Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.     

Enhanced resolution of fluorescence anisotropy decays by simultaneous analysis of progressively quenched samples. Applications to anisotropic rotations and to protein dynamics.

Enhanced resolution of rapid and complex anisotropy decays was obtained by measurement and analysis of data from progressively quenched samples. Collisional quenching by acrylamide was used to vary the mean decay time of indole or of the tryptophan fluorescence from melittin. Anisotropy decays were obtained from the frequency-response of the polarized emission at frequencies from 4 to 2,000 MHz. Quenching increases the fraction of the total emission, which occurs on the subnanosecond timescale, and thereby provides increased information on picosecond rotational motions or local motions in proteins. For monoexponential subnanosecond anisotropy decays, enhanced resolution is obtained by measurement of the most highly quenched samples. For complex anisotropy decays, such as those due to both local motions and overall protein rotational diffusion, superior resolution is obtained by simultaneous analysis of data from quenched and unquenched samples. We demonstrate that measurement of quenched samples greatly reduces the uncertainty of the 50-ps correlation time of indole in water at 20 degrees C, and allows resolution of the anisotropic rotation of indole with correlation times of 140 and 720 ps. The method was applied to melittin in the monomeric and tetrameric forms. With increased quenching, the anisotropy data showed decreasing contributions from overall protein rotation and increased contribution from picosecond tryptophan motions. The tryptophan residues in both the monomeric and the tetrameric forms of melittin displayed substantial local motions with correlation times near 0.16 and 0.06 ns, respectively. The amplitude of the local motion is twofold less in the tetramer. These highly resolved anisotropy decays should be valuable for comparison with molecular dynamics simulations of melittin.     

Frustration‐guided motion planning reveals conformational transitions in proteins

Proteins exist as conformational ensembles, exchanging between substates to perform their function. Advances in experimental techniques yield unprecedented access to structural snapshots of their conformational landscape. However, computationally modeling how proteins use collective motions to transition between substates is challenging owing to a rugged landscape and large energy barriers. Here, we present a new, robotics‐inspired motion planning procedure called dCC‐RRT that navigates the rugged landscape between substates by introducing dynamic, interatomic constraints to modulate frustration. The constraints balance non‐native contacts and flexibility, and instantaneously redirect the motion towards sterically favorable conformations. On a test set of eight proteins determined in two conformations separated by, on average, 7.5 Å root mean square deviation (RMSD), our pathways reduced the Cα atom RMSD to the goal conformation by 78%, outperforming peer methods. We then applied dCC‐RRT to examine how collective, small‐scale motions of four side‐chains in the active site of cyclophilin A propagate through the protein. dCC‐RRT uncovered a spatially contiguous network of residues linked by steric interactions and collective motion connecting the active site to a recently proposed, non‐canonical capsid binding site 25 Å away, rationalizing NMR and multi‐temperature crystallography experiments. In all, dCC‐RRT can reveal detailed, all‐atom molecular mechanisms for small and large amplitude motions. Source code and binaries are freely available at https://github.com/ExcitedStates/KGS/ .     

Elbow‐ and hinge‐bending motions of IgG: Dielectric response and dynamic feature

Immunoglobulin G (IgG) is a Y‐shaped globular protein consisting of two Fab segments connecting to an Fc segment with a flexible hinge region, in which the Fab segments show secondary flexibility at an “elbow” region. In the present work, the hinge‐bending and elbow‐bending motions of aqueous solutions of IgG by microwave dielectric measurements below the freezing point of bulk water was observed. The presence of unfreezable water around the macromolecules reduced the effects of steric hindrance normally generated by ice and enabled the intramolecular motions of IgG. At the same time, the overall IgG molecule rotation was restricted by ice. Papain digestion and reduction of the disulfide linkage at the hinge region was used to generate Fab and Fc fragments. In solutions of these fragments, the dielectric relaxation process of the hinge‐bending motion was absent, although the elbow‐bending motion remained. Three relaxation processes were observed for papain‐digested IgG. The high, middle, and low frequency processes were attributed to unfrozen water, local peptide motions cooperating with bound water, and the elbow‐bending motion, respectively. In the case of the intact IgG, an additional relaxation process due to the hinge‐bending motion was observed at frequencies lower than that of the elbow‐bending motion. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 626–632, 2016.     

