PMID: 10535107;PMCID: PMC1690213;Abstract:
Transmissible spongiform encephalopathies such as scrapie are caused by a protein-only infectious agent, known as a prion. It is not clear how a protein can be capable of replicating itself, and the mechanism remains controversial. One influential model hypothesizes that prions are nucleated, macroscopically linear polymers. We investigated the theoretical kinetics of this model and derived predictions which could be used to test the model. In the model, the polymerization and depolymerization rates are independent of polymer size. This leads to an exponential size distribution at equilibrium. In agreement with a prediction stemming from this size distribution, the average size of PrP-res polymers was proportional to the square root of the concentration of PrP-res in a published study of in vitro conversion. Prion digestion by proteinase K (PK) is predicted to be biphasic. The second phase of digestion should be virtually independent of the PK concentration and should depend on the initial size distribution of prion polymers. For initially equilibrated polymers with an exponential size distribution, phase two digestion is exponential at a predicted rate. This rate varies in a defined way with the concentration used for equilibration and with other parameters which affect the average polymer size.
PMID: 19486147;PMCID: PMC2770902;Abstract:
Reversible phenotypic switching can be caused by a number of different mechanisms including epigenetic inheritance systems and DNA-based contingency loci. Previous work has shown that reversible switching systems may be favored by natural selection. Many switches can be characterized as "on/off" where the "off" state constitutes a temporary and reversible loss of function. Loss-of-function phenotypes corresponding to the "off" state can be produced in many different ways, all yielding identical fitness in the short term. In the long term, however, a switch-induced loss of function can be reversed, whereas many loss-of-function mutations, especially deletions, cannot. We refer to these loss-of-function mutations as "irreversible mimics" of the reversible switch. Here, we develop a model in which a reversible switch evolves in the presence of both irreversible mimics and metapopulation structure. We calculate that when the rate of appearance of irreversible mimics exceeds the migration rate, the evolved reversible switching rate will exceed the bet-hedging rate predicted by panmictic models. © 2009 The Society for the Study of Evolution.
The existence of complex (multiple-step) genetic adaptations that are irreducible (i.e., all partial combinations are less fit than the original genotype) is one of the longest standing problems in evolutionary biology. In standard genetics parlance, these adaptations require the crossing of a wide adaptive valley of deleterious intermediate stages. Here, we demonstrate, using a simple model, that evolution can cross wide valleys to produce irreducibly complex adaptations by making use of previously cryptic mutations. When revealed by an evolutionary capacitor, previously cryptic mutants have higher initial frequencies than do new mutations, bringing them closer to a valley-crossing saddle in allele frequency space. Moreover, simple combinatorics implies an enormous number of candidate combinations exist within available cryptic genetic variation. We model the dynamics of crossing of a wide adaptive valley after a capacitance event using both numerical simulations and analytical approximations. Although individual valley crossing events become less likely as valleys widen, by taking the combinatorics of genotype space into account, we see that revealing cryptic variation can cause the frequent evolution of complex adaptations.
PMID: 22576789;Abstract:
Population genetics is often taught in introductory biology classes, starting with the Hardy-Weinberg principle (HWP) and genetic drift. Here I argue that teaching these two topics first aligns neither with current expert knowledge, nor with good pedagogy. Student difficulties with mathematics in general, and probability in particular, make population genetics difficult to teach and learn. I recommend an alternative, historically inspired ordering of population genetics topics, based on progressively increasing mathematical difficulty. This progression can facilitate just-in-time math instruction. This alternative ordering includes, but does not privilege, the HWP and genetic drift. Stochastic events whose consequences are felt within a single generation, and the deterministic accumulation of the effects of selection across multiple generations, are both taught before tackling the stochastic accumulation of the effects of accidents of sampling. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
PMID: 15911577;PMCID: PMC1451192;Abstract:
Evolutionary capacitors phenotypically reveal a stock of cryptic genetic variation in a reversible fashion. The sudden and reversible revelation of a range of variation is fundamentally different from the gradual introduction of variation by mutation. Here I study the invasion dynamics of modifiers of revelation. A modifier with the optimal rate of revelation mopt has a higher probability of invading any other population than of being counterinvaded. mopt varies with the population size N and the rate θ at which environmental change makes revelation adaptive. For small populations less than a minimum cutoff Nmin, all revelation is selected against. Nmin is typically quite small and increases only weakly, with θ-1/2. For large populations with N > 1/θ, mopt is ∼1/N. Selection for the optimum is highly effective and increases in effectiveness with larger N ≫ 1/θ. For intermediate values of N, mopt is typically a little less than θ and is only weakly favored over less frequent revelation. The model is analogous to a two-locus model for the evolution of a mutator allele. It is a fully stochastic model and so is able to show that selection for revelation can be strong enough to overcome random drift. Copyright © 2005 by the Genetics Society of America.
