The knowledge of multiple conformational states is a prerequisite to understand the function of membrane transport proteins. Unfortunately, the determination of detailed atomic structures for all these functionally important conformational states with conventional high-resolution approaches is often difficult and unsuccessful. In some cases, biophysical and biochemical approaches can provide important complementary structural information that can be exploited with the help of advanced computational methods to derive structural models of specific conformational states. In particular, functional and spectroscopic measurements in combination with site-directed mutations constitute one important source of information to obtain these mixed-resolution structural models. A very common problem with this strategy, however, is the difficulty to simultaneously integrate all the information from multiple independent experiments involving different mutations or chemical labels to derive a unique structural model consistent with the data. To resolve this issue, a novel restrained molecular dynamics structural refinement method is developed to simultaneously incorporate multiple experimentally determined constraints (e.g., engineered metal bridges or spin-labels), each treated as an individual molecular fragment with all atomic details. The internal structure of each of the molecular fragments is treated realistically, while there is no interaction between different molecular fragments to avoid unphysical steric clashes. The information from all the molecular fragments is exploited simultaneously to constrain the backbone to refine a three-dimensional model of the conformational state of the protein. The method is illustrated by refining the structure of the voltage-sensing domain (VSD) of the Kv1.2 potassium channel in the resting state and by exploring the distance histograms between spin-labels attached to T4 lysozyme. The resulting VSD structures are in good agreement with the consensus model of the resting state VSD and the spin-spin distance histograms from ESR/DEER experiments on T4 lysozyme are accurately reproduced.

Nuclear pore complexes (NPCs) form gateways for material transfer across the nuclear envelope of eukaryotic cells. Disordered proteins, rich in phenylalanine-glycine repeat motifs (FG-nups), form the central transport channel. Understanding how nups are arranged in the interior of the NPC may explain how NPC functions as a selectivity filter for transport of large molecules and a sieve-like filter for diffusion of small molecules (<9 nm or 40 kDa). We employed molecular dynamics to model the structures formed by various assemblies of one kind of nup, namely the 609-aa-long FG domain of Nsp1 (Nsp1-FG). The simulations started from different initial conformations and geometrical arrangements of Nsp1-FGs. In all cases Nsp1-FGs collectively formed brush-like structures with bristles made of bundles of 2-27 nups, however, the bundles being cross-linked through single nups leaving one bundle and joining a nearby one. The degree of cross-linking varies with different initial nup conformations and arrangements. Structural analysis reveals that FG-repeats of the nups not only involve formation of bundle structures, but are abundantly present in cross-linking regions where the epitopes of FG-repeats are highly accessible. Large molecules that are assisted by transport factors (TFs) are selectively transported through NPC apparently by binding to FG-nups through populated FG-binding pockets on the TF surface. Therefore, our finding suggests that TFs bind concertedly to multiple FGs in cross-linking regions and break-up the bundles to create wide pores for themselves and their cargoes to pass. In addition, the cross-linking between Nsp1-FG bundles, arising from simulations, is found to set a molecular size limit of <9 nm (40 kDa) for passive diffusion of molecules. Our simulations suggest that the NPC central channel, near the periphery where tethering of nups is dominant, features brush-like moderately cross-linked bundles, but in the central region, where tethering loses its effect, features a sieve-like structure of bundles and frequent cross-links.

Interplay between cellular membranes and their peripheral proteins drives many processes in eukaryotic cells. Proteins of the Bin/Amphiphysin/Rvs (BAR) domain family, in particular, play a role in cellular morphogenesis, for example curving planar membranes into tubular membranes. However, it is still unclear how F-BAR domain proteins act on membranes. Electron microscopy revealed that, in vitro, F-BAR proteins form regular lattices on cylindrically deformed membrane surfaces. Using all-atom and coarse-grained (CG) molecular dynamics simulations, we show that such lattices, indeed, induce tubes of observed radii. A 250 ns all-atom simulation reveals that F-BAR domain curves membranes via the so-called scaffolding mechanism. Plasticity of the F-BAR domain permits conformational change in response to membrane interaction, via partial unwinding of the domains 3-helix bundle structure. A CG simulation covering more than 350 µs provides a dynamic picture of membrane tubulation by lattices of F-BAR domains. A series of CG simulations identified the optimal lattice type for membrane sculpting, which matches closely the lattices seen through cryo-electron microscopy.

