An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Abstract

Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.

Domain motions in dihydrofolate reductase: a molecular dynamics study

“…see McCammon & Harvey, 1987;Dean, 1987;Brooks et al, 1988). A number of such studies have been carried out on dhfr: molecular mechanics calculations to explore the conformational energy landscape of ligands (Spark et al, 1982) and ligand binding DauberOsguthorpe et al, 1988); molecular dynamics to examine mutations and free-energy calculations to study active sites and ligands (Singh, 1988;Singh & Benkovic, 1988;Fleischman & Brooks, 1990;McDonald & Brooks, 1991, 1992Gerber et al, 1993). In addition, use of density functional methods to estimate charge density changes on binding of ligands (Bajorath et al, 1991) and ab initio quantum mechanics for exploring the catalytic mechanism (Gready, 1985) have been reported.…”

Ensemble variance in free energy calculations by thermodynamic integration: Theory, optimal “Alchemical” path, and practical solutions

“…The optimal path for the van der Waals and electrostatics shown in Figure 2 is reminiscent of the “soft core” van der Waals 6, 7. This suggests that analysis with eq.…”

“…It is also possible to change the shape of the potential during the transition. The soft core van der Waals is an example where the mathematical singularity is removed by displacement and modification of the distance scale 6, 7. Attempting to soften van der Waals terms coupled with an electrostatic attraction by removing the charges before modifying the van der Waals terms and then restoring the new charges is an other example.…”

Modelling and Informatics in the Analysis of P. falciparum DHFR Enzyme Inhibitors

“…There are various types of molecular docking algorithms that could generate and identify complementary match between ligands and macromolecular targets [73,96]. It involves a combination of methods for locating binding sites and evaluating the strength/weakness of the binding or energy of binding [92,[96][97][98][99][100][101][102][103][104][105][106][107]. Docking is also used in the virtual screening of compounds during drug discovery process in which a virtual library of ligands are screened to identify their binding affinities through docking approach using protein target of known 3D-structure [98,108,109].…”