Determination of equilibrium properties of biomolecular systems using multidimensional adaptive umbrella sampling

Two-dimensional adaptive umbrella sampling with the first umbrella coordina te equal to the potential energy of the system and the second umbrella coor dinate equal to a function that discriminates important folded conformation s from unfolded conformations is used to determine the equilibrium properti es of complex biological systems. Compared to one-dimensional adaptive umbr ella sampling with the potential energy as umbrella coordinate (multicanoni cal sampling), more reliable results can be obtained in certain cases. The method is applied to a helical peptide (RN24) with an analytical continuum solvent potential in combination with the PARAM19 force field of CHARMM. Th is effective potential energy function has been shown to describe the struc tural preferences of solvated peptides. With the two-dimensional approach a nd the deviation from the helical structure as the second umbrella coordina te, a converged description of the structural properties and the thermodyna mics of the peptide RN24 is obtained. In particular, we find that the forma tion of the helix of RN24 occurs as a transition accompanied by a character istic peak in the heat capacity. A formalism is described that uses the wei ghting factors obtained from a self-consistent solution of the weighted his togram analysis method equations to combine the results from a series of si mulations with different biases and calculate the ensemble average of any d ynamical variable as a function of the temperature without the need for ext racting the density of states from the simulations. It is shown how the for malism can be used to calculate thermodynamic properties of the system. (C) 1999 American Institute of Physics. [S0021-9606(99)50340-1].