Prospective Control in Catching: The Persistent Angle-of-Approach Effect in Lateral Interception

In lateral interception tasks balls converging onto the same interception location via different trajectories give rise to systematic differences in the kinematics of hand movement. While it is generally accepted that this angle-of-approach effect reflects the prospective (on-line) control of movement, controversy exists with respect to the information used to guide the hand to the future interception location. Based on the pattern of errors observed in a task requiring visual extrapolation of line segments to their intersection with a second line, angle-of-approach effects in lateral interception have been argued to result from perceptual biases in the detection of information about the ball''s future passing distance along the axis of hand movement. Here we demonstrate that this account does not hold under experimental scrutiny: The angle-of-approach effect still emerged when participants intercepted balls moving along trajectories characterized by a zero perceptual bias with respect to the ball''s future arrival position (Experiment 4). Designing and validating such bias-controlled trajectories were done using the line-intersection extrapolation task (Experiments 2 and 3). The experimental set-up used in the present series of experiments was first validated for the lateral interception and the line-intersection extrapolation tasks: In Experiment 1 we used rectilinear ball trajectories to replicate the angle-of-approach effect in lateral interception of virtual balls. Using line segments extracted from these rectilinear ball trajectories, in Experiment 2 we replicated the reported pattern of errors in the estimated locus of intersection with the axis of hand movement. We used these errors to develop a set of bias-free trajectories. Experiment 3 confirmed that the perceptual biases had been corrected for successfully. We discuss the implications on the information-based regulation of hand movement of our finding that the angle-of-approach effect in lateral interception cannot not explained by perceptual biases in information about the ball''s future passing distance.     

Extraction of the energetics of selected types of motion from molecular dynamics trajectories by filtering

A novel method for analyzing molecular dynamics trajectories has been developed which enables the study of selected motions and the corresponding energetics. In particular, it is possible to filter out the high-frequency motions and focus on the structural and energetic features of low-frequency collective motions. The trajectories of the properties of interest are Fourier transformed to the frequency domain, a filtering function is applied, and then an inverse transformation back to the time domain yields the filtered trajectory. The method is demonstrated for harmonic fluctuations and conformational transitions of acetamide and N-acetylalanine N-methylamide, as models for peptides and proteins.     

Analysis of transient behavior in complex trajectories: application to secretory vesicle dynamics

Analysis of trajectories of dynamical biological objects, such as breeding ants or cell organelles, is essential to reveal the interactions they develop with their environments. Many previous works used a global characterization based on parameters calculated for entire trajectories. In cases where transient behavior was detected, this usually concerned only a particular type, such as confinement or directed motion. However, these approaches are not appropriate in situations in which the tracked objects may display many different types of transient motion. We have developed a method to exhaustively analyze different kinds of transient behavior that the tracked objects may exhibit. The method discriminates stalled periods, constrained and directed motions from random dynamics by evaluating the diffusion coefficient, the mean-square displacement curvature, and the trajectory asymmetry along individual trajectories. To detect transient motions of various durations, these parameters are calculated along trajectories using a rolling analysis window whose width is variable. The method was applied to the study of secretory vesicle dynamics in the subplasmalemmal region of human carcinoid BON cells. Analysis of transitions between transient motion periods, combined with plausible assumptions about the origin of each motion type, leads to a model of dynamical subplasmalemmal organization.     

Effect of Colony, Patch Distance, And Trajectory Sense on Movement Complexity in Foraging Ants

Animals display foraging trajectories when exploiting food patches. These displacements have been studied, particularly in organisms that forage from a central place. The complexity of a movement path may be analyzed by means of the fractal dimension, an index that estimates the tortuosity of a trajectory. In field experiments we studied the effect of trajectory sense, distance to the resource patch and colony on the movement complexity in a common ant of central Chile. We found that these factors and their interactions significantly affected the complexity of movement paths. We discuss whether mortality risk determines more linear trajectories when the resource patch is distant from the nest, and whether the information acquired from the environment by workers determines less complex return trips.     

