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The flagellar motor drives the rotation of flagellar filaments, propelling the swimming of flagellated bacteria. The maximum torque the motor generates, the stall torque, is a key characteristic of the motor function. Direct measurements of the stall torque carried out 3 decades ago suffered from large experimental uncertainties, and subsequently there were only indirect measurements. Here, we applied magnetic tweezers to directly measure the stall torque in E. coli. We precisely calibrated the torsional stiffness of the magnetic tweezers and performed motor resurrection experiments at stall, accomplishing a precise determination of the stall torque per torque-generating unit (stator unit). From our measurements, each stator passes 2 protons per step, indicating a tight coupling between motor rotation and proton flux. IMPORTANCE The maximum torque the bacterial flagellar motor generates, the stall torque, is a critical parameter that describes the motor energetics. As the motor operates in equilibrium near stall, from the stall torque one can determine how many protons each torque-generating unit (stator) of the motor passes per revolution and then test whether motor rotation and proton flux are tightly or loosely coupled, which has been controversial in recent years. Direct measurements performed 3 decades ago suffered from large uncertainties, and subsequently, only indirect measurements were attempted, obtaining a range of values inconsistent with the previous direct measurements. Here, we developed a method that used magnetic tweezers to perform motor resurrection experiments at stall, resulting in a direct precise measurement of the stall torque per stator. Our study resolved the previous inconsistencies and provided direct experimental support for the tight coupling mechanism between motor rotation and proton flux.

Motile bacteria usually rely on external apparatus like flagella for swimming or pili for twitching. By contrast, gliding bacteria do not rely on obvious surface appendages to move on solid surfaces. Flavobacterium johnsoniae and other bacteria in the Bacteroidetes phylum use adhesins whose movement on the cell surface supports motility. In F. johnsoniae, secretion and helicoidal motion of the main adhesin SprB are intimately linked and depend on the type IX secretion system (T9SS). Both processes necessitate the proton motive force (PMF), which is thought to fuel a molecular motor that comprises the GldL and GldM cytoplasmic membrane proteins. Here, we show that F. johnsoniae gliding motility is powered by the pH gradient component of the PMF. We further delineate the interaction network between the GldLM transmembrane helices (TMHs) and show that conserved glutamate residues in GldL TMH2 are essential for gliding motility, although having distinct roles in SprB secretion and motion. We then demonstrate that the PMF and GldL trigger conformational changes in the GldM periplasmic domain. We finally show that multiple GldLM complexes are distributed in the membrane, suggesting that a network of motors may be present to move SprB along a helical path on the cell surface. Altogether, our results provide evidence that GldL and GldM assemble dynamic membrane channels that use the proton gradient to power both T9SS-dependent secretion of SprB and its motion at the cell surface., Competing Interests: The authors have declared that no competing interests exist.

Microtubules and kinesin motor proteins are involved in intracellular transports in living cells. Such intracellular material transport systems can be reconstructed for utilisation in synthetic environments, and they are called molecular shuttles driven by kinesin motors. The performance of the molecular shuttles depends on the nature of their trajectories, which can be characterized by the path persistence length of microtubules. It has been theoretically predicted that the path persistence length should be equal to the filament persistence length of the microtubules, where the filament persistence length is a measure of microtubule flexural stiffness. However, previous experiments have shown that there is a significant discrepancy between the path and filament persistence lengths. Here, we showed how this discrepancy arises by using computer simulation. By simulating molecular shuttle movements under external forces, the discrepancy between the path and filament persistence lengths was reproduced as observed in experiments. Our close investigations of molecular shuttle movements revealed that the part of the microtubules bent due to the external force was extended more than it was assumed in the theory. By considering the extended length, we could elucidate the discrepancy. The insights obtained here are expected to lead to better control of molecular shuttle movements., (© 2022. The Author(s).)

Tubulin dimers assemble into dynamic microtubules, which are used by molecular motors as tracks for intracellular transport. Organization and dynamics of the microtubule network are commonly thought to be regulated at the polymer ends, where tubulin dimers can be added or removed. Here, we show that molecular motors running on microtubules cause exchange of dimers along the shaft in vitro and in cells. These sites of dimer exchange act as rescue sites where depolymerizing microtubules stop shrinking and start re-growing. Consequently, the average length of microtubules increases depending on how frequently they are used as motor tracks. An increase of motor activity densifies the cellular microtubule network and enhances cell polarity. Running motors leave marks in the shaft, serving as traces of microtubule usage to organize the polarity landscape of the cell., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2021 Elsevier Inc. All rights reserved.)

Mammalian hearing depends on an amplification process involving prestin, a voltage-sensitive motor protein that enables cochlear outer hair cells (OHCs) to change length and generate force. However, it has been questioned whether this prestin-based somatic electromotility can operate fast enough in vivo to amplify cochlear vibrations at the high frequencies that mammals hear. In this study, we measured sound-evoked vibrations from within the living mouse cochlea and found that the top and bottom of the OHCs move in opposite directions at frequencies exceeding 20 kHz, consistent with fast somatic length changes. These motions are physiologically vulnerable, depend on prestin, and dominate the cochlea's vibratory response to high-frequency sound. This dominance was observed despite mechanisms that clearly low-pass filter the in vivo electromotile response. Low-pass filtering therefore does not critically limit the OHC's ability to move the organ of Corti on a cycle-by-cycle basis. Our data argue that electromotility serves as the primary high-frequency amplifying mechanism within the mammalian cochlea., Competing Interests: The authors declare no competing interest.

The basal body of the bacterial flagellum is a rotary motor that consists of several rings (C, MS and LP) and a rod. The LP ring acts as a bushing supporting the distal rod for its rapid and stable rotation without much friction. Here, we use electron cryomicroscopy to describe the LP ring structure around the rod, at 3.5 Å resolution, from Salmonella Typhimurium. The structure shows 26-fold rotational symmetry and intricate intersubunit interactions of each subunit with up to six partners, which explains the structural stability. The inner surface is charged both positively and negatively. Positive charges on the P ring (the part of the LP ring that is embedded within the peptidoglycan layer) presumably play important roles in its initial assembly around the rod with a negatively charged surface., (© 2021. The Author(s).)

