The importance of the ionic interaction due to the formation of the salt bridge between the Asp-27 and the pteridine ring in Escherichia coli dihydrofolate reductasemethotrexate complex has been studied by using the free-energy perturbation method. The calculation suggests that the ionpair contribution to the binding energy is insignificant, as the enzyme surroundings do not stabilize the salt bridge to the extent of the desolvation of the charged groups. The activation barrier for the proton exchange between the pteridine ring and the Asp-27 is calculated to be 20.1 kcal/mol (1 cal = 4.184 J) by using the coordinate-coupled perturbation method, implying that this may be a channel to the proton exchange from the pteridine ring to the solvent. The Gibbs-energy difference of binding between the Asn-27 and Ser-27 is calculated to be 3.2 kcal/mol and is mainly due to the electrostatic interactions.Since Baker (1) first proposed that the tight binding of the 2,4-diamino heterocyclic inhibitors of dihydrofolate reductase (DHFR; 5,6,7,8-tetrahydrofolate:NADP+ oxidoreductase, EC 1.5.1.3), such as methotrexate (MTX), is due to the increased basicity of the pteridine ring in the inhibitor as compared to the substrate folate, extensive experimental work has been done to substantiate his hypothesis (2-8). The crystallographic study (9) on the Escherichia coli enzyme-MTX complex clearly indicated the existence of interaction between N-1 atom of MTX and the side-chain carboxyl group of Asp-27. The strong interaction of the protonated pteridine ring of the inhibitor and the carboxyl group of Asp-27 is shown by a marked shift in the pKa of the bound inhibitor (10). Through detailed kinetic analysis, Stone and Morrison (11)
Free-Energy Perturbation MethodThe statistical perturbation theory is essentially due to Zwanzig (18) and its implementation in molecular dynamics to extract free energy is described in detail elsewhere (17). I present the essence of the method for completeness. If we assume that the total Hamiltonian of a system may be separated into two parts aswhere Ho is the Hamiltonian of an unperturbed system and H1 is the perturbation, then the free-energy contribution due to perturbation is given by G, = -1 (exp (-/3H1))o, f3 [2]where /3 = 1/kT and the average of exp (-3H1)
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