Mechanics of single kinesin molecules measured by optical trapping nanometry

ADP release can explain spatially-dependent kinesin binding times

The self-organization of cells relies on the profound complexity of protein-protein interactions. Challenges in directly observing these events have hindered progress toward understanding their diverse behaviors. One notable example is the interaction between molecular motors and cytoskeletal systems that combine to perform a variety of cellular functions. In this work, we leverage theory and experiments to identify and quantify the rate-limiting mechanism of the initial association between a cargo-bound kinesin motor and a microtubule track. Recent advances in optical tweezers provide binding times for several lengths of kinesin motors trapped at varying distances from a microtubule, empowering the investigation of competing models. We first explore a diffusion-limited model of binding. Through Brownian dynamics simulations and simulation-based inference, we find this simple diffusion model fails to explain the experimental binding times, but an extended model that accounts for the ADP state of the molecular motor agrees closely with the data, even under the scrutiny of penalizing for additional model complexity. We provide quantification of both kinetic rates and biophysical parameters underlying the proposed binding process. Our model suggests that most but not every motor binding event is limited by their ADP state. Lastly, we predict how these association rates can be modulated in distinct ways through variation of environmental concentrations and spatial distances.

Fast backward steps and detachment of single kinesin molecules measured under a wide range of loads

To understand force generation under a wide range of loads, the stepping of single kinesin molecules was measured at loads from -20 to 42 pN by optical tweezers with high temporal resolution. The optical trap has been improved to halve positional noise and increase bandwidth by using 200-nm beads. The step size of the forward and backward steps was 8.2 nm even over a wide range of loads. Histograms of the dwell times of backward steps and detachment fit well to two independent exponential equations with fast (~0.4 ms) and slow (>3 ms) time constants, indicating the existence of a fast step in addition to the conventional slow step. The dwell times of the fast steps were almost independent of the load and ATP concentration, while those of the slow backward steps and detachment depended on those. We constructed the kinetic model to explain the fast and slow steps under a wide range of loads.

Axonal transport during injury on a theoretical axon

Neurodevelopment, plasticity, and cognition are integral with functional directional transport in neuronal axons that occurs along a unique network of discontinuous polar microtubule (MT) bundles. Axonopathies are caused by brain trauma and genetic diseases that perturb or disrupt the axon MT infrastructure and, with it, the dynamic interplay of motor proteins and cargo essential for axonal maintenance and neuronal signaling. The inability to visualize and quantify normal and altered nanoscale spatio-temporal dynamic transport events prevents a full mechanistic understanding of injury, disease progression, and recovery. To address this gap, we generated DyNAMO, a Dynamic Nanoscale Axonal MT Organization model, which is a biologically realistic theoretical axon framework. We use DyNAMO to experimentally simulate multi-kinesin traffic response to focused or distributed tractable injury parameters, which are MT network perturbations affecting MT lengths and multi-MT staggering. We track kinesins with different motility and processivity, as well as their influx rates, in-transit dissociation and reassociation from inter-MT reservoirs, progression, and quantify and spatially represent motor output ratios. DyNAMO demonstrates, in detail, the complex interplay of mixed motor types, crowding, kinesin off/on dissociation and reassociation, and injury consequences of forced intermingling. Stalled forward progression with different injury states is seen as persistent dynamicity of kinesins transiting between MTs and inter-MT reservoirs. DyNAMO analysis provides novel insights and quantification of axonal injury scenarios, including local injury-affected ATP levels, as well as relates these to influences on signaling outputs, including patterns of gating, waves, and pattern switching. The DyNAMO model significantly expands the network of heuristic and mathematical analysis of neuronal functions relevant to axonopathies, diagnostics, and treatment strategies.

Versatile properties of dynein molecules underlying regulation in flagellar oscillation

Dynein is a minus-end-directed motor that generates oscillatory motion in eukaryotic flagella. Cyclic beating, which is the most significant feature of a flagellum, occurs by sliding spatiotemporal regulation by dynein along microtubules. To elucidate oscillation generated by dynein in flagellar beating, we examined its mechanochemical properties under three different axonemal dissection stages. By starting from the intact 9 + 2 structure, we reduced the number of interacting doublets and determined three parameters, namely, the duty ratio, dwell time and step size, of the generated oscillatory forces at each stage. Intact dynein molecules in the axoneme, doublet bundle and single doublet were used to measure the force with optical tweezers. The mean forces per dynein determined under three axonemal conditions were smaller than the previously reported stall forces of axonemal dynein; this phenomenon suggests that the duty ratio is lower than previously thought. This possibility was further confirmed by an in vitro motility assay with purified dynein. The dwell time and step size estimated from the measured force were similar. The similarity in these parameters suggests that the essential properties of dynein oscillation are inherent to the molecule and independent of the axonemal architecture, composing the functional basis of flagellar beating.

MINFLUX dissects the unimpeded walking of kinesin-1

We introduce an interferometric MINFLUX microscope that records protein movements with up to 1.7 nanometer per millisecond spatiotemporal precision. Such precision has previously required attaching disproportionately large beads to the protein, but MINFLUX requires the detection of only about 20 photons from an approximately 1-nanometer-sized fluorophore. Therefore, we were able to study the stepping of the motor protein kinesin-1 on microtubules at up to physiological adenosine-5'-triphosphate (ATP) concentrations. We uncovered rotations of the stalk and the heads of load-free kinesin during stepping and showed that ATP is taken up with a single head bound to the microtubule and that ATP hydrolysis occurs when both heads are bound. Our results show that MINFLUX quantifies (sub)millisecond conformational changes of proteins with minimal disturbance.

Direct Measurement of Kinetic Force Generated by Mycoplasma

Optical tweezers enable us to measure the force generated by bacterial motility and motor proteins. Here, we describe a method, using optical tweezers and related techniques, to measure the force generated during Mycoplasma gliding. An avidin-conjugated polystyrene bead trapped by a focused laser beam is bound to the surface-biotinylated Mycoplasma cell, which pulls the bead from the trap center of the laser. The force generated by Mycoplasma is calculated from a displacement measured and a spring constant of the laser trap.