The effects of knee joint kinematics on anterior cruciate ligament injury and articular cartilage damage

This study determined which knee joint motions lead to anterior cruciate ligament (ACL) rupture with the knee at 25° of flexion. The knee was subjected to internal and external rotations, as well as varus and valgus motions. A failure locus representing the relationship between these motions and ACL rupture was established using finite element simulations. This study also considered possible concomitant injuries to the tibial articular cartilage prior to ACL injury. The posterolateral bundle of the ACL demonstrated higher rupture susceptibility than the anteromedial bundle. The average varus angular displacement required for ACL failure was 46.6% lower compared to the average valgus angular displacement. Femoral external rotation decreased the frontal plane angle required for ACL failure by 27.5% compared to internal rotation. Tibial articular cartilage damage initiated prior to ACL failure in all valgus simulations. The results from this investigation agreed well with other experimental and analytical investigations. This study provides a greater understanding of the various knee joint motion combinations leading to ACL injury and articular cartilage damage.     

Superimposition of protein structures with dynamically weighted RMSD

In protein modeling, one often needs to superimpose a group of structures for a protein. A common way to do this is to translate and rotate the structures so that the square root of the sum of squares of coordinate differences of the atoms in the structures, called the root-mean-square deviation (RMSD) of the structures, is minimized. While it has provided a general way of aligning a group of structures, this approach has not taken into account the fact that different atoms may have different properties and they should be compared differently. For this reason, when superimposed with RMSD, the coordinate differences of different atoms should be evaluated with different weights. The resulting RMSD is called the weighted RMSD (wRMSD). Here we investigate the use of a special wRMSD for superimposing a group of structures with weights assigned to the atoms according to certain thermal motions of the atoms. We call such an RMSD the dynamically weighted RMSD (dRMSD). We show that the thermal motions of the atoms can be obtained from several sources such as the mean-square fluctuations that can be estimated by Gaussian network model analysis. We show that the superimposition of structures with dRMSD can successfully identify protein domains and protein motions, and that it has important implications in practice, e.g., in aligning the ensemble of structures determined by nuclear magnetic resonance.     

Rotational and translational swimming of human spermatozoa: a dynamic laser light scattering study

The rotational swimming motion of human spermatozoa is evaluated from measurements of depolarized dynamic laser light scattering at zero angle. The analysis is based on a Maxwellian angular velocity distribution and yields a rotational frequency of about 4 Hz that is ascribed to the rotation of the sperm head. From comparison with the translational swimming motion, a propelling efficiency of about 10 micron per turn is deduced. This parameter describes the linkage between the rotational and translational swimming motion and is likely to be discriminatory in the analysis of physiological and pathological sperm motions.     

Nanosecond segmental mobilities of tryptophan residues in proteins observed by lifetime-resolved fluorescence anisotropies.

Steady-state and lifetime-resolved fluorescence anisotropy measurements of protein fluorescence were used to investigate the depolarizing motions of tryptophan residues in proteins. Lifetime resolution was achieved by oxygen quenching. The proteins investigated were carbonic anhydrase, carboxypeptidase A, alpha-chymotrypsin, trypsin, pepsin, and bovine and human serum albumin. When corrected for overall protein rotation, the steady state anisotropies indicate that, on the average, the tryptophan residues in these proteins rotate 29 degrees +/- 6 degrees during the unquenched excited state lifetimes of these proteins, which range from 1.7 to 6.1 ns. The lifetime-resolved anisotropies reveal correlation times for these displacements ranging from 1 to 12 ns. On the average these correlation times are tenfold shorter than that expected for overall protein rotation. We conclude that the tryptophan residues in these proteins display remarkable freedom of motion within the protein matrix, which implies that these matrices are highly flexible on the nanosecond time scale.     

