Fast multiple methods

Watanabe, M., Karplus, M. Dynamics of Molecules with Internal Degrees of Freedom by Multiple Time-Step Methods. J. Chem. Phys. 99 (1995) 8063-8074 Figueirido, F., Levy, R. M., Zhou, R., Berne, B. J. Large Scale Simulation of Macromolecules in Solution Combining the Periodic Fast Multiple Method with Multiple Time Step Integrators. J. Chem. Phys. 106 (1997) 9835-9849 Derreumaux, P., Zhang, G., Schlick, T, Brooks, B.R. A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications. J. Comp. Chem. 15 (1994) 532-555... 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

Figure 16.4 Dlustration of the Fast Multiple Moment method...

HPLC methods are preferred if excipients would interfere, if nonspecific detection techniques (mainly in UV) would be used, or when multiple APIs (combination product) are present in a drug product. Since dissolution sample set analysis can be very long due to six samples per bath as well as multiple time points for prohle testing, fast run times are preferred to quickly determine the results. If a fast HPLC method for CU is available, then the identical HPLC method can be utilized for dissolution analysis. 

At the extremely high fluxes of a nuclear explosion, fast multiple neutron capture leads to very neutron-rich isotopes of U or Pu, respectively, changing rapidly into elements of appreciably higher atomic numbers by a quick succession of transmutations. This method of formation of heavier elements is also indicated in Fig. 14.5. The elements can be found in the debris of nuclear underground explosions. 

Despite the throughput provided by the MUX interface, several practical considerations should be noted. First, the MUX system cannot be used with flow rates that exceed 0.1 mL/min. In addition, a small amount of carryover exists between adjacent sprayers, typically on the order of 0.1%. While each of these issues can be tolerated, the overhead associated with sampling multiple effluent streams limits the number of points that can be acquired across a chromatographic peak. In a four-channel MUX system, each sprayer is accessed about every 1.2 seconds [77]. Thus, to permit the acquisition of 10 data points, the LC peak must be at least 12-seconds wide. Because typical drug-discovery runs include more than one analyte, as well as an internal standard, the MUX system is not truly compatible with fast LC methods that typically produce peak widths less than 6 seconds wide. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

The SSW form an ideal expansion set as their shape is determined by the crystal structure. Hence only a few are required. This expansion can be formulated in both real and reciprocal space, which should make the method applicable to non periodic systems. When formulated in real space all the matrix multiplications and inversions become 0(N). This makes the method comparably fast for cells large than the localisation length of the SSW. In addition once the expansion is made, Poisson s equation can be solved exactly, and the integrals over the intersitital region can be calculated exactly. 

The described computational tools provide interactive, fast, and flexible data visualizations of chemical data that help and even enhance the human thought processes. However, visualization alone is often inadequate when multiple data points must be considered. A number of data mining methods that seek to identify significant relationships in large multidimensional databases are now being used for library design. 

The PLS algorithm is relatively fast because it only involves simple matrix multiplications. Eigenvalue/eigenvector analysis or matrix inversions are not needed. The determination of how many factors to take is a major decision. Just as for the other methods the right number of components can be determined by assessing the predictive ability of models of increasing dimensionality. This is more fully discussed in Section 36.5 on validation. 

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