Use of QM/MM Surface Hopping Simulations to Understand Thermally Activated Rare-Event Nonadiabatic Transitions in the Condensed Phase.

We implement a rare-event sampling scheme for quantifying the rate of thermally activated nonadiabatic transitions in the condensed phase. Our Quantum mechanics/molecular mechanics (QM/MM) methodology uses the recently developed Interface for NonAdiabatic QM/MM in Solvent (INAQS) package to interface an elementary electronic structure package and a popular open-source molecular dynamics software (GROMACS) to simulate an electron transfer event between two stationary ions in a solution of acetonitrile solvent molecules. Nonadiabatic effects are implemented through a surface hopping scheme, and our simulations allow further quantitative insight into the participation ratio of a solvent and the effect of ion separation distance as far as facilitating electron transfer. We also demonstrate that the standard gas-phase approaches for treating frustrated hops and velocity reversal must be refined when working in the condensed phase with many degrees of freedom. The code and methodology developed here can be easily expanded upon and modified to incorporate other systems and should provide a great deal of new insight into a wide variety of condensed phase nonadiabatic phenomena.

Inferring Genome-Wide Correlations of Mutation Fitness Effects between Populations.

The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.

A grid-free approach for simulating sweep and cyclic voltammetry.

We present a computational approach to simulate linear sweep and cyclic voltammetry experiments that does not require a discretized grid in space to quantify diffusion. By using a Green's function solution coupled to a standard implicit ordinary differential equation solver, we are able to simulate current and redox species concentrations using only a small grid in time. As a result, where benchmarking is possible, we find that the current method is faster than (and quantitatively identical to) established techniques. The present algorithm should help open the door for studying adsorption effects in inner sphere electrochemistry.

Modeling voltammetry curves for proton coupled electron transfer: The importance of nuclear quantum effects.

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson-Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear-electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

When is electronic friction reliable for dynamics at a molecule-metal interface?

We investigate rates of electron transfer for generalized Anderson-Holstein models in the limit of weak molecule-metal coupling, using both surface hopping and electronic friction dynamics in one and two dimensions. Overall, provided there is an external source of friction, electronic friction can sometimes perform well even in the limit of small metal-molecule coupling and capture nonadiabatic effects. However, we show that electronic friction dynamics is likely to fail if there is a competition between nonequivalent pathways. Our conclusions provide further insight into the recent observation by Ouyang et al., [J. Chem. Theory Comput., 2016, 12, 4178] regarding the applicability of Kramer's theory in the adiabatic limit to recover Marcus theory in the nonadiabatic limit.

Triallelic Population Genomics for Inferring Correlated Fitness Effects of Same Site Nonsynonymous Mutations.

The distribution of mutational effects on fitness is central to evolutionary genetics. Typical univariate distributions, however, cannot model the effects of multiple mutations at the same site, so we introduce a model in which mutations at the same site have correlated fitness effects. To infer the strength of that correlation, we developed a diffusion approximation to the triallelic frequency spectrum, which we applied to data from Drosophila melanogaster We found a moderate positive correlation between the fitness effects of nonsynonymous mutations at the same codon, suggesting that both mutation identity and location are important for determining fitness effects in proteins. We validated our approach by comparing it to biochemical mutational scanning experiments, finding strong quantitative agreement, even between different organisms. We also found that the correlation of mutational fitness effects was not affected by protein solvent exposure or structural disorder. Together, our results suggest that the correlation of fitness effects at the same site is a previously overlooked yet fundamental property of protein evolution.

Computationally Efficient Composite Likelihood Statistics for Demographic Inference.

Many population genetics tools employ composite likelihoods, because fully modeling genomic linkage is challenging. But traditional approaches to estimating parameter uncertainties and performing model selection require full likelihoods, so these tools have relied on computationally expensive maximum-likelihood estimation (MLE) on bootstrapped data. Here, we demonstrate that statistical theory can be applied to adjust composite likelihoods and perform robust computationally efficient statistical inference in two demographic inference tools: ∂a∂i and TRACTS. On both simulated and real data, the adjustments perform comparably to MLE bootstrapping while using orders of magnitude less computational time.

Sampling strategies for frequency spectrum-based population genomic inference.

BACKGROUND: The allele frequency spectrum (AFS) consists of counts of the number of single nucleotide polymorphism (SNP) loci with derived variants present at each given frequency in a sample. Multiple approaches have recently been developed for parameter estimation and calculation of model likelihoods based on the joint AFS from two or more populations. We conducted a simulation study of one of these approaches, implemented in the Python module δaδi, to compare parameter estimation and model selection accuracy given different sample sizes under one- and two-population models. RESULTS: Our simulations included a variety of demographic models and two parameterizations that differed in the timing of events (divergence or size change). Using a number of SNPs reasonably obtained through next-generation sequencing approaches (10,000 - 50,000), accurate parameter estimates and model selection were possible for models with more ancient demographic events, even given relatively small numbers of sampled individuals. However, for recent events, larger numbers of individuals were required to achieve accuracy and precision in parameter estimates similar to that seen for models with older divergence or population size changes. We quantify i) the uncertainty in model selection, using tools from information theory, and ii) the accuracy and precision of parameter estimates, using the root mean squared error, as a function of the timing of demographic events, sample sizes used in the analysis, and complexity of the simulated models. CONCLUSIONS: Here, we illustrate the utility of the genome-wide AFS for estimating demographic history and provide recommendations to guide sampling in population genomics studies that seek to draw inference from the AFS. Our results indicate that larger samples of individuals (and thus larger AFS) provide greater power for model selection and parameter estimation for more recent demographic events.