Humans exploit the biomechanics of bipedal gait during visually guided walking over complex terrain

How do humans achieve such remarkable energetic efficiency when walking over complex terrain such as a rocky trail? Recent research in biomechanics suggests that the efficiency of human walking over flat, obstacle-free terrain derives from the ability to exploit the physical dynamics of our bodies. In this study, we investigated whether this principle also applies to visually guided walking over complex terrain. We found that when humans can see the immediate foreground as little as two step lengths ahead, they are able to choose footholds that allow them to exploit their biomechanical structure as efficiently as they can with unlimited visual information. We conclude that when humans walk over complex terrain, they use visual information from two step lengths ahead to choose footholds that allow them to approximate the energetic efficiency of walking in flat, obstacle-free environments.     

A weighted constraint satisfaction approach to human goal-directed decision making

When we plan for long-range goals, proximal information cannot be exploited in a blindly myopic way, as relevant future information must also be considered. But when a subgoal must be resolved first, irrelevant future information should not interfere with the processing of more proximal, subgoal-relevant information. We explore the idea that decision making in both situations relies on the flexible modulation of the degree to which different pieces of information under consideration are weighted, rather than explicitly decomposing a problem into smaller parts and solving each part independently. We asked participants to find the shortest goal-reaching paths in mazes and modeled their initial path choices as a noisy, weighted information integration process. In a base task where choosing the optimal initial path required weighting starting-point and goal-proximal factors equally, participants did take both constraints into account, with participants who made more accurate choices tending to exhibit more balanced weighting. The base task was then embedded as an initial subtask in a larger maze, where the same two factors constrained the optimal path to a subgoal, and the final goal position was irrelevant to the initial path choice. In this more complex task, participants’ choices reflected predominant consideration of the subgoal-relevant constraints, but also some influence of the initially-irrelevant final goal. More accurate participants placed much less weight on the optimality-irrelevant goal and again tended to weight the two initially-relevant constraints more equally. These findings suggest that humans may rely on a graded, task-sensitive weighting of multiple constraints to generate approximately optimal decision outcomes in both hierarchical and non-hierarchical goal-directed tasks.     

Selective excitation of native fluctuations during thermal unfolding simulations: horse heart cytochrome c as a case study

The effect of temperature on the activation of native fluctuation motions during molecular dynamics unfolding simulations of horse heart cytochrome c has been studied. Essential dynamics analysis has been used to analyze the preferred directions of motion along the unfolding trajectories obtained by high temperature simulations. The results of this study have evidenced a clear correlation between the directions of the deformation motions that occur in the first stage of the unfolding process and few specific essential motions characterizing the 300 K dynamics of the protein. In particular, one of those collective motions, involved in the fluctuation of a loop region, is specifically excited in the thermal denaturation process, becoming progressively dominant during the first 500 ps of the unfolding simulations. As further evidence, the essential dynamics sampling performed along this collective motion has shown a tendency of the protein to promptly unfold. According to these results, the mechanism of thermal induced denaturation process involves the selective excitation of one or few specific equilibrium collective motions.     

Stability of particle motions in a narrow channel flow

Single rows or two rows of identical circular cylinders spaced regularly in a narrow channel flow have been shown to be capable of steady flow provided the cylinders are located at equal lateral positions and with equal spacings in the flow direction. The stability of such steady flows of circular cylinders is studied for periodic perturbations of the particle positions, assuming that every other cylinder is equally perturbed in lateral position and spacing along the channel. This results in two rows which are not symmetrically placed. The suspending fluid is assumed to be an incompressible Newtonian fluid. It is assumed that no external forces or moments act on the cylinders and the effects of inertia forces on the motion of the fluid and the cylinders are negligible. The velocity field of the suspending fluid and the instantaneous velocities of the cylinders are computed by the finite element method. The translational velocities of the cylinders are obtained for a large number of particle positions, from which the trajectories of their relative motion are determined for various initial positions near the regular single-file and two-file arrangements. It is shown that when the initial arrangements of the cylinders are slightly perturbed from the regular (alternating) two-file flows, the trajectories of their relative motions become small closed loops around the regular two-file arrangements. In contrast, such small closed trajectories are not obtained when they start from the arrangements near the regular single-file flows or regular (symmetric) double-file flows, suggesting that these flows are unstable under the conditions examined.     

