Shuffling Metropolis algorithms for Monte Carlo simulations and their application to biological systems: The strand separation transition in superhelical DNA and membrane phase transitions.
Item
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Title
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Shuffling Metropolis algorithms for Monte Carlo simulations and their application to biological systems: The strand separation transition in superhelical DNA and membrane phase transitions.
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Identifier
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AAI9605668
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identifier
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9605668
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Creator
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Sun, Hongzhi.
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Contributor
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Adviser: Craig J. Benham
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Date
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1995
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Biophysics, General | Biology, Molecular
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Abstract
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Metropolis-Monte Carlo algorithms are developed to analyze the strand separation transition in circular superhelical DNA molecules and phase transitions in biological membranes. In both cases shuffling operations are introduced to the simulation algorithms in order to diminish correlations among the sampled states, and thereby speed convergence. The theoretical basis for shuffling Monte Carlo algorithms is developed first. Sufficient conditions to guarantee the formal correctness of these algorithms are proved to hold.;To treat the DNA problem, moves that randomize the locations of unpaired regions are required. The computation time required scales at most quadratically with molecular length, and is approximately independent of linking difference. Techniques are developed to estimate the sample size and other calculation parameters needed to achieve a specified accuracy. When the results of Monte Carlo calculations that use shuffling operations are compared with those from statistical mechanical calculations, excellent agreement is found. The Monte Carlo methodology makes possible calculations of transition behavior in cases where alternative approaches are intractable, such as in long molecules under circumstances where several runs of open base pairs occur simultaneously. It also allows the analysis of transitions in cases where the base pair separation energies vary in complex manners, such as through near neighbor interactions, or in DNA containing modified bases, abasic sites, or bound molecules.;Since ergodicity is not a required property for shuffling operations, it is easy to construct these operations according to the specific of the system. The design, application and efficiency of the shuffling operations in Monte Carlo simulations are also demonstrated on an Ising model of the phase transition of a one-component phospholipid membrane. The results of the simple two-state membrane model agree with the calorimetric data. According to the simulation the gel-to-liquid crystalline transition of dipalmitoyl-phosphatidylcholine multilamellar vesicles (DPPC MLV) is a second-order phase transition, which is close to the critical point.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
