Date Published: March 21, 2019
Publisher: Public Library of Science
Author(s): Asal Atakhani, Farshid Mohammad-Rafiee, Azam Gholami, Keng-Hwee Chiam.
The forces that arise from the actin cortex play a crucial role in determining the membrane deformation. These include protrusive forces due to actin polymerization, pulling forces due to transient attachment of actin filaments to the membrane, retrograde flow powered by contraction of actomyosin network, and adhesion to the extracellular matrix. Here we present a theoretical model for membrane deformation resulting from the feedback between the membrane shape and the forces acting on the membrane. We model the membrane as a series of beads connected by springs and determine the final steady-state shape of the membrane arising from the interplay between pushing/pulling forces of the actin network and the resisting membrane tension. We specifically investigate the effect of the gel dynamics on the spatio-temporal deformation of the membrane until a stable lamellipodium is formed. We show that the retrograde flow and the cross-linking velocity play an essential role in the final elongation of the membrane. Interestingly, in the simulations where motor-induced contractility is switched off, reduced retrograde flow results in an increase in the rate and amplitude of membrane protrusion. These simulations are consistent with experimental observations that report an enhancement in protrusion efficiency as myosin II molecular motors are inhibited.
Cell motility is essential for many biological processes including development, immune response, wound healing, phagocytosis and tumor metastasis. In order to crawl, many cells form a wide flat membrane protrusion, known as the lamellipodium, in the direction of movement. The main driving mechanism for lamellipodium formation is the force generated by treadmilling actin network underneath the membrane . Actin treadmilling is a nonequilibrium process, requires the consumption of ATP  and is regulated by several proteins . In this process, the barbed ends of actin filaments polymerize and push against the membrane, whereas their pointed ends are anchored in the gel bulk formed by strongly entangled and highly cross-linked actin filaments. The gel bulk is attached to the extracellular matrix via trans-membrane receptors providing a mechanical support for the weakly cross-linked actin brush at the leading edge to push against the membrane. A schematic presentation of the membrane, gel bulk and the actin brush in the so called semiflexible region, is shown in Fig 1.
The model we present here is the combination of series of events that are happening at the leading edge of the lamellipodium, and are influenced by the presence of plasma membrane. The system is made of three parts, the membrane, the gel boundary and the region confined between the gel boundary and the membrane, the so called semiflexible region (SR). Actin filaments in the SR can polymerize, depolymerize, attach to and detach from the membrane. These processes exert pushing or pulling forces to the point of contact of filaments with the membrane. While attached filaments are mostly under tension and pull back the membrane, detached filaments and the compressed attached filaments push the membrane forward. The free fluctuating tips of actin filaments are constantly polymerizing and depolymerizing with force dependent rates. They also attach to the membrane via linker proteins, with constant rate ka, and detach with force dependent rate kd . All filaments are firmly anchored in a cross-linked actin gel. The dynamics of the gel boundary is determined by retrograde flow and the cross-linking velocity. Retrograde flow is primarily generated by myosin contractile forces and depends on the strength of adhesion between the actin gel and extracellular matrix . The gel is constantly formed by cross-linking process and acts as a mechanical support for the filaments in the SR to push against the membrane. Growing actin filaments push forward on the plasma membrane, resulting in membrane tension . Forces on the membrane at any point equilibrate within milliseconds so that, on the time-scales relevant for motility, membrane tension is spatially homogeneous along the leading edge . Moreover, membrane tension slows actin polymerization by pushing back on growing filaments [20–22]. When adhesion to the substrate is weak or absent, membrane tension pushing back on the filaments also generates retrograde flow of the actin network.
Combination of three sets of equations for membrane, gel boundary and actin filaments in the SR, as described above, breaks the initial flat configuration of the membrane and leads to the formation of a dynamic membrane protrusion. Our aim is to follow actin-driven spatio-temporal dynamics of the membrane and explore the effect of the gel dynamics on the membrane shape until a steady protrusion is established.
A lamellipodium is a flat and broad membrane extension filled with a dense and highly cross-linked filament network. Force generation through actin polymerization has been believed to be the essential driving mechanism in formation of membrane protrusion. The main purpose of this article is to understand how the presence of resistive restoring force of the plasma membrane affects force generation of polymerizing actin filaments and membrane protrusion dynamics. We modeled the membrane as a series of beads connected by springs which deform in the presence of protrusive forces of the underlying actin network. We coupled explicitly stochastic attachment/detachment and growth processes of actin filaments with fluctuation dynamics of the plasma membrane to investigate membrane protrusion as a function of various control parameters such as cross-linking velocity, retrograde flow driven by molecular motors and membrane tension.