Obtaining the Morse parameter for large bond-stretching using Murrell-Sorbie parameters

Although the second derivative approach has been shown to provide good parameter relationships between any two interatomic potential functions, these relations are valid only at and near the equilibrium point. Arising from the significant discrepancy between connected potential functions for large stretching of covalent bonds by the second derivative approach, an integral approach is developed herein. By equating interatomic energy integral from equilibrium to bond dissociation, the overall discrepancy is minimized for that range between the Morse and Murrell-Sorbie potential functions. Plotted results reveal two observations. First of all, the second derivative approach is appropriate for bond compression and infinitesimal bond stretching, while the integral approach is more suitable when the extent of bond stretching is significant. Secondly, the Morse function exactly fits the Murrell-Sorbie curve when the Morse shape parameters based on the second derivative and integral approaches are equal. Hence a criterion for determining the accuracy level of Murrell-Sorbie parameters for conversion to Morse parameter is established. Finally, a demonstration was made for cases where a clear discrepancy was observed in the potential energy curves. It was found that the integral approach gives a more conservative and more realistic interatomic force curve than those of derivative approach. Figure Morse potential force using Murrell-Sorbie parameters     

Hawkmoths’ innate flower preferences: a potential selective force on floral biomechanics

While plant–pollinator interactions are a classic model system for evolutionary relationships, the relationship between forager energetics and floral motions remains little explored. In this study, we show that hawkmoths preferentially feed on horizontally oscillating flowers, which have previously been shown to yield higher energy gains during feeding bouts than looming flowers. We also analyze natural flower motions exhibited by four hawkmoth-pollinated species. Our analysis shows these flowers have higher amplitude motions in the horizontal axis than that in the looming axis. This work demonstrates the potential for adaptation between the biomechanical determinates of flower motions and the feeding performance of hawkmoths.     

Morse potential in DNA molecule – An experiment proposal

We rely on the helicoidal Peyrard-Bishop model for DNA dynamics. Interaction between nucleotides at a same site belonging to different strands is modelled by a Morse potential energy. This potential depends on two parameters that are different for AT and CG pairs, which is a possible source for inhomogeneity. It was shown recently (Zdravkovic and Sataric 2011) that certain values of these parameters bring about a negligible influence of inhomogeneity on the solitonic dynamics. We propose an experiment that should be carried out in order to determine the values of both of these parameters.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

A musculo-skeletal model of rat ankle motion and its experimental test on rat

A biomechanical musculo-skeletal model of functional electrical stimulation (FES)-induced rat ankle motion was implemented and tested in rat experiments. The muscle model is a new Hill-based model which includes established physiological relations of force-velocity and force-length-frequency. However, the series-elastic component and the activation component of previous Hill-based models are replaced by a new component which accounts for dynamic time delays and recruitment that occur in real muscle force generation during limb movements. The skeletal model includes gravity and dynamic forces that occur in real rat ankle motions. In computer simulations, various FES patterns were applied to the tibialis anterior (TA) and soleus (SO) model muscles to produce walk-like ankle motions. In lab experiments, the same stimulation patterns were applied by epimysial electrodes implanted in the TA and SO muscles of live rats cordotomized at level T7. The resulting rat motions were recorded by video camera. Video data was converted to ankle angle-vs-time files for comparison with corresponding model angle-vs-time files. Over a physiologically significant range of ankle motions, model parameters were adjustable to yield model motions that agreed with rat motions to within 2 degrees (root mean square differences of rat and model ankle angles). This is shown in plots of model and rat motions presented here for representative cases of FES. The accuracy of our model in reproducing real ankle motions supports the hypothesis that our new muscle model generates correct muscle forces over a useful range of limb motions. It suggests that the model may be useful in the design of FES neural prostheses.     

A Bio-Inspired,Motion-Based Analysis of Crowd Behavior Attributes Relevance to Motion Transparency,Velocity Gradients,and Motion Patterns

The analysis of motion crowds is concerned with the detection of potential hazards for individuals of the crowd. Existing methods analyze the statistics of pixel motion to classify non-dangerous or dangerous behavior, to detect outlier motions, or to estimate the mean throughput of people for an image region. We suggest a biologically inspired model for the analysis of motion crowds that extracts motion features indicative for potential dangers in crowd behavior. Our model consists of stages for motion detection, integration, and pattern detection that model functions of the primate primary visual cortex area (V1), the middle temporal area (MT), and the medial superior temporal area (MST), respectively. This model allows for the processing of motion transparency, the appearance of multiple motions in the same visual region, in addition to processing opaque motion. We suggest that motion transparency helps to identify “danger zones” in motion crowds. For instance, motion transparency occurs in small exit passages during evacuation. However, motion transparency occurs also for non-dangerous crowd behavior when people move in opposite directions organized into separate lanes. Our analysis suggests: The combination of motion transparency and a slow motion speed can be used for labeling of candidate regions that contain dangerous behavior. In addition, locally detected decelerations or negative speed gradients of motions are a precursor of danger in crowd behavior as are globally detected motion patterns that show a contraction toward a single point. In sum, motion transparency, image speeds, motion patterns, and speed gradients extracted from visual motion in videos are important features to describe the behavioral state of a motion crowd.     

