Studies of meiotic recombination have revealed an evolutionary paradox. Molecular and genetic analysis has shown that crossing over initiates at specific sites called hotspots, by a recombinational-repair mechanism in which the initiating hotspot is replaced by a copy of its homolog. We have used computer simulations of large populations to show that this mechanism causes active hotspot alleles to be rapidly replaced by inactive alleles, which arise by rare mutation and increase by recombination-associated conversion. Additional simulations solidified the paradox by showing that the known benefits of recombination appear inadequate to maintain its mechanism. Neither the benefits of accurate segregation nor those of recombining f lanking genes were sufficient to preserve active alleles in the face of conversion. A partial resolution to this paradox was obtained by introducing into the model an additional, nonmeiotic function for the sites that initiate recombination, consistent with the observed association of hotspots with functional sites in chromatin. Provided selection for this function was sufficiently strong, active hotspots were able to persist in spite of frequent conversion to inactive alleles. However, this explanation is unsatisfactory for two reasons. First, it is unlikely to apply to obligately sexual species, because observed crossover frequencies imply maintenance of many hotspots per genome, and the viability selection needed to preserve these would drive the species to extinction. Second, it fails to explain why such a genetically costly mechanism of recombination has been maintained over evolutionary time. Thus the paradox persists and is likely to be resolved only by significant changes to the commonly accepted mechanism of crossing over.Meiotic crossing over between homologous chromosomes plays two important roles in the genetic reshuffling caused by sexual reproduction: it creates new combinations of alleles within each chromosome, and it prevents nondisjunction during chromosome segregation (1). Crossovers are initiated primarily at specific sites called hotspots (2, 3). Most studies of the mechanism have been done in ascomycete fungi, where meiosis can be synchronously induced and all the meiotic products recovered in the ascus. Biased gene conversion is a typical consequence of recombination at hotspots (4-6). For example, a cross between active and inactive alleles of the ARG4 hotspot in the yeast Saccharomyces cerevisiae exhibits a 22-fold bias toward conversion of the active allele to its inactive homolog (6). Physical studies have shown that recombination events in S. cerevisiae are initiated by site-specific doublestrand DNA breaks at hotspots, before the visible pairing of the chromosomes (7, 8). As illustrated in Fig. 1, these breaks are thought to be repaired by DNA synthesis that uses the strands of the homologous chromosomes as templates, with resolution of the repair intermediate frequently creating a crossover between the participating chromosomes (9, 10). This and rela...

We describe an algorithm which uses a finite number of differentiations and algebraic operations to simplify a given analytic nonlinear system of partial differential equations to a form which includes all its integrability conditions. This form can be used to test whether a given differential expression vanishes as a consequence of such a system and may be more amenable to numerical or analytical solution techniques than the original system. It is also useful for determining consistent initial conditions for such a system. A computer implementable version of our algorithm is given for polynomially nonlinear systems of partial differential equations. This version uses Grobner basis techniques for constructing the radical of the polynomial ideal generated by the equations of such systems.

No abstract

No abstract