Abstract

The problem of predicting the 3D native conformation of a polypeptide given the primary sequence is of fundamental importance in contemporary biology. Here we present a novel Genetic algorithm method to obtain the optimal geometry of a pentapeptide. The pentapeptide moiety is found in wide set of configurations in protein databases. A genetic algorithm utilizes optimization procedure similar to natural genetic evolution. Unlike other genetic algorithms, which are constrained to operate on bit strings, the algorithm used here operates on real values. A random population of conformations is generated taking into account the constraints of Ramachandran plot. This population advances through successive generations in which the solutions evolve via genetic operators (Mutate, Variate and Crossover); in such a way that it gives both better survival chance to fitter soluctions and a larger diversity within the population. More attention will be given to favorable local structures while unfavorable local structures will be rapidly abandoned on the basis of their fitness functions (potential energy), which are calculated using the GROMOS-96 force field of Spdbv version-3.7. The SCWRL3.0 program developed at Dunbrack lab is used for placing side chains to a fixed backbone coordinates. This algorithm proved to be very efficient for the penta-peptide Met-Enkephalin, a natural Opioid polypeptide produced in the brain. The algorithm converged only in 41 minutes and in 23 generations keeping the population size fixed (20 individual per population). The converged structure is energetically as stable as the native conformation of the protein. Its shows a RMSD of 5.9 from the original native conformation.

Abstract

With availability of fast computers, electronic structure and properties calculations of small to medium sized systems using quantum chemical methods are now commonplace. Several options in addition to obtaining structures with energy optimisation are now easily realisable, e.g., carrying out calculations of electrostatic potential interations, atoms in molecule approach of Bader, Natural Bonding orbital method, etc. We discuss results obtained in specific cases using these options. We have recently carried out studies on several such systems including amino-methyl furan carboxylic acid system and binding of gold nanoclusters with size expanded DNA bases, xA, xC, xG, and xT. We will present the motivation behind such works and discuss the results obtained using different methods. Geometries of these molecular systems were fully optimized using the Hartree Fock SCF method and using B3LYP density functional method (DFT). The calculations provide a theoretical understanding beyond a phenomenological observation of the preferential cyclotrimerization of 5- (aminomethyl)-2-furancarboxylic acid (AMFC). Other than calculations of thermodynamic free energy, a detailed analysis of the molecular properties is carried out. The electrostatic potentials (ESP) in the region around molecular skeletons are investigated to provide justication for the preferential formation of the cyclic tripeptide over the cyclic dipeptide from the building block, AMFC. The ESP are calculated and computed on the molecular surfaces of the oligopeptides. There are repulsions observed in the dimer due to the proximity of the ethereal oxygen atoms of the furan rings. Natural bond orbital (NBO) analysis is done to find the second-order interactions, and atoms in molecules (AIM) calculations are performed to explore the interactions between the donor and acceptor moieties in the molecule. Our results on the gold complexed x-bases show that the gold clusters around xA and xT adopt triangular geometries, whereas irregular structures are obtained in the case of gold clusters complexed around xC and xG. The lengths of the bonds between atoms in the x-bases increase on gold complexation. The aromaticcharacter of the x-bases also increases on gold complexation except for the five member rings. A significant charge transfer from the x-base to gold atoms is seen in these complexes. Second-order interactions are observed in addition to direct covalent bonds between gold atoms and x bases.

Abstract

The last two decades have seen increasing interest in the area of controlling dynamics at the atomic level. Among the several approaches used, Optimal Control Theory (OCT) has emerged as a powerful method for designing laser pulses to achieve prescribed dynamical goals. We have used OCT to obtain infrared laser pulses for the selective vibrational excitation of several different systems, from a simple diatomic to triatomics located in complex molecular environments. We use time dependent quantum mechanics to monitor the evolution of the system subject to a varying laser field. We have obtained fields for vibrational control of the diatomic system HF applying OCT using different algorithms, namely an iterative method, conjugate gradient method and genetic algorithms. The time-dependent quantum mechanical propagation of the system is achieved using the split operator form of the time evolution operator together with Fast Fourier transforms and grid methods. For the modelling of FeCO in carboxy-myoglobin, we use a two mathematical dimensional model. Density functional theory is used to obtain the potential energy and dipole moment surfaces of the active site model, while the conjugate gradient method is employed within the OCT optimization procedure to obtain the laser pulses. Optimized laser fields are found which give virtually 100% excitation probability to preselected vibrational levels. A similar application to a hydrogen bonded system of biological significance will also be presented. In all cases, detailed analyses of the field are carried out in terms of its power spectrum and the time variation of the contributions from the frequencies involved.

Abstract

The backbone conformation of amino acids in proteins is represented mainly by two torsion angles; phi and psi. Ramachandran map is a way to visualize these torsion angles in protein structures. Here we analyze the nature and distribution of disallowed Ramachandran conformations of amino acid residues observed in protein structures. A non redundant data set consisting of 405 high resolution protein crystal structures from the Brookhaven Protein Data Bank was examined. The data set consisted of a total of 78,213 non-Gly residues, which were characterized on the basis of their backbone dihedral angles phi and psi. Residues falling outside the defined "broad allowed limits" on the Ramachandran map were analyzed. The results suggested that very small fraction of residues (approximately 0.4%) lie in appreciably disallowed regions. Interestingly, small polar/charged residues showed significantly greater probability of adopting unusual backbone with the largest number of examples being observed for Asn, Asp, Ser and Thr residues. The bulky charged residues Glu, Lys, Gln and Arg have a relatively low propensity for backbone distortions. Bulky hydrophobic residues which are found predominantly in well packed interiors of proteins like Ile, Val and aromatic amino acids like Phe, Trp and Tyr do not generally adopt disallowed conformations. In the allowed region irrespective of the type of amino acid except Gly, there is a high propensity for phi value of the range -70 to -60 and for psi value 140 to 150.

