  We report a single-copy tempering method for simulating large complex
systems. In a generalized ensemble, the method uses runtime estimate of the
thermal average energy computed from a novel integral identity to guide a
continuous temperature-space random walk. We first validated the method in a
two-dimensional Ising model and a Lennard-Jones liquid system. It was then
applied to folding of three small proteins, trpzip2, trp-cage, and villin
headpiece in explicit solvent. Within 0.5~1 microsecond, all three systems were
folded into atomic accuracy: the alpha carbon root mean square deviations of
the best folded conformations from the native states were 0.2 A, 0.4 A, and 0.4
A, for trpzip2, trp-cage, and villin headpiece, respectively.