Force generation of KIF1C is impaired by pathogenic mutations

Intracellular transport is essential for neuronal function and survival. The most effective plus-end-directed neuronal transporter is the kinesin-3 KIF1C, which transports large secretory vesicles and endosomes.1-4 Mutations in KIF1C cause hereditary spastic paraplegia and cerebellar dysfunction in human patients.5-8 In contrast to other kinesin-3s, KIF1C is a stable dimer and a highly processive motor in its native state.9,10 Here, we establish a baseline for the single-molecule mechanics of Kif1C. We show that full-length KIF1C molecules can processively step against the load of an optical trap and reach average stall forces of 3.7 pN. Compared with kinesin-1, KIF1C has a higher propensity to slip backward under load, which results in a lower maximal single-molecule force. However, KIF1C remains attached to the microtubule while slipping backward and re-engages quickly, consistent with its super processivity. Two pathogenic mutations, P176L and R169W, that cause hereditary spastic paraplegia in humans7,8 maintain fast, processive single-molecule motility in vitro but with decreased run length and slightly increased unloaded velocity compared with the wild-type motor. Under load in an optical trap, force generation by these mutants is severely reduced. In cells, the same mutants are impaired in producing sufficient force to efficiently relocate organelles. Our results show how its mechanics supports KIF1C's role as an intracellular transporter and explain how pathogenic mutations at the microtubule-binding interface of KIF1C impair the cellular function of these long-distance transporters and result in neuronal disease.

Time-correlation functions for odd Langevin systems

We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the anti-symmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the anti-symmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.

Kinesin Motors in the Filamentous Basidiomycetes in Light of the Schizophyllum commune Genome

Kinesins are essential motor molecules of the microtubule cytoskeleton. All eukaryotic organisms have several genes encoding kinesin proteins, which are necessary for various cell biological functions. During the vegetative growth of filamentous basidiomycetes, the apical cells of long leading hyphae have microtubules extending toward the tip. The reciprocal exchange and migration of nuclei between haploid hyphae at mating is also dependent on cytoskeletal structures, including the microtubules and their motor molecules. In dikaryotic hyphae, resulting from a compatible mating, the nuclear location, synchronous nuclear division, and extensive nuclear separation at telophase are microtubule-dependent processes that involve unidentified molecular motors. The genome of Schizophyllum commune is analyzed as an example of a species belonging to the Basidiomycota subclass, Agaricomycetes. In this subclass, the investigation of cell biology is restricted to a few species. Instead, the whole genome sequences of several species are now available. The analyses of the mating type genes and the genes necessary for fruiting body formation or wood degrading enzymes in several genomes of Agaricomycetes have shown that they are controlled by comparable systems. This supports the idea that the genes regulating the cell biological process in a model fungus, such as the genes encoding kinesin motor molecules, are also functional in other filamentous Agaricomycetes.

Autoregulation and dual stepping mode of MYA2, an Arabidopsis myosin XI responsible for cytoplasmic streaming

Arabidopsis thaliana has 13 genes belonging to the myosin XI family. Myosin XI-2 (MYA2) plays a major role in the generation of cytoplasmic streaming in Arabidopsis cells. In this study, we investigated the molecular properties of MYA2 expressed by the baculovirus transfer system. Actin-activated ATPase activity and in vitro motility assays revealed that activity of MYA2 was regulated by the globular tail domain (GTD). When the GTD is not bound to the cargo, the GTD inhibits ADP dissociation from the motor domain. Optical nanometry of single MYA2 molecules, combining total internal reflection fluorescence microscopy (TIRFM) and the fluorescence imaging with one-nanometer accuracy (FIONA) method, revealed that the MYA2 processively moved on actin with three different step sizes: − 28 nm, 29 nm, and 60 nm, at low ATP concentrations. This result indicates that MYA2 uses two different stepping modes; hand-over-hand and inchworm-like. Force measurement using optical trapping showed the stall force of MYA2 was 0.85 pN, which was less than half that of myosin V (2–3 pN). These results indicated that MYA2 has different transport properties from that of the myosin V responsible for vesicle transport in animal cells. Such properties may enable multiple myosin XIs to transport organelles quickly and smoothly, for the generation of cytoplasmic streaming in plant cells.

Microtubule Dumbbells to Assess the Effect of Force Geometry on Single Kinesin Motors

The cytoskeletal motors myosin, kinesin, and dynein and their corresponding tracks, actin and microtubules, are force generating ATPases responsible for motility and morphological changes at the intracellular, cellular, and tissue levels. The pioneering application of optical tweezers to measure the force-producing properties of cytoskeletal motors has provided an unparalleled understanding of their mechanochemistry. The mechanosensitivity of processive, microtubule-based motors has largely been studied in the optical trap using the "single-bead" assay, where a bead-attached motor is held adjacent to a cytoskeletal filament as it processively steps along it. However, because of the geometrical constraints in the conventional single-bead assay, the motor-filament bond is not only loaded parallel to the long axis of the filament, but also perpendicular to the long axis of the filament. This perpendicular force, which is inherent in the conventional single-bead assay, accelerates the motor-filament detachment and has not been carefully considered in prior experiments. An alternative approach is the "three-bead" assay, which was developed for the study of non-processive myosin motors. The vertical force component is minimized in this assay, and the total opposing force is mainly parallel to the microtubule. Experiments with kinesin show that microtubule attachment durations can be highly variable and last for up to tenfold longer times in the three-bead assay, compared to the single-bead assay. Thus, the ability of kinesin to bear mechanical load and remain attached to microtubules depends on the forces in more than one dimension. In this chapter, we provide detailed methods for preparing the proteins, buffers, flow chambers, and bead-filament assemblies for performing the three-bead assay with microtubules and their motors.

Dynamics of kinesin motor proteins under longitudinal and sideways loads

The available single-molecule data showed that different species of N-terminal kinesin molecular motors have very different features on dependences of run length and dissociation rate upon longitudinal load acting on stalks of the motors. The prior single-molecule data for Loligo pealei kinesin-1 indicated that the sideways load has only a weak effect on the velocity, but even a small sideways load can cause a large reduction in the run length. However, these puzzling experimental data remain to be explained and the underlying physical mechanisms are unclear. Here, based on our proposed model we study analytically the dynamics of the N-terminal kinesin motors such as Loligo pealei kinesin-1, Drosophila kinesin-1, truncated kinesin-5/Eg5, truncated kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB dimers under both longitudinal and sideways loads. The theoretical results explain quantitatively the available experimental data and provide predictions. The physical mechanism of different kinesin species showing very different features on the load-dependent dynamics and the physical mechanism of the effect of the sideways load on the dynamics are revealed.

