No abstract

Cofilin is essential for cell viability and for actin-based motility. Cofilin severs actin filaments to enhance the dynamics of filament assembly. We investigated the mechanism of filament severing by cofilin with direct fluorescence microscopy observation of single actin filaments in real time. In cells, actin filaments are likely to be attached at multiple points along their length, and, we found that attaching filaments in such a manner greatly increased the efficiency of filament severing by cofilin. Cofilin severing increased and then decreased with increasing cofilin concentration. Together, these results indicate that cofilin severs the actin filament by a mechanism of allosteric and cooperative destabilization. Severing is more efficient when relaxation of this cofilin-induced instability of the actin filament is inhibited by restricting the flexibility of the filament. These conclusions have particular relevance to cofilin function during actin-based motility in cells and in synthetic systems.

This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. Inspired by this framework, we construct a finite-dimensional approximation to the diffeomorphism group and its Lie algebra, thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group. The extension to MHD and complex fluid flow is then made through an appeal to the theory of Euler-Poincaré systems with advection, which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters. Upon deriving a family of structured integrators for these systems, we test their performance via a numerical implementation of the update schemes on a cartesian grid. Among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes.

Figure 1: By developing an integration scheme that exhibits zero numerical dissipation, we can achieve more predictable control over viscosity in fluid animation. Dissipation can then be modeled explicitly to taste, allowing for very low (left) or high (right) viscosities. AbstractNumerical viscosity has long been a problem in fluid animation. Existing methods suffer from intrinsic artificial dissipation and often apply complicated computational mechanisms to combat such effects. Consequently, dissipative behavior cannot be controlled or modeled explicitly in a manner independent of time step size, complicating the use of coarse previews and adaptive-time stepping methods. This paper proposes simple, unconditionally stable, fully Eulerian integration schemes with no numerical viscosity that are capable of maintaining the liveliness of fluid motion without recourse to corrective devices. Pressure and fluxes are solved efficiently and simultaneously in a time-reversible manner on simplicial grids, and the energy is preserved exactly over long time scales in the case of inviscid fluids. These integrators can be viewed as an extension of the classical energy-preserving Harlow-Welch / CrankNicolson scheme to simplicial grids.

Measurements of the unloaded sliding speed of and isometric force exerted on single thin filaments in in vitro motility assays were made to evaluate the role of regulatory proteins in the control of unloaded thin filament sliding speed and isometric force production. Regulated actin filaments were reconstituted from rabbit F‐actin, native bovine cardiac tropomyosin (nTm), and either native bovine cardiac troponin (nTn), troponin containing a TnC mutant, CBMII, in which the sole regulatory site in cardiac TnC (site II) is inactivated (CBMII‐Tn), or troponin containing a point mutation in TnT (I79N, where isoleucine at position 79 is replaced with asparagine) associated with familial hypertrophic cardiomyopathy (FHC). Addition of regulatory proteins to the thin filament increases both the unloaded sliding speed and the isometric force exerted by myosin heads on the thin filaments. Variation of thin filament activation by varying [Ca2+] or the fraction of CBMII/TnC bound to the thin filament at pCa 5, had little effect on the unloaded filament sliding speed until the fraction of the thin filament containing calcium bound to TnC was less than 0.15. These results suggest that [Ca2+] primarily affects the number of attached and cycling crossbridges. The presence of the FHC TnT mutant increased the thin filament sliding speed but reduced the isometric force that heavy meromyosin exerted on regulated thin filaments. These latter results, together with the increased sliding speed and isometric force seen in the presence of regulatory proteins, suggest that thin filament regulatory proteins exert significant allosteric effects on the interaction of crossbridges with the thin filament.