An Extension of a Model for the Evolution of Multigene Families by Unequal Crossing over

Evolution of a multigene family is studied from the standpoint of population genetics. It is assumed that the multigene family is undergoing continuous interchromosomal unequal crossing over, mutation and random frequency drift. The equilibrium properties of the probability of gene identity (clonality) are investigated, using two measures: identity probability within and between chromosomes. The measures represent homogeneity of genes within a family in one chromosome and similarity of gene families between two homologous chromosomes. The means, the variances and the covariance of these two measures of identity probability are obtained by using the diffusion equation method. It is shown that the means and the variances are generally smaller than those predicted in the previous model assuming intrachromosomal (sister chromatid) unequal crossing over (Ohta 1978a,b).     

Crossing over frequency following inbreeding inNeurospora

Crossing over frequency was determined for five marked regions covering most of a chromosome arm. The results of a 12th backcross were compared with previously published results from the noninbred f₁. Exchange frequency increased significantly following inbreeding. Chiasma interference remained positieve, but was somewhat less intense in b₁₂.Supported in part by Public Health Service Research Grants AI 01462 and GM 1882-01, by a National Science Foundation Faculty Fellowship to H. R. C., and by Public Health Service Research Career Award K6-GM-4899 to D. D. P.Technical Paper No. 2054, Oregon Agricultural Experiment Station, Corvallis.     

Crossing over...Markov meets Mendel

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition.     

Homology Requirements for Unequal Crossing over in Humans

To gain insight into mechanisms of unequal homologous recombination in vivo, genes generated by homologous unequal crossovers in the human beta-globin gene cluster were examined by nucleotide sequencing and hybridization experiments. The naturally occurring genes studied included one delta-beta Lepore-Baltimore fusion gene, one delta-beta Lepore-Hollandia fusion gene, 12 delta-beta Lepore-Boston genes, one A gamma-beta fusion Kenya gene, one A gamma-G gamma fusion (the central gene of a triplication) and one G gamma-A gamma fusion. A comparison of the nucleotide sequences of three Lepore-Boston genes indicates that they were derived from at least two independent homologous but unequal crossover events, although the crossovers occurred within the same 58-bp region. Nine additional Lepore-Boston genes from individuals of various ethnic origins were shown, by hybridization to specific oligonucleotide probes, to have been generated by a crossover in the same region as the sequenced genes. Evidence for gene conversion accompanying a homologous unequal crossover event was found in only one case (although some of the single nucleotide differences observed in other genes in this study may be related to the crossover events in ways that we do not presently understand). Thus, as judged by this limited sample, concurrent gene conversions are not commonly associated with homologous but unequal exchange in humans in vivo. Classification of the recombinant chromosomes by their polymorphic restriction sites in the beta-globin gene cluster indicated that the Lepore-Boston genes are found in at least six different haplotype backgrounds. Therefore the total number of independent examples in this study is at least 6, and at most 12. We have shown that in at least six cases of genes that have arisen by homologous but unequal crossing over in vivo, each event occurred in a relatively extensive region of uninterrupted identity between the parental genes. This preference cannot be explained by a mechanism whereby crossovers occur at random within misaligned related but not identical genes. In general, crossovers occur in regions that are among the largest available stretches of identity for a particular pair of mismatched genes. Our data are in agreement with those of other types of studies of homologous recombination, and support the idea that sequence identity, rather than general homology, is a critical factor in homologous recombination.     

Elements Causing Male Crossing over in DROSOPHILA MELANOGASTER

A second chromosome line of Drosophila melanogaster (Symbol: T-007) has previously been shown to be responsible for the induction of male recombination. In the present investigation, the genetic elements responsible for this phenomenon have been partially identified and mapped. A major element (Symbol: Mr, for Male recombination) locates on the second chromosome between the pr (2L-54.4) and c (2R-75.5) loci and is responsible for the large majority of male recombination. In addition, there appear to be "secondary elements" present which have the ability to induce male recombination in much reduced frequencies and which are diluted out through successive backcross generations when Mr is removed by recombination. The possible nature of these "secondary elements" is discussed.