Oscillating external force as a tool to tune motility characteristics of molecular motors

Molecular motors move in a dynamic environment of the cytoskeleton which generates fluctuations exceeding the thermal agitation. Their efficient motility and force generation are generally achieved via complex gating and coupling mechanisms between chemical steps, conformational changes, and mechanical steps in the working cycle. However, the motors display various force-velocity relations seemingly related (also) to the asymmetry of their unbinding from the track depending on the direction of the applied force. Here we study theoretically how the motility of molecular motors changes when they operate under an oscillating external force. We explore the roles of the shape of the force-velocity relation and the asymmetry of the force-induced unbinding. We find that a motor speeds up under force oscillations if its unbinding has a strong load dependence and a moderate asymmetry with respect to the direction of load. Motors whose unbinding is slowed down under hindering forces withstand average loads higher than the usual stall force. The relation between the function, unbinding properties, and predicted responses to the oscillating force supports the idea that the asymmetry of the load induced unbinding could serve as an adaptation of motors to their different physiological functions.

Force and Stepwise Movements of Gliding Motility in Human Pathogenic Bacterium Mycoplasma pneumoniae

Mycoplasma pneumoniae, a human pathogenic bacterium, binds to sialylated oligosaccharides and glides on host cell surfaces via a unique mechanism. Gliding motility is essential for initiating the infectious process. In the present study, we measured the stall force of an M. pneumoniae cell carrying a bead that was manipulated using optical tweezers on two strains. The stall forces of M129 and FH strains were averaged to be 23.7 and 19.7 pN, respectively, much weaker than those of other bacterial surface motilities. The binding activity and gliding speed of the M129 strain on sialylated oligosaccharides were eight and two times higher than those of the FH strain, respectively, showing that binding activity is not linked to gliding force. Gliding speed decreased when cell binding was reduced by addition of free sialylated oligosaccharides, indicating the existence of a drag force during gliding. We detected stepwise movements, likely caused by a single leg under 0.2-0.3 mM free sialylated oligosaccharides. A step size of 14-19 nm showed that 25-35 propulsion steps per second are required to achieve the usual gliding speed. The step size was reduced to less than half with the load applied using optical tweezers, showing that a 2.5 pN force from a cell is exerted on a leg. The work performed in this step was 16-30% of the free energy of the hydrolysis of ATP molecules, suggesting that this step is linked to the elementary process of M. pneumoniae gliding. We discuss a model to explain the gliding mechanism, based on the information currently available.

Optical tweezers in single-molecule biophysics

Optical tweezers have become the method of choice in single-molecule manipulation studies. In this Primer, we first review the physical principles of optical tweezers and the characteristics that make them a powerful tool to investigate single molecules. We then introduce the modifications of the method to extend the measurement of forces and displacements to torques and angles, and to develop optical tweezers with single-molecule fluorescence detection capabilities. We discuss force and torque calibration of these instruments, their various modes of operation and most common experimental geometries. We describe the type of data obtained in each experimental design and their analyses. This description is followed by a survey of applications of these methods to the studies of protein-nucleic acid interactions, protein/RNA folding and molecular motors. We also discuss data reproducibility, the factors that lead to the data variability among different laboratories and the need to develop field standards. We cover the current limitations of the methods and possible ways to optimize instrument operation, data extraction and analysis, before suggesting likely areas of future growth.

Effective behavior of cooperative and nonidentical molecular motors

Analytical formulas for effective drift, diffusivity, run times, and run lengths are derived for an intracellular transport system consisting of a cargo attached to two cooperative but not identical molecular motors (for example, kinesin-1 and kinesin-2) which can each attach and detach from a microtubule. The dynamics of the motor and cargo in each phase are governed by stochastic differential equations, and the switching rates depend on the spatial configuration of the motor and cargo. This system is analyzed in a limit where the detached motors have faster dynamics than the cargo, which in turn has faster dynamics than the attached motors. The attachment and detachment rates are also taken to be slow relative to the spatial dynamics. Through an application of iterated stochastic averaging to this system, and the use of renewal-reward theory to stitch together the progress within each switching phase, we obtain explicit analytical expressions for the effective drift, diffusivity, and processivity of the motor-cargo system. Our approach accounts in particular for jumps in motor-cargo position that occur during attachment and detachment events, as the cargo tracking variable makes a rapid adjustment due to the averaged fast scales. The asymptotic formulas are in generally good agreement with direct stochastic simulations of the detailed model based on experimental parameters for various pairings of kinesin-1 and kinesin-2 under assisting, hindering, or no load.

Modelling cytoskeletal transport by clusters of non-processive molecular motors with limited binding sites

Molecular motors are responsible for intracellular transport of a variety of biological cargo. We consider the collective behaviour of a finite number of motors attached on a cargo. We extend previous analytical work on processive motors to the case of non-processive motors, which stochastically bind on and off cytoskeletal filaments with a limited number of binding sites available. Physically, motors attached to a cargo cannot bind anywhere along the filaments, so the number of accessible binding sites on the filament should be limited. Thus, we analytically study the distribution and the velocity of a cluster of non-processive motors with limited number of binding sites. To validate our analytical results and to go beyond the level of detail possible analytically, we perform Monte Carlo latticed based stochastic simulations. In particular, in our simulations, we include sequence preservation of motors performing stepping and binding obeying a simple exclusion process. We find that limiting the number of binding sites reduces the probability of non-processive motors binding but has a relatively small effect on force-velocity relations. Our analytical and stochastic simulation results compare well to published data from in vitro and in vivo experiments.

Force production of human cytoplasmic dynein is limited by its processivity

Cytoplasmic dynein is a highly complex motor protein that generates forces toward the minus end of microtubules. Using optical tweezers, we demonstrate that the low processivity (ability to take multiple steps before dissociating) of human dynein limits its force generation due to premature microtubule dissociation. Using a high trap stiffness whereby the motor achieves greater force per step, we reveal that the motor's true maximal force ("stall force") is ~2 pN. Furthermore, an average force versus trap stiffness plot yields a hyperbolic curve that plateaus at the stall force. We derive an analytical equation that accurately describes this curve, predicting both stall force and zero-load processivity. This theoretical model describes the behavior of a kinesin motor under low-processivity conditions. Our work clarifies the true stall force and processivity of human dynein and provides a new paradigm for understanding and analyzing molecular motor force generation for weakly processive motors.

