Azam Gholami

Entropic forces generated by grafted semiflexible polymers

The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, where the persistence length of the polymer is larger than its contour length, we find that the entropic force shows scaling behavior. We identify the characteristic length scales and the explicit form of the scaling functions. In certain asymptotic regimes, we give simple analytical expressions which describe the full results to a very high numerical accuracy. Depending on the constraints imposed on the transverse fluctuations of the filament, there are characteristic differences in the functional form of the entropic forces. In a two-dimensional geometry, the entropic force exhibits a marked peak.

Membrane waves driven by forces from actin filaments

Membrane waves propagating along the cell circumference in a top down view have been observed with several eukaryotic cells (Dobereiner et al 2006 Phys. Rev. Lett. 97 10; Machacek and Danuser 2006 Biophys. J. 90 1439–52). We present a mathematical model reproducing these traveling membrane undulations during lamellipodial motility of cells on flat substrates. The model describes the interplay of pushing forces exerted by actin polymerization on the membrane, pulling forces of attached actin filaments on the cell edge, contractile forces powered by molecular motors across the actin gel and resisting membrane tension. The actin filament network in the bulk of lamellipodia obeys gel flow equations. We investigated in particular the dependence of wave properties on gel parameters and found that inhibition of myosin motors abolishes waves in some cells but not in others in agreement with experimental observations. The model provides a unifying mechanism explaining the dynamics of actin-based motility in a variety of systems.

Flow-driven instabilities during pattern formation of Dictyostelium discoideum

The slime mold Dictyostelium discoideum is a well known model system for the study of biological pattern formation. In the natural environment, aggregating populations of starving Dictyostelium discoideum cells may experience fluid flows that can profoundly change the underlying wave generation process. Here we study the effect of advection on the pattern formation in a colony of homogeneously distributed Dictyostelium discoideum cells described by the standard Martiel–Goldbeter model. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. The evolution of small perturbations in cAMP concentrations is studied analytically in the linear regime and by corresponding numerical simulations. We show that flow can significantly influence the dynamics of the system and lead to a flow-driven instability that initiate downstream traveling cAMP waves. We also show that boundary conditions have a significant effect on the observed patterns and can lead to a new kind of instability.

Flow-driven two-dimensional waves in colonies of Dictyostelium discoideum

Dictyostelium discoideum (D.d.) is a valuable model organism to study self-organization and pattern formation in biology. Recently we reported flow-driven waves in experiments with uniformly distributed populations of signaling amobae, D.d., and carried out a theoretical study in a one-dimensional model. In this work, we perform two-dimensional numerical simulations using the well-known Martiel–Golbeter model to study the effect of the flow profile and intrinsic noise on the flow-driven waves. We show that, in the presence of flow, a persistence noise due to spontaneous cell firing events can lead to sustained structures that fill the whole length of the system. We also show that external periodic stimuli of cyclic adenosine monophosphate can induce 1:1 and 2:1 entrainments which are in agreement with our experimental observations.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

Influence of fast advective flows on pattern formation of Dictyostelium discoideum.

We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction. While the wave period and transverse propagation velocity are constant, parallel wave velocity and the wave width increase linearly with the imposed flow. We also observe that the acquired wave shape is highly dependent on the wave generation site and the strength of the imposed flow. We compared the wave shape and velocity with numerical simulations performed using a reaction-diffusion model and found excellent agreement. These results are expected to play an important role in understanding the process of pattern formation and aggregation of D. discoideum that may experience fluid flows in its natural habitat.

Variability and order in cytoskeletal dynamics of motile amoeboid cells

The chemotactic motion of eukaryotic cells such as leukocytes or metastatic cancer cells relies on membrane protrusions driven by the polymerization and depolymerization of actin. Here we show that the response of the actin system to a receptor stimulus is subject to a threshold value that varies strongly from cell to cell. Above the threshold, we observe pronounced cell-to-cell variability in the response amplitude. The polymerization time, however, is almost constant over the entire range of response amplitudes, while the depolymerization time increases with increasing amplitude. We show that cell-to-cell variability in the response amplitude correlates with the amount of Arp2/3, a protein that enhances actin polymerization. A time-delayed feedback model for the cortical actin concentration is consistent with all our observations and confirms the role of Arp2/3 in the observed cell-to-cell variability. Taken together, our observations highlight robust regulation of the actin response that enables a reliable timing of cell movement.

Effects of developmental variability on the dynamics and self-organization of cell populations

We report experimental and theoretical results for spatiotemporal pattern formation in cell populations, where the parameters vary in space and time due to mechanisms intrinsic to the system, namely Dictyostelium discoideum (D.d.) in the starvation phase. We find that different patterns are formed when the populations are initialized at different developmental stages, or when populations at different initial developmental stages are mixed. The experimentally observed patterns can be understood with a modified Kessler–Levine model that takes into account the initial spatial heterogeneity of the cell populations and a developmental path introduced by us, i.e. the time dependence of the various biochemical parameters. The dynamics of the parameters agree with known biochemical studies. Most importantly, the modified model reproduces not only our results, but also the observations of an independent experiment published earlier. This shows that pattern formation can be used to understand and quantify the temporal evolution of the system parameters.