A single protofilament is sufficient to support unidirectional walking of Dynein and Kinesin

Cytoplasmic dynein and kinesin are two-headed microtubule motor proteins that move in opposite directions on microtubules. It is known that kinesin steps by a 'hand-over-hand' mechanism, but it is unclear by which mechanism dynein steps. Because dynein has a completely different structure from that of kinesin and its head is massive, it is suspected that dynein uses multiple protofilaments of microtubules for walking. One way to test this is to ask whether dynein can step along a single protofilament. Here, we examined dynein and kinesin motility on zinc-induced tubulin sheets (zinc-sheets) which have only one protofilament available as a track for motor proteins. Single molecules of both dynein and kinesin moved at similar velocities on zinc-sheets compared to microtubules, clearly demonstrating that dynein and kinesin can walk on a single protofilament and multiple rows of parallel protofilaments are not essential for their motility. Considering the size and the motile properties of dynein, we suggest that dynein may step by an inchworm mechanism rather than a hand-over-hand mechanism.     

A model of human walking energetics with an elastically-suspended load

Elastically-suspended loads have been shown to reduce the peak forces acting on the body while walking with a load when the suspension stiffness and damping are minimized. However, it is not well understood how elastically-suspended loads can affect the energetic cost of walking. Prior work shows that elastically suspending a load can yield either an increase or decrease in the energetic cost of human walking, depending primarily on the suspension stiffness, load, and walking speed. It would be useful to have a simple explanation that reconciles apparent differences in existing data. The objective of this paper is to help explain different energetic outcomes found with experimental load suspension backpacks and to systematically investigate the effect of load suspension parameters on the energetic cost of human walking. A simple two-degree-of-freedom model is used to approximate the energetic cost of human walking with a suspended load. The energetic predictions of the model are consistent with existing experimental data and show how the suspension parameters, load mass, and walking speed can affect the energetic cost of walking. In general, the energetic cost of walking with a load is decreased compared to that of a stiffly-attached load when the natural frequency of a load suspension is tuned significantly below the resonant walking frequency. The model also shows that a compliant load suspension is more effective in reducing the energetic cost of walking with low suspension damping, high load mass, and fast walking speed. This simple model could improve our understanding of how elastic load-carrying devices affect the energetic cost of walking with a load.     

Analysis of human abnormal walking using a multi-body model: joint models for abnormal walking and walking aids to reduce compensatory action

This paper proposes new models of diseased joints and evaluates the effectiveness of walking aids such as a cane and a brace for compensating for lost functions due to joint disorders. The ZMJ concept described in the previous work (Yamashita and Tagawa, 1988. In: Radharaman (Ed.), Robotics and Factories of the Future'87. Springer, New York, pp. 670-677) is modified into three joint models as follows: a passive element joint (PEJ) which has a spring at the diseased joint; a constrained range joint (CRJ), the motion of which stays within some constrained relative angle; a partial moment joint (PMJ) which can produce a partial amount of the moment produced about the joint in normal walking. A cane can enlarge a supporting area and adjust the posture of the upper torso to be upright. An ischial weight-bearing brace is effective for conservative management of hip disorders by reducing a load to the joint (Shiba et al., 1998. Clinical Orthopaedics and Related Research 351, 149-157). Walking aids like a cane or brace have been conveniently used by the handicapped. Abnormal walking was simulated for each joint model. Dynamic effects of a cane and a brace on abnormal walking were examined by the multi-body walking model.     

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188–202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.     