Theoretical Analysis of Dynamics of Kinesin Molecular Motors

Kinesin is a typical molecular motor that can step processively on microtubules powered by hydrolysis of adenosine triphosphate (ATP) molecules, playing a critical role in intracellular transports. Its dynamical properties such as its velocity, stepping ratio, run length, dissociation rate, etc. as well as the load dependencies of these quantities have been well documented through single-molecule experimental methods. In particular, the run length shows a dramatic asymmetry with respect to the direction of the load, and the dissociation rate exhibits a slip-catch-slip bond behavior under the backward load. Here, an analytic theory was provided for the dynamics of kinesin motors under both forward and backward loads, explaining consistently and quantitatively the diverse available experimental results.

Non-tight and tight chemomechanical couplings of biomolecular motors under hindering loads

Biomolecular motors make use of free energy released from chemical reaction (typically ATP hydrolysis) to perform mechanical motion or work. An important issue is whether a molecular motor exhibits tight or non-tight chemomechanical (CM) coupling. The tight CM coupling refers to that each ATPase activity is coupled with a mechanical step, while the non-tight CM coupling refers to that an ATPase activity is not necessarily coupled with a mechanical step. Here, we take kinesin, monomeric DNA helicase, ring-shaped hexameric DNA helicase and ribosome as examples to study this issue. Our studies indicate that some motors such as kinesin, monomeric helicase and ribosome exhibit non-tight CM coupling under hindering forces, while others such as the ring-shaped hexameric helicase exhibit tight or nearly tight CM coupling under any force. For the former, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the CM coupling efficiency, while the ATPase rate is independent or nearly independent of the force. For the latter, the reduction of the velocity caused by the hindering force arises mainly from the reduction of the ATPase rate, while the CM coupling efficiency is independent or nearly independent of the force.

Modulation of Kinesin's Load-Bearing Capacity by Force Geometry and the Microtubule Track

Kinesin motors and their associated microtubule tracks are essential for long-distance transport of cellular cargos. Intracellular activity and proper recruitment of kinesins is regulated by biochemical signaling, cargo adaptors, microtubule-associated proteins, and mechanical forces. In this study, we found that the effect of opposing forces on the kinesin-microtubule attachment duration depends strongly on experimental assay geometry. Using optical tweezers and the conventional single-bead assay, we show that detachment of kinesin from the microtubule is likely accelerated by forces vertical to the long axis of the microtubule due to contact of the single bead with the underlying microtubule. We used the three-bead assay to minimize the vertical force component and found that when the opposing forces are mainly parallel to the microtubule, the median value of attachment durations between kinesin and microtubules can be up to 10-fold longer than observed using the single-bead assay. Using the three-bead assay, we also found that not all microtubule protofilaments are equivalent interacting substrates for kinesin and that the median value of attachment durations of kinesin varies by more than 10-fold, depending on the relative angular position of the forces along the circumference of the microtubule. Thus, depending on the geometry of forces across the microtubule, kinesin can switch from a fast detaching motor (median attachment duration <0.2 s) to a persistent motor that sustains attachment (median attachment duration >3 s) at high forces (5 pN). Our data show that the load-bearing capacity of the kinesin motor is highly variable and can be dramatically affected by off-axis forces and forces across the microtubule lattice, which has implications for a range of cellular activities, including cell division and organelle transport.

A Generalized Kinetic Model for Coupling between Stepping and ATP Hydrolysis of Kinesin Molecular Motors

A general kinetic model is presented for the chemomechanical coupling of dimeric kinesin molecular motors with and without extension of their neck linkers (NLs). A peculiar feature of the model is that the rate constants of ATPase activity of a kinesin head are independent of the strain on its NL, implying that the heads of the wild-type kinesin dimer and the mutant with extension of its NLs have the same force-independent rate constants of the ATPase activity. Based on the model, an analytical theory is presented on the force dependence of the dynamics of kinesin dimers with and without extension of their NLs at saturating ATP. With only a few adjustable parameters, diverse available single molecule data on the dynamics of various kinesin dimers, such as wild-type kinesin-1, kinesin-1 with mutated residues in the NLs, kinesin-1 with extension of the NLs and wild-type kinesin-2, under varying force and ATP concentration, can be reproduced very well. Additionally, we compare the power production among different kinesin dimers, showing that the mutation in the NLs reduces the power production and the extension of the NLs further reduces the power production.

Behaviors and Energy Source of Mycoplasma gallisepticum Gliding

Mycoplasma gallisepticum, an avian-pathogenic bacterium, glides on host tissue surfaces by using a common motility system with Mycoplasma pneumoniae In the present study, we observed and analyzed the gliding behaviors of M. gallisepticum in detail by using optical microscopes. M. gallisepticum glided at a speed of 0.27 ± 0.09 μm/s with directional changes relative to the cell axis of 0.6 degree ± 44.6 degrees/5 s without the rolling of the cell body. To examine the effects of viscosity on gliding, we analyzed the gliding behaviors under viscous environments. The gliding speed was constant in various concentrations of methylcellulose but was affected by Ficoll. To investigate the relationship between binding and gliding, we analyzed the inhibitory effects of sialyllactose on binding and gliding. The binding and gliding speed sigmoidally decreased with sialyllactose concentration, indicating the cooperative binding of the cell. To determine the direct energy source of gliding, we used a membrane-permeabilized ghost model. We permeabilized M. gallisepticum cells with Triton X-100 or Triton X-100 containing ATP and analyzed the gliding of permeabilized cells. The cells permeabilized with Triton X-100 did not show gliding; in contrast, the cells permeabilized with Triton X-100 containing ATP showed gliding at a speed of 0.014 ± 0.007 μm/s. These results indicate that the direct energy source for the gliding motility of M. gallisepticum is ATP.IMPORTANCE Mycoplasmas, the smallest bacteria, are parasitic and occasionally commensal. Mycoplasma gallisepticum is related to human-pathogenic mycoplasmas-Mycoplasma pneumoniae and Mycoplasma genitalium-which cause so-called "walking pneumonia" and nongonococcal urethritis, respectively. These mycoplasmas trap sialylated oligosaccharides, which are common targets among influenza viruses, on host trachea or urinary tract surfaces and glide to enlarge the infected areas. Interestingly, this gliding motility is not related to other bacterial motilities or eukaryotic motilities. Here, we quantitatively analyze cell behaviors in gliding and clarify the direct energy source. The results provide clues for elucidating this unique motility mechanism.