Abstract

Depth movies provide 2-D representations of a time-varying 3D scene. Multistream depth movies arise in many structure-capturing setups and have been used for image based rendering. They are bulky and carry redundant information. We propose a proxy-based compression scheme for multistream depth movies of a scene involving dynamic human actors. The input to our system is depth movies from different viewpoints and the calibration parameters to relate depths to 3D points. We use an articulated human model as a proxy to represent the common structure of the scene. The proxy is parametrized by various bone angles.

Abstract

Graph cuts has become a powerful and popular opti-mization tool for energies defined over an MRF and havefound applications in image segmentation, stereo vision,image restoration, etc. The maxflow/mincut algorithm tocompute graph-cuts is computationally heavy. The best-reported implementation of graph cuts takes over 100 mil-liseconds even on images of size640×480and cannot beused for real-time applications or when iterated applica-tions are needed. The commodity Graphics Processor Unit(GPU) has emerged as an economical and fast computationco-processor recently. In this paper, we present an imple-mentation of the push-relabel algorithm for graph cuts onthe GPU. We can perform over 60 graph cuts per secondon1024×1024images and over 150 graph cuts per secondon640×480images on an Nvidia 8800 GTX. The time foreach complete graph-cut is about 1 millisecond when only afew weights change from the previous graph, as on dynamicgraphs resulting from videos. The CUDA code with a well-defined interface can be downloaded for anyone’s use

Abstract

Capturing dynamic scenes in 3D using a suitable depth or structure recovery mechanism has become popular today for image based modelling, 3D telelconferencing, etc. The 2 1 2 D geometric structure and the aligned texture – together called a depth image – are captured by such setups. Time varying sequences of depth images are called depth movies. Depth movies of humans performing interesting actions are being captured using specialized setups today in different research labs. The data so captured is often streamed to another location for immersive viewing using standard depth-image rendering techniques. The depth maps are bulky and need innovative algorithms for efficient representation and compression. In this paper, we present a compression scheme that uses parametric proxy models for the underlying action. We use a generic articulated human model as the proxy and the various joint angles as its parameters for each time instant. The proxy model represents common prediction of the scene structure for that time instant. It can be projected to each view and the difference or residue between the depth due to the proxy and the original depth can be used to represent the scene. The residues compress better and can exploit temporal and spatial relationship between multiple depth movies. We show results on several synthetic actions to demonstrate the usefulness of the scheme

Abstract

Augmenting virtual objects between real objectsof a video poses a challenging problem, primarily because itnecessitates accurate knowledge of the scene’s depth. In thispaper, we propose an approach that generates an approximatedepth for every pixel in the vicinity of the virtual object, which weshow is enough to decide the ordering of objects in every image.We also draw a similarity between layered segmentation andaugmentation. We argue that augmentation only needs to knowwhich layers are in front of the object and which are behind it.Our algorithm makes effective use of object boundaries detectedin an image using image segmentation. The assumption thatthese boundaries correspond to depth discontinuities provides auseful simplification of the problem, sufficient to produce realisticresults. We use a combination of segmentation and featuredetection for sparse depth assignment. Results on challengingdata sets show the effectiveness of our approach

Abstract

Capture of dynamic events is an active research area to-day. Capturingthe212D geometric structure and photomet-ric appearance of dynamic scenesnds applications in 3Dtele-conferencing systems,3DTVetc.The captured ìn depth movies îcontain aligned sequences of depth maps and tex-tures and are often streamed to a distant location for immer-siveviewing. The depth maps are heavy and needed acient compression schemes.In this paper, we present a scheme to compress depth movies of human actors using a parametric proxy model for the under lying action.We use a generic articulated human model as the proxy and the various joint angles a sits parameters for reach time in stant to represent a common prediction of the scene structure. The difference or residue between the captured depth and the depth of the proxy represents the scene to exploits patial coherence. Dif-ferences in residues across time are used to exploit temporal coherence. In tra-frame code frames and difference-coded frames provider and om access and high compression.We show results on several synthetic and real actions to demon-strate the compression ratio and resulting quality using a depth-based rendering of the decoded scene

Abstract

Terrains can be rendered efficiently with rectangular 2D grid of heights. Terrain on spheres, on the other hand, can be rendered using Hierarchical Triangular Mesh (HTM) but the representation does not fit directly with 2D grid of heights. We present a unified representation of HTM and clip mapping using Hexagonal Geome-try Clipmaps. This provides one to one correspondence of vertices and heights, low and constant memory usage, less storage space requirements, no pole singularity, fast vertex look-ups, and large range of view distances. Hexagonal clip maps fit equilateral trian-gles of HTM and achieve uniform triangle count on the screen. We keep the clipmaps on the GPU for fast access from shaders and usevertex buffer objects for fast triangle rendering.