Linxi Zhang

Elastic behavior of short compact polymers

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance R(2) and the ratio of R(2)/S(2) increase with lambda. However, when the elongation ratio becomes larger, the curves of R(2)/S(2) become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90 degrees, 180 degrees, and 270 degrees). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio lambda. In the meantime, the elastic force per bond (f ) also increases with elongation ratio lambda, and the energy contribution to the elastic force (f(U)) increases first and then drops, and there exists the maximum of f(U) in the region of lambda=1.40-1.80 for different sequences. The entropy contribution to force (f(S)) is close to zero at a small elongation ratio lambda and then increases with lambda. Some comparisons with different sequences (including nonfolding and folding sequences) are also made.

Folding rate prediction based on neural network model

One of the most important challenges in biology is to understand the relationship between the folded structure of a protein and its primary amino acid sequence. A related and challenging task is to understand the relationship between sequences and folding rates of proteins. Previous studies found that one of contact order (CO), long-range order (LRO), and total contact distance (TCD) has a significant correlation with folding rate of protein. Although the predicted results from TCD can provide better results, the deviation is also large for some proteins. In this paper, we adopt back-propagation neural network to study the relationship between folding rate and protein structure. In our model, the input nodes are CO, LRO, and TCD, and the output node is folding rate. The number of nodes in the hidden layer is seven. Our results show that the relative errors for the predicted results are even lower than other methods in the literature. We also observe a best excellent correlation between the folding rate and contact parameters (including CO, LRO, and TCD), and find that the folding rate depends on CO, LRO and TCD simultaneously. This means that CO, LRO and TCD are similarly important in folding rate of protein. Some comparisons are made with other methods.

A Molecular Model of the Elastic Behavior of Polymethylene Chains

In this paper, the elastic behavior of a polymethylene (PM) chain is investigated by using a realistic rotational-isomeric-state (RIS) model. In our calculation, the non-local interactions between pairs of segments in polymethylene chain are also considered, and the Lennard-Jones (L-J) potential function is adopted. Chain dimensions and thermodynamics statistical properties of PM chains with various elongation ratios λ are calculated. We find, that the elastic force increases slowly with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant, especially for large λ. Our calculations may provide some insight into the macroscopic phenomena of rubber elasticity.

Statics and dynamics of adsorbed ring polymer chains

Abstract Monte Carlo calculations of the statics and dynamics behavior of ring polymers adsorbed on a short-range attractive wall (xy-plane) are described using the bond-fluctuation model. Chain conformation, fraction of segment adsorbed and chain dimensions are measured over a wide range of temperatures. An adsorbed layer begins to form at the larger adsorption transition temperature Ta than a single linear polymer chain. For the dynamics, the mean square displacements and the diffusion coefficients parallel and perpendicular to the z-axis are also calculated. Some comparisons with linear chains are made.

Predicting protein structure from long-range contacts.

Short-range and long-range contacts are important in forming protein structure. The proteins can be grouped into four different structural classes according to the content and topology of alpha-helices and beta-strands, and there are all-alpha, all-beta, alpha/beta and alpha+beta proteins. However, there is much difference in statistical property for those classes of proteins. In this paper, we will discuss protein structure in the view of the relative number of long-range (short-range) contacts for each residue. We find the percentage of residues having a large number of long-range contacts in protein is small in all-alpha class of proteins, and large in all-beta class of proteins. However, the percentage of residues is almost the same in alpha/beta and alpha+beta classes of proteins. We calculate the percentage of residues having the number of long-range contacts greater than or equal to (>/=) N(L)=5, and 7 for 428 proteins. The average percentage is 13.3%, 54.8%, 41.4% and 37.0% for all-alpha, all-beta, alpha/beta and alpha+beta classes of proteins with N(L)=5, respectively. With N(L) increasing, the percentage decreases, especially for all-alpha class of proteins. In the meantime, the percentage of residues having the number of short-range contacts greater than or equal to N(S) (>/=N(S)) in protein samples is large for all-alpha class of proteins, and small for all-beta class of proteins, especially for large N(S). We also investigate the ability of amino residues in forming a large number of long-range and short-range contacts. Cys, Val, Ile, Tyr, Trp and Phe can form a large number of long-range contacts easily, and Glu, Lys, Asp, Gln, Arg and Asn can form a large number of long-range contacts, but with difficulty. We also discuss the relative ability in forming short-range contacts for 20 amino residues. Comparison with Fauchere-Pliska hydrophobicity scale and the percentage of residues having large number of long-range contacts is also made. This investigation can provide some insights into the protein structure.

