Reaching the global minimum in docking simulations: A Monte Carlo energy minimization approach using Bezier splines

The docking problem faces two major challenges: the global optimization of a multivariable function, such as the energy, and the ability to discriminate between true and false positive results, i,e., native from nonnative structures based on the input energy function. Among all energy evaluation tools, only a local energy-minimization method using an accurate enough potential function is able to discriminate between native and nonnative structures. To meet these requirements, a Monte Carlo with energy-minimization method has been incorporated into a new ECEPP/3 docking program. The efficiency of the simulation results from the use of an energy-grid technique based on Bezier splines and from a simplification of the receptor by switching on the energy of only important residues of the active site. Simulations of a thrombin-inhibitor complex show that the global minimum of the energy function was reached in every independent run within less than 3 min of time on an IBM RX 6000 computer. For comparison, 10 standard independent Monte Carlo simulations with 10(6) steps in each were carried out. Only three of them led to a conformation close to the x-ray structure. The latter simulations required an average of 24 min and about 10 hr with acid without the grid, respectively. Another important result is that the Bezier spline technique not only speeds up the calculation by reducing the number of operations during the energy evaluation but also helps in reaching the global minimum by smoothing out the potential energy surface.