User:BärtigerBäcker/Mechanics of the cell cortex

This article concerns the physical properties of the cell cortex, as well as attempts to form mechanistic models of cell cortex function. Modeling efforts consider both discrete components and continuum descriptions. In recent years, notable progress has been made in understanding cortex mechanics through new experimental findings, application of active matter physics and increased computational power.

Salient constituents and their properties
The principal components responsible for cortex function are semiflexible actin fibers and myosin motors. The actin fibers form a cross-linked network of filaments and are oriented largely parallel to the surface of the cell membrane. As polymers, actin filaments are characterized by a persistence length. This gives a length scale below which a filament is stiff against bending due to thermal fluctuations. For actin, this length is on the order of 10 to 15 micrometers. Myosin motors latch on to actin filaments and apply contractile forces that can drive the cell cortex far from thermal equilibrium. The stiffness of the cell cortex gives support to the cell membrane, while the contractile dynamics produced by myosin facilitate purposeful shape change that facilitates a variety of cell functions.

Application of Continuum Mechanics
On the scale of a cell, the fine grained structure of the cell cortex may be replaced with a description using the tools of continuum mechanics. In particular, the cell cortex provides a rich example of biological active matter.

Active Gel Theory
Recent analytical and computational progress has been made toward understanding the cell cortex using the theory of polar active gels. Actin filaments are polar in that they have a long axis about which they are radially symmetric, with two distinct ends - a plus end and a minus end. The actin filaments preferentially add monomers, or polymerize at the plus end and shed monomers, or depolymerize, at the minus end. A minimal active polar gel model of the cortex considers number densities of free and polymerized actin monomers, and of free myosin motors and myosin motors bound to actin filaments. The movement of these quantities is then described by current densities, vector whose direction indicates the direction of flow and whose magnitude indicates that amount of a quantity that passes through a given surface area per unit time. . Ordinary fluids obey a continuity condition enforcing the condition that the rate of change of the quantity of some substance within a closed volume is due to the net flow of that quantity through the boundary of the volume. This can be violated in active gel models of cell cortex constituents, as myosin motors become bound to or released from actin filaments, and actin monomers are added to and removed from filaments. The orientation of actin fibers is described by a vector field, often denoted by $$\vec{p}$$. The value of the field at a given point is a vector of unit length, pointing from the minus end to the plus end of an actin filament at this location. . In principle the dynamics this system are understood if the dynamics of the polarization field and of the actin and myosin currents are known.

Elastic and Rheological Properties
The cell cortex exhibits viscoelasticity, meaning that on one time scale it behaves like an elastic solid, while on a separate time scale it behaves like a viscous fluid. In a deformed elasic medium near its equilibrium configuration, forces proportional to the size of the deformation arise that tend to restore the material to its initial form. Viscous fluids may be permanantly deformed as their constituents are rearranged to accommodate a deformation, and resist rearrangement with forces proportional to the time rate of change of deformation. The cell cortex tends to be elastic on short time scales, while on larger time scales, turnover of its building blocks and of network structure due to forces exerted by myosin allows for flow. The simplest treatment of a system of a system that is elastic on short time scales and viscous at larger time scales is the Maxwell model. At large deformations, the cortex exhibits pronounced strain stiffening. This is a property generic to networks of semiflexible polymers such as the actin network in the cortex.

Contractile Dynamics
Contractile forces exerted on individual actin filaments by myosin motors can lead to coordinated, cortex-spanning contractile dynamics. Recent experimental work on filamentous networks driven by molecular motors suggests an optimal level of contractile activity for molecular motors in order to coordinate large scale contractions. Below this concentration, contraction is found to be restricted to isolated clusters, while above an optimal concentration, active forces exerted by molecular motors remove an excessive number of cross-links.

Cell Division
Studies have found the cell cortex to be essential in throughout the process of cell division. Cells undergoing mitosis are frequently observed to assume a more spherical shape. This is preceded by an increase in RhoA, a chemical associated with an increase in myosin activity. . With the onset of increased myosin activity, the cell cortex undergoes pronounced stiffening. Increased myosin activity is also essential for the formation of a furrow during cytokinesis. Increased contractility at a north and south pole on the surface of an initially spheroidal shell lead to a deepening furrow beginning from these poles, with a net flow of cortical constituents toward the furrow, and a thinning of the cortex away from the furrow.

Cell motility
The cortex plays a role in various types of cell motion, which can take place in free suspension or on a substrate, and with varying degrees of confinement. A long-studied model of amoeboid motion is that of a squirmer, in which contractile forces in the cortex lead to periodic aberrations from a spheroidal shape. Wu et al. note a characteristic time scale for rearrangement of the surrounding fluid that increases with the viscocity of the fluid and decreases with the magnitude of the active forces in the cortex. Fluctuations must occur on a longer time scale. Cells may also be able to take advantage confinement to perform more efficient locomotion, although excessive confinement may excessively restrict shape changes necessary for locomotion.