Experimental and Theoretical Approach to Hydrogen-Bonded Diastereomeric Interactions in a Model Complex

Abstract

Binding affinities of (R,R)-1,2-cyclohexanediamine (R) to (R,R)-1,2-cyclopentanediol (R 5 ) and (S,S)-1,2-cyclopentanediol (S 5 ) and to the corresponding cyclohexanediols (R 6 and S 6 ) have been measured in benzene and in CCl4 at 298 K by microcalorimetry, and unexpected differences between the diastereomeric complexes are observed. Long time scale (0.1 μs) molecular-dynamics simulations of the two smaller diastereomeric complexes, R/R 5 and R/S 5 , in a simplified solvent model are reported. A direct free energy calculation gives results in good agreement with the experimental values measured in benzene for the first pair, but nearly identical results for the second pair, which is at variance with experiment. A systematic analysis of the dependence of simulation results on model parameters is performed, and no possibility is found to improve the enantioselectivity by parameter tuning. Other possible causes for discrepancies are specific solute−solvent or solvent−solvent interactions, electronic charge redistribution effects, or formation of clusters of more than two molecules. Owing to the long time scales reached, a well-converged picture of the dynamics is obtained, and the species present at equilibrium can be studied in detail. The average lifetime of the complex is found to be about 200 ps, whereas that of a hydrogen bond is only about 5 ps. Besides the unbound state, the dominant species observed in the simulations for both diastereomeric pairs are singly hydrogen-bonded complexes, with a clear preference for a O to N over the N to O hydrogen bond. Many other hydrogen-bonding patterns (bridged, double) are also observed in minor amounts.

Determining equilibrium constants for dimerization reactions from molecular dynamics simulations

“…(12) and (13)], yields correct free energies, whereas direct application of the law of mass action provides wrong results. Nevertheless, as the above results show, the law of mass action can be derived from the Boltzmann approach and is in this sense compatible -as must be.…”

“…Such an approach has been applied to, for example, the dimerization of chirally related organic molecules, 12 folding / unfolding of small peptides, 13,14 dimerization of methane molecules 15 as well as of charged 16 and hydrophobic 17 amino acid pairs in water, and a dimer of transmembrane helices in a lipid bilayer. 18 However, contradicting approaches and formulae have been employed to calculate free energy differences.…”

“…In particular, as further explained in the Theory section, directly using the ratio of the observed Boltzmann probabilities 13,14,16,17,19 yields different results compared to approaches adopting the law of mass action to simulations of two dimerizing molecules. 12,15,18 For example, if the system is found in a dimerized state during a fraction P 1 of the total simulation time, and in a monomeric state during a fraction P 0 = 1 − P 1 , the free energy difference would in the first case be given by an equation of the form G ∝ ln(P 1 /P 0 ), whereas in the latter case, it is ∝ ln(P 1 /P 2 0 ). Which of the two approaches is correct?…”

Using one‐step perturbation to predict the effect of changing force‐field parameters on the simulated folding equilibrium of a β‐peptide in solution

“…So, only relative free energy differences were obtained. In a different context, Hünenberger et al 28 have analyzed the sensitivity of simulated strengths of hydrogenbonded diastereomeric interactions in organic solvents to systematic perturbations of model parameters with respect to a single reference Hamiltonian.…”

Computation of Free Energy

“…An example of the use of Eqn. 4 to determine the difference in free energy of binding for a pair of chirally related molecules can be found in [12]. Direct counting has the advantage that it does not depend on the definition of a reaction coordinate.…”