Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model

Much of the current theory of adaptation is based on Gillespie's mutational landscape model (MLM), which assumes that the fitness values of genotypes linked by single mutational steps are independent random variables. On the other hand, a growing body of empirical evidence shows that real fitness landscapes, while possessing a considerable amount of ruggedness, are smoother than predicted by the MLM. In the present article we propose and analyse a simple fitness landscape model with tunable ruggedness based on the Rough Mount Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79 (2000)] in the context of protein evolution. We provide a comprehensive collection of results pertaining to the topographical structure of RMF landscapes, including explicit formulae for the expected number of local fitness maxima, the location of the global peak, and the fitness correlation function. The statistics of single and multiple adaptive steps on the RMF landscape are explored mainly through simulations, and the results are compared to the known behavior in the MLM model. Finally, we show that the RMF model can explain the large number of second-step mutations observed on a highly-fit first step backgound in a recent evolution experiment with a microvirid bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number of fitness maxim

Exact Results for Amplitude Spectra of Fitness Landscapes

Starting from fitness correlation functions, we calculate exact expressions for the amplitude spectra of fitness landscapes as defined by P.F. Stadler [J. Math. Chem. 20, 1 (1996)] for common landscape models, including Kauffman's NK-model, rough Mount Fuji landscapes and general linear superpositions of such landscapes. We further show that correlations decaying exponentially with the Hamming distance yield exponentially decaying spectra similar to those reported recently for a model of molecular signal transduction. Finally, we compare our results for the model systems to the spectra of various experimentally measured fitness landscapes. We claim that our analytical results should be helpful when trying to interpret empirical data and guide the search for improved fitness landscape models.Comment: 13 pages, 5 figures; revised and final versio

Greedy adaptive walks on a correlated fitness landscape

We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length $L$. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient $c$ is a parameter that interpolates between the limits of an uncorrelated random landscape ($c = 0$) and an effectively additive landscape ($c \to \infty$). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for $L \to \infty$, different from its values for $c=0$ and $c = \infty$, if $c$ is scaled with $L$ in an appropriate combination.Comment: minor change

Multidimensional epistasis and the transitory advantage of sex

Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional fitness landscapes in the presence of sign epistasis. Here we present a comparative numerical study of sexual and asexual evolutionary dynamics of haploids on tunably rugged model landscapes under strong selection, paying special attention to the temporal development of the evolutionary advantage of recombination and the link between population diversity and the rate of adaptation. We show that the adaptive advantage of recombination on static rugged landscapes is strictly transitory. At early times, an advantage of recombination arises through the possibility to combine individually occurring beneficial mutations, but this effect is reversed at longer times by the much more efficient trapping of recombining populations at local fitness peaks. These findings are explained by means of well established results for a setup with only two loci. In accordance with the Red Queen hypothesis the transitory advantage can be prolonged indefinitely in fluctuating environments, and it is maximal when the environment fluctuates on the same time scale on which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final versio

Theoretical Examination of Solvent and R Group Dependence in Gold Thiolate Nanoparticle Synthesis

The growth of gold thiolate nanoparticles can be affected by the solvent and the R group on the ligand. In this work, the difference between methanol and benzene solvents as well as the effect of alkyl (methyl) and aromatic (phenyl) thiols on the reaction energies and barrier heights is investigated theoretically. Density functional theory (DFT) calculations using the BP86 functional and a triple ζ polarized basis set show that the overall reaction favors methylthiol over phenylthiol with reaction energies of −0.54 and −0.39 eV in methanol, respectively. At the same level of theory, the methanol solvent is favored over the benzene solvent for reactions forming ions; in benzene, the overall reaction energies for methylthiol and phenylthiol reacting with AuCl4− to form Au(HSR)2+ are 0.37 eV and 0.44 eV, respectively. Methylthiol in methanol also has the lowest barrier heights at about 0.3 eV, whereas phenylthiol has barrier heights around 0.4 eV. Barrier heights in benzene are significantly larger than those in methanol

A colorimetric competitive displacement assay for the evaluation of catalytic peptides

An assay based on competitive dye displacement was adapted to detect the formation of aldol product in crude reaction mixtures, and was used to evaluate minimal peptide aldol catalysts.</p

Collecting Saliva by Mail for Genetic and Cotinine Analyses in Participants Recruited through the Internet

The authors assessed whether collection by mail of saliva and buccal cells for genetic analysis was feasible in participants recruited through the Internet. In 2003, 14,773 visitors of a smoking cessation website were invited by e-mail to take part in the study. Salivettes (plastic vials containing a cotton roll) were mailed to participants, for collection of saliva and buccal cells. Because of limited resources, the authors stopped recruitment when 392 participants (3% of 14,733) were registered. They received 315 saliva samples back (80% of 392). Salivary cotinine was analyzed in 145 daily smokers. Cotinine concentration could be assessed in 141 samples (97%) (range 0.7-899ng/ml, median 260ng/ml). DNA extraction was achieved in all the 285 samples in which it was attempted. Quality of DNA was assessed by optical density measurements and by polymerase chain reaction amplification of a gene coding for the α-4 nicotinic receptor, with the detection of a known polymorphism. Successful results were obtained in 235 samples (82% of 285). Thus collecting saliva by mail for cotinine and DNA analysis in participants recruited through the internet produced samples of good quality at a reasonable cost. This approach should be valuable for genetic epidemiology and pharmacogenetic researc