While often believed to be a passive agent that merely exploits its host's metabolism, the influenza virus has recently been shown to actively move across glycan-coated surfaces. This form of enzymatically driven surface motility is currently not well understood and has been loosely linked to burnt-bridge Brownian ratchet mechanisms. Starting from known properties of influenza's spike proteins, we develop a physical model that quantitatively describes the observed motility. It predicts a collectively emerging dynamics of spike proteins and surface-bound ligands that combined with the virus' geometry give rise to a self-organized rolling propulsion. We show that in contrast to a Brownian ratchet, the rotary spike drive is not fluctuation driven but operates optimally as a macroscopic engine in the deterministic regime. The mechanism also applies to relatives of influenza and to man-made analogs like DNA monowheels and should give guidelines for their optimization.

ClpXP in Escherichia coli is a proteasome degrading protein substrates. It consists of one hexamer of ATPase (ClpX) and two heptamers of peptidase (ClpP). The ClpX binds ATP and translocates the substrate protein into the ClpP chamber by binding and hydrolysis of ATP. At single molecular level, ClpX harnesses cycles of power stroke (dwell and burst) to unfold the substrates, then releases the ADP and Pi. Based on the construction and function of ClpXP, especially the recent progress on how ClpX unfold protein substrates, in this mini-review, a currently proposed single ClpX molecular model system detected by optical tweezers, and its prospective for the elucidation of the mechanism of force generation of ClpX in its power stroke and the subunit interaction with each other, were discussed in detail., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Many bacteria swim by means of flagella that are rotated by a nanoscale motor embedded in the cell membrane. Torque is generated by the interaction between ion-conducting membrane proteins that comprise the stator and ring-shaped structures that form the rotor. Although the structure and function of the motor have been extensively studied, many mysteries remain, including the force-generation mechanism, the path of ion flow through the stator, the activation mechanism of the stator, and the mechanism of switching between clockwise (CW) and counterclockwise (CCW) rotation. We summarize recent knowledge of the Na + -driven flagellar motor, especially the Vibrio polar motor that rotates much faster than the H + -driven motor and provides a useful model system for examining comparative aspects of flagellar function., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

Axonal transport is integral for maintaining neuronal form and function, and defects in axonal transport have been correlated with several neurological diseases, making it a subject of extensive research over the past several years. The anterograde and retrograde transport machineries are crucial for the delivery and distribution of several cytoskeletal elements, growth factors, organelles and other synaptic cargo. Molecular motors and the neuronal cytoskeleton function as effectors for multiple neuronal processes such as axon outgrowth and synapse formation. This review examines the molecular mechanisms governing axonal transport, specifically highlighting the contribution of studies conducted in C. elegans , which has proved to be a tractable model system in which to identify both novel and conserved regulatory mechanisms of axonal transport.

The bacterial flagellar motor converts the energy of proton flow through the MotA/MotB complex into mechanical works required for motor rotation. The rotational force is generated by electrostatic interactions between the stator protein MotA and the rotor protein FliG. The Arg-90 and Glu-98 from MotA interact with Asp-289 and Arg-281 of FliG, respectively. An increase in the expression level of the wild-type MotA/MotB complex inhibits motility of the gfp-motB fliG(R281V) mutant but not the fliG(R281V) mutant, suggesting that the MotA/GFP-MotB complex cannot work together with wild-type MotA/MotB in the presence of the fliG(R281V) mutation. However, it remains unknown why. Here, we investigated the effect of the GFP fusion to MotB at its N-terminus on the MotA/MotB function. Over-expression of wild-type MotA/MotB significantly reduced the growth rate of the gfp-motB fliG(R281V) mutant. The over-expression of the MotA/GFP-MotB complex caused an excessive proton leakage through its proton channel, thereby inhibiting cell growth. These results suggest that the GFP tag on the MotB N-terminus affects well-regulated proton translocation through the MotA/MotB proton channel. Therefore, we propose that the N-terminal cytoplasmic tail of MotB couples the gating of the proton channel with the MotA-FliG interaction responsible for torque generation.

The friction between cytoskeletal filaments is of central importance for the formation of cellular structures such as the mitotic spindle and the cytokinetic ring. This friction is caused by passive cross-linkers, yet the underlying mechanism and the dependence on cross-linker density are poorly understood. Here, we use theory and computer simulations to study the friction between two filaments that are cross-linked by passive proteins, which can hop between discrete binding sites while physically excluding each other. The simulations reveal that filaments move via rare discrete jumps, which are associated with free-energy barrier crossings. We identify the reaction coordinate that governs the relative microtubule movement and derive an exact analytical expression for the free-energy barrier and the friction coefficient. Our analysis not only elucidates the molecular mechanism underlying cross-linker-induced filament friction, but also predicts that the friction coefficient scales superexponentially with the density of cross-linkers.

We examine the effect of cargo-motor linkage stiffness on the mechanobiological properties of the molecular motor myosin VI. We use the programmability of DNA nanostructures to modulate cargo-motor linkage stiffness and combine it with high-precision optical trapping measurements to measure the effect of linkage stiffness on the motile properties of myosin VI. Our results reveal that a stiff cargo-motor linkage leads to shorter step sizes and load-induced anchoring of myosin VI, while a flexible linkage results in longer steps with frequent detachments from the actin filament under load. Our findings suggest a novel regulatory mechanism for tuning the dual cellular roles of the anchor and transporter ascribed to myosin VI.