Kinesin and Dynein Mechanics: Measurement Methods and Research Applications

Motor proteins play critical roles in the normal function of cells and proper development of organisms. Among motor proteins, failings in the normal function of two types of proteins, kinesin and dynein, have been shown to lead many pathologies, including neurodegenerative diseases and cancers. As such, it is critical to researchers to understand the underlying mechanics and behaviors of these proteins, not only to shed light on how failures may lead to disease, but also to guide research toward novel treatment and nano-engineering solutions. To this end, many experimental techniques have been developed to measure the force and motility capabilities of these proteins. This review will (a) discuss such techniques, specifically microscopy, atomic force microscopy (AFM), optical trapping, and magnetic tweezers, and (b) the resulting nanomechanical properties of motor protein functions such as stalling force, velocity, and dependence on adenosine triphosophate (ATP) concentrations will be comparatively discussed. Additionally, this review will highlight the clinical importance of these proteins. Furthermore, as the understanding of the structure and function of motor proteins improves, novel applications are emerging in the field. Specifically, researchers have begun to modify the structure of existing proteins, thereby engineering novel elements to alter and improve native motor protein function, or even allow the motor proteins to perform entirely new tasks as parts of nanomachines. Kinesin and dynein are vital elements for the proper function of cells. While many exciting experiments have shed light on their function, mechanics, and applications, additional research is needed to completely understand their behavior.

Collective dynamics of microtubule-based 3D active fluids from single microtubules

Self-organization of kinesin-driven, microtubule-based 3D active fluids relies on the collective dynamics of single microtubules. However, the connection between macroscopic fluid flows and microscopic motion of microtubules remains unclear. In this work, the motion of single microtubules was characterized by means of 2D gliding assays and compared with the flows of 3D active fluids. While the scales of the two systems differ by ∼1000×, both were driven by processive, non-processive or an equal mixture of both molecular motor proteins. To search for the dynamic correlation between both systems, the motor activities were tuned by varying temperature and ATP concentration, and the changes in both systems were compared. Motor processivity played an important role in active fluid flows but only when the fluids were nearly motionless; otherwise, flows were dominated by hydrodynamic resistance controlled by sample size. Furthermore, while the motors' thermal reaction led active fluids to flow faster with increasing temperature, such temperature dependence could be reversed by introducing temperature-varying depletants, emphasizing the potential role of the depletant in designing an active fluid's temperature response. The temperature response of active fluids was nearly immediate (⪅10 s). Such a characteristic enables active fluids to be controlled with a temperature switch. Overall, this work not only clarifies the role of temperature in active fluid activity, but also sheds light on the underlying principles of the relationship between the collective dynamics of active fluids and the dynamics of their constituent single microtubules.

Motor torque measurement of Halobacterium salinarum archaellar suggests a general model for ATP-driven rotary motors

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.

The Orphan Kinesin PAKRP2 Achieves Processive Motility via a Noncanonical Stepping Mechanism

Phragmoplast-associated kinesin-related protein 2 (PAKRP2) is an orphan kinesin in Arabidopsis thaliana that is thought to transport vesicles along phragmoplast microtubules for cell plate formation. Here, using single-molecule fluorescence microscopy, we show that PAKRP2 is the first orphan kinesin to exhibit processive plus-end-directed motility on single microtubules as individual homodimers. Our results show that PAKRP2 processivity is achieved despite having an exceptionally long (32 residues) neck linker. Furthermore, using high-resolution nanoparticle tracking, we find that PAKRP2 steps via a hand-over-hand mechanism that includes frequent side steps, a prolonged diffusional search of the tethered head, and tight coupling of the ATP hydrolysis cycle to the forward-stepping cycle. Interestingly, truncating the PAKRP2 neck linker to 14 residues decreases the run length of PAKRP2; thus, the long neck linker enhances the processive behavior. Based on the canonical model of kinesin stepping, such a long neck linker is expected to decrease the processivity and disrupt the coupling of ATP hydrolysis to forward stepping. Therefore, we conclude that PAKRP2 employs a noncanonical strategy for processive motility, wherein a long neck linker is coupled with a slow ATP hydrolysis rate to allow for an extended diffusional search during each step without sacrificing processivity or efficiency.

Metabolon formation by chemotaxis

Enzymes that participate in reaction cascades have been shown to assemble into metabolons, in the presence of the first enzyme's substrate. However, the mechanism of metabolon formation is still an open question. We applied microfluidic and fluorescent spectroscopy techniques to study the coordinated movement of the first four enzymes of the glycolysis cycle: hexokinase, phosphoglucose isomerase, phosphofructokinase, and aldolase and showed that each enzyme independently follows its own specific substrate gradient, which is produced by the preceding enzymatic reaction. The extent of enzyme migration is proportional to the time the enzyme is exposed to the substrate gradient. Significantly, the chemotactic migration of enzymes is fairly rapid even under conditions that mimic cytosolic crowding. The observed rate was very similar to the reported rate of enzyme diffusion in living cells. Thus, chemotaxis may be a basis for the organization of metabolic networks in the cytosol of the cell.

ATP-Concentration- and Force-Dependent Chemomechanical Coupling of Kinesin Molecular Motors

A model is presented for the chemomechanical coupling of kinesin motors, which proposes that the rate constants of the chemical reaction are independent of the external force. On the basis of the model, we study theoretically the movement dynamics of the motors under varying external force and ATP concentration, such as the forward to backward stepping ratio, velocity, dwell time between two mechanical steps, stall force, and so on. The theoretical results reproduce quantitatively the diverse and even contradictory available single-molecule experimental data for different species of the motors. Furthermore, we study the dependence of the chemomechanical coupling ratio on ATP concentration and external force, with both ATP concentration and external force having large effects on the chemomechanical coupling.

Nonequilibrium Energetics of Molecular Motor Kinesin

Nonequilibrium energetics of single molecule translational motor kinesin was investigated by measuring heat dissipation from the violation of the fluctuation-response relation of a probe attached to the motor using optical tweezers. The sum of the dissipation and work did not amount to the input free energy change, indicating large hidden dissipation exists. Possible sources of the hidden dissipation were explored by analyzing the Langevin dynamics of the probe, which incorporates the two-state Markov stepper as a kinesin model. We conclude that internal dissipation is dominant.

