Figure 2. Schematic representation of energy surface and simulation trajectories.

The x and y axes represent conformation and energy for a two-molecular system, respectively. The black curved line represents the energy surface, where energy minima and energy barriers are distributed. Although the conformation of the system is defined originally in a high-dimensional space, the space shown in this figure is one-dimensional (i.e. x axis). Molecular structures are also shown schematically. R_UB is a region where unbound or slightly touching molecules are distributed, and R_B a region where various complex forms are distributed. Although R_UB is divided into two in this figure, the two may be connected in the original high-dimensional space. (a) Broken lines represent simulation trajectories at room temperature starting from conformations at P₁ and P₂, which are far from the native complex structure (P_nat). The conformation moves slowly in the space because energy barriers interfere with the motion. (b) Simulation trajectories (broken lines) at high temperature. The trajectories fluctuate in a high-energy range (shaded energy range), which involves R_UB, and the room temperature range (checkered range) is not sampled. The volume of R_B is considerably narrower than that of R_UB in the original high-dimensional space. (c) Trajectory from multi-canonical simulation, which samples the high- and low-energy ranges evenly.