Vertebrate myosin-5a is an ATP-utilizing processive motor associated with the actin network and responsible for the transport and localization of several vesicle cargoes. To transport cargo efficiently and prevent futile ATP hydrolysis, myosin-5a motor function must be tightly regulated. The globular tail domain (GTD) of myosin-5a not only functions as the inhibitory domain but also serves as the binding site for a number of cargo adaptor proteins, including melanophilin (Mlph) and Rab-interacting lysosomal protein-like 2 (RILPL2). In this study, using various biochemical approaches, including ATPase, single-molecule motility, GST pulldown assays, and analytical ultracentrifugation, we demonstrate that the binding of both Mlph and RILPL2 to the GTD of myosin-5a is required for the activation of myosin-5a motor function under physiological ionic conditions. We also found that this activation is regulated by the small GTPase Rab36, a binding partner of RILPL2. In summary, our results indicate that RILPL2 is required for Mlph-mediated activation of Myo5a motor activity under physiological conditions and that Rab36 promotes this activation. We propose that Rab36 stimulates RILPL2 to interact with the myosin-5a GTD; this interaction then induces exposure of the Mlph-binding site in the GTD, enabling Mlph to interact with the GTD and activate myosin-5a motor activity., (© 2019 Cao et al.)

The bacterial flagellar motor is a molecular machine that can rotate the flagellar filament at high speed. The rotation is generated by the stator-rotor interaction, coupled with an ion flux through the torque-generating stator. Here we employed cryo-electron tomography to visualize the intact flagellar motor in the Lyme disease spirochete, Borrelia burgdorferi . By analyzing the motor structures of wild-type and stator-deletion mutants, we not only localized the stator complex in situ, but also revealed the stator-rotor interaction at an unprecedented detail. Importantly, the stator-rotor interaction induces a conformational change in the flagella C-ring. Given our observation that a non-motile mutant, in which proton flux is blocked, cannot generate the similar conformational change, we propose that the proton-driven torque is responsible for the conformational change required for flagellar rotation., Competing Interests: YC, KM, XZ, SN, MM, JL No competing interests declared, (© 2019, Chang et al.)

Outer hair cells (OHCs) of the mammalian cochlea behave like actuators: they feed energy into the cochlear partition and determine the overall mechanics of hearing. They do this by generating voltage-dependent axial forces. The resulting change in the cell length, observed by microscopy, has been termed "electromotility." The mechanism of force generation OHCs can be traced to a specific protein, prestin, a member of a superfamily SLC26 of transporters. This short review will identify some of the more recent findings on prestin. Although the tertiary structure of prestin has yet to be determined, results from the presence of its homologs in nonmammalian species suggest a possible conformation in mammalian OHCs, how it can act like a transport protein, and how it may have evolved., (Copyright © 2019 Cold Spring Harbor Laboratory Press; all rights reserved.)

Motor proteins are the driving force behind muscle contraction and are responsible for the active transportation of most proteins and vesicles in the cytoplasm. There are three superfamilies of cytoskeletal motor proteins with various molecular functions and structures: dynein, kinesin, and myosin. The functional loss of a specific motor protein molecular function has linked to a variety of human diseases, e.g., Charcot-Marie-Tooth disease, kidney disease. Therefore, creating a precise model to classify motor proteins is essential for helping biologists understand their molecular functions and design drug targets according to their impact on human diseases. Here we attempt to classify cytoskeleton motor proteins using deep learning, which has been increasingly and widely used to address numerous problems in a variety of fields resulting in state-of-the-art results. Our effective deep convolutional neural network is able to achieve an independent test accuracy of 97.5%, 96.4%, and 96.1% for each superfamily, respectively. Compared to other state-of-the-art methods, our approach showed a significant improvement in performance across a range of evaluation metrics. Through the proposed study, we provide an effective model for classifying motor proteins and a basis for further research that can enhance the performance of protein function classification using deep learning., (Copyright © 2019 Elsevier Inc. All rights reserved.)

The bacterial flagellar motor powers the rotation that propels the swimming bacteria. Rotational torque is generated by harnessing the flow of ions through ion channels known as stators which couple the energy from the ion gradient across the inner membrane to rotation of the rotor. Here, we used error-prone PCR to introduce single point mutations into the sodium-powered Vibrio alginolyticus/Escherichia coli chimeric stator PotB and selected for motors that exhibited motility in the presence of the sodium-channel inhibitor phenamil. We found single mutations that enable motility under phenamil occurred at two sites: (i) the transmembrane domain of PotB, corresponding to the TM region of the PomB stator from V. alginolyticus and (ii) near the peptidoglycan binding region that corresponds to the C-terminal region of the MotB stator from E. coli. Single cell rotation assays confirmed that individual flagellar motors could rotate in up to 100 µM phenamil. Using phylogenetic logistic regression, we found correlation between natural residue variation and ion source at positions corresponding to PotB F22Y, but not at other sites. Our results demonstrate that it is not only the pore region of the stator that moderates motility in the presence of ion-channel blockers., (© 2019 John Wiley & Sons Ltd.)

It is unknown how the archaellum-the rotary propeller used by Archaea for motility-works. To further understand the molecular mechanism by which the hexameric ATPase motor protein FlaI drives rotation of the membrane-embedded archaellar motor, we determined motor torque by imposition of various loads on Halobacterium salinarum archaella. Markers of different sizes were attached to single archaella, and their trajectories were quantified using three-dimensional tracking and high-speed recording. We show that rotation slows as the viscous drag of markers increases, but torque remains constant at 160 pN·nm independent of rotation speed. Notably, the estimated work done in a single rotation is twice the expected energy that would come from hydrolysis of six ATP molecules in the hexamer, indicating that more ATP molecules are required for one rotation of archaellum. To reconcile the apparent contradiction, we suggest a new and general model for the mechanism of ATP-driven rotary motors., Competing Interests: Competing interestsThe authors declare no competing interests.

