Microtubule Depolymerization by the Kinesin-8 Motor Kip3p: A Mathematical Model

Proteins from the kinesin-8 family promote microtubule (MT) depolymerization, a process thought to be important for the control of microtubule length in living cells. In addition to this MT shortening activity, kinesin 8s are motors that show plus-end directed motility on MTs. Here we describe a simple model that incorporates directional motion and destabilization of the MT plus-end by kinesin 8. Our model quantitatively reproduces the key features of length-versus-time traces for stabilized MTs in the presence of purified kinesin 8, including length-dependent depolymerization. Comparison of model predictions with experiments suggests that kinesin 8 depolymerizes processively, i.e., one motor can remove multiple tubulin dimers from a stabilized MT. Fluctuations in MT length as a function of time are related to depolymerization processivity. We have also determined the parameter regime in which the rate of MT depolymerization is length dependent: length-dependent depolymerization occurs only when MTs are sufficiently short; this crossover is sensitive to the bulk motor concentration.     

Atropisomerism as a probe of restrictions to motion above and below the glass transition temperature of Polymers

This short review and interpretation of work conducted in the authors' laboratory concerns the use of atropisomeric 1,1'-binaphthyl derivatives to gain information about the glassy properties of polymers. Bridged binaphthyls appended with oligophenyl paddles are found to yield a series of probes whose racemization kinetics reveal new kinds of information concerning the basis of the time scale and length scale for the restrictions to motion and the heterogeneity of the polymeric glassy state. Because the time scale of the racemization is slower than all other glass probes used previously, new kinds of information were gained for the first time below the glass transition temperature.     

Enforced telomere elongation increases the sensitivity of human tumour cells to ionizing radiation

More than 85% of all human cancers possess the ability to maintain chromosome ends, or telomeres, by virtue of telomerase activity. Loss of functional telomeres is incompatible with survival, and telomerase inhibition has been established in several model systems to be a tractable target for cancer therapy. As human tumour cells typically maintain short equilibrium telomere lengths, we wondered if enforced telomere elongation would positively or negatively impact cell survival. We found that telomere elongation beyond a certain length significantly decreased cell clonogenic survival after gamma irradiation. Susceptibility to irradiation was dosage-dependent and increased at telomere lengths exceeding 17 kbp despite the fact that all chromosome ends retained telomeric DNA. These data suggest that an optimal telomere length may promote human cancer cell survival in the presence of genotoxic stress.     

Flagellar hook flexibility is essential for bundle formation in swimming Escherichia coli cells

Swimming Escherichia coli cells are propelled by the rotary motion of their flagellar filaments. In the normal swimming pattern, filaments positioned randomly over the cell form a bundle at the posterior pole. It has long been assumed that the hook functions as a universal joint, transmitting rotation on the motor axis through up to ～90° to the filament in the bundle. Structural models of the hook have revealed how its flexibility is expected to arise from dynamic changes in the distance between monomers in the helical lattice. In particular, each of the 11 protofilaments that comprise the hook is predicted to cycle between short and long forms, corresponding to the inside and outside of the curved hook, once each revolution of the motor when the hook is acting as a universal joint. To test this, we genetically modified the hook so that it could be stiffened by binding streptavidin to biotinylated monomers, impeding their motion relative to each other. We found that impeding the action of the universal joint resulted in atypical swimming behavior as a consequence of disrupted bundle formation, in agreement with the universal joint model.     

Reconstitution of an active human CENP-E motor

CENP-E is a large kinesin motor protein which plays pivotal roles in mitosis by facilitating chromosome capture and alignment, and promoting microtubule flux in the spindle. So far, it has not been possible to obtain active human CENP-E to study its molecular properties. Xenopus CENP-E motor has been characterized in vitro and is used as a model motor; however, its protein sequence differs significantly from human CENP-E. Here, we characterize human CENP-E motility in vitro. Full-length CENP-E exhibits an increase in run length and longer residency times on microtubules when compared to CENP-E motor truncations, indicating that the C-terminal microtubule-binding site enhances the processivity when the full-length motor is active. In contrast with constitutively active human CENP-E truncations, full-length human CENP-E has a reduced microtubule landing rate in vitro, suggesting that the non-motor coiled-coil regions self-regulate motor activity. Together, we demonstrate that human CENP-E is a processive motor, providing a useful tool to study the mechanistic basis for how human CENP-E drives chromosome congression and spindle organization during human cell division.     