Disaccharide conformational flexibility. II. Molecular dynamics simulations of sucrose

Molecular dynamics simulations have been used to study the motions in vacuum of the disaccharide sucrose. Ensembles of trajectories were calculated for each of the five local minimum energy conformations identified in the adiabatic conformational energy mapping of this molecule. The model sucrose molecules were found to exhibit a variety of motions, although the global minimum energy conformation was found to be dynamically stable, and no transitions away from this structure were observed to occur spontaneously. In all but one of these vacuum trajectories, the intramolecular hydrogen bond between residues was maintained, in accord with recent nmr studies of this molecule in aqueous solution. Considerable flexibility of the furanoid ring was found in the trajectories. No "flips" to the opposite puckering for this ring were found in the simulations starting from the global minimum, although such a transition was observed for a trajectory initiated with one of the higher local minimum energy conformations. Overall, the observed structural fluctuations were consistent with the experimental picture of sucrose as a relatively rigid molecule.     

Smooth Pursuit Eye Movements Improve Temporal Resolution for Color Perception

Human observers see a single mixed color (yellow) when different colors (red and green) rapidly alternate. Accumulating evidence suggests that the critical temporal frequency beyond which chromatic fusion occurs does not simply reflect the temporal limit of peripheral encoding. However, it remains poorly understood how the central processing controls the fusion frequency. Here we show that the fusion frequency can be elevated by extra-retinal signals during smooth pursuit. This eye movement can keep the image of a moving target in the fovea, but it also introduces a backward retinal sweep of the stationary background pattern. We found that the fusion frequency was higher when retinal color changes were generated by pursuit-induced background motions than when the same retinal color changes were generated by object motions during eye fixation. This temporal improvement cannot be ascribed to a general increase in contrast gain of specific neural mechanisms during pursuit, since the improvement was not observed with a pattern flickering without changing position on the retina or with a pattern moving in the direction opposite to the background motion during pursuit. Our findings indicate that chromatic fusion is controlled by a cortical mechanism that suppresses motion blur. A plausible mechanism is that eye-movement signals change spatiotemporal trajectories along which color signals are integrated so as to reduce chromatic integration at the same locations (i.e., along stationary trajectories) on the retina that normally causes retinal blur during fixation.     

Concerted motions in copper plastocyanin and azurin: an essential dynamics study

Essential dynamics analysis of molecular dynamics simulation trajectories (1.1 ns) of two copper containing electron transfer proteins, plastocyanin and azurin, has been performed. The protein essential modes have been analysed in order to identify large concerted motions which could be relevant for the electron transfer function exerted by these proteins. The analysis, conducted for temporal windows of different lengths along the protein trajectories, shows a rapid convergence and indicates that for both the proteins the predominant internal motions occur in a subspace of only a few degrees of freedom. Moreover, it is found that for both the proteins the likely binding sites (i.e. the hydrophobic and negative patches) with the reaction partners move in a concerted fashion with a few structural regions far from the active site. Such results are discussed in connection with the possible involvement of large concerted motions in the recognition and binding interaction with physiological electron transfer partners.     

Formation and control of optimal trajectory in human multijoint arm movement

In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.     

Characterization of protein dynamics from residual dipolar couplings using the three dimensional Gaussian axial fluctuation model

Residual dipolar couplings are potentially very powerful probes of slower protein motions, providing access to dynamic events occurring on functionally important timescales up to the millisecond. One recent approach uses the three dimensional Gaussian Axial Fluctuation model (3D GAF) to determine the major directional modes and associated amplitudes of motions along the peptide chain. In this study we have used standard and accelerated molecular dynamics simulations to determine the accuracy of 3D GAF-based approaches in characterizing the nature and extent of local molecular motions. We compare modes determined directly from the trajectories with motional parameterization derived from RDCs simulated from the same trajectories. Three approaches are tested, that either suppose a known three-dimensional structure, simultaneously determine backbone structure and dynamics, or determine dynamic modes in the absence of a structural model. The results demonstrate the robustness of the 3D GAF analysis even in the presence of large-scale motions, and illustrate the remarkably quantitative nature of the extracted amplitudes. These observations suggest that the approach can be generally used for the study of functionally interesting biomolecular motions.     