Influence of inhibitor binding on the internal motions of lysozyme

Time-resolved laser-induced fluorescence depolarization measurements of internal motions in lysozyme are presented. The fluorescent dye eosin binds in a one-to-one complex with the enzyme, and is used both to measure the overall tumbling time constants and to probe the motions of residues in the region of binding. The precision and accuracy of the present method for determining the overall tumbling time constants compare favorably with those from other methods used in the literature. The extent of the internal motions, as described by a model independent order parameter, S2, is temperature dependent, and changes when the inhibitor N,N',N"-triacetylchitotriose, (GlcNAc)3, is bound to the active site of the enzyme. The observed temperature dependence and changes in S2 upon binding of (GlcNAc)3 are interpreted in terms of a nonharmonic model of the effective potential that is consistent with the picture of concerted motions in the protein. The values of the parameters of the potential that reproduce the data with and without the bound inhibitor imply that (GlcNAc)3 binding causes an increase in the rigidity of the protein, which agree qualitatively with other results on the lysozyme-(GlcNAc)3 system.     

Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method

In this paper we develop a lattice Boltzmann algorithm to simulate red blood cell (RBC) behavior in shear flows. The immersed boundary method is employed to incorporate the fluid-membrane interaction between the flow field and deformable cells. The cell membrane is treated as a neo-Hookean viscoelastic material and a Morse potential is adopted to model the intercellular interaction. Utilizing the available mechanical properties of RBCs, multiple cells have been studied in shear flows using a two-dimensional approximation. These cells aggregate and form a rouleau under the action of intercellular interaction. The equilibrium configuration is related to the interaction strength. The end cells exhibit concave shapes under weak interaction and convex shapes under strong interaction. In shear flows, such a rouleau-like aggregate will rotate or be separated, depending on the relative strengths of the intercellular interaction and hydrodynamic viscous forces. These behaviors are qualitatively similar to experimental observations and show the potential of this numerical scheme for future studies of blood flow in microvessels.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

Biomechanics of cranial kinesis in birds: Testing linkage models in the white-throated sparrow (Zonotrichia albicollis)

Cranial kinesis in sparrows refers to the rotation of the upper jaw around its kinetic joint with the braincase. Avian jaw mechanics may involve the coupled motions of upper and lower jaws, in which the postorbital ligament transfers forces from the lower jaw, through the quadrate, pterygoid, and jugal bones, to the upper jaw. Alternatively, jaw motions may be uncoupled, with the upper jaw moving independently of the lower jaw. We tested hypotheses of cranial kinesis through the use of quantitative computer models. We present a biomechanical model of avian jaw kinetics that predicts the motions of the jaws under assumptions of both a coupled and an uncoupled mechanism. In addition, the model predicts jaw motions under conditions of force transfer by either the jugal or the pterygoid bones. Thus four alternative models may be tested using the proposed model (coupled jugal, coupled pterygoid, uncoupled jugal, uncoupled pterygoid). All models are based on the mechanics of four-bar linkages and lever systems and use morphometric data on cranial structure as the basis for predicting cranial movements. Predictions of cranial motions are tested by comparison to kinematics of white-throated sparrows (Zonotrichia albicollis) during singing. The predicted relations between jaw motions for the coupled model are significantly different from video observations. We conclude that the upper and lower jaws are not coupled in white-throated sparrows. The range of jaw motions during song is consistent with a model in which independent contractions of upper and lower jaw muscles control beak motion. © 1996 Wiley-Liss, Inc.     

