Elastic Behavior And Conformation Properties Of Compact Polymer Chains

It's important to investigate the native conformation, folding mechanism and thermodynamic properties of biomacromolecules. The relation between the structure and the function can be found in biomacromolecular sequences. In this dissertation, we investigate the conformation properties, the elastic behavior of biomacromolecules and long-range correlation of DNA sequences in order to help us to understand the organism clearly.In Chapter 2, we use coarse-grained model to calculate statistical properties of residue-residue contacts based on a large number of proteins from PDB. By analyzing the effects of amino acid residues on long-and short-range contacts, we can get the conclusion that hydrophobic residues are easy to form long-range contacts, while hydrophilic residues are difficult. However short-range contacts only depend on residue sequence. Long-range contacts play an active role in protein folding and the stability of proteins. We also discuss the statistical properties of residues for (α/β)8 barrel proteins using a new model in which Ca is replaced by the center position, and find that the average residue contacts per residue in all residue pairs is good to differentiate the interior and the exterior residues. At the same time, a simple two-dimensional HP compact lattice model is used to investigate the conformation change during folding process. We find that the size of compact chains is small at the beginning of folding process, and the size distribution depends on residue sequence. Statistical properties of long-and short-contacts based on 428 globular proteins are also studied. Proteins with different secondary structures have different ability of forming contacts. All-a proteins are easy to form short-range contacts while all-βproteins are easy to form long-range contacts. Andα/βproteins are similar toα+βproteins. This investigation can provide a new path to understand the properties of protein structure and folding mechanism.With the development of computer technique, we can dig out hidden and available information in DNA sequences. So in Chapter 3, the long-range correlation in DNA sequences using two-dimensional DNA walk are firstly discussed. The mean-square distance, root-mean-square fluctuation and autocorrelation function are obey the power law< R2(l)>-lr, F(l)-lHr and C(l)-l-μrespectively. On the other hand, the statistical properties of CG clusters in coding and non-coding DNA sequences are investigated through calculating the cluster-size distribution of CG clusters P(S) and the breadth of the distribution of the root-mean-square size of CG clustersξ(m) in consecutive, non-overlapping blocks of m bases, and we also find the relation of P(s)∝e-as andξ(m)∝m-r. There exist some differences between coding and non-coding sequences by analyzing the exponents a and y, and the behavior of coding sequences is more similar to random sequences. These results can provide some insights into the long-range correlations of DNA sequences.In Chapter 4, the elastic behavior of single polymer chains adsorbed on the attractive surface is calculated by Metropolis Monte Carlo simulation method and the bond fluctuation model. And compact polymer chains can form stable structures by intra-molecular contacts, which can represent the native conformation of proteins well. So we first consider the rate of intra-molecular contact formation in short two-dimensional compact polymers. The rate of contact formation decreases with the number of bonds, and approximately conforms to the scaling relation of K(N)∝N-α, where the value ofαincreases with the contact radius a and also depends on the percentage of hydrophobic residues in different sequences. We also calculate some statistical properties, such as mean-square end-to-end distance< R2>, mean-square radii of gyration and shape factor<δ> in order to illuminate how the size and shape of adsorbed compact chains change during the process of tensile elongation.Thermodynamic properties are also studied in Chapter 5. Different elastic behaviors are obtained for adsorbed compact polymer chains. Elastic force has a long plateau during the tensile elongation for strong adsorption interaction, which agrees well with experimental and theoretical results. These calculations can help us to understand the elastic behavior of compact polymer chains and find out the relation between the structure and the function.