PMC

Charge optimization of binding affinity. (a) The net binding free energy, which is the sum of the desolvation effects and Coulomb interaction, has a quadratic dependence on the ligand charge with a unique minimum corresponding to the optimal charge. (b) Charge selectivity, Sq, is defined as the energy increase upon an absolute deviation of 1e from the optimal charge. The ligand charge is constrained within a chemically meaningful range of [−1; +1] e (unshaded) during optimization of binding affinity. For optimal charges capped at ±1e, Sq represents the energy increase upon the charge deviation from the capped value to zero.

Hydration free energies and asymmetries as a function of bracelet size, for the distributed scheme. Shown, for solutes where the neutralizing charge is distributed, are (a) calculated hydration free energies in TIP3P water as a function of bracelet (polygon) size and (b) the asymmetry in hydration free energies between solutes where the large charge is positive, and those where the large charge is negative, for TIP3P water, as a function of bracelet size. In the legend, “positive” and “negative” denote the sign of the largest charge; in all cases the solutes are net neutral. Cartoon representations at the bottom are for the “negative” case; red atoms are negative and blue are positive, with color intensity denoting the charge magitude. Lines are a guide for the eye.

For a strain = .0.002, the effect of free charge on (a) piezoelectric potential and (b) H₂ production for various piezocatalysis systems.

Comparison of charge optimization results obtained in the probing approach with those obtained by optimization of charge distribution for actual ligands. (a) Benzamidine binding site of trypsin. (b) Free-carboxylate C-terminal valine binding site of the PDZ domain. Left panels show the calculated optimal charge distribution over the atomic charges of the actual ligand for binding to its respective target. The theoretical charge distribution of the actual ligand is shown in parenthesis and italicized. Also shown are the A_ii coefficients of the charge dependence of binding free energy corresponding to the atomic centers of the actual ligands (i.e., the diagonal elements of the ligand desolvation matrix A in , which indicate the charge selectivity at a given atomic center with the charges of the other atomic centers fixed at their optimal value). Stereo views on the right show the charge complementarity profile (top) and charge selectivity profile (bottom). These profiles are represented by the charged “center” of the probe-ligand at various positions within 2 Å from the actual ligand. Centers are displayed as spheres color coded by optimal charge and charge selectivity (see legends).