Diffusion coefficients of segmentally flexible macromolecules with two subunits: a study of broken rods

A general treatment for the solution dynamics of segmentally flexible macromolecules having two subunits is presented. Bead modeling allows for a complete inclusion of hydrodynamic interactions in this treatment. The finite size of the beads is also considered, so that it is therefore possible to account properly for torsional motions of the subunits. Expressions for the components of the resistance matrix are derived. From them, the translational and rotational diffusion coefficients can be calculated. Distinction is made between hinged macromolecules, whose only internal motion is bending, and swivel-jointed macromolecules, for which torsions of the subunits are also allowed. Numerical results are presented for broken rods with the two types of flexibility. The effects of hydrodynamic interaction between arms of broken rods are about 25% for translation and under 10% for rotation. These findings give support to the treatments of Harvey, Wegener, and co-workers in which interactions were neglected. The rotational dynamics of hinged and swivel-jointed rods are compared. Although there are differences in the short-time behavior, the longest relaxation time is the same for the two cases. Finally, the validity of Wegener's rotational diffusion constants is discussed.     

Shaping the dynamics of a bidirectional neural interface

Progress in decoding neural signals has enabled the development of interfaces that translate cortical brain activities into commands for operating robotic arms and other devices. The electrical stimulation of sensory areas provides a means to create artificial sensory information about the state of a device. Taken together, neural activity recording and microstimulation techniques allow us to embed a portion of the central nervous system within a closed-loop system, whose behavior emerges from the combined dynamical properties of its neural and artificial components. In this study we asked if it is possible to concurrently regulate this bidirectional brain-machine interaction so as to shape a desired dynamical behavior of the combined system. To this end, we followed a well-known biological pathway. In vertebrates, the communications between brain and limb mechanics are mediated by the spinal cord, which combines brain instructions with sensory information and organizes coordinated patterns of muscle forces driving the limbs along dynamically stable trajectories. We report the creation and testing of the first neural interface that emulates this sensory-motor interaction. The interface organizes a bidirectional communication between sensory and motor areas of the brain of anaesthetized rats and an external dynamical object with programmable properties. The system includes (a) a motor interface decoding signals from a motor cortical area, and (b) a sensory interface encoding the state of the external object into electrical stimuli to a somatosensory area. The interactions between brain activities and the state of the external object generate a family of trajectories converging upon a selected equilibrium point from arbitrary starting locations. Thus, the bidirectional interface establishes the possibility to specify not only a particular movement trajectory but an entire family of motions, which includes the prescribed reactions to unexpected perturbations.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

Human centromere protein B induces translational positioning of nucleosomes on alpha-satellite sequences

The human centromere proteins A (CENP-A) and B (CENP-B) are the fundamental centromere components of chromosomes. CENP-A is the centromere-specific histone H3 variant, and CENP-B specifically binds a 17-base pair sequence (the CENP-B box), which appears within every other alpha-satellite DNA repeat. In the present study, we demonstrated centromere-specific nucleosome formation in vitro with recombinant proteins, including histones H2A, H2B, H4, CENP-A, and the DNA-binding domain of CENP-B. The CENP-A nucleosome wraps 147 base pairs of the alpha-satellite sequence within its nucleosome core particle, like the canonical H3 nucleosome. Surprisingly, CENP-B binds to nucleosomal DNA when the CENP-B box is wrapped within the nucleosome core particle and induces translational positioning of the nucleosome without affecting its rotational setting. This CENP-B-induced translational positioning only occurs when the CENP-B box sequence is settled in the proper rotational setting with respect to the histone octamer surface. Therefore, CENP-B may be a determinant for translational positioning of the centromere-specific nucleosomes through its binding to the nucleosomal CENP-B box.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

The dynamics of protein hydration water: a quantitative comparison of molecular dynamics simulations and neutron-scattering experiments

We present results from an extensive molecular dynamics simulation study of water hydrating the protein Ribonuclease A, at a series of temperatures in cluster, crystal, and powder environments. The dynamics of protein hydration water appear to be very similar in crystal and powder environments at moderate to high hydration levels. Thus, we contend that experiments performed on powder samples are appropriate for discussing hydration water dynamics in native protein environments. Our analysis reveals that simulations performed on cluster models consisting of proteins surrounded by a finite water shell with free boundaries are not appropriate for the study of the solvent dynamics. Detailed comparison to available x-ray diffraction and inelastic neutron-scattering data shows that current generation force fields are capable of accurately reproducing the structural and dynamical observables. On the time scale of tens of picoseconds, at room temperature and high hydration, significant water translational diffusion and rotational motion occur. At low hydration, the water molecules are translationally confined but display appreciable rotational motion. Below the protein dynamical transition temperature, both translational and rotational motions of the water molecules are essentially arrested. Taken together, these results suggest that water translational motion is necessary for the structural relaxation that permits anharmonic and diffusive motions in proteins. Furthermore, it appears that the exchange of protein-water hydrogen bonds by water rotational/librational motion is not sufficient to permit protein structural relaxation. Rather, the complete exchange of protein-bound water molecules by translational displacement seems to be required.     

