Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the divergence time between two populations, specifically designed for the analysis of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were derived, assuming that the population dynamics of rare alleles can be described by using a birth–death process approximation and that each mutation arose before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes and few alleles, whose age can be approximated, whereas the RDc estimator appears preferable when this is not the case. When applied to three cystic fibrosis mutations, the estimator RD could not exclude a very recent time of divergence among three Mediterranean populations. On the other hand, the divergence time between these populations and the Danish population was estimated to be, on the average, 4,500 or 15,000 years, assuming or not a selective advantage for cystic fibrosis carriers, respectively. Confidence intervals are large, however, and can probably be reduced only by analyzing more alleles or loci.

Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source–sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

A maximum likelihood algorithm for genome mapping of cytogenetic loci from meiotic configuration data.

Frequencies of meiotic configurations in cytogenetic stocks are dependent on chiasma frequencies in segments defined by centromeres, breakpoints, and telomeres. The expectation maximization algorithm is proposed as a general method to perform maximum likelihood estimations of the chiasma frequencies in the intervals between such locations. The estimates can be translated via mapping functions into genetic maps of cytogenetic landmarks. One set of observational data was analyzed to exemplify application of these methods, results of which were largely concordant with other comparable data. The method was also tested by Monte Carlo simulation of frequencies of meiotic configurations from a monotelodisomic translocation heterozygote, assuming six different sample sizes. The estimate averages were always close to the values given initially to the parameters. The maximum likelihood estimation procedures can be extended readily to other kinds of cytogenetic stocks and allow the pooling of diverse cytogenetic data to collectively estimate lengths of segments, arms, and chromosomes.