Monte Carlo simulations of ionic channel selectivity

Monte Carlo simulations have been developed to study the selectivityof ionic channels in biological membranes. The channel is consideredto be in either of two possible states: (i) densely packed withions, the ions moving in single file in one direction, or alternatively,(ii) sparsely packed, where holes could appear at any particulartime thereby allowing bidirectional movement of ions. The twomodels enable us to envisage a quantitative flux of permeableions in the presence of smaller sized ions, taking into considerationtheir concentrations in the bulk solutions, the ion-channelinteractions and probability with which they fill up the channel.The programs are written in FORTRAN-77 (MS-FORTRAN) for an IBM-compatiblepersonal computer. From the simulation results we observe anenzymatic function of the channel and also note that the smallersized ions tend to block the movement of permeable ions. Thesimulations represent a technique for visualization of the factorsthat decide ionic permeability and help in manipulating theireffects with ease and speed which would otherwise involve intricateexperimental setups. Received on September 7, 1990; accepted on January 14, 1991     

Transient kinetic studies of substrate inhibition in the horse liver alcohol dehydrogenase reaction

The rate-limiting step of ethanol oxidation by alcohol dehydrogenase (E) at substrate inhibitory conditions (greater than 500 mM ethanol) is shown to be the dissociation rate of NADH from the abortive E-ethanol-NADH complex. The dissociation rate constant of NADH decreased hyperbolically from 5.2 to 1.4 s-1 in the presence of ethanol causing a decrease in the Kd of NADH binding from 0.3 microM for the binary complex to 0.1 microM for the abortive complex. Correspondingly, ethanol binding to E-NADH (Kd = 37 mM) was tighter than to enzyme (Kd = 109 mM). The binding rate of NAD+ (7 X 10(5) M-1s-1) to enzyme was not affected by the presence of ethanol, further substantiating that substrate inhibition is totally due to a decrease in the dissociation rate constant of NADH from the abortive complex. Substrate inhibition was also observed with the coenzyme analog, APAD+, but a single transient was not found to be rate limiting. Nevertheless, the presence of substrate inhibition with APAD+ is ascribed to a decrease in the dissociation rate of APADH from 120 to 22 s-1 for the abortive complex. Studies to discern the additional limiting transient(s) in turnover with APAD+ and NAD+ were unsuccessful but showed that any isomerization of the enzyme-reduced coenzyme-aldehyde complex is not rate limiting. Chloride increases the rate of ethanol oxidation by hyperbolically increasing the dissociation rate constant of NADH from enzyme and the abortive complex to 12 and 2.8 s-1, respectively. The chloride effect is attributed to the binding of chloride to these complexes, destabilizing the binding of NADH while not affecting the binding of ethanol.     

Effective water model for Monte Carlo simulations of proteins

We present an effective theory for water. Our goal is to formulate on accurate model for the effects of solvation on protein dynamics, without incurring the huge computational cost and the slow temporal evolution typical of molecular dynamics simulations of liquids. We replace the individual water molecules in an all-atom potential with a local dielectric density field, with self interactions given by the Landau-Ginzburg free energy and external interactions by Lennard-Jones forces at the surface of the protein atoms. We explore conformational space with finite temperature Monte Carlo dynamics, using parallel Langevin and Fourier acceleration algorithms well suited to data-parallel computer architectures such as the Connection Machine. To establish the validity of our approximations, we compare our electrostatic contribution to the solvalion energy with the results of Lim, Bashford, and Karplus using a conventional static continuum dielectric cavity model, and the non electrostatic contributions with estimates of hydrophohic surface free energy. Our model can also accommodate ionic charges and temperature fluctuations, We propose future investigations extending our effective theory of solvation to include explicit orientational entropy and hydroxen-bonding terms. © 1995 John Wiley & Sons, Inc.     

Investigation of formate transport through the substrate channel of formate dehydrogenase by steered molecular dynamics simulations

Steered molecular dynamics simulation has revealed the mechanism of formate transport via the substrate channel of formate dehydrogenase. It is shown that the structural organization of the channel promotes the transport of formate anion in spite of the fact that the channel is too narrow even for such a small molecule. The conformational mobility of Arg284 residue, one of the residues forming the wall of the substrate channel, provides for the binding and delivery of formate to the active site.     

Grazers and grass: Monte Carlo simulations

To illustrate the interplay between grazers and grass, we present a novel Monte Carlo model including grass-island growth, consumption of grass by grazers, and birth, migration and death of grazers. The rates of the former and three latter processes are assumed to depend on the environment so that the conventional mean-field approximation does not hold (in particular, the model takes into account that grass grows on the grass-island boundaries, and grazers are mobile and prefer to stay on the areas covered by grass). Due to the feedback between various processes, as expected, the model predicts stable regimes and irregular oscillations of the area of the grass islands and grazer population. The patterns observed are however different compared to those predicted by conventional Monte Carlo prey-predator models. Specifically, there is no tendency for grazers and grass to segregate. The mean-field version of the model is briefly discussed as well.     

Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics

A formal partially dynamical approach to ergodic sampling, hybrid Monte Carlo, has been adapted for the first time from its proven application in quantum chromodynamics to realistic molecular systems. A series of simulations of pancreatic trypsin inhibitor were run using temperature-rescaled molecular dynamics and hybrid Monte Carlo. It was found that simulations run using hybrid Monte Carlo equilibrated an order of magnitude faster than those run using temperature-rescaled molecular dynamics. Certain aspects of improved performance obtained using hybrid Monte Carlo are probably due to the increased efficiency with which this algorithm explores phase space. To discuss this we introduce the notion of “trajectory stiffness”. © 1993 John Wiley & Sons, Inc.     

Carboxymethylated liver alcohol dehydrogenase. Transient kinetic studies and effect of substrate structure on alcohol oxidation.

1. The rate constants for NADH binding and dissociation for carboxymethylated alcohol dehydrogenase have been determined and compared to those for the native enzyme. 2. Steady-state and transient kinetic experiments have shown that the hydrogen transfer step is rate-determining for oxidation of ethanol by carboxymethylated alcohol dehydrogenase. The rate constant of 0.19 s-1 is considerably slower than that for the native enzyme. 3. The steady-state parameter, V/[E], was obtained for each of a series of alcohols and correlated with the Taft sigma parameter. The linear relationship obtained indicates that the same step, hydrogen transfer, is rate-determining for all the alcohols. The sigma value obtained is the same as for the native enzyme; the implications of this for the mechanism of hydrogen transfer are discussed.     

Open-state conformation of the KcsA K+ channel: Monte Carlo normal mode following simulations

Potassium channels fluctuate between closed and open states. The detailed mechanism of the conformational changes opening the intracellular pore in the K+ channel from Streptomyces lividans (KcsA) is unknown. Applying Monte Carlo normal mode following, we find that gating involves rotation and unwinding of the TM2 bundle, lateral movement of the TM2 helices away from the channel axis, and disappearance of the TM2 bundle. The open-state conformation of KcsA exhibits a very wide inner vestibule, with a radius approximately 5-7 A and inner helices bent at the A98-G99 hinge. Computed conformational changes demonstrate that spin labeling and X-ray experiments illuminate different stages in gating: transition begins with clockwise rotation of the TM2 helices ending at a final state with the TM2 bend hinged near residues A98-G99. The concordance between the computational and experimental results provides atomic-level insights into the structural rearrangements of the channel's inner pore.     

Monte Carlo studies of lipid / water interfaces

The results of a series of numerical simulations of the aqueous interface near several types of lipid bilayer headgroups are presented. The Monte Carlo method was used to study 172 water molecules located between two lipid bilayers separated by 24.5 Å. The types of headgroups used in the studies include phosphorylcholine, -ethanolamine and -serine. The quantities calculated were molecular density, dipolar orientation and number of hydrogen bonds as functions of the distance from the interfacial regions. The data point out important differences in the organization of the interfacial water for each of the three different lipids.     

X-ray studies of the binding of Cibacron blue F3GA to liver alcohol dehydrogenase

The binding of Cibacron F3GA to orthorhombic crystals of liver alcohol dehydrogenase has been studied to 0.37-nm resolution. Similarities in the binding of this dye were found for rings B, C and D with the binding of the coenzyme NAD+. However, ring A of the dye and the nicotinamide ribose part of the coenzyme are quite differently bound to the enzyme.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Bioinorganic and bioorganic studies of liver alcohol dehydrogenase

