Computational Analysis of Heat Capacity Effects in Protein-Ligand Binding

Abstract

Heat capacity effects in protein-ligand binding as measured by calorimetric experiments have recently attracted considerable attention, particularly in the field of enzyme inhibitor design. A significant negative heat capacity change upon ligand binding implies a marked temperature dependence of the binding enthalpy, which is of high relevance for attempts to optimize protein-ligand interactions. In this work, we address the question of how well such heat capacity changes can be predicted by computer simulations. We examine a series of human thrombin inhibitors that all bind with ΔC_p values of about -0.4 kcal/mol/K and calculate heat capacity changes from plain molecular dynamics simulations of the bound and free states of the enzyme and ligand. The results show that accurate ΔC_p estimates within a few tenths of a kcal/mol/K of the experimental values can be obtained with this approach. This allows us to address the structural and energetic origin of the negative heat capacity changes for the thrombin inhibitors, and it is found that conformational equilibria of the free ligands in solution make a major contribution to the observed effect.

Figure 1

Thermodynamic process describing the calculation of binding heat capacities from four different MD simulations: apoenzyme, holoenzyme, free ligand in water, and pure water. For each separate system, the derivative of the total energy is calculated as a function of temperature. Black triangles schematically denote solvent molecules that are displaced by the ligand. The total number of solvent molecules is kept constant both in the upper and lower processes so that the overall process does not involve any change in the number of degrees of freedom.

Figure 2

(a) The three Melagatran derivatives (2, 3, 4) considered in this work. (b) Crystallographic structures of the three inhibitors bound to the active site of human thrombin (yellow = 2, cyan = 3, pink = 4). The only noticeable difference between the three complexes is that Glu192 is pushed away by the larger substituent of 3, which allows the entry of one additional water molecule (red sphere).

Figure 3

Calculated average total potential energies for ligand 3 as a function of temperature for (a) the apo- and holoenzymes (without hirugen bound) and (b) for the ligand in water and for pure water. The corresponding plots for ligands 2 and 4 are virtually indistinguishable.

Figure 4

Average MD structures of the apoenzyme (pink) and the complexes (yellow) with the three ligands (cyan), overlaid at all five temperatures without (a) and with (b) hirugen bound (green). The crystallographically unresolved loop region is indicated. (c) Illustration of the conformational sampling of the apoenzyme by overlaying 30 snapshots at 298 and 303 K (interspaced by 1 ns). (d) Superimposed crystallographic apo (pink) and holo (yellow–inhibitor in cyan) structures of thrombin from ref (28)

Figure 5

Calculated average backbone r.m.s. positional fluctuations per residue along the amino acid sequence at 303 K for the apoenzyme (red curve) and the complex with ligand 3 (blue curve), (a) without and (b) with hirugen bound. Also shown are the corresponding RMSF curves calculated from the crystallographic B-factors of the inhibitor complexes 4BAM(5) and 3U8R(28) (dashed green) and the apo structure 3U69(28) (dashed black). Note that the contiguous sequence numbering here is that of PDB entry 4BAM.

Figure 6

(a) Temperature dependence of the apparent binding enthalpy for inhibitor 3 predicted by the equilibrium model (eq 4), using the average fitted values of ΔH_eq and ΔS_eq for all six ligands in ref (5). Experimental ITC data points for ligand 3 are shown as black squares. (b) Temperature dependence of the apparent binding heat capacity obtained from the average values of ΔH_eq and ΔS_eq. The insets show the behavior of ΔH_app and ΔC_p over a larger temperature interval.

Figure 7

(a) Probability distribution for the end-to-end distance of ligand 3 in water at 25 °C (blue bars) compared to the corresponding distribution in its complex with thrombin (red bars). The average intramolecular (b) and intermolecular (ligand–water) interaction energy (c) for inhibitor 3 in water at 25 °C as a function of the end-to-end distance.