Simulation of enzyme-substrate encounter with gated active sites

Orientational steering in enzyme-substrate association: ionic strength dependence of hydrodynamic torque effects

The effect of hydrodynamic torques on the association rate constants for enzyme-ligand complexation is investigated by Brownian dynamics simulations. Our hydrodynamic models of the enzyme and ligand are composed of spherical elements with friction forces acting at their centers. A quantitative measure of hydrodynamic torque orientational effects is introduced by choosing, as a reference system, an enzyme-ligand model with the same average hydrodynamic interactions but without orientational dependence. Our simple models show a 15% increase in the rate constant caused by hydrodynamic torques at physiological ionic strength. For more realistic hydrodynamic models, which are not computationally feasible at present, this effect is probably higher. The most important finding of this work is that hydrodynamic complementarity in shape (i.e. like the fitting together of pieces of a puzzle) is most effective for interactions between molecules at physiological ionic strength.

Electrostatic and hydrodynamic orientational steering effects in enzyme-substrate association

Diffusional encounters between a dumbbell model of a cleft enzyme and a dumbbell model of an elongated ligand are simulated by Brownian dynamics. The simulations take into account electrostatic and hydrodynamic interactions between the molecules. It is shown that the primary effect of inclusion of hydrodynamic interactions into the simulation is an overall decrease in the rate constant. Hydrodynamic orientational effects are of modest size for the systems considered here. They are manifested when changes in the rate constants for diffusional encounters favored by hydrodynamic interactions are compared with those favored by electrostatic interactions as functions of the overall strength of electrostatic interactions. The electrostatic interactions modify the hydrodynamic torques by modifying the drift velocity of the substrate toward the enzyme. We conclude that simulations referring only to electrostatic interactions between an enzyme and its ligand may yield rate constants that are somewhat (e.g., 20%) too high, but provide realistic descriptions of the orientational steering effects in the enzyme-ligand encounters.

Acetylcholinesterase: diffusional encounter rate constants for dumbbell models of ligand

For some enzymes, virtually every substrate molecule that encounters the entrance to the active site proceeds to reaction, at low substrate concentrations. Such diffusion-limited enzymes display high apparent bimolecular rate constants ((kcat/KM)), which depend strongly upon solvent viscosity. Some experimental studies provide evidence that acetylcholinesterase falls into this category. Interestingly, the asymmetric charge distribution of acetylcholinesterase, apparent from the crystallographic structure, suggests that its electrostatic field accelerates the encounter of its cationic substrate, acetylcholine, with the entrance to the active site. Here we report simulations of the diffusion of substrate in the electrostatic field of acetylcholinesterase. We find that the field indeed guides the substrate to the mouth of the active site. The computed encounter rate constants depend upon the particular relative geometries of substrate and enzyme that are considered to represent successful encounters. With loose reaction criteria, the computed rates exceed those measured experimentally, but the rate constants vary appropriately with ionic strength. Although more restrictive reaction criteria lower the computed rates, they also lead to unrealistic variation of the rate constants with ionic strength. That these simulations do not agree well with experiment suggests that the simple diffusion model is incomplete. Structural fluctuations in the enzyme or events after the encounter may well contribute to rate limitation.

Receptor binding properties of four-helix-bundle growth factors deduced from electrostatic analysis

Hormones of the hematopoietin class mediate signal transduction by binding to specific transmembrane receptors. Structural data show that the human growth hormone (hGH) forms a complex with a homodimeric receptor and that hGH is a member of a class of hematopoietins possessing an antiparallel 4-alpha-helix bundle fold. Mutagenesis experiments suggest that electrostatic interactions may have an important influence on hormone-receptor recognition. In order to examine the specificity of hormone-receptor complexation, an analysis was made of the electrostatic potentials of hGH, interleukin-2 (IL-2), interleukin-4 (IL-4), granulocyte colony-stimulating factor (G-CSF), granulocyte-macrophage colony-stimulating factor (GM-CSF), and the hGH and IL-4 receptors. The binding surfaces of hGH and its receptor, and of IL-4 and its receptor, show complementary electrostatic potentials. The potentials of the hGH and its receptor display approximately 2-fold rotational symmetry because the receptor subunits are identical. In contrast, the potentials of GM-CSF and IL-2 lack such symmetry, consistent with their known high affinity for hetero-oligomeric receptors. Analysis of the electrostatic potentials supports a recently proposed hetero-oligomeric model for a high-affinity IL-4 receptor and suggests a possible new receptor binding mode for G-CSF; it also provides valuable information for guiding structural and mutagenesis studies of signal-transducing proteins and their receptors.