Dihedral-angle information entropy as a gauge of secondary structure propensity

Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set--a sublibrary of the Protein Data Bank at the 90% sequence redundancy level--appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, (http://www.d2check.gatech.edu). Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation-namely, PROCHECK and WHAT_CHECK--is also provided.     

Representing and identifying alternative movement techniques for goal-directed manual tasks

Differences in motion patterns subserving the same movement goal can be identified qualitatively. These alternatives, which may characterize 'movement techniques' (e.g., the stoop and the squat lifting technique), may be associated with significantly different biomechanical constraints and physiological responses. Despite the widely shared understanding of the significance of alternative movement techniques, quantitative representation and identification of movement techniques have received little attention, especially for three-dimensional whole-body motions. In an attempt to systematically differentiate movement techniques, this study introduces a quantitative index termed joint contribution vector (JCV) representing a motion in terms of contributions of individual joint degrees-of-freedom to the achievement of the task goal. Given a set of uncharacterized (unlabeled) motions represented by joint angle trajectories (motion capture data), the JCV and statistical clustering methods enable automated motion classification to uncover a taxonomy of alternative movement techniques. The results of our motion data analyses show that the JCV was able to characterize and discern stoop and squat lifting motions, and also to identify movement techniques for a three-dimensional, whole-body, one-handed load-transfer task. The JCV index would facilitate consideration of alternative movement techniques in a variety of applications, including work method comparison and selection, and human motion modeling and simulation.     

Pressure – volume curves and drought injury

Leaf hygrometers were used to establish pressure-volume curves on detached leaves of four herbaceous species ( Asarum europaeum , L., Hepatica nobilis , Mill., Phyteuma spicatum , L., Pulmonaria officialis , L.). Breakdown of leaf tissues due to drought injury was independently estimated. There was good agreement between the onset of visible symptoms and beginning deviations from the straight-line portion of the pressure-volume curve. Type I transformation of data (plots of water potential vs. reciprocal relative water content) is superior for recognizing deviating data points. The results are discussed in the context of pressure-volume curve methodology; pressure-volume curves are shown to provide a promising tool for estimating and displaying drought tolerance in plants.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ambulatory measurement of 3D knee joint angle

Three-dimensional measurement of joint motion is a promising tool for clinical evaluation and therapeutic treatment comparisons. Although many devices exist for joints kinematics assessment, there is a need for a system that could be used in routine practice. Such a system should be accurate, ambulatory, and easy to use. The combination of gyroscopes and accelerometers (i.e., inertial measurement unit) has proven to be suitable for unrestrained measurement of orientation during a short period of time (i.e., few minutes). However, due to their inability to detect horizontal reference, inertial-based systems generally fail to measure differential orientation, a prerequisite for computing the three-dimentional knee joint angle recommended by the Internal Society of Biomechanics (ISB). A simple method based on a leg movement is proposed here to align two inertial measurement units fixed on the thigh and shank segments. Based on the combination of the former alignment and a fusion algorithm, the three-dimensional knee joint angle is measured and compared with a magnetic motion capture system during walking. The proposed system is suitable to measure the absolute knee flexion/extension and abduction/adduction angles with mean (SD) offset errors of -1 degree (1 degree ) and 0 degrees (0.6 degrees ) and mean (SD) root mean square (RMS) errors of 1.5 degrees (0.4 degrees ) and 1.7 degrees (0.5 degrees ). The system is also suitable for the relative measurement of knee internal/external rotation (mean (SD) offset error of 3.4 degrees (2.7 degrees )) with a mean (SD) RMS error of 1.6 degrees (0.5 degrees ). The method described in this paper can be easily adapted in order to measure other joint angular displacements such as elbow or ankle.     

Appendix to the sulfur-cyanolysis sites of serum albumin: metabolite competition studies. Tight-binding inhibitions that yield atypical Henderson plots

Ordinary tight-binding inhibition in steady-state enzyme systems is conveniently evaluated by means of the Henderson plot. This is a linear plotting form that has an ordinate intercept equal to the total enzyme concentration. However, there are two experimental situations that yield deviations from the common Henderson plot form. These are inhibitor binding in a separate, noninhibitory mode that depletes the concentration of free inhibitor, and partial inhibition, i.e., the retention of partial activity by the enzyme-inhibitor complex. Noninhibitory depletion results in Henderson plots with elevated ordinate intercepts. Competitive partial inhibition yields a characteristic pattern of parabolic Henderson plots.     