Internal dynamics and overall motion of lysozyme studied by fluorescence depolarization of the eosin lysozyme complex

Time-resolved fluorescence depolarization on the nanosecond and sub-nanosecond time scales is a powerful technique for the study of rapid motions in the condensed phase. We apply this technique to measure the motions of proteins using both extrinsic and intrinsic probes. Eosin, which absorbs and fluoresces in the visible, forms a one-to-one complex with lysozyme binding in the hydrophobic box region and is used as an extrinsic probe of lysozyme motion. The long-time anisotropy of bound eosin is used to measure the overall rotation time of lysozyme for which refined values are presented. In addition, our measurements show a rapid restricted motion of the eosin molecule on the time scale of approximately 100 ps. The order parameter, a model independent measure of the extent of the restriction of the rapid motions, decreases with increasing temperature, indicating that the motion of the eosin is less hindered as temperature increases. We compare our results with the crystallographic measurements of least square displacements for the hydrophobic box region. Our measurements provide direct time resolved confirmation that the displacements observed in this region correspond to rapid motion.     

Backbone dynamics of Tet repressor alpha8intersectionalpha9 loop

A set of single Trp mutants of class B Tet repressor (TetR), in which Trp residues are located from positions 159 to 167, has been engineered to investigate the dynamics of the loop joining the alpha-helices 8 and 9. The fluorescence anisotropy decay of most mutants can be described by the sum of three exponential components. The longest rotational correlation time, 30 ns at 10 degrees C, corresponds to the overall rotation of the protein. The shortest two components, on the subnanosecond and nanosecond time scale, are related to internal motions of the protein. The initial anisotropy, in the 0.16-0.22 range, indicates the existence of an additional ultrafast motion on the picosecond time scale. Examination of physical models for underlying motions indicates that librational motions of the Trp side chain within the rotameric chi(1) x chi(2) potential wells contribute to the picosecond depolarization process, whereas the subnanosecond and nanosecond depolarization processes are related to backbone dynamics. In the absence of inducer, the order parameters of these motions, about 0.90 and 0.80 for most positions, indicate limited flexibility of the loop backbone. Anhydrotetracycline binding to TetR induces an increased mobility of the loop on the nanosecond time scale. This suggests that entropic factors might play a role in the mechanism of allosteric transition.     

Bias-free separation of internal and overall motion of biomolecules

Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias-free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the "total amount of motion" (TAM) in the mode. Our algorithm allows to back-calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13-ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias-free separation.     

Coherent Motions in Confluent Cell Monolayer Sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.     

Coherent Motions in Confluent Cell Monolayer Sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.     

Maximising forward somersault rotation in springboard diving

Performance in the flight phase of springboard diving is limited by the amounts of linear and angular momentum generated during the takeoff phase. A planar 8-segment torque-driven simulation model combined with a springboard model was used to investigate optimum takeoff technique for maximising rotation in forward dives from the one metre springboard. Optimisations were run by varying the torque activation parameters to maximise forward rotation potential (angular momentum × flight time) while allowing for movement constraints, anatomical constraints, and execution variability. With a constraint to ensure realistic board clearance and anatomical constraints to prevent joint hyperextension, the optimised simulation produced 24% more rotation potential than a simulation matching a 2½ somersault piked dive. When 2 ms perturbations to the torque onset timings were included for the ankle, knee and hip torques within the optimisation process, the model was only able to produce 87% of the rotation potential achieved in the matching simulation. This implies that a pre-planned technique cannot produce a sufficiently good takeoff and that adjustments must be made during takeoff. When the initial onset timings of the torque generators were unperturbed and 10 ms perturbations were introduced into the torque onset timings in the board recoil phase, the optimisation produced 8% more rotation potential than the matching simulation. The optimised simulation had more hip flexion and less shoulder extension at takeoff than the matching simulation. This study illustrates the difficulty of including movement variability within performance optimisation when the movement duration is sufficiently long to allow feedback corrections.     

