Fig 1.
The physical equivalences in probing interactions of molecular recognition.
(A) A specific ligand binding to different receptors, P1∼Pn represent the different receptor proteins with the associated binding sites. (B) Different interactions through different atomic contacts of a specific pair of ligand-receptor complex, M1∼Mn represent the different interactions with different set of contacts located at the different binding sites of a specific receptor. (C) A specific receptor binding to different ligands, N1∼Nn represent the different ligands with different sequences.
Fig 2.
Funneled energy landscape of the biomolecular binding.
Panel (A) shows the energy landscape of the receptor-ligand binding with a funneled shape towards the native state. Panel (B) shows the density of states of the ligand binding landscape. The intrinsic specificity ratio , where energy gap δE and energy roughness ΔE and size of the binding funnel measured by the entropy S are shown respectively. Panel (C) shows the free energy landscape of ligand binding, cartoon showing of receptor/ligand complex corresponds to the different binding states. The affinity measured by the free energy difference between the native binding state and unbound states are shown as ΔG. It can also be measured by the equilibrium constant K where ΔG = −RTlnK. Panel (D) shows the energy landscape and free energy profiles on different reaction coordinates.
Fig 3.
The entropy S(E) as a function of energy for the random energy model.
The curve is entropy S(E) = ln[n(E)], where n(E) is the density of states with energy E from the spectrum, Ec is the corresponding energy of the trapping transition temperature Tc. As we see, the point M moves on the curve with the changes in the slope (1/T).
Fig 4.
Validation of Autodock scoring to predict the binding affinities for 20 drugs against the Cox-2.
Fig 5.
The distribution of the free energy with 720 compounds binding to the Cox2.
the vertical axis represents the number of states or probability for the free energy, gaussian curve: in the center; exponential curve: near the tail. The parameter values for these distributions are presented. The analytical function consisting of a Gaussian and two exponential functions is highlighted with red line.
Fig 6.
The distribution of the logarithm of equilibrium constant with 720 compounds binding to the Cox2.
the vertical axis represents the number of states or probability for the equilibrium constant, gaussian curve: in the center; exponential curve: near the tail. The parameter values for these distributions are presented. The analytical function consisting of a Gaussian and two exponential functions is highlighted with red line.
Fig 7.
The distribution of the specificity(ISR) with 720 compounds binding to the Cox2.
the vertical axis represents the number of states or probability for the specificity, gaussian curve: in the center; exponential curve: near the tail. The parameter values for these distributions are presented. The analytical function consisting of a Gaussian and two exponential functions is highlighted with red line.
Fig 8.
The relationship between the predicted and experimental kinetic specificities for 22 drugs against the Cox-2.
represents the relative predicted residence time and Timeoff0pred is the constant weighting factor, is the experimental residence time.
Fig 9.
The distribution of the predicted kinetic specificity.
(A) The distribution of the logarithm of the predicted Timeon with 720 compounds binding to the Cox2; (B) The distribution of the logarithm of the predicted Timeoff with 720 compounds binding to the Cox2. gaussian curve: in the center; exponential curve: near the tail. The parameter values for these distributions are presented. The analytical function consisting of a Gaussian and two exponential functions is highlighted with red line.
Fig 10.
Three representative ligands analyzed in the docking simulations.
The left panels of (A), (B) and (C) show the one dimensional projection of binding free energy landscape to RMSD with high, medium and low ISR with similar affinity as well as the corresponding structures of the different ligands, where the docked pose with the most stable affinity or the strongest binding state is chosen as the reference structure to calculate the RMSDs; the Autodock score function is used to evaluate the interaction energies between the ligand and the receptor. (high:fork structure, medium:near-linear structure, low:linear structure);the right panels of them show the corresponding binding energy spectrum for each, the sparse part of the spectrum implies there are fewer states, and dense part of the spectrum implies there are more states. (D) show the kinetic time for binding for the above three different ISRs. The upper black line represents the predicted kinetic timeoff and the under black line represents the predicted kinetic timeon. The vertical axis represents the calculated kinetic time.