MYH9, a widely expressed gene encoding nonmuscle myosin heavy chain, is also expressed in podocytes and is associated with glomerular pathophysiology. However, the mechanisms underlying MYH9-related glomerular diseases associated with proteinuria are poorly understood. Therefore, we investigated the role and mechanism of MYH9 in diabetic kidney injury. MYH9 expression was decreased in glomeruli from diabetic patients and animals and in podocytes treated with Ang II in vitro. Ang II treatment and siRNA-mediated MYH9 knockdown in podocytes resulted in actin cytoskeleton reorganization, reduced cell adhesion, actin-associated protein downregulation, and increased albumin permeability. Ang II treatment increased NOX4 expression and ROS generation. The Ang II receptor blocker losartan and the ROS scavenger NAC restored MYH9 expression in Ang II-treated podocytes, attenuated disrupted actin cytoskeleton and decreased albumin permeability. Furthermore, MYH9 overexpression in podocytes restored the effects of Ang II on the actin cytoskeleton and actin-associated proteins. Ang II-mediated TRPC6 activation reduced MYH9 expression. These results suggest that Ang II-mediated MYH9 depletion in diabetic nephropathy may increase filtration barrier permeability by inducing structural and functional podocyte injury through TRPC6-mediated Ca 2+ influx by NOX4-mediated ROS generation. These findings reveal a novel MYH9 function in maintaining urinary filtration barrier integrity. MYH9 may be a potential target for treating diabetic nephropathy.

Stochastic trajectories measured in single-molecule experiments have provided key insights into the microscopic behaviour of cyclic motor proteins. However, the fundamental free-energy landscapes of motor proteins are currently only able to be determined by computationally intensive numerical methods that do not take advantage of available single-trajectory data. In this paper we present a robust method for analysing single-molecule trajectories of cyclic motor proteins to reconstruct their free-energy landscapes. We use simulated trajectories on model potential landscapes to show the reliable reconstruction of the potentials. We determine the accuracy of the reconstruction method for common precision limitations and show that the method converges logarithmically. These results are then used to determine the experimental precision required to reconstruct a potential with a desired accuracy. The key advantages of the method are that it is simple to implement, is free of numerical difficulties that plague existing methods and is easily generalizable to higher dimensions., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

MYH9 was first discovered due to thrombocytopenia caused by MYH9 mutation-related abnormalities. In recent years, researchers have increasingly found that MYH9 plays an important role in cancer as a cytokine involved in cytoskeletal reorganization, cellular pseudopodia formation, and migration. MYH9 is closely related to the progress and poor prognosis of most solid tumors, and it is now accepted that MYH9 is a suppressor gene and plays an important role on the re-Rho pathway. Recent research has been limited to the study of tissues. However, it would be more direct and informative to be able to use hematology to assess tumor prognosis and changes in MYH9 levels and NMMHC-IIA. This article summarizes recent research on MYH9 and provides a reference for future clinical research.

Organisms in the three domains of life depend on protein polymers to form a cytoskeleton that helps to establish their shapes, maintain their mechanical integrity, divide, and, in many cases, move. Eukaryotes have the most complex cytoskeletons, comprising three cytoskeletal polymers-actin filaments, intermediate filaments, and microtubules-acted on by three families of motor proteins (myosin, kinesin, and dynein). Prokaryotes have polymers of proteins homologous to actin and tubulin but no motors, and a few bacteria have a protein related to intermediate filament proteins., (Copyright © 2018 Cold Spring Harbor Laboratory Press; all rights reserved.)

The voltage-dependent protein SLC26a5 (prestin) underlies outer hair cell electromotility (eM), which is responsible for cochlear amplification in mammals. The electrical signature of eM is a bell-shaped nonlinear capacitance (NLC), deriving from prestin sensor-charge (Q p ) movements, which peaks at the membrane voltage, V h , where charge is distributed equally on either side of the membrane. Voltage dependencies of NLC and eM differ depending on interrogation frequency and intracellular chloride, revealing slow intermediate conformational transitions between anion binding and voltage-driven Q p movements. Consequently, NLC exhibits low-pass characteristics, substantially below prevailing estimates of eM frequency response. Here we study in guinea pig and mouse of either sex synchronous prestin electrical (NLC, Q p ) and mechanical (eM) activity across frequencies under voltage clamp (whole cell and microchamber). We find that eM and Q p magnitude and phase correspond, indicating tight piezoelectric coupling. Electromechanical measures (both NLC and eM) show dual-Lorentzian, low-pass behavior, with a limiting (τ 2 ) time constant at V h of 32.6 and 24.8 μs, respectively. As expected for voltage-dependent kinetics, voltage excitation away from V h has a faster, flatter frequency response, with our fastest measured τ 2 for eM of 18.2 μs. Previous observations of ultrafast eM (τ ≈ 2 μs) were obtained at offsets far removed from V h We hypothesize that trade-offs in eM gain-bandwith arising from voltage excitation at membrane potentials offset from V h influence the effectiveness of cochlear amplification across frequencies. SIGNIFICANCE STATEMENT Of two types of hair cells within the organ of Corti, inner hair cells and outer hair cells, the latter evolved to boost sensitivity to sounds. Damage results in hearing loss of 40-60 dB, revealing amplification gains of 100-1000× that arise from voltage-dependent mechanical responses [electromotility (eM)]. eM, driven by the membrane protein prestin, may work beyond 70 kHz. However, this speed exceeds, by over an order of magnitude, kinetics of typical voltage-dependent membrane proteins. We find eM is actually low pass in nature, indicating that prestin bears kinetics typical of other membrane proteins. These observations highlight potential difficulties in providing sufficient amplification beyond a cutoff frequency near 20 kHz. Nevertheless, observed trade-offs in eM gain-bandwith may sustain cochlear amplification across frequency., (Copyright © 2018 the authors 0270-6474/18/385495-12$15.00/0.)