Hepatitis C virus (HCV) p7 is a membrane-associated oligomeric protein harboring ion channel activity. It is essential for effective assembly and release of infectious HCV particles and an attractive target for antiviral intervention. Yet, the self-assembly and molecular mechanism of p7 ion channelling are currently only partially understood. Using molecular dynamics simulations (aggregate time 1.2 µs), we show that p7 can form stable oligomers of four to seven subunits, with a bias towards six or seven subunits, and suggest that p7 self-assembles in a sequential manner, with tetrameric and pentameric complexes forming as intermediate states leading to the final hexameric or heptameric assembly. We describe a model of a hexameric p7 complex, which forms a transiently-open channel capable of conducting ions in simulation. We investigate the ability of the hexameric model to flexibly rearrange to adapt to the local lipid environment, and demonstrate how this model can be reconciled with low-resolution electron microscopy data. In the light of these results, a view of p7 oligomerization is proposed, wherein hexameric and heptameric complexes may coexist, forming minimalist, yet robust functional ion channels. In the absence of a high-resolution p7 structure, the models presented in this paper can prove valuable as a substitute structure in future studies of p7 function, or in the search for p7-inhibiting drugs.

BACKGROUND: Biological molecules are often asymmetric with respect to stereochemistry, and correct stereochemistry is essential to their function. Molecular dynamics simulations of biomolecules have increasingly become an integral part of biophysical research. However, stereochemical errors in biomolecular structures can have a dramatic impact on the results of simulations. RESULTS: Here we illustrate the effects that chirality and peptide bond configuration flips may have on the secondary structure of proteins throughout a simulation. We also analyze the most common sources of stereochemical errors in biomolecular structures and present software tools to identify, correct, and prevent stereochemical errors in molecular dynamics simulations of biomolecules. CONCLUSIONS: Use of the tools presented here should become a standard step in the preparation of biomolecular simulations and in the generation of predicted structural models for proteins and nucleic acids.

Integrins may undergo large conformational changes during activation, but the dynamic processes and pathways remain poorly understood. We used molecular dynamics to simulate forced unbending of a complete integrin α(v)β₃ ectodomain in both unliganded and liganded forms. Pulling the head of the integrin readily induced changes in the integrin from a bent to an extended conformation. Pulling at a cyclic RGD ligand bound to the integrin head also extended the integrin, suggesting that force can activate integrins. Interactions at the interfaces between the hybrid and β tail domains and between the hybrid and epidermal growth factor 4 domains formed the major energy barrier along the unbending pathway, which could be overcome spontaneously in ~1 µs to yield a partially-extended conformation that tended to rebend. By comparison, a fully-extended conformation was stable. A newly-formed coordination between the α(v) Asp457 and the α-genu metal ion might contribute to the stability of the fully-extended conformation. These results reveal the dynamic processes and pathways of integrin conformational changes with atomic details and provide new insights into the structural mechanisms of integrin activation.

Oseltamivir (Tamiflu) is currently the frontline antiviral drug employed to fight the flu virus in infected individuals by inhibiting neuraminidase, a flu protein responsible for the release of newly synthesized virions. However, oseltamivir resistance has become a critical problem due to rapid mutation of the flu virus. Unfortunately, how mutations actually confer drug resistance is not well understood. In this study, we employ molecular dynamics (MD) and steered molecular dynamics (SMD) simulations, as well as graphics processing unit (GPU)-accelerated electrostatic mapping, to uncover the mechanism behind point mutation induced oseltamivir-resistance in both H5N1 "avian" and H1N1pdm "swine" flu N1-subtype neuraminidases. The simulations reveal an electrostatic binding funnel that plays a key role in directing oseltamivir into and out of its binding site on N1 neuraminidase. The binding pathway for oseltamivir suggests how mutations disrupt drug binding and how new drugs may circumvent the resistance mechanisms.

