Ryan N Gutenkunst

PMID: 17925353;Abstract:

Successful predictions are among the most compelling validations of any model. Extracting falsifiable predictions from nonlinear multiparameter models is complicated by the fact that such models are commonly sloppy, possessing sensitivities to different parameter combinations that range over many decades. Here we discuss how sloppiness affects the sorts of data that best constrain model predictions, makes linear uncertainty approximations dangerous, and introduces computational difficulties in Monte-Carlo uncertainty analysis. We also present a useful test problem and suggest refinements to the standards by which models are communicated. © 2007 New York Academy of Sciences.

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on approximating the second largest eigenvalue in the spectrum of the MCMC operator using a variational principle and the approach is applicable to problems with continuous state spaces. We apply the method to one dimensional examples with Gaussian and quartic target densities, and we contrast the performance of the random walk Metropolis-Hastings algorithm with a "smart" variant that incorporates gradient information into the trial moves, a generalization of the Metropolis adjusted Langevin algorithm. We find that the variational method agrees quite closely with numerical simulations. We also see that the smart MCMC algorithm often fails to converge geometrically in the tails of the target density except in the simplest case we examine, and even then care must be taken to choose the appropriate scaling of the deterministic and random parts of the proposed moves. Again, this calls into question the utility of smart MCMC in more complex problems. Finally, we apply the same method to approximate the rate of convergence in multidimensional Gaussian problems with and without importance sampling. There we demonstrate the necessity of importance sampling for target densities which depend on variables with a wide range of scales.

Protein tyrosine phosphorylation is a key regulatory modification in metazoans, and the corresponding kinase enzymes have diversified dramatically. This diversification is correlated with a genome-wide reduction in protein tyrosine content, and it was recently suggested that this reduction was driven by selection to avoid promiscuous phosphorylation that might be deleterious. We tested three predictions of this intriguing hypothesis. 1) Selection should be stronger on residues that are more likely to be phosphorylated due to local solvent accessibility or structural disorder. 2) Selection should be stronger on proteins that are more likely to be promiscuously phosphorylated because they are abundant. We tested these predictions by comparing distributions of tyrosine within and among human and yeast orthologous proteins. 3) Selection should be stronger against mutations that create tyrosine versus remove tyrosine. We tested this prediction using human population genomic variation data. We found that all three predicted effects are modest for tyrosine when compared with the other amino acids, suggesting that selection against deleterious phosphorylation was not dominant in driving metazoan tyrosine loss.

Partially recessive variants under positive selection are expected to go to fixation more quickly on the X chromosome as a result of hemizygosity, an effect known as faster-X. Conversely, purifying selection is expected to reduce substitution rates more effectively on the X chromosome. Previous work in humans contrasted divergence on the autosomes and X chromosome, with results tending to support the faster-X effect. However, no study has yet incorporated both divergence and polymorphism to quantify the effects of both purifying and positive selection, which are opposing forces with respect to divergence. In this study, we develop a framework that integrates previously developed theory addressing differential rates of X and autosomal evolution with methods that jointly estimate the level of purifying and positive selection via modeling of the distribution of fitness effects (DFE). We then utilize this framework to estimate the proportion of nonsynonymous substitutions fixed by positive selection (α) using exome sequence data from a West African population. We find that varying the female to male breeding ratio (β) has minimal impact on the DFE for the X chromosome, especially when compared with the effect of varying the dominance coefficient of deleterious alleles (h). Estimates of α range from 46% to 51% and from 4% to 24% for the X chromosome and autosomes, respectively. While dependent on h, the magnitude of the difference between α values estimated for these two systems is highly statistically significant over a range of biologically realistic parameter values, suggesting faster-X has been operating in humans.

PMID: 19713326;PMCID: PMC2782326;Abstract:

Balancing selection is potentially an important biological force for maintaining advantageous genetic diversity in populations, including variation that is responsible for long-term adaptation to the environment. By serving as a means to maintain genetic variation, it may be particularly relevant to maintaining phenotypic variation in natural populations. Nevertheless, its prevalence and specific targets in the human genome remain largely unknown. We have analyzed the patterns of diversity and divergence of 13,400 genes in two human populations using an unbiased single-nucleotide polymorphism data set, a genome-wide approach, and a method that incorporates demography in neutrality tests. We identified an unbiased catalog of genes with signatures of long-term balancing selection, which includes immunity genes as well as genes encoding keratins and membrane channels; the catalog also shows enrichment in functional categories involved in cellular structure. Patterns are mostly concordant in the two populations, with a small fraction of genes showing population-specific signatures of selection. Power considerations indicate that our findings represent a subset of all targets in the genome, suggesting that although balancing selection may not have an obvious impact on a large proportion of human genes, it is a key force affecting the evolution of a number of genes in humans.