Rotary ATPases are unique rotary molecular motors that function as energy conversion machines. Among all known rotary ATPases, F 1 -ATPase is the best characterized rotary molecular motor. There are many high-resolution crystal structures and the rotation dynamics have been investigated in detail by extensive single-molecule studies. In contrast, knowledge on the structure and rotation dynamics of V 1 -ATPase, another rotary ATPase, has been limited. However, recent high-resolution structural studies and single-molecule studies on V 1 -ATPase have provided new insights on how the catalytic sites in this molecular motor change its conformation during rotation driven by ATP hydrolysis. In this review, we summarize recent information on the structural features and rotary dynamics of V 1 -ATPase revealed from structural and single-molecule approaches and discuss the possible chemomechanical coupling scheme of V 1 -ATPase with a focus on differences between rotary molecular motors.

Mitotic kinesin-5 bipolar motor proteins perform essential functions in mitotic spindle dynamics by crosslinking and sliding antiparallel microtubules (MTs) apart within the mitotic spindle. Two recent studies have indicated that single molecules of Cin8, the Saccharomyces cerevisiae kinesin-5 homolog, are minus end-directed when moving on single MTs, yet switch directionality under certain experimental conditions (Gerson-Gurwitz et al., EMBO J 30:4942-4954, 2011; Roostalu et al., Science 332:94-99, 2011). This finding was unexpected since the Cin8 catalytic motor domain is located at the N-terminus of the protein, and such kinesins have been previously thought to be exclusively plus end-directed. In addition, the essential intracellular functions of kinesin-5 motors in separating spindle poles during mitosis can only be accomplished by plus end-directed motility during antiparallel sliding of the spindle MTs. Thus, the mechanism and possible physiological role of the minus end-directed motility of kinesin-5 motors remain unclear. Experimental and theoretical studies from several laboratories in recent years have identified additional kinesin-5 motors that are bidirectional, revealed structural determinants that regulate directionality, examined the possible mechanisms involved and have proposed physiological roles for the minus end-directed motility of kinesin-5 motors. Here, we summarize our current understanding of the remarkable ability of certain kinesin-5 motors to switch directionality when moving along MTs.

Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. Here, we study a computational model for a cross-linked network with active motors based on minimal requirements for production and dissipation of contractile stress: Asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. We characterize how the production and dissipation of network stress depend, individually, on cross-link dynamics and filament turnover, and how these dependencies combine to determine overall rates of cortical flow. Our analysis predicts that filament turnover is required to maintain active stress against external resistance and steady state flow in response to external stress. Steady state stress increases with filament lifetime up to a characteristic time τm, then decreases with lifetime above τm. Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. These individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular our model predicts that when filament lifetimes are shorter than both τc and τm, the dependencies of effective viscosity and steady state stress on filament turnover cancel one another, such that flow speed is insensitive to filament turnover, and shows a simple dependence on motor activity and crosslink dynamics. These results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.

D'Arcy Thompson was a proponent of applying mathematical and physical principles to biological systems, an approach that is becoming increasingly common in developmental biology. Indeed, the recent integration of quantitative experimental data, force measurements and mathematical modeling has changed our understanding of morphogenesis - the shaping of an organism during development. Emerging evidence suggests that the subcellular organization of contractile cytoskeletal networks plays a key role in force generation, while on the tissue level the spatial organization of forces determines the morphogenetic output. Inspired by D'Arcy Thompson's On Growth and Form , we review our current understanding of how biological forms are created and maintained by the generation and organization of contractile forces at the cell and tissue levels. We focus on recent advances in our understanding of how cells actively sculpt tissues and how forces are involved in specific morphogenetic processes., Competing Interests: Competing interestsThe authors declare no competing or financial interests., (© 2017. Published by The Company of Biologists Ltd.)

Rotation of the bacterial flagellar motor is driven by multiple torque-generating units (stator elements). The torque-generating dynamics can be understood in terms of the "duty ratio" of the stator elements, that is, the fraction of time a stator element engages with the rotor during its mechanochemical cycle. The dependence of the limiting speed (zero-load speed) of the motor on the number of stator elements is the determining test of the duty ratio, which has been controversial experimentally and theoretically over the past decade. Here, we developed a method combining laser dark-field microscopy and optical trapping to resolve this controversy. We found that the zero-load speed is independent of the number of stator elements for the bacterial flagellar motor in Escherichia coli , demonstrating that these elements have a duty ratio close to 1., Competing Interests: The authors declare no conflict of interest.

It is known from the wave-like motion of microtubules in motility assays that the piconewton forces that motors produce can be sufficient to bend the filaments. In cellular phenomena such as cytosplasmic streaming, molecular motors translocate along cytoskeletal filaments, carrying cargo which entrains fluid. When large numbers of such forced filaments interact through the surrounding fluid, as in particular stages of oocyte development in Drosophila melanogaster , complex dynamics are observed, but the detailed mechanics underlying them has remained unclear. Motivated by these observations, we study here perhaps the simplest model for these phenomena: an elastic filament, pinned at one end, acted on by a molecular motor treated as a point force. Because the force acts tangential to the filament, no matter what its shape, this 'follower-force' problem is intrinsically non-variational, and thereby differs fundamentally from Euler buckling, where the force has a fixed direction, and which, in the low-Reynolds-number regime, ultimately leads to a stationary, energy-minimizing shape. Through a combination of linear stability theory, analytical study of a solvable simplified 'two-link' model and numerical studies of the full elastohydrodynamic equations of motion, we elucidate the Hopf bifurcation that occurs with increasing forcing of a filament, leading to flapping motion analogous to the high-Reynolds-number oscillations of a garden hose with a free end., (© 2017 The Author(s).)

