Classical and quantum simulations of tryptophan in solution

We use path integral molecular dynamics to study the effect of nuclear tunneling on the structure, fluctuations, and energetics of tryptophan in water. Tryptophan is important as a spectroscopic probe; it can also serve as a miniature model of a protein, possessing charged, polar, hydrophobic, and aromatic groups, hard and soft degrees of freedom, and conformational heterogeneity around its dihedral angles. At room temperature, nuclear tunneling increases the fluctuations of hard internal degrees of freedom by a factor of approximately 2; dihedral fluctuations are not affected. Water structure is weakened, and the solvation energies of the amino, carboxyl, and indole groups change by 1-2 kcal/mol. Solvation energies and free energies of the 1La and 1Lb excited states were analyzed, using semiempirical and ab initio atomic charges, and a free energy perturbation approach. The dielectric relaxation free energy, from Marcus theory, is 1/2 of the dielectric relaxation energy, for a wide class of systems; this is used to relate the free energy results to experimental Stokes shifts. CNDO/S charges, with the classical ground state simulations, predict a 5.5 kcal/mol red shift for 1La, a large solvent broadening and Stokes shift, in approximate agreement with experimental data for methylindole, with a smaller red shift, solvent broadening, and relaxation for 1Lb. Nuclear tunneling increases the red shift, decreases the solvent broadening, and decreases the solvent dielectric relaxation by 20-30%, consistent with the weaker solvent structure seen in the quantum simulations.