PMID: 10326247;Abstract:
The mechanism of protein-only prion replication is controversial. A detailed mathematical model of prion replication by nucleated polymerisation is developed, and its parameters are estimated from published data. PrP-res decay is around two orders of magnitude slower than PrP-sen decay, a plausible ratio of two parameters estimated from very different experiments. By varying the polymer breakage rate, we reveal that systems of short polymers grow the fastest. Drugs which break polymers could therefore accelerate disease progression. Growth in PrP-res seems slower than growth in infectious titre. This can be explained either by a novel hypothesis concerning inoculum clearance from a newly infected brain, or by the faster growth of compartments containing smaller polymers. The existence of compartments can also explain why prion growth sometimes reaches a plateau. Published kinetic data are all compatible with our mathematical model, so the nucleated polymerisation hypothesis cannot be ruled out on dynamic grounds. Copyright (C) 1999 Elsevier Science B.V. All rights reserved.
PMID: 21888925;PMCID: PMC3218209;Abstract:
Clonal reproduction of diploids leads to an increase in heterozygosity over time. A single round of selfing will then create new homozygotic genotypes. Given the same allele frequencies, heritable genetic variation is larger when there are more extreme, i.e. homozygotic genotypes. So after a long clonal expansion, one round of selfing increases heritable genetic variation, but any fully or partially recessive deleterious alleles simultaneously impose a fitness cost. Here we calculate that the cost of selfing in the yeast Saccharomyces is experienced only by a minority of zygotes. This allows a round of selfing to act as an evolutionary capacitor to unlock genetic variation previously found in a cryptic heterozygous form. We calculate the evolutionary consequences rather than the evolutionary causes of sex. We explore a range of parameter values describing sexual frequencies, focusing especially on the parameter values known for wild Saccharomyces. Our results are largely robust to many other parameter value choices, so long as meiosis is rare relative to the strength of selection on heterozygotes. Results may also be limited to organisms with a small number of genes. We therefore expect the same phenomenon in some other species with similar reproductive strategies. © 2011 Elsevier Inc.
PMID: 19661199;PMCID: PMC2912466;Abstract:
Recent empirical studies of taxa including humans, fish, and birds have shown elevated rates of molecular evolution between species that diverged recently. Using the Moran model, we calculate expected divergence as a function of time. Our findings suggest that the observed phenomenon of elevated rates at short timescales is consistent with standard population genetics theory. The apparent acceleration of the molecular clock at short timescales can be explained by segregating polymorphisms present at the time of the ancestral population, both neutral and slightly deleterious, and not newly arising slightly deleterious mutations as has been previously hypothesized. Our work also suggests that the duration of the rate elevation depends on the effective population size, providing a method to correct time estimates of recent divergence events. Our model concords with estimates of divergence obtained from African cichlid fish and humans. As an additional application of our model, we calculate that Ka/Ks is elevated within a population before decaying slowly to its long-term value. Similar to the molecular clock, the duration and magnitude of Ka/Ks elevation depend on the effective population size. Unlike the molecular clock, however, Ka/Ks elevation is caused by newly arising slightly deleterious mutations. This elevation, although not as severe in magnitude as had been previously predicted in models neglecting ancestral polymorphism, persists slightly longer.
PMID: 16387877;PMCID: PMC1456269;Abstract:
Cryptic genetic variation accumulates under weakened selection and has been proposed as a source of evolutionary innovations. Weakened selection may, however, also lead to the accumulation of strongly deleterious or lethal alleles, swamping the effect of any potentially adaptive alleles when they are revealed. Here I model variation that is partially shielded from selection, assuming that unconditionally deleterious variation is more strongly deleterious than variation that is potentially adaptive in a future environment. I find that cryptic genetic variation can be substantially enriched for potential adaptations under a broad range of realistic parameter values, including those applicable to alternative splices and readthrough products generated by the yeast prion [PSI+]. This enrichment is dramatically stronger when multiple simultaneous changes are required to generate a potentially adaptive phenotype. Cryptic genetic variation is likely to be an effective source of useful adaptations at a time of environmental change, relative to an equivalent source of variation that has not spent time in a hidden state. Copyright © 2006 by the Genetics Society of America.
Abstract:
The purpose of this paper is to extend the framework for binary topological interactions to spaces up to 4-D. It includes descriptions of the various interactions between objects of various dimensions in various spaces, covering all interactions between all types of objects up to 4-D, in spaces up to 4-D. The need for topology in GIS is briefly discussed, in the instance of a vector-based 4-D GIS. The requirements for spatio-temporal indexing of data in a 4-D GIS are discussed briefly, together with the current dearth of information on query types and temporal analysis needs. This absence limits how well system designers can optimize the indexing, and consequently performance, of a 4-D GIS. This information will become available only after systems are in regular use and their modes of use analyzed. © 1992.
