Session V11: Physics of Cytoskeleton Across Scales V

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Conotoxins are short, disulfide-rich peptide toxins produced by aquatic snails. Due to their strong selectivity for receptors involved in neuromuscular transmission, they are promising therapeutic leads. Because the number of disulfide connectivities grows rapidly with the number of cysteines, it can be difficult to ascertain the native folded structure or whether there even is a native fold rather than an ensemble of "disulfide isomers." The μ conotoxins contain six cysteines and exist in a folding spectrum. In this article, we employ the composite diffusion map approach to study their unified folding landscape with unconnected disulfides. We identify important nonlinear collective modes and demonstrate that hirudin-like folders occupy a region associated with hydrophobic collapse, while BPTI-like folders occupy a region associated with extended states. This work sheds important light on the free energy landscapes of μ-conotoxins and quantifies the sequence contribution to these landscapes.   

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Intracellular transport of particles often consists of two phases - an active, molecular motor-driven phase along cytoskeletal filaments, and a passive, diffusive transport phase in the cytoplasm, with a stochastic rate of switching between the two phases. An interesting feature results when cytoskeletal filaments form aster-like traps, in which motors along different filaments arrive to a common point. Escape of cargo from such traps takes place by diffusion in the cytoplasm until a particle finds itself outside of the advective basin of attraction of a trap. To calculate the mean time for this escape, we constructed a one-dimensional model that consists of two layers: the advective layer (AL) - representing filaments, and a diffusive layer (DL) - representing the cytoplasm. The velocity field in the AL contains an attracting fixed point - representing the trap. A particle escapes the basin of attraction of a trap when it reaches the absorbing boundaries in the DL. Remarkably, the biophysical parameters are such that escape from basin of attraction of a trap is a rare event. The results are very sensitive to the placement of the trap within its basin of attraction and also display a non-trivial dependence on the initial position of the cargo.   

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Abstract We investigate the dynamics of microtubules (MTs) under the influence of the electric field using the Ising model. The mean-field theory is used to compute the thermodynamic properties of the model such as polarization, critical temperature, and free energy in the absence and presence of the external electric field. The results show that the magnitude of the external electric field plays a critical role in symmetry breaking in MTs. However, when the magnitude of the external electric field is weak and the environmental temperature is below the critical value, the system adopts a favorable configuration where the transmission process occurs.   

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In active matter systems, dense nematic suspensions of self-propelled agents spontaneously exhibit large-scale, chaotic flow structures. Descriptions of the dynamics of these systems have predominately focused on characterization of spatiotemporal correlation of the velocity field, but their transport and mixing properties remain largely unknown. In this work, we use Lagrangian analysis techniques to study the chaotic flow fields generated by ``bacterial turbulence'' in dense suspensions of a model bacterium (Bacillus subtilis). High-resolution velocity fields are measured using particle image velocimetry across a range of bacterial swimming speeds and cell densities. We quantify the kinematic deformations of these flows through the Lagrangian stretching field to visualize the induced stretching and folding, characteristic of mixing. Close inspection of the finite-time Lyapunov exponent (FTLE) field reveals for the first time swimming-speed dependent FTLE-distribution transitions reminiscent of intermittent dynamics in classical chaotic dynamical systems.   

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Actomyosin networks are active systems with a central role in mechanical interactions between the cell and its environment. Actomyosin networks are formed by actin filaments, myosin motors, and actin-binding proteins (ABPs) such as α-actinin and Arp2/3. ABPs allow the transformation of small independent movements of myosin motors into large-scale motions in the actomyosin networks by connecting actin filaments together. The influence of the connectivity of actomyosin networks on the structure, rheology and mechanics of the network has been previously studied experimentally and using coarse-grained molecular simulations.
In this work we model the actomyosin networks using the Flory-Stockmayer theory to describe the conditions under which connectivity percolation occurs. We also compare our model to a mechanochemical coarse-grained model of actomyosin networks. We find that the connectivity of the network is modulated by Arp2/3 in a non-monotonic way. Finally, we relate the connectivity percolation to the rigidity percolation and propose different connectivity states that give rise to distinct behaviors of the actomyosin network.   