A complete set of control equations for the human musculo-skeletal system

A mathematical model of the total human musculo-skeletal system is presented. The model comprises a link-mechanical and a musculo-mechanical set of ordinary first-order differential equations which describe the dynamics of the segment model and muscle model respectively. The interdependence of the two sets of equations is demonstrated. The set of musculo-mechanical equations contains the two neuromuscular control parameters motor unit recruitment and stimulation rate, and the significance of such a representation for a control-theoretical treatment of musculo-skeletal systems is discussed. Finally, after a short discussion of the successful application of the present model in the prediction of an optimal human motion, further possibilities are indicated of the use of the model for investigations into the control behaviour of musculo-skeletal systems.     

Short Telomeres Initiate Telomere Recombination in Primary and Tumor Cells

Human tumors that lack telomerase maintain telomeres by alternative lengthening mechanisms. Tumors can also form in telomerase-deficient mice; however, the genetic mechanism responsible for tumor growth without telomerase is unknown. In yeast, several different recombination pathways maintain telomeres in the absence of telomerase—some result in telomere maintenance with minimal effects on telomere length. To examine non-telomerase mechanisms for telomere maintenance in mammalian cells, we used primary cells and lymphomas from telomerase-deficient mice (mTR−/− and Eμmyc+mTR−/−) and CAST/EiJ mouse embryonic fibroblast cells. These cells were analyzed using pq-ratio analysis, telomere length distribution outliers, CO-FISH, Q-FISH, and multicolor FISH to detect subtelomeric recombination. Telomere length was maintained during long-term growth in vivo and in vitro. Long telomeres, characteristic of human ALT cells, were not observed in either late passage or mTR−/− tumor cells; instead, we observed only minimal changes in telomere length. Telomere length variation and subtelomeric recombination were frequent in cells with short telomeres, indicating that length maintenance is due to telomeric recombination. We also detected telomere length changes in primary mTR−/− cells that had short telomeres. Using mouse mTR+/− and human hTERT+/− primary cells with short telomeres, we found frequent length changes indicative of recombination. We conclude that telomere maintenance by non-telomerase mechanisms, including recombination, occurs in primary cells and is initiated by short telomeres, even in the presence of telomerase. Most intriguing, our data indicate that some non-telomerase telomere maintenance mechanisms occur without a significant increase in telomere length.     

Visuomotor transformation in the fly gaze stabilization system

For sensory signals to control an animal's behavior, they must first be transformed into a format appropriate for use by its motor systems. This fundamental problem is faced by all animals, including humans. Beyond simple reflexes, little is known about how such sensorimotor transformations take place. Here we describe how the outputs of a well-characterized population of fly visual interneurons, lobula plate tangential cells (LPTCs), are used by the animal's gaze-stabilizing neck motor system. The LPTCs respond to visual input arising from both self-rotations and translations of the fly. The neck motor system however is involved in gaze stabilization and thus mainly controls compensatory head rotations. We investigated how the neck motor system is able to selectively extract rotation information from the mixed responses of the LPTCs. We recorded extracellularly from fly neck motor neurons (NMNs) and mapped the directional preferences across their extended visual receptive fields. Our results suggest that-like the tangential cells-NMNs are tuned to panoramic retinal image shifts, or optic flow fields, which occur when the fly rotates about particular body axes. In many cases, tangential cells and motor neurons appear to be tuned to similar axes of rotation, resulting in a correlation between the coordinate systems the two neural populations employ. However, in contrast to the primarily monocular receptive fields of the tangential cells, most NMNs are sensitive to visual motion presented to either eye. This results in the NMNs being more selective for rotation than the LPTCs. Thus, the neck motor system increases its rotation selectivity by a comparatively simple mechanism: the integration of binocular visual motion information.     

