1Department of Physical Chemistry, Faculty of Science, Palacký University, tř. Svobody 26, 771 46 Olomouc, Czech Republic
2Department of Organic Chemistry, Faculty of Chemical Technology, University of Pardubice, Čs. Legií 565, 532 10 Pardubice, Czech Republic
3National Centre for Biomolecular Research, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
The near attack conformation (NAC) concept was introduced by Bruice et al. . This concept proposes that the main reason for catalytic power of enzymes is reduction of the configuration space of reacting atoms and bringing them together to a typical arrangement defined as NAC. Bruice and coworkers revealed linear relationship between log of relative rate constants (log krel) and log of NAC population concluding that the rate constants are directly dependent on the NAC population [1-3].
Haloalkane dehalogenases (HADs, EC 188.8.131.52) are bacterial enzymes catalysing the cleavage of the carbon-halogen bond in haloorganic compounds by a hydrolytic mechanism. The first step of the dehalogenation is SN2 attack of Asp124 carboxyl group oxygen to haloalkane carbon atom followed by AdN of water molecule to ester intermediate. Bruice and coworkers postulated that NAC of the substrate molecule positioned in the active site of HAD involves two atoms forming the bond (Asp124-COO–…C-Cl). These two atoms should ideally be within the van der Waals contact distance (< 3.2 Å) and the attack angle (Asp124--COO–…C-Cl) within ±15° deviation from the bonding angle in the TS for the SN2 displacement of Cl–. Here we propose effective tool for definition and calculation of NAC or any other configuration subspace population in clear statistical terms.
The NAC configuration can be described in terms of geometrical parameters, e.g. distances, angles, and dihedrals. Hence, the NAC configuration can be characterized by n-dimensional vector m made from selected n parameters. During the simulation the n selected parameters make for each time step a realization of n-dimensional stochastic vector n. If the system populates NAC, the realizations of vector n fluctuate with n-dimensional Gauss distribution with main value m and covariance matrix Σ. For each MD simulation it is possible to test a hypothesis, whether the parametrical vector is or isn’t in NAC. The hypothesis can be easily tested using Mahalanobis distance representing a distance between NAC described by vector m and snapshot configuration ni. The Mahalanobis distance has Fisher-Snedecor distribution with n and N–n degrees of freedom, where N is the number of steps in model simulation used for covariance matrix Σ estimation, n is dimension of vectors m and n, vector ni denotes the vector n realization in i-th simulation snapshot. Finally, the acceptation region for the hypothesis of snapshot being in NAC is represent by an unequal
Presented method is based on testing the Mahalanobis distance of a molecular arrangement from the NAC in the configuration space. The way to estimate vector m as well as matrix Σ will be discussed. Practical examples from the application of developed method on quantitative estimation of NAC for HAD will be presented.
Plot of angle (Asp124--COO–…C-Cl) against distance (Asp124-COO– … C-Cl) for all HAD/chlorohexane complex MD simulation snapshots. The ellipse represents critical Mahalanobis distance from NAC at which the hypothesis that the configuration does not significantly differ from NAC is acceptable (the point inside the ellipse can be considered as NAC conformation).
1. F. Lightstone, T.C. Bruice, J. Amer. Chem. Soc., 118 (1996) 2595-2605
2. T.C. Bruice, F. Lightstone, Acc. Chem. Res. 32 (1999) 127-136
3. T.C. Bruice, Acc. Chem. Res. 35 (2002) 139-148