Echolocating bats use a nearly time-optimal strategy to intercept prey

Acquisition of food in many animal species depends on the pursuit and capture of moving prey. Among modern humans, the pursuit and interception of moving targets plays a central role in a variety of sports, such as tennis, football, Frisbee, and baseball. Studies of target pursuit in animals, ranging from dragonflies to fish and dogs to humans, have suggested that they all use a constant bearing (CB) strategy to pursue prey or other moving targets. CB is best known as the interception strategy employed by baseball outfielders to catch ballistic fly balls. CB is a time-optimal solution to catch targets moving along a straight line, or in a predictable fashion--such as a ballistic baseball, or a piece of food sinking in water. Many animals, however, have to capture prey that may make evasive and unpredictable maneuvers. Is CB an optimum solution to pursuing erratically moving targets? Do animals faced with such erratic prey also use CB? In this paper, we address these questions by studying prey capture in an insectivorous echolocating bat. Echolocating bats rely on sonar to pursue and capture flying insects. The bat's prey may emerge from foliage for a brief time, fly in erratic three-dimensional paths before returning to cover. Bats typically take less than one second to detect, localize and capture such insects. We used high speed stereo infra-red videography to study the three dimensional flight paths of the big brown bat, Eptesicus fuscus, as it chased erratically moving insects in a dark laboratory flight room. We quantified the bat's complex pursuit trajectories using a simple delay differential equation. Our analysis of the pursuit trajectories suggests that bats use a constant absolute target direction strategy during pursuit. We show mathematically that, unlike CB, this approach minimizes the time it takes for a pursuer to intercept an unpredictably moving target. Interestingly, the bat's behavior is similar to the interception strategy implemented in some guided missiles. We suggest that the time-optimal strategy adopted by the bat is in response to the evolutionary pressures of having to capture erratic and fast moving insects.     

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female's pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction.     

Conditional prediction of consecutive tumor evolution using cancer progression models: What genotype comes next?

Accurate prediction of tumor progression is key for adaptive therapy and precision medicine. Cancer progression models (CPMs) can be used to infer dependencies in mutation accumulation from cross-sectional data and provide predictions of tumor progression paths. However, their performance when predicting complete evolutionary trajectories is limited by violations of assumptions and the size of available data sets. Instead of predicting full tumor progression paths, here we focus on short-term predictions, more relevant for diagnostic and therapeutic purposes. We examine whether five distinct CPMs can be used to answer the question “Given that a genotype with n mutations has been observed, what genotype with n + 1 mutations is next in the path of tumor progression?” or, shortly, “What genotype comes next?”. Using simulated data we find that under specific combinations of genotype and fitness landscape characteristics CPMs can provide predictions of short-term evolution that closely match the true probabilities, and that some genotype characteristics can be much more relevant than global features. Application of these methods to 25 cancer data sets shows that their use is hampered by a lack of information needed to make principled decisions about method choice. Fruitful use of these methods for short-term predictions requires adapting method’s use to local genotype characteristics and obtaining reliable indicators of performance; it will also be necessary to clarify the interpretation of the method’s results when key assumptions do not hold.     

Trajectory formation based on physiological characteristics of skeletal muscles

Human arm trajectories in natural unrestricted reaching movements were studied. They have particular properties such that a hand path is a rather simple straight or curved line, and a tangential velocity profile of hand is bell-shaped. Also these properties are invariant, independent of movement duration and hand-held load. In this study, trajectory formation is investigated on the basis of physiological characteristics of skeletal muscles, and a criterion prescribed by a derivative of isometric muscle torque is proposed. Subsequently, optimal trajectories are formulated under various conditions of movement to account for a planning strategy of human arm trajectories. In addition to such a theoretical approach, human arm trajectories are experimentally observed by a measuring system which provides a visual sensor and a target tracking device, enabling totally unrestricted movements. Then, optimal trajectories are quantitatively evaluated in comparison with experimental data in which essential properties of human arm trajectories are demonstrated. These results support the idea that human arm trajectories are planned in order to minimize the proposed criterion which is determined from physiological aspects. Finally, the physiological advantages of human arm trajectories are discussed with regard to the analysis of observed and optimal trajectories. Received: 2 December 1997 / Accepted in revised form: 20 March 1998     

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that the geometry-based FRODA occasionally sampled the pathway space of force field-based DIMS MD. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.     

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.