Structural reorganization of parallel actin bundles by crosslinking proteins: incommensurate states of twist

Memory in the hippocampus

To date, there is no clear evidence for memory formation. In this article, we provide a framework to understand how memory is formed. The information collected by sensory organs is converted to a digital current that enters the presynaptic neuron through axonal conductance. Digital waves are converted to analog waves in the synapses. The analog current of information flows into the postsynapse. The degree of Ca²⁺ influx in the postsynapse is proportional to the voltage of each wave of analog current. The activation (via dephosphorylation) of the phosphorylated phosphatase, Slingshot, is regulated by Ca²⁺ concentration in the spine. After dephosphorylation by Slingshot, activated cofilin binds the parallel actin bundle. The wide helical twist angle of an actin filament that has been decorated with cofilin confers high electric potential to the filament. Phosphorylation results in the deactivation of the actin filament bound to cofilin, which in turn results in the cleavage of cofilin and actin filament, followed by a decrease in the twist angle of the actin filament. Next, the electric potential energy is discharged by the actin filament as it returns to its non-cofilin bound state, resulting in the formation of additional analog waves in the postsynapse.

Shape Selection of Surface-Bound Helical Filaments: Biopolymers on Curved Membranes

Motivated to understand the behavior of biological filaments interacting with membranes of various types, we employ a theoretical model for the shape and thermodynamics of intrinsically helical filaments bound to curved membranes. We show that filament-surface interactions lead to a host of nonuniform shape equilibria, in which filaments progressively unwind from their native twist with increasing surface interaction and surface curvature, ultimately adopting uniform-contact curved shapes. The latter effect is due to nonlinear coupling between elastic twist and bending of filaments on anisotropically curved surfaces such as the cylindrical surfaces considered here. Via a combination of numerical solutions and asymptotic analysis of shape equilibria, we show that filament conformations are critically sensitive to the surface curvature in both the strong- and weak-binding limits. These results suggest that local structure of membrane-bound chiral filaments is generically sensitive to the curvature radius of the surface to which it is bound, even when that radius is much larger than the filament's intrinsic pitch. Typical values of elastic parameters and interaction energies for several prokaryotic and eukaryotic filaments indicate that biopolymers are inherently very sensitive to the coupling between twist, interactions, and geometry and that this could be exploited for regulation of a variety of processes such as the targeted exertion of forces, signaling, and self-assembly in response to geometric cues including the local mean and Gaussian curvatures.

Stability of actin-lysozyme complexes formed in cystic fibrosis disease

Finding the conditions for destabilizing actin-lysozyme complexes is of biomedical importance in preventing infections in cystic fibrosis. In this manuscript, the effects of different charge-mutants of lysozyme and salt concentration on the stability of actin-lysozyme complexes are studied using Langevin dynamics simulation. A coarse-grained model of F-actin is used in which both its twist and bending rigidities are considered. We observe that the attraction between F-actins is stronger in the presence of wild-type lysozymes relative to the mutated lysozymes of lower charges. By calculating the potential of mean force between F-actins, we conclude that the stability of actin-lysozyme complexes is decreased by reducing the charge of lysozyme mutants. The distributions of different lysozyme charge-mutants show that wild-type (+9e) lysozymes are mostly accumulated in the center of triangles formed by three adjacent F-actins, while lysozyme mutants of charges +7e and +5e occupy the bridging regions between F-actins. Low-charge mutants of lysozyme (+3e) distribute uniformly around F-actins. A rough estimate of the electrostatic energy for these different distributions proves that the distribution in which lysozymes reside in the center of triangles leads to more stable complexes. Also our results in the presence of a salt suggest that at physiological salt concentration of airway, F-actin complexes are not formed by charge-reduced mutants of lysozyme. The findings are interesting because if we can design charge-reduced lysozyme mutants with considerable antibacterial activity, they are not sequestered inside F-actin aggregates and can play their role as antibacterial agents against airway infection.

Semiflexible Biopolymers in Bundled Arrangements

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.

Exploring the stability limits of actin and its suprastructures

Actin is the main component of the microfilament system in eukaryotic cells and can be found in distinct morphological states. Global (G)-actin is able to assemble into highly organized, supramolecular cellular structures known as filamentous (F)-actin and bundled (B)-actin. To evaluate the structure and stability of G-, F-, and B-actin over a wide range of temperatures and pressures, we used Fourier transform infrared spectroscopy in combination with differential scanning and pressure perturbation calorimetry, small-angle x-ray scattering, laser confocal scanning microscopy, and transmission electron microscopy. Our analysis was designed to provide new (to our knowledge) insights into the stabilizing forces of actin self-assembly and to reveal the stability of the actin polymorphs, including in conditions encountered in extreme environments. In addition, we sought to explain the limited pressure stability of actin self-assembly observed in vivo. G-actin is not only the least temperature-stable but also the least pressure-stable actin species. Under abyssal conditions, where temperatures as low as 1-4°C and pressures up to 1 kbar are reached, G-actin is hardly stable. However, the supramolecular assemblies of actin are stable enough to withstand the extreme conditions usually encountered on Earth. Beyond ∼3-4 kbar, filamentous structures disassemble, and beyond ∼4 kbar, complete dissociation of F-actin structures is observed. Between ∼1 and 2 kbar, some disordering of actin assemblies commences, in agreement with in vivo observations. The limited pressure stability of the monomeric building block seems to be responsible for the suppression of actin assembly in the kbar pressure range.

Cofilin-induced changes in F-actin detected via cross-linking with benzophenone-4-maleimide

Cofilin is a member of the actin depolymerizing factor (ADF)/cofilin family of proteins. It plays a key role in actin dynamics by promoting disassembly and assembly of actin filaments. Upon its binding, cofilin has been shown to bridge two adjacent protomers in filamentous actin (F-actin) and promote the displacement and disordering of subdomain 2 of actin. Here, we present evidence for cofilin promoting a new structural change in the actin filament, as detected via a switch in cross-linking sites. Benzophenone-4-maleimide, which normally forms intramolecular cross-linking in F-actin, cross-links F-actin intermolecularly upon cofilin binding. We mapped the cross-linking sites and found that in the absence of cofilin intramolecular cross-linking occurred between residues Cys374 and Asp11. In contrast, cofilin shifts the cross-linking by this reagent to intermolecular, between residue Cys374, located within subdomain 1 of the upper protomer, and Met44, located in subdomain 2 of the lower protomer. The intermolecular cross-linking of F-actin slows the rate of cofilin dissociation from the filaments and decreases the effect of ionic strength on cofilin-actin binding. These results are consistent with a significant role of filament flexibility in cofilin-actin interactions.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.