doi: 10.1371/journal.pcbi.1004771.
eCollection 2016 Jun.
The Context-Dependence of Mutations: A Linkage of Formalisms
Affiliations
- PMID: 27337695
- PMCID: PMC4919011
- DOI: 10.1371/journal.pcbi.1004771
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The Context-Dependence of Mutations: A Linkage of Formalisms
PLoS Comput Biol.
.
No abstract available
Conflict of interest statement
The authors have declared that no competing interests exist.
Figures
Representation of (A) single mutant, (B) double mutant, and (C) triple mutant experiments. Phenotypes are denoted by yg, where g is the underlying genotype. g = {gN,…,g1} with gi ∈{0,1}; “0” or “1” indicates the state of the mutable site (e.g., amino acid position). The effect of a single, double, and triple mutation is given by the red arrows. Pairwise (or second-order) epistasis is defined as the differential effect of a mutation depending on the background in which it occurs; for example, in (B) it is the degree to which the effect of one mutation (e.g., y10−y00) deviates in the background of the second mutation (y11−y01). Thus, the expression for second-order epistasis is (y11−y10)−(y01−y00). The third order and higher cases are considered in the main text.
(A) PDZ domains are small, mixed αβ proteins that bind target peptide ligand (in yellow stick bonds) in a groove formed between the β2 and α2 elements (PSD95pdz3 shown, Protein Data Bank (PDB) accession 1BE9). The study discussed in the main text and in Table 1 is focused on the epistatic interactions between three amino acid positions—two in the PDZ domain (H372 and G330) and one in the ligand (T-2) (red spheres). (B) a thermodynamic cube representing the energetics of mutations at the three positions; values are equilibrium dissociation constants (Kd) for the target ligand (CRIPT [58]) in μM for all eight possible combination of mutations; errors represent standard deviation. (C) structure of the homotetrameric KcsA K+ ion channel (PDB accession 1K4C), showing the four positions selected for mutation in Sadovsky and Yifrach (in red spheres, shown only for one subunit for clarity) [60]. Note that the experiments were carried out in the Shaker K+ ion channel, and the positions in Shaker numbering are given in parentheses. The positions form a network that roughly links the intracellular activation gate and the selectivity filter.
(A) Z2 for when data for mutants up to second-order is available and (B) Z1 for when only first-order mutants are available. Both matrices are self-similar, which allows their generation for arbitrary order, and are related to the logic Sierpinski triangle. For example, Z2 = 1−AΣ, where A is the anti-diagonal identity matrix and Σ is the Sierpinski matrix (i.e., multigrade AND in Boolean logic) for three inputs.
References
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- Wells JA (1990) Additivity of mutational effects in proteins. Biochemistry 29:8509 - PubMed
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