How dinoflagellates swim

Dinoflagellates possess two flagella; usually these are directed perpendicular to one another constituting a transversal flagellum and a longitudinal, trailing flagellum, respectively. The transversal flagellum causes the cell to rotate around its length axis. The trailing flagellum is responsible for the translation of the cell; due to its asymmetric insertion it also causes a rotation of the cell around an axis perpendicular to the longitudinal axis. Together, these two rotational components result in a helical swimming path. Cells can vary the two rotational components independently as well as the translational velocity. With these three degrees of freedom, cells can vary the parameters of their helical swimming paths for steering. Dinoflagellates use this mechanism for orientation in chemical concentration gradients (“helical klinotaxis”).     

Sequence dependence of translational positioning of core nucleosomes

The basis for the choice of translational position of a histone octamer on DNA is poorly understood. To gain further insights into this question we have studied the translational and rotational settings of core particles assembled on a simple repeating 20 bp positioning sequence. We show that the translational positions of the core particles assembled on this sequence are invariant with respect to the DNA sequence and occur at 20 bp intervals. Certain modifications of the original sequence reduce the spacing of possible dyads to 10 bp. At least one of these alters both the translational and rotational settings. We conclude that the translational position of a core particle is specified by sequence determinants additional to those specifying rotational positioning. The rotational settings on either side of the dyads of core particles assembled on the wild-type and a mutant sequence differ by +2 bp, corresponding to an overall helical periodicity of approximately 10.15 bp. The average helical periodicity of the central two to four turns is 10.5-11 bp whilst that of the flanking DNA is closer to 10 bp. The DNA immediately flanking the dyad is also characterised by a more extensive susceptibility to cleavage by hydroxyl radical.     

Analysis of kinematic invariances of multijoint reaching movement

 There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joint angle or intrinsic space in the general condition of joint redundancy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate systems. We show that the cartesian trajectory can be planned based on the task parameters (target coordinates, etc.) prior to and independently of angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in cartesian and angular spaces simultaneously is proposed. Due to joint redundancy, each cartesian trajectory corresponds to a family of angular trajectories which can account for the substantial variability of the latter. A set of strategies for multijoint motor control following from this model is considered; one of them coincides with the frog wiping reflex model and resolves the kinematic inverse problem without inversion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, straight end-point paths, bell-shaped tangential velocity profiles, speed-sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajectory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb configuration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian space. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control used in planning. All the results are given analytically and, in order to compare the model with experimental results, by computer simulations. Received: 6 April 1994/Accepted in revised form: 25 April 1995     

Directional bias of soft-tissue artifacts on the acromion during recording of 3D scapular kinematics

Scapular kinematics during sports performances can be recorded using skin-mounted trackers attached to the skin overlying the acromion for continuous data collection without restricting natural motions of the subject relative to medical imaging analyses limiting its use for wide-range or high-speed motions. This study aimed to describe the existence of a directional bias in the translational and rotational errors of skin-mounted trackers using a 3D magnetic resonance imaging (3D-MRI) protocol. 3D-MRI scans of the healthy right shoulders of 19 males were acquired in 12 arm positions. The relative transformation of the scapular configuration determined to be the measurement error, as recorded by the configuration of the small cuboid imitating a skin-mounted tracker relative to the actual scapular configuration measured by the voxel-based registration. These measurement errors were expressed with either positive or negative values to describe the bias. Overall translational errors in the lateral, anterior, and superior directions were 3.7 ± 8.4 mm, 9.5 ± 6.4 mm, and 6.2 ± 4.6 mm, respectively. Overall rotational errors in protraction, upward rotation, and posterior tilt were 7.8 ± 8.4°, 0.2 ± 7.4°, and − 4.0 ± 7.5°, respectively. The skin-mounted tracker displayed a high probability of displacement in antero-superior (93% and 91%) directions and rotates in a protracting manner (82%) relative to the position of the underlying bone with the gradual nature of its change. The existence of the directional bias with its gradual change suggests a statistical predictability in measurement errors, which can be used to predict accurate scapular translation and rotation.     

