Modelling Cell Polarization Driven by Synthetic Spatially Graded Rac Activation

The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization

Collective Motion of Cells Mediates Segregation and Pattern Formation in Co-Cultures

Pattern formation by segregation of cell types is an important process during embryonic development. We show that an experimentally yet unexplored mechanism based on collective motility of segregating cells enhances the effects of known pattern formation mechanisms such as differential adhesion, mechanochemical interactions or cell migration directed by morphogens. To study in vitro cell segregation we use time-lapse videomicroscopy and quantitative analysis of the main features of the motion of individual cells or groups. Our observations have been extensive, typically involving the investigation of the development of patterns containing up to 200,000 cells. By either comparing keratocyte types with different collective motility characteristics or increasing cells' directional persistence by the inhibition of Rac1 GTP-ase we demonstrate that enhanced collective cell motility results in faster cell segregation leading to the formation of more extensive patterns. The growth of the characteristic scale of patterns generally follows an algebraic scaling law with exponent values up to 0.74 in the presence of collective motion, compared to significantly smaller exponents in case of diffusive motion

Factors limiting the transmission of HIV mutations conferring drug resistance: fitness costs and genetic bottlenecks

Transmission of HIV strains with drug-resistance mutations (DRMs) causes public health problems in resource-rich countries. We use a stochastic model, with data from viral competition experiments, to analyze the effect of fitness costs (FCs) and genetic bottlenecks on limiting transmission of 10 clinically significant DRMs. Transmission of DRMs with low FCs (∼0.2%) is similar to wild-type; transmission chains last ∼8 generations causing clusters of ∼60 infected individuals. Genetic bottlenecks substantially limit transmission of DRMs with moderately high FCs (∼0.6%); chains last ∼1–3 generations with transmission clusters of 2–7. Transmission of DRMs with extremely high FCs (>6%) only occurs from ∼5% of index cases. DRMs can revert to wild-type and remain as minority strains, within treatment-naïve individuals, undetectable by current resistance assays. We calculate, based on assay sensitivity, the length of time each DRM is detectable within individuals. Taken together, our results imply a hidden epidemic of transmitted resistance may exist

Theoretical Model for Cellular Shapes Driven by Protrusive and Adhesive Forces

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted