Session K11: Physics of the Cytoskeleton II

Twist Response of Actin Filaments

Actin cytoskeleton force generation, sensing, and adaptation are dictated by the bending and twisting mechanics of filaments.  We use magnetic tweezers and microfluidics to twist and pull individual actin filaments and evaluate their response to applied loads.  Twisted filaments bend and dissipate torsional strain by adopting a supercoiled plectoneme.  Pulling prevents plectoneme formation, which causes twisted filaments to sever.  Analysis over a range of twisting and pulling forces as well as direct visualization of filament and single-subunit twisting fluctuations yield an actin filament torsional persistence length of ~10 µm, similar to the bending persistence length.  Filament severing by cofilin is driven by local twist strain at boundaries between bare and decorated segments and is accelerated by low pN pulling forces.  This work explains how contractile forces generated by myosin motors accelerate filament severing by cofilin and establishes a role for filament twisting in the regulation of actin filament stability and assembly dynamics.

    

Active microrheology of actin-vimentin intermediate filaments composite networks

The cytoskeleton--a complex dynamic network of biopolymers comprising actin, microtubules, and intermediate filaments--plays a vital role in several cellular processes ranging from the stability and rigidity of biological cells to cell motility and shape change. Central to this multifunctionality are the inherent stiffness of each filament and the myriad binding proteins that serve to crosslink, bundle, and stabilize these filaments. Exploring the mechanics and dynamics of in vitro reconstituted networks consisting of only one of these cytoskeletal components has been the subject of extensive experimental work. However, the role each cytoskeletal component plays in their composite networks' mechanical properties and structural dynamics is yet to be well understood. Here, we couple optical tweezers microrheology with confocal imaging to measure the nonlinear viscoelastic response and structural dynamics of in vitro reconstituted filamentous actin (F-actin)--vimentin intermediate filaments (VIFs) composite networks by varying the relative concentration of actin and vimentin. Our measurements shed new light on how VIFs and F-actin work synergistically during the various cellular processes.   

Collective behaviors of actin filaments in the motility assay with mobile myosin motors

Cells require mechanical forces for their biological functions. The mechanical forces are generated mainly from molecular interactions between actin filaments and myosin motors in the actin cytoskeleton. To better understand their molecular interactions, many studies employed myosin motility assays with actin filaments propelled by myosin heads fixed on a surface. Although these previous studies have shown a wide variety of collective behaviors of actin filaments, the assumption of spatially fixed myosin motors is less physiologically relevant. We employed our computational model for the motility assay with consideration of motor mobility. In agreement with recent experimental results obtained with myosin motors coupled to a lipid bilayer, our simulations showed that actin filaments form large aggregates as opposed to thin bundles as motor mobility increases. Furthermore, this aggregate formation is characterized by the polarity sorting of filaments. Analysis of our simulations shows that polarity sorting and aggregate formation can be explained by a change in collusion statistics between filaments and a phase separation between filaments and motors.

    

Stress Relaxation in Actin Networks and Solutions via Severing

Actin Filaments are maintained in the cytoskeleton along with the monomeric actin in dynamic self-assembly. These biopolymers form highly dynamic networks that contribute to force generation and mechanical stability in the cytoskeleton. They undergo reactions such as polymerization, depolymerization, and severing, which play a crucial role in self-assembly and affect the rheology of the networks. Recent experiments and theory have identified novel stress relaxation due to severing. Inspired by prior studies, we focus on the effects of severing and its rheological implications in both solution and network limits. We develop computational models to predict specific signatures in stress relaxation due to severing in both limits. We also consider the possible effects of mechano-chemical feedback of stress on severing reactions.   

Range and distribution of forces induced by myosin motors in the disordered actin network

Mechanical forces generated by myosin motors in actin networks is responsible for a variety of processes such as cell shape changes and locomotion. These forces may be transmitted through the disordered elastic crosslinked actin network, potentially mediating mechanical interactions between distant myosin motors. We model myosin motors as contractile force dipoles embedded in a bond-diluted triangular lattice, representing the actin network, with bonds that resist bending and stretching. These model fiber networks show a transition from stretching to bending dominated regimes with increasing bond dilution. We quantify the range of force transmission and mechanical heterogeneity of these networks in response to force dipoles. Force propagates over longer ranges in stretching-dominated networks than in the dilute bending regime. Increasing the bending stiffness however restores long-range force transmission even in the dilute regime. By quantifying the decay of mean strain energy with distance, we show that a little bond dilution enhances range of force transmission relative to the ordered lattice. We also investigate the differences between tensile and compressive force propagation by analysing clusters comprising nodes connected to highly stretched or compressed bonds.   

Cell polarity, motility, and shape

Eukaryotic cells are often highly polarized, with very different concentrations of proteins on different sides of the cell: this gives the cell directionality in migration or asymmetric division. I will discuss the group's recent work on how reactions of polarity proteins at the cell's surface can become sensitive to the cell's shape. This shape sensing can lead to surprising new behaviors, like single cells developing a spontaneous circular motion, but can be disrupted by membrane roughness. I will discuss the implications of this idea both for how cells respond to electrical cues and how cells in different environments polarize.   

