the front vs. back. Relatively fast PI diffusion also leads to selection of a unique pattern of Rho distribution from a collection of possible patterns. We use the model to explore the importance of specific hypothesized interactions, to explore mutant phenotypes, and to study the role of actin polymerization in the maintenance of the PI asymmetry. Collaborators on this work include A.T. Dawes, A. Jilkine, and A.F.M. Maree.   

Migration of a Model Lamellipodium by Actin Polymerization: A Molecular Dynamics Simulation Approach

We performed molecular dynamics simulation of a model lamellipodium with growing F-actin filaments in order to study the effect of stiffness of the F-actin filament, the G-actin monomer concentration, and the number of polymerization sites on lamellipodium motion. The lamellipodium is modeled as a two-end capped cylinder formed by triangulated particles on its surface. It is assumed that F-actin filaments are firmly attached to a lamellipodium surface where polymerization sites are located and actin polymerization takes place by connecting a G-actin monomer to a polymerization site and the first monomer of a growing F-actin filament. It is found that there is an optimal number of polymerization sites for rapid lamellipodium motion. This appearance of the maximum speed is related to the competition between the number of polymerization sites and the number of available G-actin monomers, and the degree of pulling and holding the lamellipodium surface by non-polymerized actin filaments. The model lamellipodium speed distribution is found to be Maxwellian for particles with random motion in two dimensions and is in agreement with experiment.   

Intracellular dynamics during directional sensing of chemotactic cells

We use an experimental approach based on the photo-chemical release of signaling molecules in microfluidic environments to expose chemotactic cells to well controlled chemoattractant stimuli. We apply this technique to study intracellular translocation of fluorescently labeled PH-domain proteins in the social ameba \textit{Dictyostelium discoideum. }Single chemotactic \textit{Dictyostelium }cells are exposed to localized, well defined gradients in the chemoattractant cAMP and their translocation response is quantified as a function of the external gradient.   

Searching strategies in Dictyostelium

Levy walks are known to be the best strategy for optimizing non-destructive search times, while an intermittent two-state searching process optimizes the destructive case. Here we ask about hunting strategy in Dictyostelium amoebae when they cannot know where their food is. We show that correlated random walks with two typical correlation time scales bias their search, improving the search outcome. Further analysis indicates that cell trajectories consist of runs and turns. Strikingly, amoebae remember the last turn, and have a strong turning preference away from the last turn. Autocorrelation analysis of turn sequences indicates that this tendency does not persist beyond the nth+1 turn. Computer simulations reveal that this bias contributes to the longer of the two correlation times. The search rules are essentially the same when cells are continuously stimulated by cAMP, with different persistence times and lengths. Interestingly, new pseudopods form in an orientation opposite to the following turn. One of the correlation timescales is approximately 30 seconds in all cases, thus indicating a short-lived cellular process, while the other is 9 to 15 minutes suggesting a process sensitive to external signals, perhaps pseudopod extensions during turning.   

Perturbing Streaming in Dictyostelium Discoideum

Upon starvation the social amoebae \textit{Dictyostelium discoideum} aggregate to form multicellular organisms. During the transition from single cells to full aggregates, cells relay the chemotactic signal, align in a head-to-tail fashion, and follow each other in streams. To gain more insight into streaming behavior we investigated its robustness by perturbing the strength of the relayed chemoattractant. We measured the effects of plating the cells at varying densities, placing them in excess extracellular fluid thereby diluting cell-cell signals, or directly mixing up the local external fluid using ultrasound-induced bubble-driven flow. We compared wild type cells to cells devoid of signal relay and measured how streaming affects cell speed, directionality, and extent of directed migration. Results will be discussed and a model describing our findings will be presented.   

Traction cytometry applied to chemotacting \textit{Dictyostelium discoideum}

The motion of \textit{Dictyostelium discoideum} cells moving on a elastic substrate has been studied. Joint analysis of time-lapse DIC movies of the cells and UV fluorescence from the beads embedded in the substrate, allows for identification of characteristic time scales of the motion and the quantitative description of the crawling cycle. From the measured displacements of the beads, forces can be computed by analytically solving the elasto-static equation in a finite thickness slab. We found that the finite thickness of the substrate and the distance of the beads to its surface have a substantial effect and that the previous traction cytometry techniques based on the Boussinesq solution effectively low-pass-filtered the force field, reducing the spatial resolution and damping the range of the measured forces by as much as 50{\%}. The improved spatial resolution of this method enables us to determine the spatial extent of the regions where the cells apply force on the substrate and, consequently, the magnitude of the elastic energy spent in its deformation. The measured forces, as well as the elastic energy communicated by the cell to the substrate, will be correlated to the different stages of the crawling cycle for various cell strains.   

Stem cell cytoskeleton is slaved to active motors

Cells feel their physical microenvironment through their adhesion and respond to it in various ways. Indeed, matrix elasticity can even guide the differentiation of human adult mesenchymal stem cells (MSCs) [Engler et al. \textit{Cell} 2006]. Sparse cultures of MSCs on elastic collagen--coated substrates that are respectively soft, stiff, or extremely stiff were shown to induce neurogenesis, myogenesis, and osteogenesis. Lineage commitment was evaluated by morphological analysis, protein expression profiles, and transcription microarrays. Differentiation could be completely blocked with a specific non-muscle myosin II (NMM II) inhibitor, suggesting that contractile motor activity is essential for the cells to sense matrix elasticity. Current studies by AFM and near-field fluorescence imaging show that NMM II inhibition in stem cells on rigid glass surfaces promotes actin-rich dendritic outgrowth resembling neurite extension. Dynamic cell studies have been conducted to elucidate the complex molecular interplay of the contractile apparatus in response to selected physical and biochemical stimuli. Additional insight is being gained by using AFM to investigate the local elasticity of the cell's cytoskeletal force sensing machinery.   

