Relationship between protein thermodynamic constraints and variation of evolutionary rates among sites
Excerpt: “…a two-variable model that combines stability and stress significantly improves predictions. Therefore, both the overall stability [symbol] and the stress [symbol] seem to capture distinct thermodynamic constraints on protein evolution.”
My comment: Proteins do not evolve. Nutrients are required. Metabolism of nutrients to species-specific pheromones controls the physiology of reproduction in species from microbes to man. The nutrient-dependent pheromone-controlled physiology of reproduction enables epistasis via nutrient-dependent RNA-directed DNA methylation and RNA-mediated amino acid substitutions that differentiate cell types in the context of thermodynamic cycles of protein biosynthesis and degradation.
Species-specific pheromones control the physiology of reproduction and “fix” the amino acid substitutions in populations. The substitutions stabilize the DNA in organized genomes and the substitutions prevent most of the damage that would otherwise result from accumulated mutations.
Nutrient-dependent DNA repair mechanisms also typically prevent the accumulation of damage that might otherwise occur during life history transitions. For example, vitamin D uptake or natural production links ecological adaptations in populations where malaria is endemic via substitution of the amino acid associated with the hemoglobin S (sickle cell) variant.
The idea of protein evolution is foreign to me because protein evolution is not exemplified in model organisms. The universal trend of amino acid gain and loss in proteins occurs when nutrient-dependent substitutions stabilize the DNA in organized genomes. Accumulated mutations that cause too much dysfunction are typically eliminated — until nutrient stress and/or social stress overwhelm the ability of organisms that might otherwise continue to ecologically adapt as if they were immortal.
Two external factors cause changes in amino acid compositions of proteins in all genera that lead to biodiversity via mortality of individuals. The external factors are nutrient uptake and the pheromone-controlled physiology of reproduction. Together, they link the epigenetic landscape to the physical landscape of DNA in organized genomes via the bio-physically constrained chemistry of protein folding. That is how protein folding can be linked to the conserved molecular mechanisms of ecological adaptations in all species via amino acid substitutions.
biomolbioandco My comment about the Relationship between protein thermodynamic constraints and variation of evolutionary rates among sites was posted at this site after it was blocked by the moderator at the BioRxiv article site.
The stability model they detail is a model in which mutations are either neutral or completely deleterious. However, their evolutionary inferences link the mutations to biodiversity.
The same thing is done in Biophysics of protein evolution and evolutionary protein biophysics.
My comment: These are people who “…expect to witness increasing collaboration between the fields of biophysics and evolution as well as between theory/computation and experiment to decipher many aspects of the evolutionary forces that have been shaping the biological roles of proteins.”
I expect them to be humiliated by serious scientists who are less likely to think that mutations link perturbed protein folding to the increasing organismal complexity manifested in nutrient-dependent pheromone-controlled biodiversity.
See for example, a 5.5 minute video representation of: Nutrient-dependent / Pheromone-controlled adaptive evolution: (a mammalian model of thermodynamics and organism-level thermoregulation)
This model refutes a book-length revision of a comparable theory: ‘Mutation-driven evolution’ 
Chemical ecology drives adaptive evolution via ecological, social, neurogenic, and socio-cognitive niche construction. Nutrients are metabolized to pheromones that epigenetically effect hormones that affect behavior in the same way food odors classically condition behavior associated with food preferences. In mammals, the epigenetic effects of olfactory/pheromonal input are on gonadotropin releasing hormone (GnRH) neurosecretory neurons of brain tissue. For example: glucose and pheromones alter the secretion of GnRH and luteinizing hormone (LH). Secretion of LH is the measurable proxy for genetically predisposed differences in hypothalamic GnRH pulse frequency and amplitude and the downstream effects of GnRH, which is the central regulator of genetically predisposed nutrient-dependent individual survival and pheromone-controlled species survival.
This model of systems biology represents the conservation of bottom-up organization and top-down activation via the 1) thermodynamics of nutrient stress-induced and social stress-induced intracellular changes in the microRNA / messenger RNA (miRNA/mRNA) balance; 2) intermolecular changes in DNA (genes) and alternative splicing; 3) non-random experience-dependent stochastic variations in de novo gene expression and biosynthesis of odor receptors; 4) the required gene-cell-tissue-organ-organ system pathway that links sensory input directly to gene activation in neurosecretory cells and to miRNA-facilitated learning and memory in the amygdala of the adaptively evolved mammalian brain; and 5) the reciprocity that links the thermodynamics of gene expression to behavior and altered organism-level thermoregulation in species from microbes to man.
Examples of nutrient-dependent amino acid substitutions clarify the involvement of seemingly futile thermodynamic control of intracellular and intermolecular interactions, which result in de novo creation of olfactory receptor genes. Thermodynamically controlled cycles of RNA transcription and protein degradation are responsible for organism-level changes in pheromone production, which enable accelerated changes in the miRNA/mRNA balance and thermoregulation of controlled nutrient-dependent adaptive evolution.
In this mammalian model, food odors associated with nutrient uptake and species-specific social odors cause changes in the miRNA/mRNA balance. Those changes enable differential gene expression in GnRH neurons during developmental transitions required for successful nutrient-dependent pheromone-controlled reproduction, which occurs in species from microbes to man. Recent data extend this mammalian model of conserved molecular mechanisms across the continuum of adaptive evolution to selection for phenotypic expression associated with pheromones in a human population.
Across species comparisons of epigenetic effects on pangenomic microbial nutrient-dependent reproduction and on hormone-controlled invertebrate and vertebrate social and sexual behavior indicate that human pheromones alter the development of the brain and behavior via the molecular mechanisms conserved across all species.