Harbor Seals (Phoca vitulina) Can Perceive Optic Flow under Water

Optic flow, the pattern of apparent motion elicited on the retina during movement, has been demonstrated to be widely used by animals living in the aerial habitat, whereas underwater optic flow has not been intensively studied so far. However optic flow would also provide aquatic animals with valuable information about their own movement relative to the environment; even under conditions in which vision is generally thought to be drastically impaired, e. g. in turbid waters. Here, we tested underwater optic flow perception for the first time in a semi-aquatic mammal, the harbor seal, by simulating a forward movement on a straight path through a cloud of dots on an underwater projection. The translatory motion pattern expanded radially out of a singular point along the direction of heading, the focus of expansion. We assessed the seal''s accuracy in determining the simulated heading in a task, in which the seal had to judge whether a cross superimposed on the flow field was deviating from or congruent with the actual focus of expansion. The seal perceived optic flow and determined deviations from the simulated heading with a threshold of 0.6 deg of visual angle. Optic flow is thus a source of information seals, fish and most likely aquatic species in general may rely on for e. g. controlling locomotion and orientation under water. This leads to the notion that optic flow seems to be a tool universally used by any moving organism possessing eyes.     

Power analysis to determine sample size for monitoring vegetation change in salt marsh habitats

Numerous initiatives are underway throughout New England and elsewhere to quantify salt marsh vegetation change, mostly in response to habitat restoration, sea level rise, and nutrient enrichment. To detect temporal changes in vegetation at a marsh or to compare vegetation among different marshes with a degree of statistical certainty an adequate sample size is required. Based on sampling 1 m² vegetation plots from 11 New England salt marsh data sets, we conducted a power analysis to determine the minimum number of samples that were necessary to detect change between vegetation communities. Statistical power was determined for sample sizes of 5, 10, 15, and 20 vegetation plots at an alpha level of 0.05. Detection of subtle differences between vegetation data sets (e.g., comparing vegetation in the same marsh over two consecutive years) can be accomplished using a sample size of 20 plots with a reasonable probability of detecting a difference when one truly exists. With a lower sample size, and thus lower power, there is an increased probability of not detecting a difference when one exists (e.g., Type II error). However, if investigators expect to detect major changes in vegetation (e.g., such as those between an un-impacted and a highly impacted marsh) then a sample size of 5, 10, or 15 plots may be appropriate while still maintaining adequate power. Due to the relative ease of collecting vegetation data, we suggest a minimum sample size of 20 randomly located 1 m² plots when developing monitoring designs to detect vegetation community change of salt marshes. The sample size of 20 plots per New England salt marsh is appropriate regardless of marsh size or permanency (permanent or non-permanent) of the plots.     

Analysis of three-dimensional ciliary beating by means of high-speed stereomicroscopy.

Results are presented on the analysis of three-dimensional motion of compound cilia or cirri in voltage-clamped specimens of the protozoan Stylonychia mytilus. Time series of three-dimensional data were obtained by using the anaxial illumination method for simultaneous recording of stereoscopic video images. Data processing involved the following steps: determination of a reference coordinate system based solely on features present in each stereo-pair; tracing of cirral axes in digitized images, conversion to parameter curves by means of least-squares polynomial approximation, conversion of pairs of two-dimensional data to a series of three-dimensional data; correction for distortion due to projective shortening and conversion to a series of polynomial triplets, and analysis of the periodical components of the motion pattern in the frequency domain. Reconstructed beating cycles show typical differences between hyperpolarization-induced ciliary activity and depolarization-induced ciliary activity. Reconstructions of the motion of the basal segment of a cirrus are in agreement with existing data. Analysis of the curvature and torsion of a cirral axis during beating does not reveal any simple pattern of propagated activity within the axoneme. The return stroke may be subdivided into two phases. First, a curvature peak develops proximally. Secondly, a region with increased torsion arises more distally and spreads out in proximal direction. Both curvature and torsion return to minimal values by the beginning of the power stroke.     