The Collective Contractile Dynamics of Confluent Epithelial Cells is Highly Coherent

We have studied the collective contractile dynamics of confluent Cos-7 epithelial cells in several contexts. We patterned cells in single file lines on confined PDMS 'rubber bands', and quantified substrate deformation by tracking embedded fluorescent particles over the course of approximately 10 hours. Deformations confined to one dimension, well over ten microns in magnitude, correlated over distances exceeding the millimeter scale, were observed. On unpatterened PDMS, collective substrate deformations in two dimensions were over ten times smaller, and exhibited a propagating mechanical excitation. Three dimensional matrix deformation was studied by embedding cells at high density in 1mg/ml collagen. Since collective network deformations are difficult to quantify in the microscope, a dynamic small angle light scattering technique was adapted. With this technique, we have spectrally characterized the three dimensional mechanical network deformations, and observed collective behavior similar to the measurements on compliant surfaces.   

Membrane fluctuations driven by actin and myosin: waves and quantized division.

We present a model which couples the membrane with the protrusive forces of actin polymerization and contractile forces of molecular motors, such as myosin. The actin polymerization at the membrane is activated by freely diffusing membrane proteins, that may have a distinct spontaneous curvature. Molecular motors are recruited to the polymerizing actin filaments, from a constant reservoir, and produce a contractile force. All the forces and variables are treated in the linear limit, which allows us to derive analytic solutions. Our results show that for convex membrane proteins the myosin activity gives rise to propagating membrane waves similar to those observed on different cells. For concave membrane proteins the myosin activity gives rise to an unstable contraction, which yields a length-quantization of the mitosis process.   

Simulation of Actin-Polymerization-Mediated Propulsion

An important component of the cellular cytoskeleton is F-actin, a biopolymer whose self-assembly is key to the process of cell crawling. The polymerization and branching of F-actin near the cell membrane is known to drive cell crawling, but the precise mechanism by which these processes lead to the generation of a mechanical force is still controversial. We have constructed a Brownian dynamics simulation of F-actin polymerizing near a surface, which includes all known important processes, including polymerization, depolymerization, branching, severing and capping. Using this model, we are able to simulate the cell movement. We measure the speed as function of concentration of different proteins involved in the process. We find the speed to be non-monotonic, consistent with experimental results [Louis et al. Nature \textbf{401} 613 (1999)].   

Symmetry breaking in actin gels - Implications for cellular motility

The physical origin of cell motility is not fully understood. Recently minimal model systems have shown, that polymerizing actin itself can produce a motile force, without the help of motor proteins. Pathogens like Shigella or Listeria use actin to propel themselves forward in their host cell. The same process can be mimicked with polystyrene beads covered with the activating protein ActA, which reside in a solution containing actin monomers. ActA induces the growth of an actin gel at the bead surface. Initially the gel grows symmetrically around the bead until a critical size is reached. Subsequently one observes a symmetry breaking and the gel starts to grow asymmetrically around the bead developing a tail of actin at one side. This symmetry breaking is accompanied by a directed movement of the bead, with the actin tail trailing behind the bead. Force generation relies on the combination of two properties: growth and elasticity of the actin gel. We study this phenomenon theoretically within the framework of a linear elasticity theory and linear flux-force relationships for the evolution of an elastic gel around a hard sphere. Conditions for a parity symmetry breaking are identified analytically and illustrated numerically with the help of a phasefield model.   

A kinematic description of the trajectories of Listeria monocytogenes propelled by actin comet tails

The bacterial pathogen Listeria monocytogenes propels itself in the cytoplasm of the infected cells by forming a filamentous comet tail assembled by the polymerization of the cytoskeletal protein, actin. While a great deal is known about the molecular processes that lead to actin based movement, most macroscale aspects of motion, including the nature of the trajectories traced out by the motile bacteria are not well understood. Listeria moving between a glass-slide and cover slip in a Xenopus frog egg extract motility assay is observed to display a number of geometrically fascinating trajectories including sine curves, serpentine shapes, circles, and a variety of spirals. We have developed a dynamic model that provides a unified description of these seemingly unrelated trajectories. A key ingredient of the model is a torque (not included in any microscopic models to date) that arises from the rotation of the propulsive force about the body-axis of the bacterium. The trajectories of bacteria executing both steady and saltatory motion are found to be in excellent agreement with the predictions of our dynamic model. When the constraints that lead to planar motion are removed, our model predicts motion along regular helical trajectories, observed in recent experiments. We discover from the analysis of the trajectories of spherical beads that the comet tail revolves around the bead.   

Steady-state configurations and dynamics of the MreB helix within bacteria

We present a quantitative model of the actin-like MreB cytoskeleton that is present in many prokaryotes. Individual MreB polymers are bundled into a supra-molecular array to make up helical cables. The cell wall imposes constraint forces through a global elasticity model. With variational techniques and stochastic simulations we obtain relationships between observable quantities such as the pitch of the helix, the total abundance of MreB molecules, and the thickness of the MreB cables. We address changes expected with slow cell growth, as well as turnover dynamics that are relevant to FRAP studies. We also address polarized macromolecular trafficking along the MreB cables without motor proteins.