In protein molecules each residue has a different ability to form contacts. In this paper

we calculated the number of contacts per residue and investigated the distribution of residue-residue contacts from 495 globular protein molecules using Contacts of Structural Units (CSU) software. It was found that the probability P(n) of amino acid residues having n pairs of contacts in all contacts fits Gaussian distribution very well. The distribution function of residue-residue contacts can be expressed as: P(n) = P0 + aexp[-b(n - nc)2]. In our calculation

P0 = -0.06

a = 11.4

b = -0.04 and nc = 9.0. According to distribution function

we found that those hydrophobic (H) residues including Leu

Val

Ile

Met

Phe

Tyr

Cys

and Trp residues have large values of the most probable number of contact nc

and hydrophilic (P) residues including Ala

Gly

Thr

His

Glu

Gln

Asp

Asn

Lys

Ser

Arg

and Pro residues have the small ones. We also compare with Fauchere-Pliska hydrophobicity scale (FPH) and the most probable number of contact nc for 20 amino acid residues

and find that there exists a linear relationship between Fauchere-Pliska hydrophobicity scale (FPH) and the most probable number of contact nc

and it is expressed as: nc = a + b × FPH

here a=8.87

and b=1.15. It is important to further explain protein folding and its stability from residue-residue contacts.