OpenSim Moco: Musculoskeletal optimal control

Musculoskeletal simulations are used in many different applications, ranging from the design of wearable robots that interact with humans to the analysis of patients with impaired movement. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. OpenSim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation. Moco frees researchers from implementing direct collocation themselves—which typically requires extensive technical expertise—and allows them to focus on their scientific questions. The software can handle a wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyography-driven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which enable modeling of kinematic loops (e.g., cycling models) and complex anatomy (e.g., patellar motion). To show the abilities of Moco, we first solved for muscle activity that produced an observed walking motion while minimizing squared muscle excitations and knee joint loading. Next, we predicted how muscle weakness may cause deviations from a normal walking motion. Lastly, we predicted a squat-to-stand motion and optimized the stiffness of an assistive device placed at the knee. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand the movement of humans and other animals.     

Gait analysis using gravitational acceleration measured by wearable sensors

A novel method for measuring human gait posture using wearable sensor units is proposed. The sensor units consist of a tri-axial acceleration sensor and three gyro sensors aligned on three axes. The acceleration and angular velocity during walking were measured with seven sensor units worn on the abdomen and the lower limb segments (both thighs, shanks and feet). The three-dimensional positions of each joint are calculated from each segment length and joint angle. Joint angle can be estimated mechanically from the gravitational acceleration along the anterior axis of the segment. However, the acceleration data during walking includes three major components; translational acceleration, gravitational acceleration and external noise. Therefore, an optimization analysis was represented to separate only the gravitational acceleration from the acceleration data. Because the cyclic patterns of acceleration data can be found during constant walking, a FFT analysis was applied to obtain some characteristic frequencies in it. A pattern of gravitational acceleration was assumed using some parts of these characteristic frequencies. Every joint position was calculated from the pattern under the condition of physiological motion range of each joint. An optimized pattern of the gravitational acceleration was selected as a solution of an inverse problem. Gaits of three healthy volunteers were measured by walking for 20 s on a flat floor. As a result, the acceleration data of every segment was measured simultaneously. The characteristic three-dimensional walking could be shown by the expression using a stick figure model. In addition, the trajectories of the knee joint in the horizontal plane could be checked by visual imaging on a PC. Therefore, this method provides important quantitive information for gait diagnosis.     

Three-dimensional finite element modelling of muscle forces during mastication

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.     

Disaccharide conformational maps: 3D contours or 2D plots?

The potential energy surfaces of several alpha-(1-->3)- and beta-(1-->4)-linked disaccharides were obtained and plotted in terms of energy versus psi glycosidic angle. These plots were compared to those obtained previously in the way of the usual 3D contour maps, which relate the energy with the two glycosidic angles (phi and psi). Given the usually small variations of the phi angle in the low-energy regions (at least using MM3), both kinds of graphs lead to similar conclusions concerning flexibility measurements by two different methods and assessment of the effects of sulfation and/or hydroxyl group orientation. Only second-order effects were found with some sulfated disaccharides, not changing the general conclusions. The computational efforts required to produce those plots are smaller, and the plots are easier to interpret. Besides, the conversion of a 3D map into a 2D plot leaves the possibility of constructing 3D maps of carbohydrates including a second variable different to phi, e.g., the second psi angle of a trisaccharide or the omega angle of a 6-linked disaccharide.     

Trait-related flowering patterns in submediterranean mountain meadows

The research aims were to identify the flowering pattern and the related functional strategies in submediterranean mountain meadows (central Italy) and understand their relationships with some environmental and community structure variables. The number of flowering shoots per species was counted and environmental data were collected in 40 plots during 2009. Analysis of the species and trait data sets highlighted a flowering pattern and an underlying functional pattern. Dominant species tend to bloom in the central phases of the growing season when no stress acts in the system and a long time is available for plant growth and seed maturation. This kind of species does not need functional strategies allowing the canopy fast pre-emption or the tolerance to drought stress. Non-dominant species have two groups of functional strategies that allow them to share the same flowering period of dominant ones by a different type of space occupation (spatial niche partitioning) or to flower before or after their flowering period (temporal niche partitioning). The functional strategies involved in the temporal niche partitioning have a dual ecological meaning, limiting competition with dominant species by fast growth and seed maturation (e.g., short stature, mobilisation of stored reserves, colonization of unexploited soil niches by clonal growth organs and light seeds) and enabling tolerance to drought stress (e.g., scleromorphic and succulent leaves, persistent green leaves, tap roots) and to the low light availability at the ground level owing to the change of grassland structure (e.g., tall size and upright growth form).     