Graphics processing units (GPUs) have become an attractive option for accelerating scientific computations as a result of advances in the performance and flexibility of GPU hardware, and due to the availability of GPU software development tools targeting general purpose and scientific computation. However, effective use of GPUs in clusters presents a number of application development and system integration challenges. We describe strategies for the decomposition and scheduling of computation among CPU cores and GPUs, and techniques for overlapping communication and CPU computation with GPU kernel execution. We report the adaptation of these techniques to NAMD, a widely-used parallel molecular dynamics simulation package, and present performance results for a 64-core 64-GPU cluster.

We have implemented a system termed Interactive Molecular Dynamics (IMD), which permits manipulation of molecules in molecular dynamics simulations with real-time force feedback and graphical display. Communication is achieved throughanefficientsocketconnectionbetweenthevisualization program (VMD) and a molecular dynamics program (NAMD) running on single or multiple machines. A natural force feedback interface for molecular steering is provided by a haptic device. We model the effect of simulation speed on the haptic feedback, and discuss results of an IMD study of a 4,000 atom system, the gramicidin A channel.

The abundance of information provided by completely sequenced genomes defines a starting point for new insights in the multi-level organization of organisms and their evolution. At the lowest level enzymes and other protein complexes are formed by aggregating multiple polypeptides. At a higher level enzymes group conceptually into metabolic pathways as part of a dynamic information processing system substrates are processed by enzymes yielding other substrates. A new method based on a combination of sequence information with graph-topology of the underlying pathway is presented. By this approach pathways of different organisms are related to each other by phylogenetic analysis: Metabolic pathways in organisms are assigned by the presence of genes with corresponding functions. A global distance between pathways is defined by using individual distances between sequences of the same functional role. Gap-penalties are introduced for existing pathways with missing functional roles. As an example the method is applied to pathways related to the utilization of ferredoxin as redox-agent. First results report a high versatility and controversial phylogenies. Pathway which evolve early in evolution are present in organisms of all three domains (Archaea, Bacteria and Eucarya). Functional roles which are utilized in these very pathways are common in many pathways of the cell. Pathways which are only present in organisms of a single (or at maximum two) domains often perform ”pathologic” tasks with rare and specialized functional roles. As example serves NADPH – Hg Electron transport with mercury(II) reductase reaction as enzyme. Beside a more comprehensive understanding of similarities and differences between organisms, this method already indicates different evolutionary rates between substrates and enzymes. It is also capable to hint towards variation and specialization of pathways in the sense of an evolution of metabolisms.

Knowledge of the complex molecular structures of living cells is being accumulated at a tremendous rate. Key technologies enabling this success have been, high performance computing and powerful molecular graphics applications, but the technology is beginning to seriously lag behind challenges posed by the size and number of new structures and by the emerging opportunities in drug design and genetic engineering. A visual computing environment is being developed which permits interactive modeling of biopolymers by linking a 3D molecular graphics program with an efficient molecular dynamics simulation program executed on remote high-performance parallel computers. The system will be ideally suited for distributed computing environments, by utilizing both local 3D graphics facilities and the peak capacity of high-performance computers for the purpose of interactive biomolecular modeling. To create an interactive 3D environment three input methods will be explored: (1) a six degree of freedom "mouse" for controlling the space shared by the model and the user; (2) voice commands monitored through a microphone and recognized by a speech recognition interface; (3) hand gestures, detected through cameras and interpreted using computer vision techniques. Controlling 3D graphics connected to real time simulations and the use of voice with suitable language semantics, as well as hand gestures, promise great benefits for many types of problem solving environments. Our focus on structural biology takes advantage of existing sophisticated software, provides concrete objectives, defines a well-posed domain of tasks and offers a well-developed vocabulary for spoken communication.

Recent progress in 3-D, immersive display and virtual reality (VR) technologies has made possible many exciting applications, for example interactive visualization of complex scientific data. To fully exploit this potential there is a need for "natural" interfaces that allow the manipulation of such displays without cumbersome attachments. In this paper we describe the use of visual hand gesture analysis and speech recognition for developing a speech/gesture interface for controlling a 3-D display. The interface enhances an existing application, VMD, which is a VR visual computing environment far molecular biologists. The free hand gestures are used for manipulating the 3-D graphical display together with a set of speech commands. We describe the visual gesture analysis and the speech analysis techniques used in developing this interface. The dual modality of speech/gesture is found to greatly aid the interaction capability.