Long-latency reflexes of the human arm reflect an internal model of limb dynamics

A key feature of successful motor control is the ability to counter unexpected perturbations. This process is complicated in multijoint systems, like the human arm, by the fact that loads applied at one joint will create motion at other joints [1-3]. Here, we test whether our most rapid corrections, i.e., reflexes, address this complexity through an internal model of the limb's mechanical properties. By selectively applying torque perturbations to the subject's shoulder and/or elbow, we revealed a qualitative difference between the arm's short-latency/spinal reflexes and long-latency/cortical reflexes. Short-latency reflexes of shoulder muscles were linked exclusively to shoulder motion, whereas its long-latency reflexes were sensitive to both shoulder and elbow motion, i.e., matching the underlying shoulder torque. In fact, a long-latency reflex could be evoked without even stretching or lengthening the shoulder muscle but by displacing just the elbow joint. Further, the shoulder's long-latency reflexes were appropriately modified across the workspace to account for limb-geometry changes that affect the transformation between joint torque and joint motion. These results provide clear evidence that long-latency reflexes possess an internal model of limb dynamics, a degree of motor intelligence previously reserved for voluntary motor control [3-5]. The use of internal models for both voluntary and reflex control is consistent with substantial overlap in their neural substrates and current notions of intelligent feedback control [6-8].     

Manuo-ocular coordination in target tracking. II. Comparing the model with human behavior

Several studies have shown that humans track a moving visual target with their eyes better if the movement of this target is directly controlled by the observer's hand. The improvement in performance has been attributed to coordination control between the arm motor system and the smooth pursuit (SP) system. In such a task, the SP system shows characteristics that differ from those observed during eye-alone tracking: latency (between the target-arm and the eye motion onsets) is shorter, maximum SP velocity is higher and the maximum target motion frequency at which the SP can function effectively is also higher. The aim of this article is to qualitatively evaluate the behavior of a dynamical model simulating the oculomotor system and the arm motor system when both are involved in tracking visual targets. The evaluation is essentially based on a comparison of the behavior of the model with the behavior of human subjects tracking visual targets under different conditions. The model has been introduced and quantitatively evaluated in a companion paper. The model is based on an exchange of internal information between the two sensorimotor systems, mediated by sensory signals (vision, arm muscle proprioception) and motor signals (arm motor command copy). The exchange is achieved by a specialized structure of the central nervous system, previously identified as a part of the cerebellum. Computer simulation of the model yielded results that fit the behavior of human subjects observed during previously reported experiments, both qualitatively and quantitatively. The parallelism between physiology and human behavior on the one hand, and structure and simulation of the model on the other hand, is discussed. Received: 6 March 1997 / Accepted in revised form: 15 July 1997     

Biochemical and molecular characterization of diseases linked to motor proteins

Recent studies have revealed that kinesin, dynein and myosin each form large superfamilies and participate in many different intracellular transport systems. Importantly, these motor proteins play significant roles in the pathogenesis of a variety of diseases. Studies using knockout mice for kinesin KIF1B have led to the identification of the cause of a human hereditary neuropathy, Charcot-Marie-Tooth disease type 2A. The function of members of the dynein superfamily whose existence has previously only been confirmed through genome databases, has been revealed by studies of immotile cilia syndrome. Unconventional myosins have been shown to function in the inner-ear cells by examination of hereditary human hearing impairment and studies using mouse models. In addition, some diseases are caused by mutations, not in the motor itself, but in the proteins associated with the motor proteins. Here, we discuss the relationship of these motor proteins and how they contribute to disease in molecular terms.     