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Long cell protrusions are effectively one-dimensional dynamic subcellular structures. The length of such a protrusion can keep fluctuating about the mean value even in the steady state. For its optimal performance as a sensor, the length of a protrusion must not cross a narrow band bounded by two thresholds. However, fluctuations may drive the length beyond these thresholds. Using the generic stochastic models of length control of long cell protrusions and exploiting the techniques of level crossings developed for random excursions of stochastic processes, we have derived analytical expressions of (a) passage times for hitting various thresholds, (b) sojourn times of random excursions beyond the threshold and (c) the extreme lengths attained during the lifetime of these protrusions. We apply our general formulae to flagella (also called cilia) of eukaryotic cells thereby getting estimates of the typical length scales and time scales associated with the various aspects of random length fluctuations. Since most of the earlier works investigated only the mean length of cell protrusions, our study of the fluctuations opens a new horizon in the field of subcellular size control.   

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The structure and dynamics of the cytoskeleton dictate the stability and motility of the cell, but a full understanding of how the global behavior of the network is influenced by the detailed microscopic interactions remains lacking. In particular, the ability of the cytoskeletal network to support a compressive load, necessary for both growth and response to external stimulation, depends strongly on the statistics of the individual filaments and the crosslinks between them. Using a mean field approach, I identify a critical strain at which buckling will occur for a single filament. Strongly bent configurations are predicted to be stable for compressions beyond this critical strain. The mean compressive force required to attain these strains is also computed, with the filament unable to support greater applied forces. I further show that a pair of filaments crosslinked by passive linkers (modeled as permanent harmonic interactions) can be treated on the mean field level as well, and determine the buckling transition for these bundles in two dimensions. These predictions give greater quantitative insight into how the topology of the passive crosslinking between filaments can affect the strength of the system.   

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In engineered materials, bond lifetimes shorten under an applied load. By contrast, biological materials such as the cell cytoskeleton also contain bonds that increase their lifetime under stress. These “catch bonds” can break detailed balance at the molecular scale and increase the toughness of passive materials to externally applied stresses. However, the catch bonds found in the cell cytoskeleton are molecular motors that generate stresses internally via ATP hydrolysis. Through coarse-grained molecular dynamics simulations of the actomyosin cytoskeleton, we explore the effect of the resulting feedback between active stresses and force-dependent binding kinetics on large-scale material and thermodynamic properties of active materials. We show that active catch bonds induce a macroscopic fluid-solid transition, where the extent of broken detailed balance and distinct time-reversal symmetries characterize each material phase. Our work illustrates how the combination of non-equilibrium binding and active stresses mounts an adaptive mechanical response in biological materials.   

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We investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments as well as the global features of actomyosin networks by first mapping the networks into graph representations, then implementing network-theory order parameters that provide principles for combining multiple local models into a joint global model accounting for heterogeneous observations. We find that ABPs with a valency greater than two promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosin-like motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosins detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.   

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Abnormal shapes of red blood cells (RBC) have been associated with various diseases. Here, we focus on sickle-shaped RBC, which form due to the abnormal growth of semi-rigid hemoglobin (HbS) fibers confined in RBC. Using the area difference elasticity (ADE) model for RBC and worm-like chain model for the confined HbS fibers, we explore shape deformations at equilibrium using Monte-Carlo simulations. We show that while a single HbS fiber is not rigid enough to produce sickle-like deformation, a fiber bundle can do so. We also consider multiple disjoint filaments and find that confinement can generate multipolar RBC shapes and even promote helical filament conformations, which have not been discussed before. When applied to microtubules confined in phospholipid vesicles, we show that the same model predicts vesicle tubulation. Also, we reproduce the tube collapse transition and tennis racket type vesicle shapes, as reported in experiments.
The highlight of this work is several important non-axisymmetric RBC and vesicle shapes, which have never been explored in simulations.


References:
1. Lim et al., Proc. Natl. Acad. Sci., 99, 16766 (2002).
2. Fygenson et al., Phys. Rev. Lett., 79, 4497 (1997).   

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Nearly all eukaryotic cells contain mitochondria, which can change their shape, divide, or fuse with each other. We use super-resolution microscopy and fluorescent sensors of physiological and biophysical states to understand how mitochondrial division and transcription are physically regulated and organized. Where do mitochondria divide along their surface? How is the location of division determined? We find that division occurs spatially in a non-random, regulated manner, giving rise to mitochondria with different fates. How are mitochondrial transcripts organized? Mitochondrial RNA granules are highly enriched in mitochondrial RNA, and we find that they behave as liquid condensates, although they are remarkably stable. Why does one mitochondria constrict and divide where another relaxes? We find that membrane tension plays a key role in deciding the fates of individual fission sites.