Saturation-transfer electron spin resonance studies on the mobility of spin-labeled sodium and potassium ion activated adenosinetriphosphatase in membranes from Squalus acanthias

The sodium and potassium ion activated adenosinetriphosphatase [(Na+,K+)-ATPase] in membranous preparations from Squalus acanthias has been spin-labeled on sulfhydryl groups after prelabeling with N-ethylmaleimide. Saturation-transfer electron spin resonance spectroscopy has been used to study the rotational motions of the labeled protein on the microsecond time scale. Effective rotational correlation times deduced from the diagnostic line-height ratios in the second-harmonic, 90 degrees out-of-phase (V2') spectra are much larger than those deduced from the spectral integrals, indicating the presence of large-scale segmental motions, in addition to rotation of the protein as a whole. Experiments involving controlled cross-linking of the protein by glutaraldehyde, as well as measurements of the line broadening of the conventional electron spin resonance spectra, support this interpretation. Both the spectral integrals and diagnostic line-height ratios are found to increase irreversibly with time on incubation at temperatures greater than 20 degrees C, corresponding to a decrease in the segmental motion of the protein and probably also in the overall protein rotation. The native enzyme displays a marked nonlinearity in the Arrhenius temperature dependence of the activity at temperatures above 20 degrees C, and the activity decreases with a half-life of ca. 70 min on incubation at 37 degrees C (but not on incubation at low temperature), paralleling the time- and temperature-dependent changes in the saturation-transfer spectra of the labeled protein. Both of these observations suggest that the changes observed in the molecular dynamics could correspond to functional properties of the protein.(ABSTRACT TRUNCATED AT 250 WORDS)     

A Biological Micro Actuator: Graded and Closed-Loop Control of Insect Leg Motion by Electrical Stimulation of Muscles

In this study, a biological microactuator was demonstrated by closed-loop motion control of the front leg of an insect (Mecynorrhina torquata, beetle) via electrical stimulation of the leg muscles. The three antagonistic pairs of muscle groups in the front leg enabled the actuator to have three degrees of freedom: protraction/retraction, levation/depression, and extension/flexion. We observed that the threshold amplitude (voltage) required to elicit leg motions was approximately 1.0 V; thus, we fixed the stimulation amplitude at 1.5 V to ensure a muscle response. The leg motions were finely graded by alternation of the stimulation frequencies: higher stimulation frequencies elicited larger leg angular displacement. A closed-loop control system was then developed, where the stimulation frequency was the manipulated variable for leg-muscle stimulation (output from the final control element to the leg muscle) and the angular displacement of the leg motion was the system response. This closed-loop control system, with an optimized proportional gain and update time, regulated the leg to set at predetermined angular positions. The average electrical stimulation power consumption per muscle group was 148 µW. These findings related to and demonstrations of the leg motion control offer promise for the future development of a reliable, low-power, biological legged machine (i.e., an insect–machine hybrid legged robot).     

Internal Dynamics and Overall Motion of Lysozyme Studied by Fluorescence Depolarization of the Eosin Lysozyme Complex

Abstract

Time-resolved fluorescence depolarization on the nanosecond and sub-nanosecond time scales is a powerful technique for the study of rapid motions in the condensed phase. We apply this technique to measure the motions of proteins using both extrinsic and intrinsic probes. Eosin, which absorbs and fluoresces in the visible, forms a one-to-one complex with lysozyme binding in the hydrophobic box region and is used as an extrinsic probe of lysozyme motion. The long-time anisotropy of bound eosin is used to measure the overall rotation time of lysozyme for which refined values are presented. In addition, our measurements show a rapid restricted motion of the eosin molecule on the time scale of ～ 100 ps. The order parameter, a model independent measure of the extent of the restriction of the rapid motions, decreases with increasing temperature, indicating that the motion of the eosin is less hindered as temperature increases. We compare our results with the crystallographic measurements of least square displacements for the hydrophobic box region. Our measurements provide direct time resolved confirmation that the displacements observed in this region correspond to rapid motion.     