Modular control of human walking: A simulation study

Recent evidence suggests that performance of complex locomotor tasks such as walking may be accomplished using a simple underlying organization of co-active muscles, or “modules”, which have been assumed to be structured to perform task-specific biomechanical functions. However, no study has explicitly tested whether the modules would actually produce the biomechanical functions associated with them or even produce a well-coordinated movement. In this study, we generated muscle-actuated forward dynamics simulations of normal walking using muscle activation modules (identified using non-negative matrix factorization) as the muscle control inputs to identify the contributions of each module to the biomechanical sub-tasks of walking (i.e., body support, forward propulsion, and leg swing). The simulation analysis showed that a simple neural control strategy involving five muscle activation modules was sufficient to perform the basic sub-tasks of walking. Module 1 (gluteus medius, vasti, and rectus femoris) primarily contributed to body support in early stance while Module 2 (soleus and gastrocnemius) contributed to both body support and propulsion in late stance. Module 3 (rectus femoris and tibialis anterior) acted to decelerate the leg in early and late swing while generating energy to the trunk throughout swing. Module 4 (hamstrings) acted to absorb leg energy (i.e., decelerate it) in late swing while increasing the leg energy in early stance. Post-hoc analysis revealed an additional module (Module 5: iliopsoas) acted to accelerate the leg forward in pre- and early swing. These results provide evidence that the identified modules can act as basic neural control elements that generate task-specific biomechanical functions to produce well-coordinated walking.     

A numerical method for simulating the dynamics of human walking

This paper presents a general method for simulating the movement of the lower extremity during human walking. It is based upon two separate algorithms: one for single support (an open kinematic chain), and the other for the double support phase (a closed-loop linkage). Central to each of these is the recursive Newton-Euler inverse dynamics algorithm, applicable, as given, to any serial, spatial linkage.

For the unconstrained single support model, the Newton-Euler scheme is applied directly to numerically generate the equations of motion. In the case of double support, however, the kinematic constraint equations are used to first eliminate the redundant degrees of freedom, and then solve for the unknown ground reactions under the constrained limb.

The attractiveness of the method is that it offers a compact alternative to manually deriving the equations defining a mathematical model for human gait.     

A self-organizing model of walking patterns of insects

Insects generate walking patterns which depend upon external conditions. For example, when an insect is exposed to an additional load parallel to the direction in which it is walking, the walking pattern changes according to the magnitude of the load. Furthermore, even after some of its legs have been amputated, an insect will produce walking patterns with its remaining legs. These adaptations in insect walking could not previously be explained by a mathematical model, since the mathemati cal models were based upon the hypothesis that the relationship between walking velocity and walking patterns is fixed under all conditions. We have produced a mathematical model which describes self-organizing insect walking patterns in real-time by using feedback information regarding muscle load (Kimura et al. 1993). As part of this model, we introduced a new rule to coordinate leg movement, in which the information is circulated to optimize the efficiency of the energy transduction of each effector orga n. We describe this mechanism as ‘the least dissatisfaction for the greatest number of elements’. In this paper, we introduce the following aspects of this model, which reflect adaptability to changing circumstances: (1) after one leg is exposed to a transient perturbation, the walking pattern recovers swiftly; (2) when the external load parallel to the walking direction is continuously increased or decreased, the pattern transition point is shifted according to the magnitude of the load increme nt or decrement. This model generates a walking pattern which optimizes energy consumption at a given walking velocity even under these conditions; and (3) when some of the legs are amputated, the model generates walking patterns which are consistent with experimental results. We also discuss the ability of a hierarchical self-organizing model to describe a swift and flexible information processing system. Received: 8 February 1993/Accepted in revised form: 12 November 1993     

A self-organizing model of walking patterns of insects

It is well known that the motor systems of animals are controlled by a hierarchy consisting of a brain, central pattern generator, and effector organs. An animal's walking patterns change depending on its walking velocities, even when it has been decerebrated, which indicates that the walking patterns may, in fact, be generated in the subregions of the neural systems of the central pattern generator and the effector organs. In order to explain the self-organization of the walking pattern in response to changing circumstances, our model incorporates the following ideas: (1) the brain sends only a few commands to the central pattern generator (CPG) which act as constraints to self-organize the walking patterns in the CPG; (2) the neural network of the CPG is composed of oscillating elements such as the KYS oscillator, which has been shown to simulate effectively the diversity of the neural activities; and (3) we have introduced a rule to coordinate leg movement, in which the excitatory and inhibitory interactions among the neurons act to optimize the efficiency of the energy transduction of the effector organs. We describe this mechanism as the least dissatisfaction for the greatest number of elements, which is a self-organization rule in the generation of walking patterns. By this rule, each leg tends to share the load as efficiently as possible under any circumstances. Using this self-organizing model, we discuss the control mechanism of walking patterns.     

