Multiple-site titration and molecular modeling: two rapid methods for computing energies and forces for ionizable groups in proteins

Computer models of proteins frequently treat the energies and forces associated with ionizable groups as if they were purely electrostatic. This paper examines the validity of the purely electrostatic approach, and concludes that significant errors in energies can result from the neglect of ionization changes. However, a complete treatment of ionizable groups presents substantial computational obstacles, because of the large number of ionization states which must be examined in systems having multiple interacting titratable groups. In order to address this problem, two novel methods for treating the energetics and forces associated with ionizable groups with a minimum of computer time have been developed. The most rapid method yields approximate energies by computing the free energy of a single highly occupied ionization state. The second method separates ionizable groups into clusters, and treats intracluster interactions exactly, but intercluster interactions approximately. This method yields both accurate energies and fractional charges. Good results are obtained in tests of both methods on proteins having has many as 123 ionizable groups. The more rapid method requires computer times of 0.01 to 0.34 sec, while the more accurate method requires 0.7 to 15 sec. These methods may be fast enough to permit the incorporation of ionization effects in iterative computations, such as energy minimizations and conformational searches.