The bacterial flagellar motor (BFM) rotates hundreds of times per second to propel bacteria driven by an electrochemical ion gradient. The motor consists of a rotor 50 nm in diameter surrounded by up to 11 ion-conducting stator units, which exchange between motors and a membrane-bound pool. Measurements of the torque-speed relationship guide the development of models of the motor mechanism. In contrast to previous reports that speed near zero torque is independent of the number of stator units, we observe multiple speeds that we attribute to different numbers of units near zero torque in both Na + - and H + -driven motors. We measure the full torque-speed relationship of one and two H + units in Escherichia coli by selecting the number of H + units and controlling the number of Na + units in hybrid motors. These experiments confirm that speed near zero torque in H + -driven motors increases with the stator number. We also measured 75 torque-speed curves for Na + -driven chimeric motors at different ion-motive force and stator number. Torque and speed were proportional to ion-motive force and number of stator units at all loads, allowing all 77 measured torque-speed curves to be collapsed onto a single curve by simple rescaling., Competing Interests: The authors declare no conflict of interest., (Published under the PNAS license.)

Microtubules (MTs) are protein filaments that provide structure to the cytoskeleton of cells and a platform for the movement of intracellular substances. The spatial organization of MTs is crucial for a cell's form and function. MTs interact with a class of proteins called motor proteins that can transport and position individual filaments, thus contributing to overall organization. In this paper, we study the mathematical properties of a coupled partial differential equation (PDE) model, introduced by White et al. in 2015, that describes the motor-induced organization of MTs. The model consists of a nonlinear coupling of a hyperbolic PDE for bound motor proteins, a parabolic PDE for unbound motor proteins, and a transport equation for MT dynamics. We locally smooth the motor drift velocity in the equation for bound motor proteins. The mollification is not only critical for the analysis of the model, but also adds biological realism. We then use a Banach Fixed Point argument to show local existence and uniqueness of mild solutions. We highlight the applicability of the model by showing numerical simulations that are consistent with in vitro experiments.

Self-propelled bacteria can be integrated into synthetic micromachines and act as biological propellers. So far, proposed designs suffer from low reproducibility, large noise levels or lack of tunability. Here we demonstrate that fast, reliable and tunable bio-hybrid micromotors can be obtained by the self-assembly of synthetic structures with genetically engineered biological propellers. The synthetic components consist of 3D interconnected structures having a rotating unit that can capture individual bacteria into an array of microchambers so that cells contribute maximally to the applied torque. Bacterial cells are smooth swimmers expressing a light-driven proton pump that allows to optically control their swimming speed. Using a spatial light modulator, we can address individual motors with tunable light intensities allowing the dynamic control of their rotational speeds. Applying a real-time feedback control loop, we can also command a set of micromotors to rotate in unison with a prescribed angular speed.

Multiscale modeling of muscular-skeletal systems-the materials and structures that help organisms support themselves and move-is a rapidly growing field of study that has contributed key elements to the understanding of these systems, especially from a multiscale perspective. The systems, including materials such as bone and muscle, have hierarchical structures ranging from the nano- to the macroscale, and it is difficult to understand their macroscopic behaviors, both physiological and pathological, without knowledge of their hierarchical structures and properties. In this review, we discuss the methods of multiscale modeling. Through a series of case studies about key materials in muscular-skeletal systems, we describe how different methods can bridge the gap between hierarchical structures and their roles in the systems' mechanical properties. In particular, we emphasize the importance of the quality of minerals in bone. Finally, we discuss biomimetic material designs facilitated by additive manufacturing technology.

Downstream of gene expression, effectors such as the actomyosin contractile machinery drive embryo morphogenesis. During Drosophila embryonic axis extension, actomyosin has a specific planar-polarised organisation, which is responsible for oriented cell intercalation. In addition to these cell rearrangements, cell shape changes also contribute to tissue deformation. While cell-autonomous dynamics are well described, understanding the tissue-scale behaviour challenges us to solve the corresponding mechanical problem at the scale of the whole embryo, since mechanical resistance of all neighbouring epithelia will feedback on individual cells. Here we propose a novel numerical approach to compute the whole-embryo dynamics of the actomyosin-rich apical epithelial surface. We input in the model specific patterns of actomyosin contractility, such as the planar-polarisation of actomyosin in defined ventro-lateral regions of the embryo. Tissue strain rates and displacements are then predicted over the whole embryo surface according to the global balance of stresses and the material behaviour of the epithelium. Epithelia are modelled using a rheological law that relates the rate of deformation to the local stresses and actomyosin anisotropic contractility. Predicted flow patterns are consistent with the cell flows observed when imaging Drosophila axis extension in toto, using light sheet microscopy. The agreement between model and experimental data indicates that the anisotropic contractility of planar-polarised actomyosin in the ventro-lateral germband tissue can directly cause the tissue-scale deformations of the whole embryo. The three-dimensional mechanical balance is dependent on the geometry of the embryo, whose curved surface is taken into account in the simulations. Importantly, we find that to reproduce experimental flows, the model requires the presence of the cephalic furrow, a fold located anteriorly of the extending tissues. The presence of this geometric feature, through the global mechanical balance, guides the flow and orients extension towards the posterior end.

Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematical model representing core interactions involved in the spatial localization of junctional RhoA signaling. We demonstrate how the interplay between biochemical signaling through positive feedback, combined with diffusion on the cell membrane and mechanical forces generated in the cortex, can determine the spatial distribution of RhoA signaling at cell-cell junctions. This dynamical mechanism relies on the balance between a propagating bistable signal that is opposed by an advective flow generated by an actomyosin stress gradient. Experimental observations on the behavior of the system when contractility is inhibited are in qualitative agreement with the predictions of the model.