Dynamics of superhelical DNA studied by photon correlation spectroscopy

We have conducted photon correlation spectroscopy (PCS) studies on the plasmid pUC8 (2717 bp) in order to elucidate the internal dynamics of this superhelical DNA. We confirm that the first-order autocorrelation function of the scattered light from pUC8 solutions can be separated into two distinct exponential decay components, as first shown by Lewis et al. (R. Lewis, J.H. Huang and P. Pecora, Macromolecules 18 (1985) 944). A thorough analysis of the dependence on scattering vector K of the rates and amplitudes of the two components enables us to assign the slowly relaxing part to the center-of-mass diffusion of the DNA, while the faster component corresponds to rotational, bending and twisting motions of the superhelix. For larger K values the internal motions can be formally expressed in terms of an 'internal diffusion coefficient' Di, whose value of 2.0-2.5 X 10(-11) m2 s-1 is approximately equal to the translational diffusion coefficient predicted for a stiff DNA piece of the persistence length, 65 nm. Comparison of our measured Di values to those predicted from a recent theory of circular worm-like coils (K. Soda, Macromolecules 17 (1984) 2365) shows that the internal motions are faster than the theoretical values. One of the reasons for this discrepancy could be that the theory does not take into account torsional motions, which contribute significantly to the internal dynamics (J.C. Thomas, S.A. Allison, C.J. Appelof and J.M. Schurr, Biophys. Chem. 12 (1980) 177). At low K values, the fast relaxation of superhelical pUC8 is no longer proportional to K2, but reaches a constant value as K approaches zero. This behavior, not seen for the linearized DNA, can be interpreted in terms of rotational diffusion of a flexible rod-like molecule (T. Maeda and S. Fujime, Macromolecules 17 (1984) 2381) and supports an interwound rod-like structure for pUC8 DNA with an average end-to-end distance of 220 nm.     

Light-Scattering Spectrum Due to Wiggling Motions of Bacteria

Simple models are used to calculate the inelastic light scattering spectrum of motile bacteria when wiggling motions are included in addition to translational displacement. Computations of spectra lead to the conclusion that nontranslational motions can be neglected when swimming speeds are deduced from light-scattering data for normal vigorously motile strains. On the other hand, for slowly translating bacteria, or for strains exhibiting noticeable wiggling motion when viewed in a microscope, additional spectral components may be significant. Such components are best distinguished when measurements are made at small and intermediate scattering angles; at large angles the spectra have approximately the same scaling properties (functionals of Qt, Q being the Bragg wave vector) as those associated with simple translational motility.     

Proprioceptive Interaction between the Two Arms in a Single-Arm Pointing Task

Proprioceptive signals coming from both arms are used to determine the perceived position of one arm in a two-arm matching task. Here, we examined whether the perceived position of one arm is affected by proprioceptive signals from the other arm in a one-arm pointing task in which participants specified the perceived position of an unseen reference arm with an indicator paddle. Both arms were hidden from the participant’s view throughout the study. In Experiment 1, with both arms placed in front of the body, the participants received 70–80 Hz vibration to the elbow flexors of the reference arm (= right arm) to induce the illusion of elbow extension. This extension illusion was compared with that when the left arm elbow flexors were vibrated or not. The degree of the vibration-induced extension illusion of the right arm was reduced in the presence of left arm vibration. In Experiment 2, we found that this kinesthetic interaction between the two arms did not occur when the left arm was vibrated in an abducted position. In Experiment 3, the vibration-induced extension illusion of one arm was fully developed when this arm was placed at an abducted position, indicating that the brain receives increased proprioceptive input from a vibrated arm even if the arm was abducted. Our results suggest that proprioceptive interaction between the two arms occurs in a one-arm pointing task when the two arms are aligned with one another. The position sense of one arm measured using a pointer appears to include the influences of incoming information from the other arm when both arms were placed in front of the body and parallel to one another.     

Acceleration Workspace of Cooperating Multi-Finger Robot Systems

We present a mathematical method for acceleration workspace analysis of cooperating multi-finger robot systems using a model of point-contact with friction. A new unified formulation from dynamic equations of cooperating multi-finger robots is derived considering the force and acceleration relationships between the fingers and the object to be handled. From the dynamic equation, maximum translational and rotational acceleration bounds of an object are calculated under given constraints of contact conditions, configurations of fingers, and bounds on the torques of joint actuators for each finger. Here, the rotational acceleration bounds can be applied as an important manipulability index when the multi-finger robot grasps an object. To verify the proposed method, we used a set of case studies with a simple multi-finger mechanism system. The achievable acceleration boundary in task space can be obtained successfully with the proposed method and the acceleration boundary depends on the configurations of fingers.     

Magnetosome dynamics in magnetotactic bacteria.