Filament sliding in simulations of CaMKII-actin bundles

Neuronal synapses form in the brain when the axons of presynaptic neurons connect to the dendrites of postsynaptic neurons. During the synapse formation, small protrusions form on the dendrites of the presynaptic neurons, called dendritic spines, after stimulation with high-frequency electric signals in a process known as long-term potentiation. Calcium/calmodulin-dependent protein kinase II (CaMKII) is crucial in long-term potentiation because it can decode signals, initiate phosphorylation cascades, and interact with actin filaments to form blunt-ended bundles. We modeled CaMKII-actin bundles using a coarse-grained model of four particles per actin promoter and a docking simulation performed in our group. We show that the geometry of CaMKII allows it to slide easily along actin filaments compared to other crosslinkers such as α-actinin and fascin. We also show that the sliding of CaMKII depends on the affinity and properties of the CaMKII-actin docking arrangement. Finally, we propose a mechanism that explains how CaMKII sliding leads to the formation of blunt-ended actin bundles.   

Coarse-grained Molecular Dynamics Modeling of Actin Self-assembly

Actin filaments, microtubules, and intermediate filaments are major components of the cytoskeleton. The self-assembly process of actin filaments, where actin proteins transition from their free monomer form (G-actin) to be part of a long, double-stranded, helical polymer microfilament (F-actin), is of fundamental importance to biology and also serves as a platform to inspire the design of new biomimetic materials. A coarse-grained model is developed to capture the geometric features of G-actin and the assembly characteristics of microfilaments. The model monomer has the shape of a slightly bent, twisted rod with binding sites on its lateral and top/bottom surfaces. Such monomers are found to form a variety of structures, including double-stranded actin filaments. A machine learning approach is developed to classify the monomer states in a self-assembling system by computing the Smooth Overlap of Atomic Positions (SOAP) descriptor for each monomer. Probabilistic Analysis of Molecular Motifs (PAMM), based on a principal component analysis along with an unsupervised clustering algorithm, is adopted to identify free monomers, monomers in the middle and at the end of a filament, and defects. We further define a metric on the basis of such classification information to capture the type and extent of the self-assembly ordering of a given system. This metric enables us to quantify the relation between monomer-monomer binding strengths, self-assembly structures, and defects. Overall, we obtain an understanding of the self-assembly process of actin filaments.   

Shape change in cytoskeleton surface by active self-organization of nematic structures.

Morphogenetic events in the actin cytoskeleton surface result from an interplay between  nematic structures, hydrodynamic flow, density accumulation, geometry, topology, and shape deformation. In this work, we propose a theoretical model to explore the physical mechanisms, regulated by the aforementioned interplay, that leads to self-organized shape changes in a cytoskeleton surface. This model is based on Onsager's formalism, according to which the dynamics result from a variational principle where free-energy release, dissipation, and activity compete. We perform a linear stability analysis of the model to predict an unstable regime that results in the various deformation modes in a cytoskeleton surface. Lastly, we used a finite element-based computational framework to explore the model in a fully non-linear regime and investigate the role of the deformation modes in morphogenetic events such as cellular oscillation, division, motility and wound healing.

    

Cytoskeletal networks at Interfaces

Cytoskeletal networks play a key role in multiple mechanical and dynamical processes in cells. Recently, a continuum theory has been developed [1], allowing for the prediction of the material properties of highly crosslinked cytoskeletal networks from a phenomenological modelling of the microscopic interactions between the cytoskeleton filaments. We extend this theoretical framework to account for external forces, allowing us to explore how the  properties of cytoskeletal networks are affected by the presence of various interfaces. This extended theory allows to study the interplay between cytoskeletal networks and the organelles that it interacts with, such as the centrosomes in spindles, vesicles embedded in intracellular actin networks, or even cortex-membrane interactions at the cell periphery.

[1] S. Fürthauer, D. J. Needleman, M. J. Shelley,  New J. Phys. 23, 013012 (2021).   

Simulating confined cytoskeletal structures with explicit motors and crosslinkers

Confined cytoskeletal filaments, motor proteins, and passive crosslinkers organize into networks whose structure and dynamics depend on the interplay of filament mechanical rigidity, kinetics of polymerization, and interaction with confining boundaries. Several experimental studies have reconstituted a variety of confined structures in vitro, such as asters and contractile rings, paving the way for synthetic cell applications. However, understanding the space of all possible confined cytoskeletal patterns requires the development of computational methods that allow systematic variation of molecular interactions, at varying concentrations, over micron scales. To overcome the limitations of prior methods, we used and modified the high-performance, open-source software aLENS. In aLENS, a constraint method enforces hard-core repulsion between rigid spherosylinders with crosslinking and motor forces incorporated in a unified implicit solver. We further implemented filament flexibility by connecting short spherocylinders by pairs of springs, under the same aLENS solver, tuned to reproduce the desired persistence length. Polymerization was simulated as the addition of segments at a rate that decreases according to a depleting uniform monomer pool. We use this method to show how confined actin filaments form structures such as contractile rings or bundled networks in the presence of myosin motors, passive crosslinkers, and surface-attached linkers or motors.