The function of the heart valve interstitial cells (VICs) is intimately connected to heart valve tissue remodeling and repair, as well as the onset and progression of valvular pathological processes. There is yet only very limited knowledge and extant models for the complex three-dimensional VIC internal stress-bearing structures, the associated cell-level biomechanical behaviors, and how they change under varying activation levels. Importantly, VICs are known to exist and function within the highly dynamic valve tissue environment, including very high physiological loading rates. Yet we have no knowledge on how these factors affect VIC function. To this end, we extended our previous VIC computational continuum mechanics model (Sakamoto, et al., 2016, "On Intrinsic Stress Fiber Contractile Forces in Semilunar Heart Valve Interstitial Cells Using a Continuum Mixture Model," J. Mech. Behav. Biomed. Mater., 54(244-258)). to incorporate realistic stress-fiber geometries, force-length relations (Hill model for active contraction), explicit α-smooth muscle actin (α-SMA) and F-actin expression levels, and strain rate. Novel micro-indentation measurements were then performed using cytochalasin D (CytoD), variable KCl molar concentrations, both alone and with transforming growth factor β1 (TGF-β1) (which emulates certain valvular pathological processes) to explore how α-SMA and F-actin expression levels influenced stress fiber responses under quasi-static and physiological loading rates. Simulation results indicated that both F-actin and α-SMA contributed substantially to stress fiber force generation, with the highest activation state (90 mM KCL + TGF-β1) inducing the largest α-SMA levels and associated force generation. Validation was performed by comparisons to traction force microscopy studies, which showed very good agreement. Interestingly, only in the highest activation state was strain rate sensitivity observed, which was captured successfully in the simulations. These unique findings demonstrated that only VICs with high levels of αSMA expression exhibited significant viscoelastic effects. Implications of this study include greater insight into the functional role of α-SMA and F-actin in VIC stress fiber function, and the potential for strain rate-dependent effects in pathological states where high levels of α-SMA occur, which appear to be unique to the valvular cellular in vivo microenvironment.

Cells assemble numerous types of actomyosin bundles that generate contractile forces for biological processes, such as cytokinesis and cell migration. One example of contractile bundles is a transverse arc that forms via actomyosin-driven condensation of actin filaments in the lamellipodia of migrating cells and exerts significant forces on the surrounding environments. Structural reorganization of a network into a bundle facilitated by actomyosin contractility is a physiologically relevant and biophysically interesting process. Nevertheless, it remains elusive how actin filaments are reoriented, buckled, and bundled as well as undergo tension buildup during the structural reorganization. In this study, using an agent-based computational model, we demonstrated how the interplay between the density of myosin motors and cross-linking proteins and the rigidity, initial orientation, and turnover of actin filaments regulates the morphological transformation of a cross-linked actomyosin network into a bundle and the buildup of tension occurring during the transformation., Competing Interests: The authors have declared that no competing interests exist.

The role of flagellar motors in bacterial motility and chemotaxis is well-understood. Recent discoveries suggest that flagellar motors are able to remodel in response to a variety of environmental stimuli and are among the triggers for surface colonization and infections. The precise mechanisms by which motors remodel and promote cellular adaptation likely depend on key motor attributes. The photomultiplier-based bead-tracking technique presented here enables accurate biophysical characterization of motor functions, including adaptations in motor speeds and switch-dynamics. This approach offers the advantage of real-time tracking and the ability to probe motor behavior over extended durations. The protocols discussed can be readily extended to study flagellar motors in a variety of bacterial species.

Rho kinases (ROCK1 and ROCK2) function downstream of the small GTPase RhoA to drive actomyosin cytoskeletal remodeling. It has often been believed that ROCK1 and ROCK2 may be functionally redundant, as they share a highly conserved kinase domain. However, in this study, we report differential functional effects for these ROCKs at the epithelial zonula adherens (ZA). Using specific siRNA, we found that ROCK1 depletion disrupted cadherin organization at the ZA, accompanied by loss of F-actin and NMIIA, whereas ROCK2 knockdown had no significant effect. Further, ROCK1, but not ROCK2, was necessary to stabilize GTP-RhoA at the ZA, thereby sustaining junctional tension and inhibiting intraepithelial cell movement. We also found that nonmuscle myosin IIA is a major determinant of ROCK1 cortical stability. Thus, despite sharing the catalytic domain with ROCK2, ROCK1 appears to be the dominant kinase essential for junctional integrity and contractile tension at epithelial ZA., (© 2017 Priya et al. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).)

Apicomplexa exhibit a unique form of substrate-dependent gliding motility central for host cell invasion and parasite dissemination. Gliding is powered by rearward translocation of apically secreted transmembrane adhesins via their interaction with the parasite actomyosin system. We report a conserved armadillo and pleckstrin homology (PH) domain-containing protein, termed glideosome-associated connector (GAC), that mediates apicomplexan gliding motility, invasion, and egress by connecting the micronemal adhesins with the actomyosin system. TgGAC binds to and stabilizes filamentous actin and specifically associates with the transmembrane adhesin TgMIC2. GAC localizes to the apical pole in invasive stages of Toxoplasma gondii and Plasmodium berghei, and apical positioning of TgGAC depends on an apical lysine methyltransferase, TgAKMT. GAC PH domain also binds to phosphatidic acid, a lipid mediator associated with microneme exocytosis. Collectively, these findings indicate a central role for GAC in spatially and temporally coordinating gliding motility and invasion., (Copyright © 2016 Elsevier Inc. All rights reserved.)

