Performance of hybrid methods for large-scale unconstrained optimization as applied to models of proteins.

Energy minimization plays an important role in structure determination and analysis of proteins, peptides, and other organic molecules; therefore, development of efficient minimization algorithms is important. Recently, Morales and Nocedal developed hybrid methods for large-scale unconstrained optimization that interlace iterations of the limited-memory BFGS method (L-BFGS) and the Hessian-free Newton method (Computat Opt Appl 2002, 21, 143-154). We test the performance of this approach as compared to those of the L-BFGS algorithm of Liu and Nocedal and the truncated Newton (TN) with automatic preconditioner of Nash, as applied to the protein bovine pancreatic trypsin inhibitor (BPTI) and a loop of the protein ribonuclease A. These systems are described by the all-atom AMBER force field with a dielectric constant epsilon = 1 and a distance-dependent dielectric function epsilon = 2r, where r is the distance between two atoms. It is shown that for the optimal parameters the hybrid approach is typically two times more efficient in terms of CPU time and function/gradient calculations than the two other methods. The advantage of the hybrid approach increases as the electrostatic interactions become stronger, that is, in going from epsilon = 2r to epsilon = 1, which leads to a more rugged and probably more nonlinear potential energy surface. However, no general rule that defines the optimal parameters has been found and their determination requires a relatively large number of trial-and-error calculations for each problem.

n-p short-range correlations from (p,2p+n) measurements.

We studied the 12C(p,2p+n) reaction at beam momenta of 5.9, 8.0, and 9.0 GeV/c. For quasielastic (p,2p) events p(f), the momentum of the knocked-out proton before the reaction, was compared (event by event) with p(n), the coincident neutron momentum. For |p(n)|>k(F)=0.220 GeV/c (the Fermi momentum) a strong back-to-back directional correlation between p(f) and p(n) was observed, indicative of short-range n-p correlations. From p(n) and p(f) we constructed the distributions of c.m. and relative motion in the longitudinal direction for correlated pairs. We also determined that 49+/-13% of events with |p(f)|>k(F) had directionally correlated neutrons with |p(n)|>k(F).

Energy dependence of nuclear transparency in C (p,2p) scattering.

The transparency of carbon for (p,2p) quasielastic events was measured at beam momenta ranging from 5.9 to 14.5 GeV/c at 90 degrees c.m. The four-momentum transfer squared (Q2) ranged from 4.7 to 12.7 (GeV/c)(2). We present the observed beam momentum dependence of the ratio of the carbon to hydrogen cross sections. We also apply a model for the nuclear momentum distribution of carbon to obtain the nuclear transparency. We find a sharp rise in transparency as the beam momentum is increased to 9 GeV/c and a reduction to approximately the Glauber level at higher energies.