The universal asymptotic scaling laws proposed by Amari et al. are studied in large scale simulations using a CM5. Small stochastic multilayer feedforward networks trained with backpropagation are investigated. In the range of a large number of training patterns t, the asymptotic generalization error scales as 1/t as predicted. For a medium range t a faster 1/t2 scaling is observed. This effect is explained by using higher order corrections of the likelihood expansion. It is shown for small t that the scaling law changes drastically, when the network undergoes a transition from strong overfitting to effective learning.

Orientation and ocular dominance maps in the primary visual cortex of mammals are among the most thoroughly investigated of the patterns in the cerebral cortex. A considerable amount of work has been dedicated to unraveling both their detailed structure and the neural mechanisms that underlie their formation and development. Many schemes have been proposed, some of which are in competition. Some models focus on development of receptive fields while others focus on the structure of cortical maps, i.e., the arrangement of receptive field properties across the cortex. Each model used different means to determine its success at reproducing experimental map patterns, often relying principally on visual comparison. Experimental data are becoming available that allow a more careful evaluation of models. In this contribution more than 10 of the most prominent models of cortical map formation and structure are critically evaluated and compared with the most recent experimental findings from macaque striate cortex. Comparisons are based on properties of the predicted or measured cortical map patterns. We introduce several new measures for comparing experimental and model map data that reveal important differences between models. We expect that the use of these measures will improve current models by helping determine parameters to match model maps to experimental data now becoming available from a variety of species. Our study reveals that (1) despite apparent differences, many models are based on similar principles and consequently make similar predictions, (2) several models produce orientation map patterns that are not consistent with the experimental data from macaques, regardless of the plausibility of the models' suggested physiological implementations, and (3) no models have yet fully accounted for both the local and the global relationships between orientation and ocular dominance map patterns.

More than ten of the most prominent models for the structure and for the activity dependent formation of orientation and ocu(cid:173) lar dominance columns in the striate cort(>x have been evaluated. We implemented those models on parallel machines, we extensively explored parameter space, and we quantitatively compared model predictions with experimental data which were recorded optically from macaque striate cortex. In our contribution we present a summary of our results to date. Briefly, we find that (i) despite apparent differences, many models are based on similar principles and, consequently, make similar pre(cid:173) dictions, (ii) certain "pattern models" as well as the developmental "correlation-based learning" models disagree with the experimen(cid:173) tal data, and (iii) of the models we have investigated, "competitive Hebbian" models and the recent model of Swindale provide the best match with experimental data. 1 Models and Data The models for the formation and structure of orientation and ocular dominance columns which we have investigated are summarized in table 1. Models fall into two categories: "Pattern models" whose aim is to achieve a concise description of the observed patterns and "developmental models" which are focussed on the pro- 94 E. Erwin, K. Obermayer, K. Schulten Class Pattern Models Models

The macaque lateral geniculate nucleus (LGN) exhibits an intricate lamination pattern, which changes midway through the nucleus at a point coincident with small gaps due to the blind spot in the retina. We present a three-dimensional model of morphogenesis in which local cell interactions cause a wave of development of neuronal re(cid:173) ceptive fields to propagate through the nucleus and establish two distinct lamination patterns. We examine the interactions between the wave and the localized singularities due to the gaps, and find that the gaps induce the change in lamination pattern. We explore critical factors which determine general LGN organization.