It is now clear how an environmental drive evolved from that of nutrient uptake in unicellular organisms to that of pheromone-controlled socialization in insects. This makes it clearer that, in mammals, nutrients associated with food odors and pheromones associated with body odors cause controlled changes in hormones, which have developmental affects on the control of behavior in nutrient-dependent reproductively fit individuals that signal their fitness via pheromones. For contrast, in theory, mutations are not physiologically controlled, but control is required for adaptive evolution to occur .
An epigenetic continuum of nutrient-dependent pheromone-controlled adaptive evolution
Nematodes: Species incompatibilities are associated with cysteine-to-alanine substitutions . Differences in behavior are determined by nutrient-dependent rewiring of their primitive nervous system .
Insects: Neurogenic niche construction in nematodes  is also exemplified in the honeybee model organism of nutrient-dependent pheromone-controlled adaptive evolution of the brain and behavior. In flies, nutrient-dependent changes in mitochondrial tRNA and a nuclear-encoded tRNA synthetase enable the attachment an amino acid that facilitates the reaction required for efficient and accurate protein synthesis . In wasps, the change in a pre-existing signaling molecule triggered by a glucose-dependent  stereochemical inversion  leads to species-specific pheromone production. In Ostrinia moth species, substitution of a critical amino acid, is sufficient to create a new pheromone blend .
Mammals: The association of the nutrient choline in humans and its metabolism to trimethylamine odor in different species of mice was the best example of how a change in diet becomes associated with the presence of mammalian conspecifics whose androgen estrogen ratio-associated odor distinguishes them sexually, and also as nutrient-dependent physically fit mates . The mouse model makes it clearer that glucose uptake changes cellular thermodynamic equilibrium  and differential pathway regulation that results in adaptively evolved fitness in species from microbes  to mammals.
Humans: Two reports link substitution of the amino acid alanine for the amino acid valine  to nutrient-dependent pheromone-controlled adaptive evolution. Cause and effect was established in mice . These two reports [13, 14] tell a new short story of nutrient-dependent pheromone-controlled adaptive evolution. The story begins with what was probably a nutrient-dependent variant allele that arose in central China ~ 30,000 years ago. In other mammals, like the mouse, the effect of the allele is manifested in sweat, skin, hair, and teeth, and the effect is clearly due to the epigenetic effect of nutrients on hormones responsible for the tweaking of immense gene networks that metabolize nutrients to pheromones. In the model here, the pheromones control the nutrient-dependent hormone-dependent organization and activation of reproductive sexual behavior in mammals such as mice and humans, and also in invertebrates as previously indicated . Therefore, the adaptive evolution of the human population, which is detailed in these two reports, is also likely to be nutrient-dependent and pheromone-controlled sans mutations theory. See also 
1. Nei, M., Mutation-Driven Evolution. 2013, Oxford, UK: Oxford Univesity Press.
2. Noble, D., Physiology is rocking the foundations of evolutionary biology. Experimental Physiology, 2013: 10.1113/expphysiol.2012.071134.
3. Wilson, L., et al., Fertilization in C. elegans requires an intact C-terminal RING finger in sperm protein SPE-42. BMC Dev Biol 2011. 11(1): 10.
4. Bumbarger, Daniel J., et al., System-wide Rewiring Underlies Behavioral Differences in Predatory and Bacterial-Feeding Nematodes. Cell, 2013. 152(1): 109-119.
5. Kohl, J.V., Human pheromones and food odors: epigenetic influences on the socioaffective nature of evolved behaviors. Socioaffective Neuroscience & Psychology, 2012. 2(17338).
6. Meiklejohn, C.D., et al., An Incompatibility between a Mitochondrial tRNA and Its Nuclear-Encoded tRNA Synthetase Compromises Development and Fitness in Drosophila. PLoS Genet, 2013. 9(1): e1003238.
7. Yadav, J.S., B.V. Joshi, and M.K. Gurjar, An enantiospecific synthesis of (4R,5R)-5-hydroxy-4-decanolide from d-glucose. Carbohydr Res, 1987. 165(1): 116-119.
8. Niehuis, O., et al., Behavioural and genetic analyses of Nasonia shed light on the evolution of sex pheromones. Nature, 2013. 494: 345–348.
9. Lassance, J.-M., et al., Functional consequences of sequence variation in the pheromone biosynthetic gene pgFAR for Ostrinia moths. Proceedings of the National Academy of Sciences, 2013. in press.
10. Stensmyr, M. and F. Maderspacher, Olfactory Evolution: Mice Rethink Stink. Curr Biol, 2013. 23(2): R59-R61.
11. Kohl, J.V., Nutrient-dependent / Pheromone-controlled thermodynamics and thermoregulation. http://dx.doi.org/10.6084/m9.figshare.643393, 2013.
12. Kondrashov, F.A., Gene duplication as a mechanism of genomic adaptation to a changing environment. Proc Biol Sci, 2012. 279 (1749): 5048-5057.
13. Grossman, Sharon R., et al., Identifying Recent Adaptations in Large-Scale Genomic Data. Cell, 2013. 152(4): 703-713.
14. Kamberov, Yana G., et al., Modeling Recent Human Evolution in Mice by Expression of a Selected EDAR Variant. Cell, 2013. 152(4): 691-702.
15. Kohl, J.V., Nutrient–dependent / pheromone–controlled adaptive evolution: a model. Socioaffective Neuroscience & Psychology, 2013. 3(20553).