hdANM: a new comprehensive dynamics model for protein hinges

Hinge motions are essential for many protein functions, and their dynamics are important to understand underlying biological mechanisms. The ways that these motions are represented by various computational methods differ significantly. By focusing on a specific class of motion, we have developed a new hinge-domain anisotropic network model (hdANM) that is based on the prior identification of flexible hinges and rigid domains in the protein structure and the subsequent generation of global hinge motions. This yields a set of motions in which the relative translations and rotations of the rigid domains are modulated and controlled by the deformation of the flexible hinges, leading to a more restricted, specific view of these motions. hdANM is the first model, to our knowledge, that combines information about protein hinges and domains to model the characteristic hinge motions of a protein. The motions predicted with this new elastic network model provide important conceptual advantages for understanding the underlying biological mechanisms. As a matter of fact, the generated hinge movements are found to resemble the expected mechanisms required for the biological functions of diverse proteins. Another advantage of this model is that the domain-level coarse graining makes it significantly more computationally efficient, enabling the generation of hinge motions within even the largest molecular assemblies, such as those from cryo-electron microscopy. hdANM is also comprehensive as it can perform in the same way as the well-known protein dynamics models (anisotropic network model, rotations-translations of blocks, and nonlinear rigid block normal mode analysis), depending on the definition of flexible and rigid parts in the protein structure and on whether the motions are extrapolated in a linear or nonlinear fashion. Furthermore, our results indicate that hdANM produces more realistic motions as compared to the anisotropic network model. hdANM is an open-source software, freely available, and hosted on a user-friendly website.     

Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method

A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen–iron and the iron–iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden’s Algorithm—a quasi-Newton method—provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples.     

Kinetics of unfolding and folding from amide hydrogen exchange in native ubiquitin

Amide hydrogen (NH) exchange is one of the few experimental techniques with the potential for determining the thermodynamics and kinetics of conformational motions at nearly every residue in native proteins. Quantitative interpretation of NH exchange in terms of molecular motions relies on a simple two-state kinetic model: at any given slowly exchanging NH, a closed or exchange-incompetent conformation is in equilibrium with an open or exchange-competent conformation. Previous studies have demonstrated the accuracy of this model in measuring conformational equilibria by comparing exchange data with the thermodynamics of protein unfolding. We report here a test of the accuracy of the model in determining the kinetics of conformational changes in native proteins. The kinetics of folding and unfolding for ubiquitin have been measured by conventional methods and compared with those derived from a comprehensive analysis of the pH dependence of exchange in native ubiquitin. Rate constants for folding and unfolding from these two very different types of experiments show good agreement. The simple model for NH exchange thus appears to be a robust framework for obtaining quantitative information about molecular motions in native proteins.     

A Monte Carlo Simulation of Nematic and Discotic Ordering in a Polymeric Liquid Crystal

A cyclic polymeric liquid crystal system is simulated using the Metropolis Monte Carlo method in the NVT ensemble. The polymeric system consists of mesogenic moieties attached by alkyl chain spacers to siloxane ring polymers. In the model, the mesogenic moieties are represented individually by an anisotropic Lennard-Jones potential and the polymer ring is represented solely as a constraint on the relative motions of the attached mesogens. A transition from calamitic ordering to discotic ordering is observed as the ring-mesogen bond is varied from full flexible to rigid.     

Elastic network models capture the motions apparent within ensembles of RNA structures

The role of structure and dynamics in mechanisms for RNA becomes increasingly important. Computational approaches using simple dynamics models have been successful at predicting the motions of proteins and are often applied to ribonucleo-protein complexes but have not been thoroughly tested for well-packed nucleic acid structures. In order to characterize a true set of motions, we investigate the apparent motions from 16 ensembles of experimentally determined RNA structures. These indicate a relatively limited set of motions that are captured by a small set of principal components (PCs). These limited motions closely resemble the motions computed from low frequency normal modes from elastic network models (ENMs), either at atomic or coarse-grained resolution. Various ENM model types, parameters, and structure representations are tested here against the experimental RNA structural ensembles, exposing differences between models for proteins and for folded RNAs. Differences in performance are seen, depending on the structure alignment algorithm used to generate PCs, modulating the apparent utility of ENMs but not significantly impacting their ability to generate functional motions. The loss of dynamical information upon coarse-graining is somewhat larger for RNAs than for globular proteins, indicating, perhaps, the lower cooperativity of the less densely packed RNA. However, the RNA structures show less sensitivity to the elastic network model parameters than do proteins. These findings further demonstrate the utility of ENMs and the appropriateness of their application to well-packed RNA-only structures, justifying their use for studying the dynamics of ribonucleo-proteins, such as the ribosome and regulatory RNAs.     

Global ribosome motions revealed with elastic network model

The motions of large systems such as the ribosome are not fully accessible with conventional molecular simulations. A coarse-grained, less-than-atomic-detail model such as the anisotropic network model (ANM) is a convenient informative tool to study the cooperative motions of the ribosome. The motions of the small 30S subunit, the larger 50S subunit, and the entire 70S assembly of the two subunits have been analyzed using ANM. The lowest frequency collective modes predicted by ANM show that the 50S subunit and 30S subunit are strongly anti-correlated in the motion of the 70S assembly. A ratchet-like motion is observed that corresponds well to the experimentally reported ratchet motion. Other slow modes are also examined because of their potential links to the translocation steps in the ribosome. We identify several modes that may facilitate the E-tRNA exiting from the assembly. The A-site t-RNA and P-site t-RNA are found to be strongly coupled and positively correlated in these slow modes, suggesting that the translocations of these two t-RNAs occur simultaneously, while the motions of the E-site t-RNA are less correlated, and thus less likely to occur simultaneously. Overall the t-RNAs exhibit relatively large deformations. Animations of these slow modes of motion can be viewed at.     

