Browsing by Author "Zhang, William"

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    Evolutionary Dynamics in an Individual Spatial and a Mean Field Differential Equation Host-Pathogen Model
    (2013-04-30) Zhang, William
    We examine a host-pathogen model in which three types of species exist: empty sites, healthy hosts, and infected hosts. In this model six different transitions can occur: empty sites can be colonized by healthy hosts, healthy hosts can be infected, and infected hosts can either recover or die. We implement this general model in both a spatial context with discrete time and in a homogeneously mixing model in continuous time. We then explore evolution for pairs of parameters, calculating viable regions in the ODE model and and evolutionary vector fields in both models. Our results show that results from the spatial model do not always converge to our ODE model results, that stochasticity in the spatial evolutionary vector field can be used as a measure of the magnitude of evolutionary pressure and as an indicator of non-viable parameters, and that the evolutionary pressures on different parameters are not necessarily independent. For example, a lower transmissibility greatly lowers the magnitude of evolutionary pressure for all parameters associated with transitions from infected hosts.
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    ItemOpen Access
    Evolutionary Dynamics in an Individual Spatial and a Mean Field Differential Equation Host-Pathogen Model
    (2014-01-29) Zhang, William
    We examine a host-pathogen model in which three types of species exist: empty sites, healthy hosts, and infected hosts. In this model six different transitions can occur: empty sites can be colonized by healthy hosts, healthy hosts can be infected, and infected hosts can either recover or die. We implement this general model in both a spatial context with discrete time and in a homogeneously mixing model in continuous time. We then explore evolution for pairs of parameters, calculating viable regions in the ODE model and and evolutionary vector fields in both models. Our results show that results from the spatial model do not always converge to our ODE model results, that stochasticity in the spatial evolutionary vector field can be used as a measure of the magnitude of evolutionary pressure and as an indicator of non-viable parameters, and that the evolutionary pressures on different parameters are not necessarily independent. For example, a lower transmissibility greatly lowers the magnitude of evolutionary pressure for all parameters associated with transitions from infected hosts.
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    ItemOpen Access
    Sequence-Dependence of DX DNA Electronic Properties and Thermal Fluctuations
    (2013-04-30) Zhang, William
    The Watson-Crick base-pairing of DNA has been exploited through sticky-end cohesion and branched junctions to create complex self-assemblying nanostructures. The double-crossover (DX) junction is a common motif in these structures. Interest in nanoelectronics has led to previous experimental studies of the DX structure as a nanoscale current splitter. Here, we build atomic-level models of both the original sequence and redesigned improved sequences. We produce 10 ns of molecular dynamics simulation snapshots for each sequence, which indicate a universally stable central core and fluctuating forks. We then use CNDO, a semi-empirical quantum mechanics method assuming zero differential overlap, to compute electronic structures for various segments of each system. Using the basic equation of Marcus theory, we find that our redesigned "Duke" sequence achieves a maximum cross-helical hopping rate fifty times greater than the original sequence. Our results form a foundation for atomic-level models of larger DNA nanostructures, and indicate that a careful consideration of three-dimensional geometry is crucial to sequence design in DNA nanotechnology.