Cytoskeleton

A network of protein filaments within a biological cell that contributes to shape, mechanical support and motion. Its coupling to the lipid bilayer adds mechanical responses, including shear elasticity, absent from an isolated fluid bilayer.

An intermediate filament is a rope-like protein assembly of the cytoskeleton, typically about 10 nanometres in diameter, between an actin filament and a microtubule in thickness. Different cells use different constituent proteins: keratins reinforce many epithelial cells, vimentin forms networks in many connective-tissue cells, and lamins support the cell nucleus. Their assembled subunits do not establish the uniform head-to-tail polarity characteristic of an actin filament.^[ref]

The mechanical role can be tested outside a biological cell. In 1991, P. A. Janmey and colleagues compared purified vimentin, actin and microtubule networks under deformation. The vimentin networks tolerated larger deformations before disruption, illustrating how an intermediate filament network can combine compliance with resistance to damage. This helps explain why load-bearing tissues need a network that can stretch rather than simply a rigid internal frame.^[ref]

Spectrin is a flexible cytoskeletal protein that forms a meshwork beneath the cell membrane, often through assemblies of alpha and beta chains. Connections to membrane-associated components and actin help distribute mechanical stress. The red blood cell provides a striking example: its membrane skeleton supports repeated deformation through narrow vessels. Spectrin is also present in other cells, where related assemblies help organize membrane domains. ^[ref]

A modular protein can release additional contour length when a folded domain crosses a mechanical unfolding barrier. At almost fixed end separation this lowers fractional extension and tension, producing a saw-tooth force record. Successive worm-like chain fits can share backbone persistence length while their contour lengths increase. Rupture force and hysteresis depend on loading history; peak force alone is not an equilibrium unfolding free energy.

An assembly of actin filaments and myosin motors. Network architecture, motor activity and attachments determine how contractile activity produces cellular or tissue deformation.

A filament-associated regulatory protein whose position along actin helps control myosin access. In skeletal muscle its coupling to troponin connects calcium regulation to cross-bridge activity.

A calcium-responsive regulatory protein complex on thin muscle filaments. Changes in its occupancy and conformation couple calcium signals to movement of tropomyosin and accessibility of myosin-binding sites on actin.

A prescribed-velocity motor can attach only over a narrow displacement window, remain attached over a protected interval, then detach with constant rate. Converting time to displacement gives a rising attachment probability, a plateau $p_b$, and an exponential tail with spatial length $v/k_{off}$. Independent successive-site encounters require detachment before the next window, not merely a large geometric site separation. Earlier attachments can be retained in a periodic availability correction.

A prescribed-speed molecular motor model in which a head attaches only within a phase window of width $x_1$, stays bound to phase $x_2$, and then detaches at a constant rate before the next period $\Delta$. If the binding window and detachment tail are short relative to the bound plateau, the phase-average force is the plateau fraction multiplied by its attachment probability and bound-head force $f_0$.

With positive opposing load magnitude $L$ and positive viscous drag coefficient $\gamma$, steady contraction requires $L=N⟨f⟩-\gamma u$. A decreasing motor force curve and an increasing drag-magnitude line have a unique intersection for each load below the limiting stall force. Using $+\gamma u$ as the signed drag would instead make drag assist forward motion, reversing its physical role.

For attached-state elastic energy $U=\kappa (x-x_0{)}^2/2$ and a binding window much narrower than $x_0$, the expected assisting work before $x_0$ is $\kappa p_b{x}_0^2/2$. The detachment tail produces resisting work $-\kappa p_b{v}^2/k_{off}^2$. Mean force per head is $W/D$ for site spacing $D$. The detachment-time second moment, not the square of its mean, fixes the resisting term. These are idealized prescribed-velocity kinetics, not a complete muscle energy budget.

A repeating contractile unit of striated muscle containing organized filament systems. Its maturation contributes to force production but does not alone establish a cell's proliferative state.

A contractile filament in striated muscle. Thin actin-containing and thick myosin-containing filaments slide relative to one another during sarcomere shortening; their individual lengths are approximately conserved over an ordinary contraction.

actomyosin contractility generates force through interactions of myosin motors with actin networks. The resulting load depends on network organization, attachments and resistance from the surroundings.