Abstract
Free energy calculated in simulations on the atomic level (Monte Carlo or Molecular Dynamics) has a systematic error, if the water shell surrounding a globular protein is finite. The error (“cluster error”) is equal to a difference of free energies obtained in simulations with an infinite and finite water shell. In this work a continuum dielectric model was used to estimate the “cluster error”. A multipole expansion of the estimate was performed for a water shell with a spherical outer boundary. The expansion has very simple form. Each term is a product of two functions, one of them depending only on the charge's conformation, and the other one only on dielectric properties of the system. There are two practical uses of the expansion. First, it may be used to estimate the “cluster error” in a simulation already made; second, it may be used to plan a simulation in such a way that the “cluster error” is minimal. Numerical values of the largest terms in the multipole expansion corresponding to a typical system in simulations of globular proteins are given.