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Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties. 

Translation of messenger RNA (mRNA) is regulated through a diverse set of RNA-binding proteins. A significant fraction of RNA-binding proteins contains prion-like domains which form functional prions. This raises the question of how prions can play a role in translational control. Local control of translation in dendritic spines by prions has been invoked in the mechanism of synaptic plasticity and memory. We show how channeling through diffusion and processive translation cooperate in highly ordered mRNA/prion aggregates as well as in less ordered mRNA/protein condensates depending on their substructure. We show that the direction of translational control, whether it is repressive or activating, depends on the polarity of the mRNA distribution in mRNA/prion assemblies which determines whether vectorial channeling can enhance recycling of ribosomes. Our model also addresses the effect of changes of substrate concentration in assemblies that have been suggested previously to explain translational control by assemblies through the introduction of a potential of mean force biasing diffusion of ribosomes inside the assemblies. The results from the model are compared with the experimental data on translational control by two functional RNA-binding prions, CPEB involved in memory and Rim4 involved in gametogenesis. 

Dendritic spines are tiny membranous protrusions on the dendrites of neurons. Dendritic spines change shape in response to input signals, thereby strengthening the connections between neurons. The growth and stabilization of dendritic spines is thought to be essential for maintaining long-term memory. Actin cytoskeleton remodeling in spines is a key element of their formation and growth. More speculatively, the aggregation of CPEB3, a functional prion that binds RNA, has been reported to be involved in the maintenance of long-term memory. Here we study the interaction between actin and CPEB3 and propose a molecular model for the complex structure of CPEB3 and an actin filament (F-actin). The results of our computational modeling, including both energetic and structural analyses, are compared with novel data from peptide array experiments. Our model of the CPEB3/F-actin interaction suggests that F-actin potentially triggers the aggregation-prone structural transition of a short CPEB3 sequence by zipping it into a beta-hairpin form. We also propose that the CPEB3/F-actin interaction might be regulated by the SUMOylation of CPEB3, based on bioinformatic searches for potential SUMOylation sites as well as SUMO interacting motifs in CPEB3. On the basis of these results and the existing literature, we put forward a possible molecular mechanism underlying long-term memory that involves CPEB3’s binding to actin, its aggregation, and its regulation by SUMOylation. 

Actomyosin networks give cells the ability to move and divide. These networks contract and expand while being driven by active energy-consuming processes such as motor protein walking and actin polymerization. Actin dynamics is also regulated by actin-binding proteins, such as the actin-related protein 2/3 (Arp2/3) complex. This complex generates branched filaments, thereby changing the overall organization of the network. In this work, the spatiotemporal patterns of dynamical actin assembly accompanying the branching-induced reorganization caused by Arp2/3 were studied using a computational model (mechanochemical dynamics of active networks [MEDYAN]); this model simulates actomyosin network dynamics as a result of chemical reactions whose rates are modulated by rapid mechanical equilibration. We show that branched actomyosin networks relax significantly more slowly than do unbranched networks. Also, branched networks undergo rare convulsive movements, “avalanches,” that release strain in the network. These avalanches are associated with the more heterogeneous distribution of mechanically linked filaments displayed by branched networks. These far-from-equilibrium events arising from the marginal stability of growing actomyosin networks provide a possible mechanism of the “cytoquakes” recently seen in experiments. 

Calcium/calmodulin-dependent kinase II (CaMKII) plays a key role in the plasticity of dendritic spines. Calcium signals cause calcium−calmodulin to activate CaMKII, which leads to remodeling of the actin filament (F-actin) network in the spine. We elucidate the mechanism of the remodeling by combining computer simulations with protein array experiments and electron microscopic imaging, to arrive at a structural model for the dodecameric complex of CaMKII with F-actin. The binding interface involves multiple domains of CaMKII. This structure explains the architecture of the micrometer-scale CaMKII/F-actin bundles arising from the multivalence of CaMKII. We also show that the regulatory domain of CaMKII may bind either calmodulin or F-actin, but not both. This frustration, along with the multipartite nature of the binding interface, allows calmodulin transiently to strip CaMKII from actin assemblies so that they can reorganize. This observation therefore provides a simple mechanism by which the structural dynamics of CaMKII establishes the link between calcium signaling and the morphological plasticity of dendritic spines.