Jan Antosiewicz

Computing ionization states of proteins with a detailed charge model

A convenient computational approach for the calculation of the p Kas of ionizable groups in a protein is described. The method uses detailed models of the charges in both the neutral and ionized form of each ionizable group. A full derivation of the theoretical framework is presented, as are details of its implementation in the UHBD program. Application to four proteins whose crystal structures are known shows that the detailed charge model improves agreement with experimentally determined pKas when a low protein dielectric constant is assumed, relative to the results with a simpler single‐site ionization model. It is also found that use of the detailed charge model increases the sensitivity of the computed pKas to the details of proton placement.

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: Role of the enzyme's charge distribution in steering charged ligands toward the active site

The electrostatic steering of charged ligands toward the active site of Torpedo californica acetylcholinesterase is investigated by Brownian dynamics simulations of wild type enzyme and several mutated forms, in which some normally charged residues are neutralized. The simulations reveal that the total ligand influx through a surface of 42 A radius centered in the enzyme monomer and separated from the protein surface by 1-14 A is not significantly influenced by electrostatic interactions. Electrostatic effects are visible for encounters with a surface of 32 A radius, which is partially hidden inside the protein, but mostly within the solvent. A clear accumulation of encounter events for that sphere is observed in the area directly above the entrance to the active site gorge. In this area, the encounter events are increased by 40% compared to the case of a neutral ligand. However, the differences among the encounter rates for the various mutants considered here are not pronounced, all rate constants being within +/- 10% of the average value. The enzyme charge distribution becomes more important as the charged ligand moves toward the bottom of the gorge, where the active site is located. We show that neither the enzymes total charge, nor its dipole moment, fully account for the electrostatic steering of ligand to the active site. Higher moments of the enzymes charge distribution are also important. However, for a series of mutations for which the direction of the enzyme dipole moment is constant within a few degrees, one observes a gradual decrease in the diffusional encounter rate constant with the number of neutralized residues. On the other hand, for other mutants that change the direction of the dipole moment from that of the wild type, the calculated encounter rate constants can be very close to that of the wild type. The present work yields two new insights to the kinetics of acetylcholinesterase. First, evolution appears to have built a redundant electrostatic steering capability into this important enzyme through the overall distribution of its thousands of partially charged atoms. And second, roughly half of the rate enhancement due to electrostatics arises from steering of the substrate outside the enzyme; the other half of the rate enhancement arises from improved trapping of the substrate after it has entered the gorge. The computational results reproduce qualitatively, and help to rationalize, many surprising experimental results obtained recently for human acetylcholinesterase.

Computation of the dipole moments of proteins

A simple and computationally feasible procedure for the calculation of net charges and dipole moments of proteins at arbitrary pH and salt conditions is described. The method is intended to provide data that may be compared to the results of transient electric dichroism experiments on protein solutions. The procedure consists of three major steps: (i) calculation of self energies and interaction energies for ionizable groups in the protein by using the finite-difference Poisson-Boltzmann method, (ii) determination of the position of the center of diffusion (to which the calculated dipole moment refers) and the extinction coefficient tensor for the protein, and (iii) generation of the equilibrium distribution of protonation states of the protein by a Monte Carlo procedure, from which mean and root-mean-square dipole moments and optical anisotropies are calculated. The procedure is applied to 12 proteins. It is shown that it gives hydrodynamic and electrical parameters for proteins in good agreement with experimental data.

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.

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.

Simulation of electrostatic and hydrodynamic properties of Serratia endonuclease

We analyze the electrostatic and hydrodynamic properties of a nuclease from the pathogenic gram-negative bacterium Serratia marcescens using finite-difference Poisson-Boltzmann methods for electrostatic calculations and a bead-model approach for diffusion coefficient calculations. Electrostatic properties are analyzed for the enzyme in monomeric and dimeric forms and also in the context of DNA binding by the nuclease. Our preliminary results show that binding of a double-stranded DNA dodecamer by nuclease causes an overall shift in the charge of the protein by approximately three units of elementary charge per monomer, resulting in a positively charged protein at physiologic pH. In these calculations, the free enzyme was found to have a negative (-1 e) charge per monomer at pH 7. The most dramatic shift in pKa involves His 89 whose pKa increases by three pH units upon DNA binding. This shift leads to a protonated residue at pH 7, in contrast to the unprotonated form in the free enzyme. DNA binding also leads to a decrease in the energetic distances between the most stable protonation states of the enzyme. Dimerization has no significant effect on the electrostatic properties of each of the monomers for both free enzyme and that bound to DNA. Results of hydrodynamic calculations are consistent with the dimeric form of the enzyme in solution. The computed translational diffusion coefficient for the dimer model of the enzyme is in very good agreement with measurements from light scattering experiments. Preliminary electrooptical calculations indicate that the dimer should possess a large dipole moment (approximately 600 Debye units) as well as substantial optical anisotropy (limiting reduced linear electric dichroism of about 0.3). Therefore, this system may serve as a good model for investigation of electric and hydrodynamic properties by relaxation electrooptical experiments.

Binding of Cations and Protons in the Active Site of Acetylcholinesterase

The active site of acetylcholinesterase contains a number of ionizable residues. The pK as of the catalytic histidine, His 440, is believed to be 6.3, based upon enzyme kinetic studies. However, the pK as of the other residues have not been measured. Here, we describe calculations of the pK a of the ionizable groups in this enzyme. Interestingly, the initial calculations predict a pK a of 9.3 for His 440. The deviation of 3 pK a units from the measured pK a is traceable to the influence of Glu 199 and Glu 443 upon His 440. We argue that the deviation does not represent a failure of the computational method. Rather it points to the need for an adjustment in the model of the protein. The adjustment we suggest involves a monovalent cation bound in the active site, near Glu 199 and His 440. Including such a cation in the calculations brings the computed pK a of His 440 into agreement with the measured value. Furthermore, the idea that a bound cation substantially reduces tbe pK a of His 440 leads to satisfying explanations of a number of otherwise puzzling experimental data.

Computer Modeling of Acetylcholinesterase and Acetylcholinesterase-Ligand Complexes

Site directed mutagenesis and computer simulations studies have become valuable tools for the understanding of function-structure relations of proteins. At the current level of computer technology, the quantitative agreement between experimental and molecular simulations results is not always satisfactory for proteins of acetylcholinesterase (AChE) size and complexity. However, the comparison of both types of results can increase dramatically our knowledge on molecular mechanisms of protein action.