Selection originating from protein stability/foldability: Relationships between protein folding free energy, sequence ensemble, and fitness
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arXiv
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2016
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| author | Miyazawa, Sanzo |
| author_facet | Miyazawa, Sanzo |
| contents | Assuming that mutation and fixation processes are reversible Markov processes, we prove that the equilibrium ensemble of sequences obeys a Boltzmann distribution with $\exp(4N_e m(1 - 1/(2N)))$, where $m$ is Malthusian fitness and $N_e$ and $N$ are effective and actual population sizes. On the other hand, the probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with $\exp(-ψ_N)$, where $ψ_N$ is represented as the sum of one body and pairwise potentials. A protein folding theory indicates that homologous sequences obey a canonical ensemble characterized by $\exp(-ΔG_{ND}/k_B T_s)$ or by $\exp(- G_{N}/k_B T_s)$ if an amino acid composition is kept constant, where $ΔG_{ND} \equiv G_N - G_D$, $G_N$ and $G_D$ are the native and denatured free energies, and $T_s$ is selective temperature. Thus, $4N_e m (1 - 1/(2N))$, $-Δψ_{ND}$, and $-ΔG_{ND}/k_B T_s$ must be equivalent to each other. Based on the analysis of the changes ($Δψ_N$) of $ψ_N$ due to single nucleotide nonsynonymous substitutions, $T_s$, and then glass transition temperature $T_g$, and $ΔG_{ND}$ are estimated with reasonable values for 14 protein domains. In addition, approximating the probability density function (PDF) of $Δψ_N$ by a log-normal distribution, PDFs of $Δψ_N$ and $K_a/K_s$, which is the ratio of nonsynonymous to synonymous substitution rate per site, in all and in fixed mutants are estimated. It is confirmed that $T_s$ negatively correlates with the mean of $K_a/K_s$. Stabilizing mutations are significantly fixed by positive selection, and balance with destabilizing mutations fixed by random drift. Supporting the nearly neutral theory, neutral selection is not significant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1612_09379 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Selection originating from protein stability/foldability: Relationships between protein folding free energy, sequence ensemble, and fitness Miyazawa, Sanzo Populations and Evolution Biomolecules Assuming that mutation and fixation processes are reversible Markov processes, we prove that the equilibrium ensemble of sequences obeys a Boltzmann distribution with $\exp(4N_e m(1 - 1/(2N)))$, where $m$ is Malthusian fitness and $N_e$ and $N$ are effective and actual population sizes. On the other hand, the probability distribution of sequences with maximum entropy that satisfies a given amino acid composition at each site and a given pairwise amino acid frequency at each site pair is a Boltzmann distribution with $\exp(-ψ_N)$, where $ψ_N$ is represented as the sum of one body and pairwise potentials. A protein folding theory indicates that homologous sequences obey a canonical ensemble characterized by $\exp(-ΔG_{ND}/k_B T_s)$ or by $\exp(- G_{N}/k_B T_s)$ if an amino acid composition is kept constant, where $ΔG_{ND} \equiv G_N - G_D$, $G_N$ and $G_D$ are the native and denatured free energies, and $T_s$ is selective temperature. Thus, $4N_e m (1 - 1/(2N))$, $-Δψ_{ND}$, and $-ΔG_{ND}/k_B T_s$ must be equivalent to each other. Based on the analysis of the changes ($Δψ_N$) of $ψ_N$ due to single nucleotide nonsynonymous substitutions, $T_s$, and then glass transition temperature $T_g$, and $ΔG_{ND}$ are estimated with reasonable values for 14 protein domains. In addition, approximating the probability density function (PDF) of $Δψ_N$ by a log-normal distribution, PDFs of $Δψ_N$ and $K_a/K_s$, which is the ratio of nonsynonymous to synonymous substitution rate per site, in all and in fixed mutants are estimated. It is confirmed that $T_s$ negatively correlates with the mean of $K_a/K_s$. Stabilizing mutations are significantly fixed by positive selection, and balance with destabilizing mutations fixed by random drift. Supporting the nearly neutral theory, neutral selection is not significant. |
| title | Selection originating from protein stability/foldability: Relationships between protein folding free energy, sequence ensemble, and fitness |
| topic | Populations and Evolution Biomolecules |
| url | https://arxiv.org/abs/1612.09379 |