Intracellular transport is an essential function in eucaryotic cells, facilitated by motor proteins-proteins converting chemical energy into kinetic energy. It is understood that motor proteins work in teams enabling unidirectional and bidirectional transport of intracellular cargo over long distances. Disruptions of the underlying transport mechanisms, often caused by mutations that alter single motor characteristics, are known to cause neurodegenerative diseases. For example, phosphorylation of kinesin motor domain at the serine residue is implicated in Huntington's disease, with a recent study of phosphorylated and phosphomimetic serine residues indicating lowered single motor stalling forces. In this article we report the effects of mutations of this nature on transport properties of cargo carried by multiple wild-type and mutant motors. Results indicate that mutants with altered stall forces might determine the average velocity and run-length even when they are outnumbered by wild type motors in the ensemble. It is shown that mutants gain a competitive advantage and lead to an increase in the expected run-length when the load on the cargo is in the vicinity of the mutant's stalling force or a multiple of its stalling force. A separate contribution of this article is the development of a semi-analytic method to analyze transport of cargo by multiple motors of multiple types. The technique determines transition rates between various relative configurations of motors carrying the cargo using the transition rates between various absolute configurations. This enables a computation of biologically relevant quantities like average velocity and run-length without resorting to Monte Carlo simulations. It can also be used to introduce alterations of various single motor parameters to model a mutation and to deduce effects of such alterations on the transport of a common cargo by multiple motors. Our method is easily implementable and we provide a software package for general use., Competing Interests: The authors have declared that no competing interests exist.

Rectal cancer treatment still fails with local and distant relapses of the disease. It is hypothesized that radiotherapy could stimulate cancer cell dissemination and metastasis. In this study, we evaluated the effect of X-radiation on collagen type I strap formation potential, i.e. matrix remodeling associated with mesenchymal cell migration, and behaviors of SW480, SW620, HCT116 p53+/+ and HCT116 p53-/- colon cancer cells. We determined a radiation-induced increase in collagen type I strap formation and migration potentials of SW480 and HCT116 p53+/+. Further studies with HCT116 p53+/+, indicated that after X-radiation strap forming cells have an increased motility. More, we detected a decrease in adhesion potential and mature integrin β1 expression, but no change in non-muscle myosin II expression for HCT116 p53+/+ after X-radiation. Integrin β1 neutralization resulted in a decreased cell adhesion and collagen type I strap formation in both sham and X-radiated conditions. Our study indicates collagen type I strap formation as a potential mechanism of colon cancer cells with increased migration potential after X-radiation, and suggests that other molecules than integrin β1 and non-muscle myosin II are responsible for the radiation-induced collagen type I strap formation potential of colon cancer cells. This work encourages further molecular investigation of radiation-induced migration to improve rectal cancer treatment outcome.

We developed a model of cardiac sarcomere contraction to study the calcium-tension relationship in cardiac muscle. Calcium mediates cardiac contraction through its interactions with troponin (Tn) and subsequently tropomyosin molecules. Experimental studies have shown that a slight increase in intracellular calcium concentration leads to a rapid increase in sarcomeric tension. Though it is widely accepted that the rapid increase is not possible without the concept of cooperativity, the mechanism is debated. We use the hypothesis that there exists a base level of cooperativity intrinsic to the thin filament that is boosted by mechanical tension, i.e. a high level of mechanical tension in the thin filament impedes the unbinding of calcium from Tn. To test these hypotheses, we developed a computational model in which a set of three parameters and inputs of calcium concentration and sarcomere length result in output tension. Tension as simulated appeared in good agreement with experimentally measured tension. Our results support the hypothesis that high tension in the thin filament impedes Tn deactivation by increasing the energy required to detach calcium from the Tn. Given this hypothesis, the model predicted that the areas with highest tension, i.e. closest to the Z-disk end of the single overlap region, show the largest concentration of active Tn's., Competing Interests: The authors have declared that no competing interests exist.

Asters nucleated by Microtubule (MT) organizing centers (MTOCs) converge on chromosomes during spindle assembly in mouse oocytes undergoing meiosis I. Time-lapse imaging suggests that this centripetal motion is driven by a biased 'search-and-capture' mechanism. Here, we develop a model of a random walk in a drift field to test the nature of the bias and the spatio-temporal dynamics of the search process. The model is used to optimize the spatial field of drift in simulations, by comparison to experimental motility statistics. In a second step, this optimized gradient is used to determine the location of immobilized dynein motors and MT polymerization parameters, since these are hypothesized to generate the gradient of forces needed to move MTOCs. We compare these scenarios to self-organized mechanisms by which asters have been hypothesized to find the cell-center- MT pushing at the cell-boundary and clustering motor complexes. By minimizing the error between simulation outputs and experiments, we find a model of "pulling" by a gradient of dynein motors alone can drive the centripetal motility. Interestingly, models of passive MT based "pushing" at the cortex, clustering by cross-linking motors and MT-dynamic instability gradients alone, by themselves do not result in the observed motility. The model predicts the sensitivity of the results to motor density and stall force, but not MTs per aster. A hybrid model combining a chromatin-centered immobilized dynein gradient, diffusible minus-end directed clustering motors and pushing at the cell cortex, is required to comprehensively explain the available data. The model makes experimentally testable predictions of a spatial bias and self-organized mechanisms by which MT asters can find the center of a large cell., Competing Interests: The authors have declared that no competing interests exist.

The centrosome is positioned at the cell center by pushing and pulling forces transmitted by microtubules (MTs). Centrosome decentering is often considered to result from asymmetric, cortical pulling forces exerted in particular by molecular motors on MTs and controlled by external cues affecting the cell cortex locally. Here we used numerical simulations to investigate the possibility that it could equally result from the redistribution of pushing forces due to a reorientation of MTs. We first showed that MT gliding along cell edges and pivoting around the centrosome regulate MT rearrangement and thereby direct the spatial distribution of pushing forces, whereas the number, dynamics, and stiffness of MTs determine the magnitude of these forces. By modulating these parameters, we identified different regimes, involving both pushing and pulling forces, characterized by robust centrosome centering, robust off-centering, or "reactive" positioning. In the last-named conditions, weak asymmetric cues can induce a misbalance of pushing and pulling forces, resulting in an abrupt transition from a centered to an off-centered position. Taken together, these results point to the central role played by the configuration of the MTs on the distribution of pushing forces that position the centrosome. We suggest that asymmetric external cues should not be seen as direct driver of centrosome decentering and cell polarization but instead as inducers of an effective reorganization of the MT network, fostering centrosome motion to the cell periphery., (© 2016 Letort et al. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).)