A non-tight chemomechanical coupling model for force-dependence of movement dynamics of molecular motors

Based on the available experimental evidence, we present a simple and general model to describe the movement dynamics of molecular motors that can move processively on their linear tracks by using the chemical energy derived from ATP hydrolysis. An important aspect of the model is the non-tight coupling between the ATP hydrolysis and mechanical stepping, in contrast to the prevailing models presented in the literature that assume the tight chemomechanical coupling. With kinesin as an example, based on the current model, we study in detail its movement dynamics under a backward load, reproducing well the diverse available single-molecule experimental data such as the forward to backward step ratio, velocity, dwell time, randomness, run length, etc., versus the load. Moreover, predicted results are provided on the force-dependence of the mean number of ATP molecules consumed per mechanical step. Additionally, the theoretical data for the dynamics of myosin-V obtained based on the model are also in good agreement with the available experimental data.

Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol

Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms.

A Unified Walking Model for Dimeric Motor Proteins

Dimeric motor proteins, kinesin-1, cytoplasmic dynein-1, and myosin-V, move stepwise along microtubules and actin filaments with a regular step size. The motors take backward as well as forward steps. The step ratio r and dwell time τ, which are the ratio of the number of backward steps to the number of forward steps and the time between consecutive steps, respectively, were observed to change with the load. To understand the movement of motor proteins, we constructed a unified and simple mathematical model to explain the load dependencies of r and of τ measured for the above three types of motors quantitatively. Our model consists of three states, and the forward and backward steps are represented by the cycles of transitions visiting different pairs of states among the three, implying that a backward step is not the reversal of a forward step. Each of r and τ is given by a simple expression containing two exponential functions. The experimental data for r and τ for dynein available in the literature are not sufficient for a quantitative analysis, which is in contrast to those for kinesin and myosin-V. We reanalyze the data to obtain r and τ of native dynein to make up the insufficient data to fit them to the model. Our model successfully describes the behavior of r and τ for all of the motors in a wide range of loads from large assisting loads to superstall loads.

Powering Motion with Enzymes

Enzymes are ubiquitous in living systems. Apart from traditional motor proteins, the function of enzymes was assumed to be confined to the promotion of biochemical reactions. Recent work shows that free swimming enzymes, when catalyzing reactions, generate enough mechanical force to cause their own movement, typically observed as substrate-concentration-dependent enhanced diffusion. Preliminary indication is that the impulsive force generated per turnover is comparable to the force produced by motor proteins and is within the range to activate biological adhesion molecules responsible for mechanosensation by cells, making force generation by enzymatic catalysis a novel mechanobiology-relevant event. Furthermore, when exposed to a gradient in substrate concentration, enzymes move up the gradient: an example of chemotaxis at the molecular level. The driving force for molecular chemotaxis appears to be the lowering of chemical potential due to thermodynamically favorable enzyme-substrate interactions and we suggest that chemotaxis promotes enzymatic catalysis by directing the motion of the catalyst and substrates toward each other. Enzymes that are part of a reaction cascade have been shown to assemble through sequential chemotaxis; each enzyme follows its own specific substrate gradient, which in turn is produced by the preceding enzymatic reaction. Thus, sequential chemotaxis in catalytic cascades allows time-dependent, self-assembly of specific catalyst particles. This is an example of how information can arise from chemical gradients, and it is tempting to suggest that similar mechanisms underlie the organization of living systems. On a practical level, chemotaxis can be used to separate out active catalysts from their less active or inactive counterparts in the presence of their respective substrates and should, therefore, find wide applicability. When attached to bigger particles, enzyme ensembles act as "engines", imparting motility to the particles and moving them directionally in a substrate gradient. The impulsive force generated by enzyme catalysis can also be transmitted to the surrounding fluid and molecular and colloidal tracers, resulting in convective fluid pumping and enhanced tracer diffusion. Enzyme-powered pumps that transport fluid directionally can be fabricated by anchoring enzymes onto a solid support and supplying the substrate. Thus, enzyme pumps constitute a novel platform that combines sensing and microfluidic pumping into a single self-powered microdevice. Taken in its entirety, force generation by active enzymes has potential applications ranging from nanomachinery, nanoscale assembly, cargo transport, drug delivery, micro- and nanofluidics, and chemical/biochemical sensing. We also hypothesize that, in vivo, enzymes may be responsible for the stochastic motion of the cytoplasm, the organization of metabolons and signaling complexes, and the convective transport of fluid in cells. A detailed understanding of how enzymes convert chemical energy to directional mechanical force can lead us to the basic principles of fabrication, development, and monitoring of biological and biomimetic molecular machines.

Processivity of dimeric kinesin-1 molecular motors

Kinesin‐1 is a homodimeric motor protein that can move along microtubule filaments by hydrolyzing ATP with a high processivity. How the two motor domains are coordinated to achieve such high processivity is not clear. To address this issue, we computationally studied the run length of the dimer with our proposed model. The computational data quantitatively reproduced the puzzling experimental data, including the dramatically asymmetric character of the run length with respect to the direction of external load acting on the coiled‐coil stalk, the enhancement of the run length by addition of phosphate, and the contrary features of the run length for different types of kinesin‐1 with extensions of their neck linkers compared with those without extension of the neck linker. The computational data on other aspects of the movement dynamics such as velocity and durations of one‐head‐bound and two‐head‐bound states in a mechanochemical coupling cycle were also in quantitative agreement with the available experimental data. Moreover, predicted results are provided on dependence of the run length upon external load acting on one head of the dimer, which can be easily tested in the future using single‐molecule optical trapping assays.

Assessing the Impact of Electrostatic Drag on Processive Molecular Motor Transport

The bidirectional movement of intracellular cargo is usually described as a tug-of-war among opposite-directed families of molecular motors. While tug-of-war models have enjoyed some success, recent evidence suggests underlying motor interactions are more complex than previously understood. For example, these tug-of-war models fail to predict the counterintuitive phenomenon that inhibiting one family of motors can decrease the functionality of opposite-directed transport. In this paper, we use a stochastic differential equations modeling framework to explore one proposed physical mechanism, called microtubule tethering, that could play a role in this "co-dependence" among antagonistic motors. This hypothesis includes the possibility of a trade-off: weakly bound trailing molecular motors can serve as tethers for cargoes and processing motors, thereby enhancing motor-cargo run lengths along microtubules; however, this introduces a cost of processing at a lower mean velocity. By computing the small- and large-time mean-squared displacement of our theoretical model and comparing our results to experimental observations of dynein and its "helper protein" dynactin, we find some supporting evidence for microtubule tethering interactions. We extrapolate these findings to predict how dynein-dynactin might interact with the opposite-directed kinesin motors and introduce a criterion for when the trade-off is beneficial in simple systems.

