Formulation of improved basis sets for the study of polymer dynamics through diffusion theory methods

Abstract

In this work a new method is proposed for the choice of basis functions in diffusion theory (DT) calculations. This method, named hybrid basis approach (HBA), combines the two previously adopted long time sorting procedure (LTSP) and maximum correlation approximation (MCA) techniques; the first emphasizing contributions from the long time dynamics, the latter being based on the local correlations along the chain. In order to fulfill this task, the HBA procedure employs a first order basis set corresponding to a high order MCA one and generates upper order approximations according to LTSP. A test of the method is made first on a melt of cis-1,4-polyisoprene decamers where HBA and LTSP are compared in terms of efficiency. Both convergence properties and numerical stability are improved by the use of the HBA basis set whose performance is evaluated on local dynamics, by computing the correlation times of selected bond vectors along the chain, and on global ones, through the eigenvalues of the diffusion operator L. Further use of the DT with a HBA basis set has been made on a 71-mer of syndiotactic trans-1,2-polypentadiene in toluene solution, whose dynamical properties have been computed with a high order calculation and compared to the "numerical experiment" provided by the molecular dynamics (MD) simulation in explicit solvent. The necessary equilibrium averages have been obtained by a vacuum trajectory of the chain where solvent effects on conformational properties have been reproduced with a proper screening of the nonbonded interactions, corresponding to a definite value of the mean radius of gyration of the polymer in vacuum. Results show a very good agreement between DT calculations and the MD numerical experiment. This suggests a further use of DT methods with the necessary input quantities obtained by the only knowledge of some experimental values, i.e., the mean radius of gyration of the chain and the viscosity of the solution, and by a suitable vacuum trajectory, with great savings in computational time required. This offers a theoretical bridge between the experimental static and dynamical properties of polymers.

Peptide dynamics by molecular dynamics simulation and diffusion theory method with improved basis sets

“…Individual local persistence lengths ranged from 2.12 to 3.83, showing significant variability of the local stiffness along the chain. The comparison of these results with the same quantities of the melt of cis-1,4-polyisoprene 7 confirms that we are indeed studying the dynamic properties of a polymer with variable local stiffness along the chain and a longer persistence length. This average persistent length of TTR can be compared furthermore with that of the melt of cis-1,4-polyisoprene 7 which was calculated to be 2.06 with a standard deviation of 0.091 and the individual local persistence lengths of the latter fall into a much narrower range between 2.01 and 2.26.…”

“…Recently, the philosophies underlying these two well-established methods were merged into a new formulation of basis sets and applied to DT. This so-called hybrid basis approach (HBA) 7 takes advantage of the strengths of both approaches and obtains higher quality results within less computational effort. Essentially, this new HBA method consisted in constructing a first order basis by the mth order MCA basis set and using it in the LTSP procedure for higher order calculations.…”

“…The HBA was tested on those flexible polymers that are characterized by the repetition of the same monomeric unit along the chain. One system was a melt of cis-1,4polyisoprene decamers, 7 and the other, a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene. 7 In both cases, the HBA was shown to fully exploit the specific viewpoints of MCA and LTSP in the formulation of the basis set.…”

“…One system was a melt of cis-1,4polyisoprene decamers, 7 and the other, a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene. 7 In both cases, the HBA was shown to fully exploit the specific viewpoints of MCA and LTSP in the formulation of the basis set. Those calculations yielded in fact the same results of LTSP but with a much smaller number of basis functions employed in the numerical computations.…”

“…These polymers exhibit, of course, different local and global dynamic properties against those cases considered previously. 6,7 Proteins are important examples of these kinds of polymers and, given their relevance in the life processes, it is of great theoretical interest to assess the extent to which the HBA method can be exploited to improve the description of their dynamics. As in flexible synthetic polymers, both MCA and LTSP have been previously applied to biological systems also, such as the rat microsomal cytochrome b 5 , 8 peptide met-enkephalin, 5,9,10 DNA oligomer, 11 protein fragment NK-2, 12 RNA fragment, 13 etc.…”