Manuo-ocular coordination in target tracking. I. A model simulating human performance

During eye tracking of a self-moved target, human subjects' performance differs from eye-alone tracking of an external target. Typical latency between target and eye motion onsets is shorter, ocular smooth pursuit (SP) saturation velocity increases and the maximum target motion frequency at which the SP system functions correctly is higher. Based on a previous qualitative model, a quantitative model of the coordination control between the arm motor system and the SP system is presented and evaluated here. The model structure maintains a high level of parallelism with the physiological system. It contains three main parts: the eye motor control (containing a SP branch and a saccadic branch), the arm motor control and the coordination control. The coordination control is achieved via an exchange of information between the arm and the eye sensorimotor systems, mediated by sensory signals (vision, proprioception) and motor command copy. This cross-talk results in improved SP system performance. The model has been computer simulated and the results have been compared with human subjects' behavior observed during previous experiments. The model performance is seen to quantitatively fit data on human subjects. Received: 6 March 1997 / Accepted in revised form: 15 July 1997     

The phosphorylation state of an aurora-like kinase marks the length of growing flagella in Chlamydomonas

Flagella and cilia are structurally polarized organelles whose lengths are precisely defined, and alterations in length are related to several human disorders. Intraflagellar transport (IFT) and protein signaling molecules are implicated in specifying flagellar and ciliary length, but evidence has been lacking for a flagellum and cilium length sensor that could participate in active length control or establishment of structural polarity. Previously, we showed that the phosphorylation state of the aurora-like protein kinase CALK in Chlamydomonas is a marker of the absence of flagella. Here we show that CALK phosphorylation state is also a marker for flagellar length. CALK is phosphorylated in cells without flagella, and during flagellar assembly it becomes dephosphorylated. Dephosphorylation is not simply a consequence of initiation of flagellar assembly or of time after experimentally induced flagellar loss, but instead requires flagella to be assembled to a threshold length. Analysis of cells with flagella of varying lengths shows that the threshold length for CALK dephosphorylation is ~6 μm (half length). Studies with short and long flagellar mutants indicate that cells detect absolute rather than relative flagellar length. Our results demonstrate that cells possess a mechanism for translating flagellar length into a posttranslational modification of a known flagellar regulatory protein.     

Step length measurement--theory and simulation for tethered bead constant-force single molecule assay

Linear molecular motors translocate along polymeric tracks using discrete steps. The step length is usually measured using constant-force single molecule experiments in which the polymer is tethered to a force-clamped microsphere. During the enzymatic cycle the motor shortens the tether contour length. Experimental conditions influence the achievable step length resolution, and ideally experiments should be conducted with high clamp-force using slow motors linked to small beads via stiff short tethers. We focus on the limitations that the polymer-track flexibility, the thermal motion of the microsphere, and the motor kinetics pose for step-length measurement in a typical optical tweezers experiment. An expression for the signal/noise ratio in a constant-force, worm-like chain tethered particle, single-molecule experiment is developed. The signal/noise ratio is related to the Fourier transform of the pairwise distance distribution, commonly used to determine step length from a time-series. Monte Carlo simulations verify the proposed theory for experimental parameter values typically encountered with molecular motors (polymerases and helicases) translocating along single- or double-stranded nucleic acids. The predictions are consistent with recent experimental results for double-stranded DNA tethers. Our results map favorable experimental conditions for observing single motor steps on various substrates but indicate that principal resolution limits are set by thermal fluctuations.     