A fast inverse dynamics model of walking for use in optimisation studies

Computer simulation of human gait, based on measured motion data, is a well-established technique in biomechanics. However, optimisation studies requiring many iterative gait cycle simulations have not yet found widespread application because of their high computational cost. Therefore, a computationally efficient inverse dynamics model of 3D human gait has been designed and compared with an equivalent model, created using a commercial multi-body dynamics package. The fast inverse dynamics model described in this paper led to an eight fold increase in execution speed. Sufficient detail is provided to allow readers to implement the model themselves.     

A model of pattern generation of cockroach walking reconsidered

Cockroaches that have been decapitated or that have cut thoracic connectives can show rhythmic bursting in motoneurons to intrinsic leg muscles. These preparations have been studied as models for walking and to evaluate the functions of leg proprioceptors. The present study demonstrates that headless cockroaches walk extremely poorly and slowly with considerable discoordination of motoneuronal activity, these preparations show rhythmic motoneuron bursting that is similar to righting responses (attempts to turn upright) of intact animals when placed on their backs, and bursting is inhibited when a headless animal is turned or turns itself upright. Thus, rhythmic motoneuron activity of these preparations is most probably attempted righting rather than walking. It is concluded that the headless cockroach is useful for understanding the motor mechanisms underlying righting and walking but is not of value in assessing the functions of proprioceptive feedback.     

Interaction of influenza virus proteins with planar lipid bilayers: A model for virion assembly

Changes in conductance of oxidized cholesterol planar lipid bilayers were measured following the incorporation of isolated surface glycoproteins; hemagglutinin and neuraminidase (HA+NA) or matrix protein (M-protein) of influenza virus. The conductance dependence of the lipid bilayers on the HA+NA or M-protein concentrations indicates different mechanisms of interaction of these viral proteins with the lipid bilayer. Adsorption of M-protein molecules on one side of the lipid bilayer affects the character of the HA+NA interaction with the opposite side. Planar lipid bilayers can be a useful model for investigation of the assembly of influenza virions and other enveloped viruses.     

From swimming to walking: a single basic network for two different behaviors

 In this paper we consider the hypothesis that the spinal locomotor network controlling trunk movements has remained essentially unchanged during the evolutionary transition from aquatic to terrestrial locomotion. The wider repertoire of axial motor patterns expressed by amphibians would then be explained by the influence from separate limb pattern generators, added during this evolution. This study is based on EMG data recorded in vivo from epaxial musculature in the newt Pleurodeles waltl during unrestrained swimming and walking, and on a simplified model of the lamprey spinal pattern generator for swimming. Using computer simulations, we have examined the output generated by the lamprey model network for different input drives. Two distinct inputs were identified which reproduced the main features of the swimming and walking motor patterns in the newt. The swimming pattern is generated when the network receives tonic excitation with local intensity gradients near the neck and girdle regions. To produce the walking pattern, the network must receive (in addition to a tonic excitation at the girdles) a phasic drive which is out of phase in the neck and tail regions in relation to the middle part of the body. To fit the symmetry of the walking pattern, however, the intersegmental connectivity of the network had to be modified by reversing the direction of the crossed inhibitory pathways in the rostral part of the spinal cord. This study suggests that the input drive required for the generation of the distinct walking pattern could, at least partly, be attributed to mechanosensory feedback received by the network directly from the intraspinal stretch-receptor system. Indeed, the input drive required resembles the pattern of activity of stretch receptors sensing the lateral bending of the trunk, as expressed during walking in urodeles. Moreover, our results indicate that a nonuniform distribution of these stretch receptors along the trunk can explain the discontinuities exhibited in the swimming pattern of the newt. Thus, separate limb pattern generators can influence the original network controlling axial movements not only through a direct coupling at the central level but also via a mechanical coupling between trunk and limbs, which in turn influences the sensory signals sent back to the network. Taken together, our findings support the hypothesis of a phylogenetic conservatism of the spinal locomotor networks generating axial motor patterns from agnathans to amphibians. Received: 12 October 2001 / Accepted in revised form: 16 May 2002 Correspondence to: T. Bem (e-mail: tiaza.bem@ibib.waw.pl)     

