Ewald summation and multiple time step methods for molecular dynamics simulation of biological molecules

Methods by which to determine conditions for a molecular dynamics (MD) simulation of biological molecules were investigated. Derivation of the optimal parameters of the Ewald summation was described so as to give same precision to the real space, the reciprocal space summations and the van der Waals interaction. Later, the procedure by which to determine the condition of the multiple time step method by RESPA (REference System Propagator Algorithm; Tuckerman et al., 1992, J. Chem. Phys., 97, 1990) was described as exemplified by MD simulations of a solvated β-sheet peptide. The conservation of the total energy in a microcanonical ensemble was measured to investigate the stability of the simulation conditions. The most feasible respective combinations of the time steps were: 0.25 fs for bond, angle and torsion interactions; 2 fs for van der Waals interaction and Ewald real-space summation; and 4 fs for Ewald reciprocal-space summation. Though it retained an acceptable accuracy, this condition accelerated the simulation ten-fold compared to that in which a simple velocity-Verlet method with a time step of 0.25 fs was used. The update of the correction term due to excluded neighbors was then investigated. Better results were obtained when the correction was updated with the real-space than when it was updated with the reciprocal-space summation. Finally, an MD simulation as long as 50 ps performed under the optimal Ewald and RESPA parameters was thus determined. The trajectory showed a good stability, indicating the feasibility of the parameters.     

LINCS: A linear constraint solver for molecular simulations

In this article, we present a new LINear Constraint Solver (LINCS) for molecular simulations with bond constraints. The algorithm is inherently stable, as the constraints themselves are reset instead of derivatives of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrices, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large molecules. At the same accuracy, the LINCS algorithm is three to four times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1463–1472, 1997     

Phenylene Ethynylene‐Tethered Perylene Bisimide Folda‐Dimer and Folda‐Trimer: Investigations on Folding Features in Ground and Excited States

In this work, we have elucidated in detail the folding properties of two perylene bisimide (PBI) foldamers composed of two and three PBI units, respectively, attached to a phenylene ethynylene backbone. The folding behaviors of these new PBI folda‐dimer and trimer have been studied by solvent‐dependent UV/Vis absorption and 1D and 2D NMR spectroscopy, revealing facile folding of both systems in tetrahydrofuran (THF). In CHCl₃ the dimer exists in extended (unfolded) conformation, whereas partially folded conformations are observed in the trimer. Temperature‐dependent ¹H NMR spectroscopic studies in [D₈]THF revealed intramolecular dynamic processes for both PBI foldamers due to, on the one hand, hindered rotation around C?N imide bonds and, on the other hand, backbone flapping; the latter process being energetically more demanding as it was observed only at elevated temperature. The structural features of folded conformations of the dimer and trimer have been elucidated by different 2D‐NMR spectroscopy (e.g., ROESY and DOSY) in [D₈]THF. The energetics of folding processes for the PBI dimer and trimer have been assessed by calculations applying various methods, particularly the semiempirical PM6‐DH2 and the more sophisticated B97D approach, in which relevant dispersion corrections are included. These calculations corroborate the results of NMR spectroscopic studies. Folding features in the excited states of these PBI foldamers have been characterized by using time‐resolved fluorescence and transient absorption spectroscopy in THF and CHCl₃, exhibiting similar solvent‐dependent behavior as observed for the ground state. Interestingly, photoinduced electron transfer (PET) process from electron‐donating backbone to electron‐deficient PBI core for extended, but not for folded, conformations was observed, which can be explained by a fast relaxation of excited PBI stacks in the folded conformation into fluorescent excimer states.