Local Move Monte Carlo with the reverse proximity criterion

Mihaly Mezei

Department of Structural and Chemical Biology
Icahn School of Medicine at Mount Sinai
New York, NY 10019

Published in the Journal of Chemical Physics 118, 3874-3879 (2003)
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Theory

Regular torsions are ineffective on long chains since even a small change in a torsion angle causes large displacements at the chain's end.

However, after the change of a torsion angle it is possible to adjust the subsequent six torsions in such a way that the rest of the chain remains unchanged - this is called a local move. This requires the solution of the geometry problem closing the just opened loop.

Such moves can satisfy detailed balance if the new torsions are selected randomly from the solution space and if the Jacobian involved in the transformation of these torsion angles is also included into the acceptance probability [L.R. Dodd, T.D. Boone, D.N. Theodorou, Molec. Phys., 78, 961-996 (1993)].

This project showed that it is possible to use the solution nearest to the original conformation if it rejected automatically when the old conformation was not the nearest solution to the new one. This results in a better tunable method and for bulky sidechains it eliminates trial moves that are unlikely to be accepted.

Results

Comparison of the new local move (LPX) with the previus best [D. Hoffmann, E.-W. Knapp, Eur. J. Biophys., 24, 387-403 (1996)] local move (LPW) and with the extension-biased torsion moves [P. Jedlovszky, M. Mezei, J. Chem. Phys., 111, 10770-10773 (1999)] on a bilayer of DMPC:

 NMCNMCeff DaxDayDazDL DLDThgDThc1DThc2
EXB 1 1.0 3.6 3.9 4.40.28 11.8 5.6 6.8 7.4
EXB 5 5.0 5.6 6.2 6.50.46 15.1 6.1 9.3 9.7
EXB1010.0 6.6 7.5 7.70.59 16.9 7.010.111.1
LPX 1 0.5 2.5 2.5 2.5 0.27 9.5 5.3 5.3 5.5
LPX 5 2.5 4.6 5.1 5.2 0.4813.2 6.1 7.6 8.2
LPX10 5.0 5.6 5.6 5.9 0.4915.2 6.5 8.810.0
LJW 1 0.6 2.8 2.5 3.0 0.26 9.9 5.2 5.6 5.7
LJW 5 2.8 4.6 4.7 5.2 0.4313.5 5.8 8.3 8.2
LJW10 5.6 5.5 5.7 5.7 0.4814.9 6.3 9.5 8.9
Dax, Day, Daz: the mean overall rotation of the molecule around the space-fixed x, y, and z axes (the bilayer is in the y-z plane
Dx, Dy, Dz: the overall mean displacement of the center of the lipid molecules during the run
DT, DThg, DThc1, DThc2: the mean overall displacement of the entire molecule, the headgroup chain and the two hydrocarbon chains, respectively, due to torsion angle changes only

Comparison of the new local move (LPX) with the previus best local move (LPW) for the aqueous solution of hexadecane with biphenyl groups attached at the 3, 7, 10, and 13 positions:

flftPacc PrrRMSDbb ftPaccPacc/nn RMSDbb
2300.750.051.95 180.270.00100.55
4180.710.061.17 180.170.00151.05
6140.570.071.82 220.210.00220.80
8220.480.121.28 220.150.00070.74
10220.440.121.43 140.150.00220.56
12180.430.161.65 300.140.00091.17
14180.390.151.19 220.110.00060.69
16180.440.081.83 180.100.00150.88
18220.350.151.32 180.100.00150.77
20180.300.171.24 140.080.00161.06
40300.210.191.04 180.040.00030.80
60180.120.241.02 300.030.00081.04
80220.080.311.02 140.030.00030.53
fl: the overall scale factor applied to the local move ranges
ft: the best overall scale factor applied to the regular torsion ranges}
Pacc: probability of acceptance
Prr: probability of reverse rejection
RMSDbb: root-mean square deviation of the driver torsion atoms
Pacc/nn: probability of acceptance for local move that did not choose the nearest solution

Some details

Findig the nearest solution of the loop-closing problem for a polymer with consecutive torsions without obtainig the full solution set: scan the circle in the middle, starting from the point nearest to the original position of the corresponding atom until positions of the other two moving atoms (derived from the point on the circle and the fixed atoms) are at the right distance.

For a peptide backbone, the 1-6 distance can be scanned similarly - assuming a value for the distance between atoms 1 and 6 the rest can be determined in a stepwise manner (to be published).

The calculations were performed with the MMC Monte Carlo program, available at http://inka.mssm.edu/~mezei/mmc


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Last modified: 11/15/2003 (MM)