Whole-body angular momentum in incline and decline walking

Angular momentum is highly regulated over the gait cycle and is important for maintaining dynamic stability and control of movement. However, little is known regarding how angular momentum is regulated on irregular surfaces, such as slopes, when the risk of falling is higher. This study examined the three-dimensional whole-body angular momentum patterns of 30 healthy subjects walking over a range of incline and decline angles. The range of angular momentum was either similar or reduced on decline surfaces and increased on incline surfaces relative to level ground, with the greatest differences occurring in the frontal and sagittal planes. These results suggest that angular momentum is more tightly controlled during decline walking when the risk of falling is greater. In the frontal plane, the range of angular momentum was strongly correlated with the peak hip and knee abduction moments in early stance. In the transverse plane, the strongest correlation occurred with the knee external rotation peak in late stance. In the sagittal plane, all external moment peaks were correlated with the range of angular momentum. The peak ankle plantarflexion, knee flexion and hip extension moments were also strongly correlated with the sagittal-plane angular momentum. These results highlight how able-bodied subjects control angular momentum differently on sloped surfaces relative to level walking and provide a baseline for comparison with pathological populations that are more susceptible to falling.     

The morph server: a standardized system for analyzing and visualizing macromolecular motions in a database framework

The number of solved structures of macromolecules that have the same fold and thus exhibit some degree of conformational variability is rapidly increasing. It is consequently advantageous to develop a standardized terminology for describing this variability and automated systems for processing protein structures in different conformations. We have developed such a system as a 'front-end' server to our database of macromolecular motions. Our system attempts to describe a protein motion as a rigid-body rotation of a small 'core' relative to a larger one, using a set of hinges. The motion is placed in a standardized coordinate system so that all statistics between any two motions are directly comparable. We find that while this model can accommodate most protein motions, it cannot accommodate all; the degree to which a motion can be accommodated provides an aid in classifying it. Furthermore, we perform an adiabatic mapping (a restrained interpolation) between every two conformations. This gives some indication of the extent of the energetic barriers that need to be surmounted in the motion, and as a by-product results in a 'morph movie'. We make these movies available over the Web to aid in visualization. Many instances of conformational variability occur between proteins with somewhat different sequences. We can accommodate these differences in a rough fashion, generating an 'evolutionary morph'. Users have already submitted hundreds of examples of protein motions to our server, producing a comprehensive set of statistics. So far the statistics show that the median submitted motion has a rotation of approximately 10 degrees and a maximum Calpha displacement of 17 A. Almost all involve at least one large torsion angle change of >140 degrees. The server is accessible at http://bioinfo.mbb.yale. edu/MolMovDB     

Rotational dynamics of the single tryptophan of porcine pancreatic phospholipase A2, its zymogen, and an enzyme/micelle complex. A steady-state and time-resolved anisotropy study

The rotational dynamics of the single tryptophan of porcine pancreatic phospholipase A2 and its zymogen (prophospholipase A2) have been studied by polarized fluorescence using steady-state and time-resolved single-photon counting techniques. The motion of Trp-3 in phospholipase A2 consists of a rapid subnanosecond wobble of the indole ring with an amplitude of about +/- 20 degrees accompanied by slower isotropic rotation of the entire protein. The rotational correlation times for overall particle rotational diffusion are consistent with conventional hydrodynamic theory. When phospholipase A2 binds to micelles of n-hexadecylphosphocholine, the amplitude of the fast ring rotation decreases. The whole particle rotational correlation time of the enzyme/micelle complex is smaller than the minimum value calculated from hydrodynamic theory. A similar result is obtained for the micelle itself by using the lipophilic probe transparinaric acid. These low values for the particle correlation times can be understood by postulating that an isotropic motion of the fluorophore in the small detergent particles contributes to the angular reorientation of the fluorophore. The internal reorientational motion of the tryptophan in the zymogen, prophospholipase A2, is of larger amplitude than that observed for the enzyme; specifically, the proenzyme exhibits a motion with a significant amplitude on the nanosecond time scale. This additional freedom of motion is attributed to segmental mobility of the N-terminal residues of prophospholipase A2. This demonstrates that this region of the protein is flexible in the zymogen but not in the processed enzyme. The implications of these findings for the mechanism of surface activation of phospholipase A2 are discussed by analogy with a trypsinogen-trypsin activation model.