Binding Constants of Neuraminidase Inhibitors:  An Investigation of the Linear Interaction Energy Method

The linear interaction energy (LIE) method has been applied to the calculation of the binding free energies of 15 inhibitors of the enzyme neuraminidase. This is a particularly challenging system for this methodology since the protein conformation and the number of tightly bound water molecules in the active site are known to change for different inhibitors. It is not clear that the basic LIE method will calculate the contributions to the binding free energies arising from these effects correctly. Application of the basic LIE equation yielded an rms error with respect to experiment of 1.51 kcal mol-1 for the free energies of binding. To determine whether it is appropriate to include extra terms in the LIE equation, a detailed statistical analysis was undertaken. Multiple linear regression (MLR) is often used to determine the significance of terms in a fitting equation; this method is inappropriate for the current system owing to the highly correlated nature of the descriptor variables. Use of MLR in other applications of the LIE equation is therefore not recommended without a correlation analysis being performed first. Here factor analysis was used to determine the number of useful dimensions contained within the data and, hence, the maximum number of variables to be considered when specifying a model or equation. Biased fitting methods using orthogonalized components were then used to generate the most predictive model. The final model gave a q 2 of 0.74 and contained van der Waals and electrostatic energy terms. This result was obtained without recourse to prior knowledge and was based solely on the information content of the data.