Chapter 8 – Theoretical Biophysics  325

(8.17)

∆p r

w r

U r

k T

i

i

i

( ) ⁼ ( )

−( )













exp

B

Thus, for undersampled states, w would be chosen to be relatively high, and for oversampled

states, w would be low, such that all microstates were roughly equally explored in the finite

simulation time. Mean values of any general thermodynamic parameter A that can be

measured from the simulation (e.g., the free energy change between different conformations)

can still be estimated as

(8.18)

〈〉= ^〈

〉

〈

〉

A

A w

w

/

/

1

FIGURE 8.2  Monte Carlo methods in molecular simulations. Simplified schematic of a typical

Monte Carlo algorithm for performing stochastic molecular simulations.