Phylogenetic dating with confidence intervals using mean path lengths

The mean path length (MPL) method, a simple method for dating nodes in a phylogenetic tree, is presented. For small trees the age estimates and corresponding confidence intervals, calibrated with fossil data, can be calculated by hand, and for larger trees a computer program gives the results instantaneously (a Pascal program is available upon request). Necessary input data are a rooted phylogenetic tree with edge lengths (internode lengths) approximately corresponding to the number of substitutions between the nodes. Given this, the MPL method produces relative age estimates with confidence intervals for all nodes of the tree. With the age of one or several nodes of the tree being known from reference fossils, the relative age estimates induce absolute age estimates and confidence intervals of the nodes of the tree. The MPL method relies on the assumptions that substitutions occur randomly and independently in different sites in the DNA sequence and that the substitution rates are approximately constant in time, i.e., assuming a molecular clock. A method is presented for identification of the nodes in the tree at which significant deviations from the clock assumption occur, such that dating may be done using different rates in different parts of the tree. The MPL method is illustrated with the Liliales, a group of monocot flowering plants.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

Evaluation of a new algorithm to determine the hip joint center

Accurately locating the hip joint center is a challenging and important step in many biomechanical investigations. The purpose of this study was to test the accuracy and robustness of a "pivoting" algorithm used to locate the hip center. We tested the performance of this algorithm with data acquired by manipulating a ball and socket model of the hip through several motion patterns. The smallest mean errors of 2.2+/-0.2 mm occurred with a circumduction motion pattern, while the largest errors of 4.2+/-1.3 mm occurred with single-plane motion (e.g., flexion/extension). Introducing random noise with an amplitude of 30 mm increased the errors by only 1.3+/-0.5 mm with a circumduction motion pattern. The pivoting algorithm performs well in the laboratory, and further work is warranted to evaluate its performance in a clinical setting.     

Yeast tRNAPhe conformation wheels: a novel probe of the monoclinic and orthorhombic models.

A series of conformation wheels is constructed from the recently refined X-ray crystallographic data of monoclinic and orthorhombic yeast tRNAPhe. These circular plots relate the primary chemical structure (i.e., base sequence) directly to the secondary and tertiary structure of the molecule. The circular sequence of backbone torsion angles displays a unique pattern that is useful both in distinguishing the ordered and disordered regions of the molecule and in comparing the three sets of experimental data. Composite conformation wheels describe the fluctuations in the "fixed" parameters (phi', phi, chi) and independent conformation wheels reveal the changes in the "variable" parameters (omega', omega, psi, psi') of the three different yeast tRNAPhe models. Additional plots of base-stacking parameters help to visualize the intimate interrelationship between chemical sequence and three-dimensional folding of yeast tRNAPhe. The composite data illustrate several conformational schemes that position the bases of adjacent nucleosides in a parallel stacked array and reveal an even larger number of conformations that introduce bends or turns in the polynucleotide chain.     

Analytic determination of the depth effect in stereokinetic phenomena without a rigidity assumption

When a circular disk with an eccentric dot is set in slow rotary motion a compelling impression of a three-dimensional cone is observed. Similarly a line segment of constant length, a bar, rotating on the frontal plane appears slanted in depth. The two stereokinetic phenomena cannot be explained on the basis of Ullman's method of extracting depth from 2-D moving stimuli i.e. the rigidity assumption. A new analytic model is here presented based on the hypothesis that the visual system minimizes the relative velocity differences among all the points of the moving pattern. Two different methods of calculating the depth displacement are described: the velocity field method and the trajectories method. Both lead to the same results. A comparison of the theoretical results with the experimental ones supports the validity of the model.