The conformational properties and elastic behaviors of protein-like single chains in the process of tensileelongation were investigated by means of Monte Carlo method.The sequences of protein-like single chains contain two typesof residues:hydrophobic(H)and hydrophilic(P).The average conformations and thermodynamics statistical properties ofprotein-like single chains with various elongation ratio λ were calculated.It was found that the mean-square end-to-enddistance(?).increases with elongation ratio λ.The tensor eigenvalues ratio of:decreases with elongationratio λ for short(HP)_x protein-like polymers,however,the ratio of:increases with elongation ratio λ,especially for long (H)_x sequence.Average energy per bond increases with elongation ratio λ,especially for (H)_xprotein-like single chains.Helmholtz free energy per bond also increases with elongation ratio λ.Elastic force(f),energycontribution to force(f_U)and entropy contribution to force(fs)for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.
The characterization of long-range correlations and fractal properties of DNA sequences has proved to be adifficult though rewarding task mainly due to the mosaic character of DNA consisting of many patches of various lengthswith different nucleotide constitutions.In this paper we investigate statistical correlations among different positions in DNAsequences using the two-dimensional DNA walk.The root-mean-square fluctuation F(l)is described by a power law.Theautocorrelation function C(l),which is used to measure the linear dependence and periodicity,exists a power law ofC(l)-l^(-μ).We also calculate the mean-square distancealong the DNA chain,and it may be expressed as-l^(?)with 2>γ>1.Our investigations can provide some insights into long-range correlations in DNA sequences.
The analysis of residue-residue contacts in protein structures can shed some light on our understanding of the folding and stability of proteins. In this paper, we study the statistical properties of long-range and short-range residue- residue contacts of 91 globular proteins using CSU software and analyze the importance of long-range contacts in globular protein structure. There are many short-range and long-range contacts in globular proteins, and it is found that the average number of long-range contacts per residue is 5.63 and the percentage of residue-residue contacts which are involved in long- range ones is 59.4%. In more detail, the distribution of long-range contacts in different residue intervals is investigated and it is found that the residues occurring in the interval range of 4-10 residues apart in the sequence contribute more long-range contacts to the stability of globular protein. The number of long-range contacts per residue, which is a measure of ability to form residue-residue contacts, is also calculated for 20 different amino acid residues. It is shown that hydrophobic residues (including Leu, Val, He, Met, Phe, Tyr, Cys and Trp) having a large number of long-range contacts easily form long-range contacts, while the hydrophilic amino acids (including Ala, Gly, Thr, His, Glu, Gln, Asp, Asn, Lys, Ser, Arg, and Pro) form long-range contacts with more difficulty. The relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of short-range and long-range contacts per residue for 20 amino acid residues is also studied. An approximately linear relationship between the Fauchere-Pliska hydrophobicity scale (FPH) and the number of long-range contacts per residue CL, is found and can be expressed as CL = a + b × FPH where a = 5.04 and b = 1.23. These results can help us to understand the role of residue-residue contacts in globular protein structure.
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)=P_0+aexp[-b(n-n_c)~2].In our calculation,P_0=-0.06,α=11.4,b=-0.04 and n_c=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 n_c,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 n_c 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 n_c, and it is expressed as:n_c=a+b×FPH,here α=8.87,and b=1.15.It is important to further explain protein folding and its stability from residue-residue contacts.
Short two-dimensional compact chains adsorbed on the attractive surface at different temperatures were investigated by using the enumeration calculation method. First we investigate the chain size and shape of adsorbed chains, such as characteristic ratios of mean-square radii of gyration 〈S^2〉x/N and 〈S^2〉y/N, shape factor 〈δ〉, and the orientation of chain bonds 〈cos^2 θ〉 to illuminate how the size and shape of adsorbed compact chains change with increasing temperatures. There are some special behaviors for the chain size and shape at low temperature, especially for strong attraction interaction. In the meantime, adsorbed compact chains have different behaviors from general adsorbed polymer chains. Some thermodynamics properties are also discussed here. Heat capacity changes non-monotonously, first increases and then reduces. The transition temperature Tc is nearly 1.0, 1.4, 2.0 and 4.2 （in the unit of To） for the case of ε = 0, -1, -2 and -4 （in the unit of kTo）, respectively. Average energy per bond increases while average Helmholtz free energy per bond decreases with increasing temperatures. From these two thermodynamics parameters we can also get another transition temperature Tc＇, and it is close to 0.7, 1.1, 1.5 and 3.4 for ε= 0, -1, -2, and -4, respectively. Therefore, Tc is greater than Tc＇ under the same condition. These investigations may provide some insights into the thermodynamics behaviors of adsorbed protein-like chains.
