Book of Abstracts: Albany 2003
June 17-21 2003
A New Chain Breakage/Closure Algorithm Yields Fast Conformational Equilibration of Nucleic Acid Structures in Monte Carlo Simulations
Recent developments of the Chain Breakage/Closure (CBC) algorithm and new results obtained for three DNA dodecamers will be presented. By using the constant bond lengths approximation and solving the CBC problem in the bond/torsion angle space, collective variables have been defined that maintain structural moves entirely local and allow for large conformational changes in Monte Carlo (MC) simulations. It is essentially this choice of independent variables that enables conformational equilibration on an acceptable CPU time scale, which is considered to be a necessary condition for deriving meaningful structural data from the trajectories of molecular simulations. As shown in the Figure, the currently implemented molecular model for nucleic acids includes 14 independent chain and ring variables per nucleotide: six rigid body variables of the base, four sugar ring variables, three torsion angles (χ, e, γ), and the bond angle at O3?. The P-O5? and O1?-C4? bonds are chosen for CBC, where the positions of atoms O5? and C4?, respectively, are determined by the closure equations. Associated Jacobians are included in the Metropolis acceptance criterion for MC moves.
Performance and results of this approach will be demonstrated by applications to three DNA dodecamers with the palindromic sequences d(CG)6, d(TA)6, and d(CGCGAATTCGCG). Here the AMBER94 force field has been used for energy calculations, and solvent electrostatic effects were taken into account by a continuum model of the aqueous solvent with explicit counter-ions for neutralizing the phosphate charges. Fast equilibration of counter-ions was found to be important in order to observe frequent conformational transitions in the DNA oligomers. Accumulated averages and fluctuations of structural parameters show the sequence effects emerging in the course of simulations. In the case of palindromic sequences, the degree of equilibration is indicated by the differences observed for equivalent base pair steps. The simulations of the example sequences indicate that such differences, compared with sequence-induced differences, are already very small after 106 MC cycles, which need less than one week CPU time on a currently available PC under Linux. This result was confirmed by some simulations started from distinctly different initial structures, where the final averaged structures with a RMSD in the order of 0.2Å are virtually the same. The averaged structures show the characteristics of B-form DNA with sequence-dependent helical step parameters that are mostly close to the averages calculated for the ten different dinucleotide steps from crystallographic data bases. Striking examples are the sequence-dependent twist differences observed for R/Y and Y/R steps. The MC trajectory however comprises a broad spectrum of different conformations, where many of them are visited more than ten times. For example, the conformational ensemble of the d(CG)6 dodecamer contains the full spectrum from A-like structures (negative x-displacement, positive inclination, low twist) to D-like structures (positive x-displacement, negative inclination, high twist) and shows that averaged structures and parameter fluctuations do not fully describe the sequence-dependent dynamics of the system. A more detailed insight is obtained from occupancy distributions and correlation analysis of relevant conformational parameters, including sugar pucker parameters, the torsion angles χ, e/ζ, and α/γ, and the helical parameters. It should be stressed that the results, thanks to the almost full conformational equilibration and in contrast with computationally much more demanding Molecular Dynamics simulations, uniquely reflect the behavior of the molecular model under the force field used for energy calculations. Accordingly, the suggested MC simulation technique easily allows for exploring the effect of modified force fields and, in particular, of the approximations used for describing solute/solvent interactions on the results in comparison with available experimental data.
Max Delbrueck Center for Molecular Medicine