Detailed Analyses of Stall Force Generation in Mycoplasma mobile Gliding

Mycoplasma mobile is a bacterium that uses a unique mechanism to glide on solid surfaces at a velocity of up to 4.5 μm/s. Its gliding machinery comprises hundreds of units that generate the force for gliding based on the energy derived from ATP; the units catch and pull sialylated oligosaccharides fixed to solid surfaces. In this study, we measured the stall force of wild-type and mutant strains of M. mobile carrying a bead manipulated using optical tweezers. The strains that had been enhanced for binding exhibited weaker stall forces than the wild-type strain, indicating that stall force is related to force generation rather than to binding. The stall force of the wild-type strain decreased linearly from 113 to 19 picoNewtons after the addition of 0-0.5 mM free sialyllactose (a sialylated oligosaccharide), with a decrease in the number of working units. After the addition of 0.5 mM sialyllactose, the cells carrying a bead loaded using optical tweezers exhibited stepwise movements with force increments. The force increments ranged from 1 to 2 picoNewtons. Considering the 70-nm step size, this small-unit force may be explained by the large gear ratio involved in the M. mobile gliding machinery.

Self-organization and stability of magnetosome chains-A simulation study

Magnetotactic bacteria orient in magnetic fields with the help of their magnetosome chain, a linear structure of membrane enclosed magnetic nanoparticles (magnetosomes) anchored to a cytoskeletal filament. Here, we use simulations to study the assembly and the stability of magnetosome chains. We introduce a computational model describing the attachment of the magnetosomes to the filament and their magnetic interactions. We show that the filamentous backbone is crucial for the robust assembly of the magnetic particles into a linear chain, which in turn is key for the functionality of the chain in cellular orientation and magnetically directed swimming. In addition, we simulate the response to an external magnetic field that is rotated away from the axis of the filament, an experimental method used to probe the mechanical stability of the chain. The competition between alignment along the filament and alignment with the external fields leads to the rupture of a chain if the applied field exceeeds a threshold value. These observations are in agreement with previous experiments at the population level. Beyond that, our simulations provide a detailed picture of chain rupture at the single cell level, which is found to happen through two abrupt events, which both depend on the field strength and orientation. The re-formation of the chain structure after such rupture is found to be strongly sped up in the presence of a magnetic field parallel to the filament, an observation that may also be of interest for the design of self-healing materials. Our simulations underline the dynamic nature of the magnetosome chain. More generally, they show the rich complexity of self-assembly in systems with competing driving forces for alignment.

Impact of a mechanical shear stress on intracellular trafficking

Intracellular trafficking mainly takes place along the microtubules, and its efficiency depends on the local architecture and organization of the cytoskeletal network. In this work, the cytoplasm of stem cells is subjected to mechanical vortexing at a frequency of up to 1 Hz, by using magnetic chains of endosomes embedded in the cell body, in order to locally perturb the network structure. The consequences are evaluated on the directionality and processivity of the spontaneous motion of endosomes. When the same chains are used both to shear the cell medium and to probe the intracellular traffic, a substantial decrease in transport efficiency is detected after applying the mechanical shear. Interestingly, when using different objects to apply the shear and to probe the spontaneous motion, no alteration of the transport efficiency can be detected. We conclude that shaking the vesicles mainly causes their unbinding from the cytoskeletal tracks, but has little influence on the integrity of the network itself. This is corroborated by active microrheology measurements, performed with chains actuated by a magnetic field, and showing that the mechanical compliance of the cytoplasm is similar before and after slow vortexing.

Dynamics of dimeric kinesins: Limping, effect of longitudinal force, effects of neck linker extension and mutation, and comparison between kinesin-1 and kinesin-2

Conventional kinesin (kinesin-1) can walk on microtubule filaments in an asymmetric hand-over-hand manner, exhibiting a marked alternation in the mean dwell time in successive steps. Here, we study computationally the asymmetric stepping dynamics of the kinesin-1 homodimer, revealing its origin and providing quantitative explanations of the available experimental data. The alternation in the mean dwell time in successive steps arises from the alternation in the mechanochemical coupling ratio, which is in turn caused by the alternation in the slight variation of the stretched neck linker length. Both the vertical and backward longitudinal forces can enhance the asymmetric ratio. Additionally, other aspects of the stepping dynamics of the dimer such as the velocity versus longitudinal force, extended neck linker, etc., are also studied. In particular, the conflicting experimental data, with some showing that the velocity does not change with the forward longitudinal load while others showing that the velocity increases largely with the forward longitudinal load, are explained quantitatively and consistently. The intriguing experimental data showing that cysteine-light Drosophila and human kinesin-1 mutants have different load-dependent velocity from the wild-type cases as well as that kinesin-2 dimers have different load-dependent velocity from the kinesin-1 are also explained consistently and quantitatively.

Manipulation of cells with laser microbeam scissors and optical tweezers: a review

The use of laser microbeams and optical tweezers in a wide field of biological applications from genomic to immunology is discussed. Microperforation is used to introduce a well-defined amount of molecules into cells for genetic engineering and optical imaging. The microwelding of two cells induced by a laser microbeam combines their genetic outfit. Microdissection allows specific regions of genomes to be isolated from a whole set of chromosomes. Handling the cells with optical tweezers supports investigation on the attack of immune systems against diseased or cancerous cells. With the help of laser microbeams, heart infarction can be simulated, and optical tweezers support studies on the heartbeat. Finally, laser microbeams are used to induce DNA damage in living cells for studies on cancer and ageing.

Optical trapping for biosensing: materials and applications

Optical trapping has been evidence as a very powerful tool for the manipulation and study of biological entities. This review explains the main concepts regarding the use of optical trapping for biosensing, focusing its attention to those applications involving the manipulation of particles which are used as handles, force transducers and sensors.