Dynamics of stiff chain

Abstract In this paper, the bending and stretching elastic potential energies are considered in calculating Hamilton actuating quantity. In the meantime, the mass density of the filament and the friction force are also considered. The normal mode analysis yields eigenfunctions and eigenvalues. In the dynamical equation of polymer chains without a Brownian force, two cases of ζ 2 −4 ρξ n >0 and ζ 2 −4 ρξ n ρ is the linear mass density of the filament, ζ is the friction constant per unit length of the filament, and ξ n is the eigenvalue. We discuss the dependence of the relaxation times on the persistence length. In the flexible limit, we obtain the relaxation times of the Rouse model. In the stiff-chain case, the relaxation times τ n are proportional to [ L /(2 n −1)] 4 .

Glassy dynamics of nanoparticles in semiflexible ring polymer nanocomposite melts

By employing molecular dynamics simulations, we explore the dynamics of NPs in semiflexible ring polymer nanocomposite melts. A novel glass transition is observed for NPs in semiflexible ring polymer melts as the bending energy (Kb) of ring polymers increases. For NPs in flexible ring polymer melts (Kb = 0), NPs move in the classic diffusive behavior. However, for NPs in semiflexible ring polymer melts with large bending energy, NPs diffuse very slowly and exhibit the glassy state in which the NPs are all irreversibly caged be the neighbouring semiflexible ring polymers. This glass transition occurs well above the classical glass transition temperature at which microscopic mobility is lost, and the topological interactions of semiflexible ring polymers play an important role in this non-classical glass transition. This investigation can help us understand the nature of the glass transition in polymer systems.

A Monte Carlo study of polymer network dynamics

Abstract Junction fluctuations in a polymer network are investigated by using the Monte Carlo method. In our calculation, a modified bond-fluctuation model is adopted. In our model, the kuhnian bond lengths are set to vary between 2 and 4, which is different from the lengths between 2 and √ 10 of the standard model. It is found that the average fluctuations of junctions i and j may be expressed in the form of ΔR i 2 / r 2 0 = a (φ−1) +b(φ=3, 4, 5, 6) 〈ΔR i ΔR j 〉/ r 2 0 = a′ (φ−1) +b′(φ=3, 4, 5, 6) where a=0.83, b=−0.076, a′=0.06, b′= 0.0075, and 〈r2〉0 is the mean-square end-to-end distance of two adjacent junction points and φ is the junction functionality. Comparisons with the Cayley tree model are also made. Our method uses real, rather than phantom, chains, and this method can be used to investigate the dynamics of polymer network chains.

Statics and dynamics of adsorbed uniform star chains

Abstract In this paper, we investigate the static and dynamic properties of uniform star chains with F=3, 6, and 9 branches of length N adsorbed on the attractive wall (xy-plane) using the bond-fluctuation model. Chain dimensions, fraction of segments adsorbed and maximum thickness of adsorbed layer are measured for systems with a different branch number of star chains over a range of temperatures. Adsorbed layers begin to form at the more adsorption transition temperature as the number of branches increases. The diffusion constants decrease with increasing number of branches. At the same time, some comparisons with linear chains are made.

A molecular study on the reinforcement of polymethylene elastomers

Abstract Monte Carlo simulations are carried out on filled networks of polymethylene (PM), which are modeled as composites of PM chains and three-dimensional cubic lattices of filler particles. Calculations are carried out for PM chains with various chain lengths n and various cubic unit dimensions a. The elastic behavior is investigated by using a realistic rotational-isomeric-state (RIS) model and enumeration calculation method. The average conformations, such as a priori probability Pη and the segmental orientation function 〈P2(cosζ)〉 of PM chains are also calculated. In the process of tensile deformation, the a priori probability Pt increases with elongation ratio λ, however, it decreases with increasing cubic unit dimensions a. The segmental orientation distribution function 〈P2(cosζ)〉 of deformed PM chains decreases with increasing cubic unit dimensions a, especially in the region of large deformation. Average Helmholtz free energy per bond becomes small when increasing cubic unit dimensions a, and average energy per bond becomes large when increasing cubic unit dimensions a. We find that the elastic force increases with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant. It is also shown that the elastic force and the energy contribution to elastic force is almost the same with various cubic unit dimensions a. The ratio fu/f ranges from −0.4 to −0.6 at T=425 K. The reinforcement effects on the Helmholtz free energy 〈A〉 and energy 〈U〉 are important; however, the effect on the elastic force is insignificant. Our calculation may provide some insight into the macroscopic phenomena of rubber elasticity.