Physicochemical distance is a measure that assesses the difference between replaced amino acids. The value of distance is based on properties of amino acids. There are 134 physicochemical properties that can be used to estimate similarity between amino acids. Each physicochemical distance is based on different composition of properties.
Grantham's distance Grantham's distance depends on three properties: composition, polarity and molecular volume. Distance difference
D for each pair of amino acid
i and
j is calculated as: D_{ij}=[\alpha(c_i-c_j)^2+\beta(p_i-p_j)^2+\gamma(v_i-v_j)^2]^{\frac{1}{2}} where
c = composition,
p = polarity, and
v = molecular volume; and are constants of squares of the inverses of the mean distance for each property, respectively equal to 1.833, 0.1018, 0.000399. According to Grantham's distance, most similar amino acids are
leucine and isoleucine and the most distant are cysteine and tryptophan.
Sneath's index Sneath's index takes into account 134 categories of activity and structure. This index that distincts the direction of exchange between amino acids, described by 2 equations: \Delta_{a\rightarrow b}=(\delta_{polarity}^2+\delta_{size}^2)^{1/2} when smaller hydrophobic residue is replaced by larger hydrophobic or polar residue \Delta_{a\rightarrow b}=(\delta_{polarity}^2+[0.5 \delta_{size}]^2)^{1/2}when polar residue is exchanged or larger residue is replaced by smaller
Miyata's distance Miyata's distance is based on 2 physicochemical properties: volume and polarity. Distance between amino acids
ai and
aj is calculated as d_{ij}=\sqrt{(\Delta p_{ij}/\sigma_p)^2+(\Delta v_{ij}/\sigma_v)^2} where \Delta p_{ij} is value of polarity difference between replaced amino acids and \Delta v_{ij} and is difference for volume; \sigma_p and \sigma_v are standard deviations for \Delta p_{ij} and \Delta v_{ij}
Experimental Exchangeability Experimental Exchangeability was devised by Yampolsky and Stoltzfus. It is the measure of the mean effect of exchanging one amino acid into a different amino acid. It is based on analysis of experimental studies where 9671 amino acids replacements from different proteins, were compared for effect on protein activity. == Typical and idiosyncratic amino acids ==