InraPorc: A model and decision support tool for the nutrition of sows

From results obtained over the last 20 years on energy and amino acid utilisation in reproductive sows, it has become possible to improve the determination of nutrient requirements (factorial approach) and the prediction of an animal's response to nutrient supplies (modelling). The objective of this project was to integrate the current state of knowledge in a nutritional model for growing pigs and for sows and make it available as a software tool to end-users, mainly nutritionists involved in the pig industry and students in animal nutrition. The aim of this paper is to describe the basis of the sow model. The sow is represented as different compartments that change over the reproductive cycle. Nutrient flows considered are those of energy and digestible amino acids. Nutrients are used with the highest priority for maintenance and uterine growth or milk production. Subsequently, deposition and/or mobilisation of body proteins and lipids are determined and used for estimating the changes in body weight and backfat thickness of the sow. A decision support tool was built from the set of equations given, with additional modules to describe animal's characteristics and adjust some model parameters to account for variations in genotypes and performance. This tool can be used to determine energy and amino acids requirements of sows according to production objectives, or to predict body composition changes according to a given feeding strategy. The use of the decision support tool is illustrated through some examples.     

A closed-form structural model of planar fibrous tissue mechanics

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress–strain law.     

A neurobiological model of the recovery strategies from perturbed walking

This paper proposes a human mimetic neuro-musculo-skeletal model to simulate the recovery reactions from perturbations during walking. The computational model incorporates nonlinear viscoelastic muscular mechanics, supraspinal control of the center-of-mass, spinal pattern generator including muscle synergy network, spinal reflexes, and long-loop reflexes. Especially the long-loop reflexes specify recovery strategies based on the experimental observations [Schillings, A.M., van Wezel, B.M.H., Mulder, T.H., Duysen, J., 2000. Muscular responses and movement strategies during stumbling over obstacles. J. Neurophysiol. 83, 2093–2102; Eng, J.J., Winter, D.A., Patla, A.E., 1994. Strategies for recovery from a trip in early and late swing during human walking. Exp. Brain Res. 102, 339–349]. The model demonstrates two typical recovery strategies, i.e., elevating and lowering strategies against pulling over a swing leg. Sensed perturbation triggers a simple tonic pulse from the cortex. Depending on the swing phase, the tonic pulse activates a different compound of muscles over lower limbs. The compound induces corresponding recovery strategies. The reproduction of principal recovery behaviors may support the model's proposed functional and/or anatomical correspondence.     

Dynamic optimization of human walking

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by slimming five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.     

A model for generalization and specification by single neurons

A rule for environmentally dependent modification of the neuronal state is examined. Under the rule, the neuron selects a trigger feature that matches either a particular pattern in the stimulus set, or the most common pattern component, depending on a certain parameter. Thus a neuron may evolve to respond to its stimulus environment in one of two capacities, namely specification or generalization. Neurons of the former variety are labelled S-cells; and those of the latter, G-cells. In the model, synaptic modification is modulated by two postsynaptic mechanisms which act antagonistically to strengthen or weaken the synaptic connectivities. The functional dependence of these mechanisms on the postsynaptic activity is shown to determine whether the neuron acts as an S-cell or a G-cell. A circuit is proposed for a module that consists of a G-cell and several S-cells sharing a common set of inputs. By inhibiting the G-cells, the S-cell acts as a contrast-enhancing element, increasing their specificities for individual patterns in the stimulus set. The output from the module is a recoded representation of the environment with respect to its general and distinctive features.This work was supported in part by United States Office of Naval Research Contract N00014-81-K-0136