Mihaela Enculescu

Actin Filament Elasticity and Retrograde Flow Shape the Force-Velocity Relation of Motile Cells

Cells migrate through a crowded environment during processes such as metastasis or wound healing, and must generate and withstand substantial forces. The cellular motility responses to environmental forces are represented by their force-velocity relation, which has been measured for fish keratocytes but remains unexplained. Even pN opposing forces slow down lamellipodium motion by three orders of magnitude. At larger opposing forces, the retrograde flow of the actin network accelerates until it compensates for polymerization, and cell motion stalls. Subsequently, the lamellipodium adapts to the stalled state. We present a mechanism quantitatively explaining the cells force-velocity relation and its changes upon application of drugs that hinder actin polymerization or actomyosin-based contractility. Elastic properties of filaments, close to the lamellipodium leading edge, and retrograde flow shape the force-velocity relation. To our knowledge, our results shed new light on how these migratory responses are regulated, and on the mechanics and structure of the lamellipodium.

Modeling of Protrusion Phenotypes Driven by the Actin-Membrane Interaction

We propose a mathematical model for simulating the leading-edge dynamics of a migrating cell from the interplay among elastic properties, architecture of the actin cytoskeleton, and the mechanics of the membrane. Our approach is based on the description of the length and attachment dynamics of actin filaments in the lamellipodium network. It is used to determine the total force exerted on the membrane at each position along the leading edge and at each time step. The model reproduces the marked state switches in protrusion morphodynamics found experimentally between epithelial cells in control conditions and cells expressing constitutively active Rac, a signaling molecule involved in the regulation of lamellipodium network assembly. The model also suggests a mechanistic explanation of experimental distortions in protrusion morphodynamics induced by deregulation of Arp2/3 and cofilin activity.

Actin-based propulsion of spatially extended objects

We propose a mathematical model of the actin-based propulsion of spatially extended obstacles. It starts from the properties of individual actin filaments and includes transient attachment to the obstacle, polymerization as well as cross-linking. Two particular geometries are discussed, which apply to the motion of protein-coated beads in a cell-like medium and the leading edge of a cell protrusion, respectively. The model gives rise to both steady and saltatory movement of beads and can explain the experimentally observed transitions of the dynamic regime with changing bead radius and protein surface density. Several spatiotemporal patterns are obtained with a soft obstacle under tension, including the experimentally observed spontaneous emergence of lateral traveling waves in crawling cells. Thus, we suggest a unifying mechanism for systems that are currently described by differential concepts.

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.

Modeling morphodynamic phenotypes and dynamic regimes of cell motion

Many cellular processes and signaling pathways converge onto cell morphology and cell motion, which share important components. The mechanisms used for propulsion could also be responsible for shape changes, if they are capable of generating the rich observed variety of dynamic regimes. Additionally, the analysis of cell shape changes in space and time promises insight into the state of the cytoskeleton and signaling pathways controlling it. While this has been obvious for some time by now, little effort has been made to systematically and quantitatively explore this source of information. First pioneering experimental work revealed morphodynamic phenotypes which can be associated with dynamic regimes like oscillations and excitability. Here, we review the current state of modeling of morphodynamic phenotypes, the experimental results and discuss the ideas on the mechanisms driving shape changes which are suggested by modeling.

Mechanisms for activity spread in a neural field model

Field models of continuous neural networks incorporate nonlocal connectivities as well as finite axonal propagation velocities and lead therefore to delayed integral equations. For special choices of the synaptic footprint it is possible to reduce the integral model to a system of partial differential equations. One example is that of the inhomogeneous damped wave equation in one space dimension derived by Jirsa and Haken for exponential synaptic footprint. We show that this equation can be put into the form of a conservation law with nonlinear source, and explore numerically this representation. We find two mechanisms for the spread of the activity from an initially excited region.