A neural map algorithm has been employed to control a five-joint pneumatic robot arm and gripper through feedback from two video cameras. The pneumatically driven robot arm (SoftArm) employed in this investigation shares essential mechanical characteristics with skeletal muscle systems. To control the position of the arm, 200 neurons formed a network representing the three-dimensional workspace embedded in a four-dimensional system of coordinates from the two cameras, and learned a three-dimensional set of pressures corresponding to the end effector positions, as well as a set of 3/spl times/4 Jacobian matrices for interpolating between these positions. The gripper orientation was achieved through adaptation of a 1/spl times/4 Jacobian matrix for a fourth joint. Because of the properties of the rubber-tube actuators of the SoftArm, the position as a function of supplied pressure is nonlinear, nonseparable, and exhibits hysteresis. Nevertheless, through the neural network learning algorithm the position could be controlled to an accuracy of about one pixel (/spl sim/3 mm) after 200 learning steps and the orientation could be controlled to two pixels after 800 learning steps. This was achieved through employment of a linear correction algorithm using the Jacobian matrices mentioned above. Applications of repeated corrections in each positioning and grasping step leads to a very robust control algorithm since the Jacobians learned by the network have to satisfy the weak requirement that the Jacobian yields a reduction of the distance between gripper and target. The neural network employed in the control of the SoftArm bears close analogies to a network which successfully models visual brain maps. It is concluded, therefore, from this fact and from the close analogy between the SoftArm and natural muscle systems that the successful solution of the control problem has implications for biological visuo-motor control.>

A neural network algorithm based on a soft-max adaptation rule is presented. This algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression. The soft-max rule employed is an extension of the standard K-means clustering procedure and takes into account a neighborhood ranking of the reference (weight) vectors. It is shown that the dynamics of the reference (weight) vectors during the input-driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of Brownian particles moving in a potential determined by the data point density. The network is used to represent the attractor of the Mackey-Glass equation and to predict the Mackey-Glass time series, with additional local linear mappings for generating output values. The results obtained for the time-series prediction compare favorably with the results achieved by backpropagation and radial basis function networks.

The implementation of two neural network algorithms for visuo-motor control of an industrial robot (Puma 562) is reported. The first algorithm uses a vector quantization technique, the ;neural-gas' network, together with an error correction scheme based on a Widrow-Hoff-type learning rule. The second algorithm employs an extended self-organizing feature map algorithm. Based on visual information provided by two cameras, the robot learns to position its end effector without an external teacher. Within only 3000 training steps, the robot-camera system is capable of reducing the positioning error of the robot's end effector to approximately 0.1% of the linear dimension of the work space. By employing adaptive feedback the robot succeeds in compensating not only slow calibration drifts, but also sudden changes in its geometry. Hardware aspects of the robot-camera system are discussed.

A hierarchical neural network structure capable of learning the control of a robot's arm and gripper is introduced. Based on T. Kohonen's algorithm (1982) for the formation of topologically correct feature maps and on an extension of the algorithm for learning of output signals, a simulated robot arm system learns the task of grasping a cylinder. The network architecture is that of a 3-D cubic lattice in which is nested at each lattice node a 2-D square lattice. The robot learns without supervision to position its arm and to orient its gripper properly by observing its own trial movements. In a simulation, the error in positioning the manipulator after training was 0.3% of the robot's dimension, and the residual error in orienting the gripper was 3.8°. Due to cooperation between neighboring neurons during the training phase, fewer than two trial movements per neuron were sufficient to learn the required control tasks

A discussion is presented of the properties of the model in the high-dimensional limit. The authors present results from a Monte Carlo simulation indicating a facilitation of the map-ordering process if the dimensionality of the input space is increased, and they provide a mathematical analysis of the development of localized receptive fields via the input-selection mechanism. The analytical results are compared with data from large-scale simulations using a Connection Machine CM-2, and very good agreement is found

The problem of predicting highly nonlinear time sequence data, where the usual approach using adaptive linear regressive models encounters difficulty, is considered. For this case, the use of an adaptive covering of the state space of the process with a set of linear regressive models, each of which is only locally used, is suggested. It is shown that such an adaptive covering, together with learning of the appropriate prediction coefficients, can be realized using Kohonen's algorithm of self-organizing maps. To illustrate the method, simulation results for a set of benchmarking problems are given

An extension of T. Kohonen's (1982) self-organizing mapping algorithm together with an error-correction scheme based on the Widrow-Hoff learning rule is applied to develop a learning algorithm for the visuomotor coordination of a simulated robot arm. Learning occurs by a sequence of trial movements without the need for an external teacher. Using input signals from a pair of cameras, the closed robot arm system is able to reduce its positioning error to about 0.3% of the linear dimensions of its work space. This is achieved by choosing the connectivity of a three-dimensional lattice consisting of the units of the neural net.