Application of Multiple Topology λ-Dynamics to a Host-Guest System: -Cyclodextrin with Substituted Benzenes K. V. Damodaran, ² Shinichi Banba, ‡ and Charles L. Brooks III* ,² Department of Molecular Biology, TPC-6, The Scripps Research Institute, La Jolla, California 92037, and Material Science Laboratory, Mitsui Chemical, Inc., 580-32 Nagaura, Sodegaura-City, Chiba 299-0265, Japan ReceiVed: January 29, 2001; In Final Form: July 6, 2001 The λ-dynamics approach to free energy simulations has been applied the host-guest system of -cyclodextrin interacting with a series of monosubstituted benzenes. Each ligand was explicitly represented, and restraining potentials [Banba, S.; Brooks, C. L., III, J. Chem. Phys. 2000, 113, 3423] were used to restrain the unselected ligands in nearly binding conformations. Using biasing potentials to enhance convergence, excellent correlation between the free energies derived from λ-dynamics and free energy perturbation results is obtained. Effects of the strength of the restraining potentials and bias potentials on the sampling of the conformational space have been examined. Ligands with smaller substituents explored alternate binding orientations in the presence of weak and moderate restraining potentials. I. Introduction Rapid and reliable assessment of binding affinities is very important for efficient screening of drugs. The common method used for computational screening, such as DOCK, 1,2 uses scoring functions based on interaction energies between the drug candidate and the receptor. However, contributions from de- solvation have to be taken into account for a more reliable assessment of ligand binding by using free energies. 3 Compu- tational evaluation of free energies using the perturbation approach is very CPU intensive. In addition to the fact that long simulations are often required to obtain satisfactory convergence, this is not a method of choice when a large number of ligands have to be screened, because it requires a large number of simulations to compare two ligands at a time. Recently, methods have been developed where multiple ligands interacting with a common environment can be sampled simultaneously. 4-9 The environment may be an enzyme active site or a host cavity or solvent. A key feature of this approach is that the coupling parameter (λ) for the interaction between the ligands and the environment (which is the equivalent of the mutation parameter in free energy perturbation calculations) is treated in a manner analogous to dynamic variables such as the Cartesian coordinates. 6,7 The sampling of the λ parameter space can be achieved using either Monte Carlo or molecular dynamics, independent of how the conformational space is sampled. Free energies are evaluated from the frequency of times that the molecules spend in the “dominant state” (i.e., strongly coupled to the environment). One immediate advantage of this approach is that a single simulation can yield the same free energy data obtained from multiple free energy perturbation calculations. This concept, along with simulated annealing has been used to explore interaction energy surfaces by Tidor and co-workers. 7,8 Pitera and Kollman have used Monte Carlo and molecular dynamics to sample the chemical (λ) and conforma- tional coordinate spaces, respectively, for a host-guest system. 9 Molecular dynamics (MD) has been used to sample both the λ- and conformational spaces in the implementation of this approach in our laboratory, called λ-dynamics. 6 This method has been applied to the screening of ligands using both hybrid topology and multiple topology representations with excellent results. 4,10 Modeling the ligands using a multiple topology representation results in enhanced sampling of the conforma- tional space and potentially rapid convergence because the ligands weakly coupled to the environment (λ ≈ 0) are not constrained to the binding orientation of the dominant ligand as in a hybrid model. However, this may also lead to slower convergence, since decoupled ligands can “wander away” from the binding site and not return during the finite simulation time. To overcome this problem Banba and Brooks added a restraining potential to the Hamiltonian. 11 The effect of the restraining potential is corrected for while calculating the free energies. The reliability of this method has also been demonstrated by using this approach to screen a set of ligands binding to an artificial cavity in cytochrome-C peroxidase. Excellent correla- tion was obtained between free energies calculated from FEP simulations and λ-dynamics. 11 The objective of this work is to further validate the technique of λ-dynamics using the multiple topology representation for the ligands in the presence of the restraining potential by applying the method to a host-guest system with explicit solvent in a periodic environment. We have also examined the ligand dynamics under restraining potentials of different strengths and biasing conditions. II. Materials and Methods A. The System. The system chosen for this investigation is a series of monosubstituted benzenes binding to a host molecule, namely -cyclodextrin. Cyclodextrins (CD) are cyclic oligosac- charides consisting of glucopyranose units linked using R-1-4 glycosidic bonds. The most widely investigated variants have six (R), seven (), and eight (γ) sugar units. 12-15 The shape of -CD is described as truncated cone with the primary hydroxyl (CH 2 OH) groups occupying the narrower rim. 16 The secondary hydroxyl (OH) groups at the 2′ and 3′ positions form hydrogen * To whom correspondence should be addressed. Electronic mail: brooks@scripps.edu. ² The Scripps Research Institute. ‡ Mitsui Chemical, Inc. 9316 J. Phys. Chem. B 2001, 105, 9316-9322 10.1021/jp010361g CCC: $20.00 © 2001 American Chemical Society Published on Web 08/25/2001