4,242 research outputs found

    Statistical properties of contact vectors

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    We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.Comment: 20 pages, 6 figure

    DNA Computing by Self-Assembly

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    Information and algorithms appear to be central to biological organization and processes, from the storage and reproduction of genetic information to the control of developmental processes to the sophisticated computations performed by the nervous system. Much as human technology uses electronic microprocessors to control electromechanical devices, biological organisms use biochemical circuits to control molecular and chemical events. The engineering and programming of biochemical circuits, in vivo and in vitro, would transform industries that use chemical and nanostructured materials. Although the construction of biochemical circuits has been explored theoretically since the birth of molecular biology, our practical experience with the capabilities and possible programming of biochemical algorithms is still very young

    Simulating chemistry using quantum computers

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    The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.Comment: 27 pages. Submitted to Ann. Rev. Phys. Che

    Critical phenomena in complex networks

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    The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende
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