Diffusive motions of the magnetosomes (enveloped Fe3O4 particles) in the magnetotactic bacterium Aquaspirillum magnetotacticum result in a very broad-line Mössbauer spectrum (T approximately 100 mm/s) above freezing temperatures. The line width increases with increasing temperature. The data are analyzed using a bounded diffusion model to yield the rotational and translational motions of the magnetosomes as well as the effective viscosity of the material surrounding the magnetosomes. The results are [theta 2] l/2 less than 1.5 degrees and [x2] 1/2 less than 8.4 A for the rotational and translational motions, respectively, implying that the particles are fixed in whole cells. The effective viscosity is 10 cP at 295 K and increases with decreasing temperature. Additional Fe3+ material in the cell is shown to be associated with the magnetosomes. Fe2+ material in the cell appears to be associated with the cell envelope.     

Cooperative Integration and Representation Underlying Bilateral Network of Fly Motion-Sensitive Neurons

How is binocular motion information integrated in the bilateral network of wide-field motion-sensitive neurons, called lobula plate tangential cells (LPTCs), in the visual system of flies? It is possible to construct an accurate model of this network because a complete picture of synaptic interactions has been experimentally identified. We investigated the cooperative behavior of the network of horizontal LPTCs underlying the integration of binocular motion information and the information representation in the bilateral LPTC network through numerical simulations on the network model. First, we qualitatively reproduced rotational motion-sensitive response of the H2 cell previously reported in vivo experiments and ascertained that it could be accounted for by the cooperative behavior of the bilateral network mainly via interhemispheric electrical coupling. We demonstrated that the response properties of single H1 and Hu cells, unlike H2 cells, are not influenced by motion stimuli in the contralateral visual hemi-field, but that the correlations between these cell activities are enhanced by the rotational motion stimulus. We next examined the whole population activity by performing principal component analysis (PCA) on the population activities of simulated LPTCs. We showed that the two orthogonal patterns of correlated population activities given by the first two principal components represent the rotational and translational motions, respectively, and similar to the H2 cell, rotational motion produces a stronger response in the network than does translational motion. Furthermore, we found that these population-coding properties are strongly influenced by the interhemispheric electrical coupling. Finally, to test the generality of our conclusions, we used a more simplified model and verified that the numerical results are not specific to the network model we constructed.     

Sensory Agreement Guides Kinetic Energy Optimization of Arm Movements during Object Manipulation

The laws of physics establish the energetic efficiency of our movements. In some cases, like locomotion, the mechanics of the body dominate in determining the energetically optimal course of action. In other tasks, such as manipulation, energetic costs depend critically upon the variable properties of objects in the environment. Can the brain identify and follow energy-optimal motions when these motions require moving along unfamiliar trajectories? What feedback information is required for such optimal behavior to occur? To answer these questions, we asked participants to move their dominant hand between different positions while holding a virtual mechanical system with complex dynamics (a planar double pendulum). In this task, trajectories of minimum kinetic energy were along curvilinear paths. Our findings demonstrate that participants were capable of finding the energy-optimal paths, but only when provided with veridical visual and haptic information pertaining to the object, lacking which the trajectories were executed along rectilinear paths.     

Prediction of protein motions from amino acid sequence and its application to protein-protein interaction

Background  

Structural flexibility is an important characteristic of proteins because it is often associated with their function. The movement of a polypeptide segment in a protein can be broken down into two types of motions: internal and external ones. The former is deformation of the segment itself, but the latter involves only rotational and translational motions as a rigid body. Normal Model Analysis (NMA) can derive these two motions, but its application remains limited because it necessitates the gathering of complete structural information.     

Contribution of translational and rotational motions to molecular association in aqueous solution

Much uncertainty and controversy exist regarding the estimation of the enthalpy, entropy, and free energy of overall translational and rotational motions of solute molecules in aqueous solutions, quantities that are crucial to the understanding of molecular association/recognition processes and structure-based drug design. A critique of the literature on this topic is given that leads to a classification of the various views. The major stumbling block to experimentally determining the translational/rotational enthalpy and entropy is the elimination of vibrational perturbations from the measured effects. A solution to this problem, based on a combination of energy equi-partition and enthalpy-entropy compensation, is proposed and subjected to verification. This method is then applied to analyze experimental data on the dissociation/unfolding of dimeric proteins. For one translational/rotational unit at 1 M standard state in aqueous solution, the results for enthalpy (H degrees (tr)), entropy (S degrees (tr)), and free energy (G degrees (tr)) are H (degrees) (tr) = 4.5 +/- 1.5RT, S (degrees) (tr) = 5 +/- 4R, and G (degrees) (tr) = 0 +/- 5RT. Therefore, the overall translational and rotational motions make negligible contribution to binding affinity (free energy) in aqueous solutions at 1 M standard state.