The dynamical Matryoshka model: 2. Modeling of local lipid dynamics at the sub-nanosecond timescale in phospholipid membranes

Biological membranes are generally formed by lipids and proteins. Often, the membrane properties are studied through model membranes formed by phospholipids only. They are molecules composed by a hydrophilic head group and hydrophobic tails, which can present a panoply of various motions, including small localized movements of a few atoms up to the diffusion of the whole lipid or collective motions of many of them. In the past, efforts were made to measure these motions experimentally by incoherent neutron scattering and to quantify them, but with upcoming modern neutron sources and instruments, such models can now be improved. In the present work, we expose a quantitative and exhaustive study of lipid dynamics on DMPC and DMPG membranes, using the Matryoshka model recently developed by our group. The model is confronted here to experimental data collected on two different membrane samples, at three temperatures and two instruments. Despite such complexity, the model describes reliably the data and permits to extract a series of parameters. The results compare also very well to other values found in the literature.     

Dynamic analysis of the structure and function of sarcomeres

We attempted to analyze the relationships between the steric structure of the sarcomere and its physiological functions by the use of a sarcomere model of muscle contraction, which includes the geometric arrangement of the thick and thin filaments of the sarcomere, as well as of the cross-bridges and actin sites. Motions of both cross-bridges and myofilaments were considered in terms of our three-state model of the elementary cycle under constraints caused by the steric structure of the sarcomere proposed by Huxley and Brown. Each cross-bridge moves in a molecular potential of our three-state model under the influence of the sliding motions of myofilaments. The sarcomere model described well the tension-velocity relation and isotonic transient processes quantitatively and consistently. In addition, it allowed independence of the no-load shortening velocity upon the overlap of the thick and thin filaments, although the motions of cross-bridges were not independent. Effects of the helical periodicities of the thick and thin filaments and of the number of cross-bridges upon muscle contraction were studied, and the conditions for smooth and efficient contraction of muscle were obtained.     

Two-arm trajectory planning in a manipulation task

This paper addresses the trajectory planning problem for a task which requires positioning and orienting an object firmly grasped by two hands at a visually specified goal configuration in the horizontal plane. The motor task involves three degrees of freedom (two translational and one rotational), and the motions of the arms are constrained by the physical coupling through the held object. Experimentally measured trajectories of two arms in the coordinated positioning/orienting task are presented. The hypothesis that the rotational and translational components of motions are decoupled and independently planned is tested. Two explicit mathematical models to account for the kinematic features of the two-arm motions are formulated, and the predictions of the models are compared with the experimental data. Both models extend the minimum-jerk model to the two-arm coordinated motions case. The trajectories predicted by the models were found to be in qualitative agreement with the experimental data. However, neither model could account for the observed configuration dependence of the motions, nor for some of the properties of the measured velocity components of the motions. Our findings support the idea that the rotational and translational components of two-arm motions in the positioning/orienting task are independently planned in extra-personal space, and are further combined in a hierarchical fashion to produce the observed motions. The tested models may serve as a basis for further investigations of issues pertinent to the generation of two-arm trajectories. Received: 27 March 1995 / Accepted in revised form: 17 September 1996     

A unit-cell-based three-dimensional molecular mechanics analysis for buckling load,effective elasticity and Poisson's ratio determination of the nanosheets

By using a three-dimensional (3D) space-frame-like model, a molecular mechanics (MM) approach is proposed for determination of the buckling loads, effective Young's modulus and Poisson's ratio of the nanosheets, using a proper unit cell. The governing equations are derived based on the 3D kinematics of deformations and the principle of minimum total potential energy. The unit-cell-based results are employed for the space-frame-like finite element model of the nanosheet. The nonlinear MM equations are solved by representing bonds of the boron nitride nanosheet (BNNS) by beam elements to extract the local characteristics. These properties are employed in modelling of the nanosheet, as a space-frame-like finite element structure. The force field constants are chosen according to the Morse, AMBER, UFF and DREIDING models to determine the buckling strength, and effective Poisson's ratio and in-plane rigidity of the whole graphene and BNNSs. Silicon Carbide nanosheets are analysed based on different force constants. These results are concordant with the results available in the literature. The comparisons reveal that the DREIDING force field usually gives the most accurate predictions.