Fine-scale time-lapse analysis of the biphasic, dynamic behaviour of the two Vibrio cholerae chromosomes

Using fluorescent repressor-operator systems in live cells, we investigated the dynamic behaviour of chromosomal origins in Vibrio cholerae, whose genome is divided between two chromosomes. We have developed a method of analysing fine-scale motion in the curved co-ordinate system of vibrioid bacteria. Using this method, we characterized two different modes of chromosome behaviour corresponding to periods between segregation events and periods of segregation. Between segregation events, the origin positions are not fixed but rather maintained within ellipsoidal caged domains, similar to eukaryotic interphase chromosome territories. These domains are approximately 0.4 microm wide and 0.6 microm long, reflecting greater restriction in the short axis of the cell. During segregation, movement is directionally biased, speed is comparable between origins, and cell growth can account for nearly 20% of the motion observed. Furthermore, the home domain of each origin is positioned by a different mechanism. Specifically, the oriC(I) domain is maintained at a constant actual distance from the pole regardless of cell length, while the oriC(II) domain is maintained at a constant relative position. Thus the actual position of oriC(II) varies with cell length. While the gross behaviours of the two origins are distinct, their fine-scale dynamics are remarkably similar, indicating that both experience similar microenvironments.     

Early motor development from partially ordered neural-body dynamics: experiments with a cortico-spinal-musculo-skeletal model

Early human motor development has the nature of spontaneous exploration and boot-strap learning, leading to open-ended acquisition of versatile flexible motor skills. Since dexterous motor skills often exploit body-environment dynamics, we formulate the developmental principle as the spontaneous exploration of consistent dynamical patterns of the neural-body-environment system. We propose that partially ordered dynamical patterns emergent from chaotic oscillators coupled through embodiment serve as the core driving mechanism of such exploration. A model of neuro-musculo-skeletal system is constructed capturing essential features of biological systems. It consists of a skeleton, muscles, spindles, tendon organs, spinal circuits, medullar circuits (CPGs), and a basic cortical model. Through a series of experiments with a minimally simple body model, it is shown that the model has the capability of generating partially ordered behavior, a mixture of chaotic exploration and ordered entrained patterns. Models of self-organizing cortical areas for primary somatosensory and motor areas are introduced. They participate in the explorative learning by simultaneously learning and controlling the movement patterns. A scaled up version of the model, a human infant model, is constructed and put through preliminary experiments. Some meaningful motor behavior emerged including rolling over and crawling-like motion. The results show the possibility that a rich variety of meaningful behavior can be discovered and acquired by the neural-body dynamics without pre-defined coordinated control circuits.     

Human motion tracking for rehabilitation—A survey

Human motion tracking for rehabilitation has been an active research topic since the 1980s. It has been motivated by the increased number of patients who have suffered a stroke, or some other motor function disability. Rehabilitation is a dynamic process which allows patients to restore their functional capability to normal. To reach this target, a patients’ activities need to be continuously monitored, and subsequently corrected. This paper reviews recent progress in human movement detection/tracking systems in general, and existing or potential application for stroke rehabilitation in particular. Major achievements in these systems are summarised, and their merits and limitations individually presented. In addition, bottleneck problems in these tracking systems that remain open are highlighted, along with possible solutions.     

Fluctuations, responses and energetics of molecular motors

A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in non-equilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of violation of the FRR in non-equilibrium systems has been under debate. Recently, the authors have found that an extent of the FRR violation is related in a simple equality to the rate of energy dissipation into the environment in non-equilibrium Langevin systems. In this paper, we fully explain the FRR, the FRR violation, and the new equality with regard to a Langevin model termed a Brownian motor model, which is considered as a simple model of a biological molecular motor. Furthermore, applications of our result to experimental studies of molecular motors are discussed, and, as an illustration, we predict the value of a new time constant regarding the motion of a KIF1A, which is a kind of single-headed kinesin.     

Short telomeres are preferentially elongated by telomerase in human cells

Short telomeres have been shown to be preferentially elongated in both yeast and mouse models. We examined this in human cells, by utilising cells with large allelic telomere length differentials and observing the relative rates of elongation following the expression of hTERT. We observed that short telomeres are gradually elongated in the first 26 PDs of growth, whereas the longer telomeres displayed limited elongation in this period. Telomeres coalesced at similar lengths irrespective of their length prior to the expression of hTERT. These data indicate that short telomeres are marked for gradual elongation to a cell strain specific length threshold.