Thermodynamics of Neutral Protein Evolution

Naturally evolving proteins gradually accumulate mutations while continuing to fold to thermodynamically stable native structures. This process of neutral protein evolution is an important mode of genetic change, and forms the basis for the molecular clock. Here we present a mathematical theory that predicts the number of accumulated mutations, the index of dispersion, and the distribution of stabilities in an evolving protein population from knowledge of the stability effects (ddG values) for single mutations. Our theory quantitatively describes how neutral evolution leads to marginally stable proteins, and provides formulae for calculating how fluctuations in stability cause an overdispersion of the molecular clock. It also shows that the structural influences on the rate of sequence evolution that have been observed in earlier simulations can be calculated using only the single-mutation ddG values. We consider both the case when the product of the population size and mutation rate is small and the case when this product is large, and show that in the latter case proteins evolve excess mutational robustness that is manifested by extra stability and increases the rate of sequence evolution. Our basic method is to treat protein evolution as a Markov process constrained by a minimal requirement for stable folding, enabling an evolutionary description of the proteins solely in terms of the experimentally measureable ddG values. All of our theoretical predictions are confirmed by simulations with model lattice proteins. Our work provides a mathematical foundation for understanding how protein biophysics helps shape the process of evolution

Protein evolution

Among the proteins that have evolved over hundreds of millions of years, with important roles in defence against invading micro-organisms, are the pentraxins. The two major members of the family are known as CRP and SAP, and they evolve due to mutations in the underlying DNA. The Study Group was asked to construct a model of this evolution in order to answer specific questions about the occurrences of these proteins in man and in the horseshoe crab

Preferential attachment in the protein network evolution

The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields this universal topology. However, it is not clear that the model assumptions hold for the protein interaction network. Using a cross genome comparison we show that (a) the older a protein, the better connected it is, and (b) The number of interactions a protein gains during its evolution is proportional to its connectivity. Therefore, preferential attachment governs the protein network evolution. The evolutionary mechanism leading to such preference and some implications are discussed.Comment: Minor changes per referees requests; to appear in PR

Machine learning-guided directed evolution for protein engineering

Machine learning (ML)-guided directed evolution is a new paradigm for biological design that enables optimization of complex functions. ML methods use data to predict how sequence maps to function without requiring a detailed model of the underlying physics or biological pathways. To demonstrate ML-guided directed evolution, we introduce the steps required to build ML sequence-function models and use them to guide engineering, making recommendations at each stage. This review covers basic concepts relevant to using ML for protein engineering as well as the current literature and applications of this new engineering paradigm. ML methods accelerate directed evolution by learning from information contained in all measured variants and using that information to select sequences that are likely to be improved. We then provide two case studies that demonstrate the ML-guided directed evolution process. We also look to future opportunities where ML will enable discovery of new protein functions and uncover the relationship between protein sequence and function.Comment: Made significant revisions to focus on aspects most relevant to applying machine learning to speed up directed evolutio

A Hierarchical Approach to Protein Molecular Evolution

Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with Monte Carlo simulations. These simulations demonstrate that non-homologous juxtaposition of encoded structure is the rate-limiting step in the production of new tertiary protein folds. Non-homologous ``swapping'' of low energy secondary structures increased the binding constant of a simulated protein by $\approx10^7$ relative to base substitution alone. Applications of our approach include the generation of new protein folds and modeling the molecular evolution of disease.Comment: 15 pages. 2 figures. LaTeX styl

Stability-mediated epistasis constrains the evolution of an influenza protein.

John Maynard Smith compared protein evolution to the game where one word is converted into another a single letter at a time, with the constraint that all intermediates are words: WORD→WORE→GORE→GONE→GENE. In this analogy, epistasis constrains evolution, with some mutations tolerated only after the occurrence of others. To test whether epistasis similarly constrains actual protein evolution, we created all intermediates along a 39-mutation evolutionary trajectory of influenza nucleoprotein, and also introduced each mutation individually into the parent. Several mutations were deleterious to the parent despite becoming fixed during evolution without negative impact. These mutations were destabilizing, and were preceded or accompanied by stabilizing mutations that alleviated their adverse effects. The constrained mutations occurred at sites enriched in T-cell epitopes, suggesting they promote viral immune escape. Our results paint a coherent portrait of epistasis during nucleoprotein evolution, with stabilizing mutations permitting otherwise inaccessible destabilizing mutations which are sometimes of adaptive value. DOI:http://dx.doi.org/10.7554/eLife.00631.001