Abstract
The distribution of protein stability effects is known to be well approximated by a Gaussian distribution from previous empirical fits. Starting from first-principles statistical mechanics, we more rigorously motivate this empirical observation by deriving per-residue-position protein stability effects to be Gaussian. Our derivation requires the number of amino acids to be large, which is satisfied by the standard set of 20 amino acids found in nature. No assumption is needed on the number of residues in close proximity in space, in contrast to previous applications of the central limit theorem to protein energetics. We support our derivation results with computational and experimental data on mutant protein stabilities across all types of protein residues.
Highlights
The overall stability of a protein is influenced by its residues and their interactions [1]
We derive from first-principles statistical mechanics that per-residue-position defining the distribution of single-mutant stability effects (DDGs) are Gaussian distributed
The finding that per-position DDGs are Gaussian distributed may not seem surprising in light of the central limit theorem
Summary
The overall stability of a protein is influenced by its residues and their interactions [1]. We apply first-principles statistical mechanics and show that per-residue-position DDG distributions are accurately approximated by Gaussians with means and variances shaped by their local (in space) sequence and structure. We transform the summation into an integral over s_mut,(i) space, picking out terms that correspond to amino acid types with Dirac delta functions and approximating each delta function as a Gaussian distribution.
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