It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly.Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution ρ(r)of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice.The probability distribution of end-to-end distance p(r)of short two-dimensional compact polymers chains may consist of two parts,i.e.p(r)=p_1(r)+p_2(r),where p_1(r)and p_2(r)are different for small r.The rate of contact formation decreases monotonically with the number of bonds N,and the rate approximately conforms to the scaling relation of k(N)∝ N^(-α).Here the value of α increases with the contact radius α and it also depends on the percentage of H(hydrophobic)residues in the sequences of compact chains and the energy parameters of ε_(HH),ε_(HP) and ε_(pp).Some comparisons of theoretical predictions with experimental results are also made.This investigation may help us to understand the protein folding.
