Biomolecular

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Barron L D, Hecht L, Bell A F and WIson G 1996 Raman optical activity an incisive probe of chirality and biomolecular structure and dynamics ICORS 96 XVth Int. Conf. on Raman Spectroscopy ed S A Asher and P B Stein (New York Wley) pp 1212-15... 

King P M 1993 Computer Simulations of Biomolecular Systems vol 2, ed W F van Gunsteren et al (Leiden ESCOM) pp315-48... 

Ramsden J J 1998 Towards zero-perturbation methods for investigating biomolecular interactions Coiioids Surfaces A 141 287-94... 

An equally important challenge for nanocrystal assembly is the fonnation of specific nanocrystal arrangements in solution. By using complementary DNA strands as tethers, Mirkin et al [102, 103] fonned aggregates of gold nanocrystals with specific sizes Alivisatos et al also used DNA to stmcture semiconductor nanocrystal molecules, though in this case the molecules contained only a few nanocrystals placed controlled distances from each other [104, 105 and 106]. The potential applications of biomolecular teclmiques to this area of nanoscience are immense, and the opportunities have been reviewed in several recent publications [107, 108, 109 and 110]. 

A contribution from the Groningen Biomolecular Sciences and Biotechnology Institute. 

Pree energy via molecular simulation A primer. In Computer Simulations of Biomolecular Systems, Vol 2, W.F. van Gunsteren, P.K. Weiner and A.J. Wilkinson, eds. Escom, Leiden (1993) 267-314. 

Procacci, P., Darden, T., Marchi, M., A very fast molecular dynamics method to simulate biomolecular systems with realistic electrostatic interactions. J. Phys. Chem. 100 (1996) 10464-10468. 

B.J. Leimkuhler, S. Reich, and R. D. Skeel. Integration methods for molecular dynamics. In Mathematical approaches to biomolecular structure and dynamics, Seiten 161-185, New York, 1996. Springer. 

T. Schlick, E. Bartha, and M. Mandziuk. Biomolecular dynamics at long timesteps Bridging the timescale gap between simulation and experiments tion. Ann. Rev. Biophys. Biom. Structure, 26 181-222, 1997. 

Volkov, S.N. Conformational transitions and the mechanism of transmission of long-range effects in DNA. Preprint ITP-88-12E, Kiev (1988) 22 Krumhansl, J.A., Alexander, D.M. Nonlinear dynamics and conformational exitations in biomolecular materials. In Structure and dynamics nucleic acids and proteins. (Clementi, E., Sarma, R.H., eds) Adenine Press, New York (1983) 61-80... 

Some Failures and Successes of Long-Timestep Approaches to Biomolecular Simulations... 

Accuracy, however, in biomolecular trajectories, must be defined somewhat subjectively. In the absence of exact reference data (from experiment or from an analytical solution), the convention has been to measure accuracy with respect to reference trajectories by a Verlet-like integrator [18, 19] at a timestep of 1 or 0.5 fs (about one tenth or one twentieth the period, respectively, of the fastest period an 0-H or N-H stretch). As pointed out by Deufihard et al. [20], these values are still larger than those needed to... 

Since the stochastic Langevin force mimics collisions among solvent molecules and the biomolecule (the solute), the characteristic vibrational frequencies of a molecule in vacuum are dampened. In particular, the low-frequency vibrational modes are overdamped, and various correlation functions are smoothed (see Case [35] for a review and further references). The magnitude of such disturbances with respect to Newtonian behavior depends on 7, as can be seen from Fig. 8 showing computed spectral densities of the protein BPTI for three 7 values. Overall, this effect can certainly alter the dynamics of a system, and it remains to study these consequences in connection with biomolecular dynamics. 

A reasonable approach for achieving long timesteps is to use implicit schemes [38]. These methods are designed specifically for problems with disparate timescales where explicit methods do not usually perform well, such as chemical reactions [39]. The integration formulas of implicit methods are designed to increase the range of stability for the difference equation. The experience with implicit methods in the context of biomolecular dynamics has not been extensive and rather disappointing (e.g., [40, 41]), for reasons discussed below. 

Because of the inherent damping, the application of IE to biomolecular dynamics only makes sense in the context of a model with a I cstoring force. 

There are three issues of concern regarding the application of LI to biomolecular dynamics (1) the governing Langevin model, (2) the implications of numerical damping, and (3) the CPU performance, given that nonlinear minimization is required at each, albeit longer, timestep. 

Though LI failed for general biomolecular applications [50], it has been found to be a useful ingredient in two other contexts macroscopic separable models, and enhanced sampling. 

The smaller the value of n (the resonance order), the larger the timestep of disturbance. For example, the linear stability for Verlet is uiAt < 2 for second-order resonance, while IM has no finite limit for stability of this order. Third-order resonance is limited by /3 ( J 1.72) for Verlet compared to about double, or 2 /3 (fa 3.46), for IM. See Table 1 for limiting values of wAt corresponding to interesting combinations of a and n. This table also lists timestep restrictions relevant to biomolecular dynamics, assuming the fastest motion has period of around 10 fs (appropriate for an O-H stretch, for example). 

The many approaches to the challenging timestep problem in biomolecular dynamics have achieved success with similar final schemes. However, the individual routes taken to produce these methods — via implicit integration, harmonic approximation, other separating frameworks, and/or force splitting into frequency classes — have been quite different. Each path has encountered different problems along the way which only increased our understanding of the numerical, computational, and accuracy issues involved. This contribution reported on our experiences in this quest. LN has its roots in LIN, which... 

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