computer modeling in molecular biology.pdf

4 Molecular Dynamics and Free Energy Calculations 95potential problem [102]. Assuming that only the rotational isomers of the mutatedsidechains contribute significantly to the free energy difference, the procedure ofStraatsma and McCammon [loo] was used to evaluate the correction that one wouldneed to apply to the computed free energy change for the Ile + Ala mutation, to adequatelyaccount for rotational isomer sampling. This correction was evaluated to beabout 0.5 kcal/mol [104], in accord with results obtained previously when computingbinding free energies of antiviral drugs to human rhinovirus [105].Another source of systematic error could be the use of an inadequate model forthe unfolded state, about which detailed information is not available. The magnitudeof the error thus introduced was evaluated in the context of a different mutation ofthe same residue: Ile 96 -+ Val [104]. The corresponding alchemical transformationwas computed in the gas phase for both the extended heptapeptide, and the sameheptapeptide taken in the a-helical conformation. The computed free energy valueswere found to differ by less than 0.5 kcal/mol between the two conformations.In conclusion, the statistical imprecision of the free energy calculations describedin this section are evaluated to be between 1-2 kcal/mol. Several of the possiblesystematic errors are estimated not to exceed 0.5 kcal/mol and hence to lie wellwithin the overall statistical error of the calculations. Systematic errors due to shortcomingof the potential function may also be of consequence, but have not been consideredhere.4.3.5 Protein Stability and the Hydrophobic EffectIn analyzing the effects of amino-acid substitutions on protein stability, parallels areoften drawn between protein denaturation and transfer processes from organicsolvents to water, or hydration free energies. In a good number of cases [89, 90,107- 1101 the change in thermodynamic stability between the wild type and mutantwas found to be roughly proportional to the free energies of transfer. But the correlationwith hydration free energy changes were much poorer [107].Similar trends are observed for the Ile-Ala mutation analyzed here. Thedifference in the transfer free energies of Ala versus Ile range from 1.5 to3.11 kcal/mol, values obtained for octanol and cyclohexane respectively [lll, 1121.These values are of the same order as the computed or experimental folding freeenergy differences between the wild type and Ala mutant. On the other hand,the hydration free energy differences between Ile and Ala are significantly smaller.The experimental values differ by - 0.21 kcal/mol and the computed difference(AAG,,,) is -0.251 - 1.15 kcal/mol.To understand the origins of these observations it is useful to consider separatelythe transfer of the side chain from the gas phase to the interior of the protein andinto the aqueous solvent (Figure 4-18). To do so, the water to protein transfer process