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

Flagella are hair-like projections from the surface of eukaryotic cells, and they play an important role in many cellular functions, such as cell-motility. The beating of flagella is enabled by their internal architecture, the axoneme, and is powered by a dense distribution of motor proteins, dyneins. The dyneins deliver the required mechanical work through the hydrolysis of ATP. Although the dynein-ATP cycle, the axoneme microstructure, and the flagellar-beating kinematics are well studied, their integration into a coherent picture of ATP-powered flagellar beating is still lacking. Here we show that a time-delayed negative-work-based switching mechanism is able to convert the individual sliding action of hundreds of dyneins into a regular overall beating pattern leading to propulsion. We developed a computational model based on a minimal representation of the axoneme consisting of two representative doublet microtubules connected by nexin links. The relative sliding of the microtubules is incorporated by modeling two groups of ATP-powered dyneins, each responsible for sliding in opposite directions. A time-delayed switching mechanism is postulated, which is key in converting the local individual sliding action of multiple dyneins into global beating. Our results demonstrate that an overall nonreciprocal beating pattern can emerge with time due to the spatial and temporal coordination of the individual dyneins. These findings provide insights in the fundamental working mechanism of axonemal dyneins and could possibly open new research directions in the field of flagellar motility.

Discrete Step Sizes of Molecular Motors Lead to Bimodal Non-Gaussian Velocity Distributions under Force

Fluctuations in the physical properties of biological machines are inextricably linked to their functions. Distributions of run lengths and velocities of processive molecular motors, like kinesin-1, are accessible through single-molecule techniques, but rigorous theoretical models for these probabilities are lacking. Here, we derive exact analytic results for a kinetic model to predict the resistive force (F)-dependent velocity [P(v)] and run length [P(n)] distribution functions of generic finitely processive molecular motors. Our theory quantitatively explains the zero force kinesin-1 data for both P(n) and P(v) using the detachment rate as the only parameter. In addition, we predict the F dependence of these quantities. At nonzero F, P(v) is non-Gaussian and is bimodal with peaks at positive and negative values of v, which is due to the discrete step size of kinesin-1. Although the predictions are based on analyses of kinesin-1 data, our results are general and should hold for any processive motor, which walks on a track by taking discrete steps.

Force per cross-sectional area from molecules to muscles: a general property of biological motors

We propose to formally extend the notion of specific tension, i.e. force per cross-sectional area-classically used for muscles, to quantify forces in molecular motors exerting various biological functions. In doing so, we review and compare the maximum tensions exerted by about 265 biological motors operated by about 150 species of different taxonomic groups. The motors considered range from single molecules and motile appendages of microorganisms to whole muscles of large animals. We show that specific tensions exerted by molecular and non-molecular motors follow similar statistical distributions, with in particular, similar medians and (logarithmic) means. Over the 10(19) mass (M) range of the cell or body from which the motors are extracted, their specific tensions vary as M(α) with α not significantly different from zero. The typical specific tension found in most motors is about 200 kPa, which generalizes to individual molecular motors and microorganisms a classical property of macroscopic muscles. We propose a basic order-of-magnitude interpretation of this result.

Small Crowders Slow Down Kinesin-1 Stepping by Hindering Motor Domain Diffusion

The dimeric motor protein kinesin-1 moves processively along microtubules against forces of up to 7 pN. However, the mechanism of force generation is still debated. Here, we point to the crucial importance of diffusion of the tethered motor domain for the stepping of kinesin-1: small crowders stop the motor at a viscosity of 5 mPa·s-corresponding to a hydrodynamic load in the sub-fN (~10^{-4} pN) range-whereas large crowders have no impact even at viscosities above 100 mPa·s. This indicates that the scale-dependent, effective viscosity experienced by the tethered motor domain is a key factor determining kinesin's functionality. Our results emphasize the role of diffusion in the kinesin-1 stepping mechanism and the general importance of the viscosity scaling paradigm in nanomechanics.

Modeling magnetosensitive ion channels in the viscoelastic environment of living cells

We propose and study a model of hypothetical magnetosensitive ionic channels which are long thought to be a possible candidate to explain the influence of weak magnetic fields on living organisms ranging from magnetotactic bacteria to fishes, birds, rats, bats, and other mammals including humans. The core of the model is provided by a short chain of magnetosomes serving as a sensor, which is coupled by elastic linkers to the gating elements of ion channels forming a small cluster in the cell membrane. The magnetic sensor is fixed by one end on cytoskeleton elements attached to the membrane and is exposed to viscoelastic cytosol. Its free end can reorient stochastically and subdiffusively in viscoelastic cytosol responding to external magnetic field changes and can open the gates of coupled ion channels. The sensor dynamics is generally bistable due to bistability of the gates which can be in two states with probabilities which depend on the sensor orientation. For realistic parameters, it is shown that this model channel can operate in the magnetic field of Earth for a small number (five to seven) of single-domain magnetosomes constituting the sensor rod, each of which has a typical size found in magnetotactic bacteria and other organisms or even just one sufficiently large nanoparticle of a characteristic size also found in nature. It is shown that, due to the viscoelasticity of the medium, the bistable gating dynamics generally exhibits power law and stretched exponential distributions of the residence times of the channels in their open and closed states. This provides a generic physical mechanism for the explanation of the origin of such anomalous kinetics for other ionic channels whose sensors move in a viscoelastic environment provided by either cytosol or biological membrane, in a quite general context, beyond the fascinating hypothesis of magnetosensitive ionic channels we explore.

Force is a signal that cells cannot ignore

Cells sense biochemical, electrical, and mechanical cues in their environment that affect their differentiation and behavior. Unlike biochemical and electrical signals, mechanical signals can propagate without the diffusion of proteins or ions; instead, forces are transmitted through mechanically stiff structures, flowing, for example, through cytoskeletal elements such as microtubules or filamentous actin. The molecular details underlying how cells respond to force are only beginning to be understood. Here we review tools for probing force-sensitive proteins and highlight several examples in which forces are transmitted, routed, and sensed by proteins in cells. We suggest that local unfolding and tension-dependent removal of autoinhibitory domains are common features in force-sensitive proteins and that force-sensitive proteins may be commonplace wherever forces are transmitted between and within cells. Because mechanical forces are inherent in the cellular environment, force is a signal that cells must take advantage of to maintain homeostasis and carry out their functions.

Increased localization precision by interference fringe analysis

We report a novel optical single-emitter-localization methodology that uses the phase induced by path length differences in a Mach-Zehnder interferometer to improve localization precision. Using information theory, we demonstrate that the localization capability of a modified Fourier domain signal generated by photon interference enables a more precise localization compared to a standard Gaussian intensity distribution of the corresponding point-spread function. The calculations were verified by numerical simulations and an exemplary experiment, where the centers of metal nanoparticles were localized to a precision of 3 nm.

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion

The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.