Liver alcohol dehydrogenase (E.C.1.1.1.1) is an NAD(+)/NADH dependent enzyme with a broad substrate specificity being active on an assortment of primary and secondary alcohols. It catalyzes the reversible oxidation of a wide variety of alcohols to the corresponding aldehydes and ketones as well as the oxidation of certain aldehydes to their related carboxylic acids. Although the bioinorganic and bioorganic aspects of the enzymatic mechanism, as well as the structures of various ternary complexes, have been extensively studied, the kinetic significance of certain intermediates has not been fully evaluated. Nevertheless, the availability of computer-assisted programs for kinetic simulation and molecular modeling make it possible to describe the biochemical mechanism more completely. Although the true physiological substrates of this zinc metalloenzyme are unknown, alcohol dehydrogenase effectively catalyzes not only the interconversion of all-trans-retinol and all-trans-retinal but also the oxidation of all-trans-retinal to the corresponding retinoic acid. Retinal and related vitamin A derivatives play fundamental roles in many physiological processes, most notably the vision process. Furthermore, retinoic acid is used in dermatology as well as in the prevention and treatment of different types of cancer. The enzyme-NAD(+)-retinol complex has an apparent pK(a) value of 7.2 and loses a proton rapidly. Proton inventory modeling suggests that the transition state for the hydride transfer step has a partial negative charge on the oxygen of retinoxide. Spectral evidence for an intermediate such as E-NAD(+)-retinoxide was obtained with enzyme that has cobalt(II) substituted for the active site zinc(II). Biophysical considerations of water in these biological processes coupled with the inverse solvent isotope effect lead to the conclusion that the zinc-bound alkoxide makes a strong hydrogen bond with the hydroxyl group of Ser48 and is thus activated for hydride transfer. Moderate pressure accelerates enzyme action indicative of a negative volume of activation. The data with retinol is discussed in terms of enzyme stability, mechanism, adaptation to extreme conditions, as well as water affinities of substrates and inhibitors. Our data concern all-trans, 9-cis, 11-cis, and 13-cis retinols as well as the corresponding retinals. In all cases the enzyme utilizes an approximately ordered mechanism for retinol-retinal interconversion and for retinal-retinoic acid transformation.     

Bioinorganic and bioorganic studies of liver alcohol dehydrogenase

Liver alcohol dehydrogenase (E.C.1.1.1.1) is an NAD⁺/NADH dependent enzyme with a broad substrate specificity being active on an assortment of primary and secondary alcohols. It catalyzes the reversible oxidation of a wide variety of alcohols to the corresponding aldehydes and ketones as well as the oxidation of certain aldehydes to their related carboxylic acids. Although the bioinorganic and bioorganic aspects of the enzymatic mechanism, as well as the structures of various ternary complexes, have been extensively studied, the kinetic significance of certain intermediates has not been fully evaluated. Nevertheless, the availability of computer-assisted programs for kinetic simulation and molecular modeling make it possible to describe the biochemical mechanism more completely. Although the true physiological substrates of this zinc metalloenzyme are unknown, alcohol dehydrogenase effectively catalyzes not only the interconversion of all-trans-retinol and all-trans-retinal but also the oxidation of all-trans-retinal to the corresponding retinoic acid. Retinal and related vitamin A derivatives play fundamental roles in many physiological processes, most notably the vision process. Furthermore, retinoic acid is used in dermatology as well as in the prevention and treatment of different types of cancer. The enzyme-NAD⁺-retinol complex has an apparent pK_a value of 7.2 and loses a proton rapidly. Proton inventory modeling suggests that the transition state for the hydride transfer step has a partial negative charge on the oxygen of retinoxide. Spectral evidence for an intermediate such as E-NAD⁺-retinoxide was obtained with enzyme that has cobalt(II) substituted for the active site zinc(II). Biophysical considerations of water in these biological processes coupled with the inverse solvent isotope effect lead to the conclusion that the zinc-bound alkoxide makes a strong hydrogen bond with the hydroxyl group of Ser48 and is thus activated for hydride transfer. Moderate pressure accelerates enzyme action indicative of a negative volume of activation. The data with retinol is discussed in terms of enzyme stability, mechanism, adaptation to extreme conditions, as well as water affinities of substrates and inhibitors. Our data concern all-trans, 9-cis, 11-cis, and 13-cis retinols as well as the corresponding retinals. In all cases the enzyme utilizes an approximately ordered mechanism for retinol–retinal interconversion and for retinal–retinoic acid transformation.     

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.     

Nuclear magnetic resonance studies of substrate interaction with cobalt substituted alcohol dehydrogenase from liver.

The role of zinc in liver alcohol dehydrogenase has been studied by replacement of 1.3 and 3.5 of the four Zn(II) ions with Co(II) and measuring the effects of the paramagnetic Co(II) on the relaxation rates of the protons of water, ethanol, and isobutyramide. Water relaxation studies at 8, 24, 100, and 220 MHz indicate two classes of bound Co(II). The similar to 2 readily replaced Co(II) ions retain one fast exchanging water proton in their inner coordination spheres, while the similar to 2 slowly exchanging Co(II) ions coordinate no detectable water protons, indicating that the former replaced Zn(II) at the "catalytic sites" and the latter replaced Zn(II) at the "structural sites" detected crystallographically. Ethanol, acetaldehyde, and isobutyramide bind with appropriate affinities to the Co(II) substituted alcohol dehydrogenases decreasing the number of fast exchanging protons at the catalytic Co(II) site by greater than or equal to 54 percent. Coenzyme binding causes smaller changes in the water relaxation rate which may be due to local conformation changes. The paramagnetic effects of Co(II) at the catalytic site on the relaxation rates of the methyl protons of isobutyramide at 100 and 220 MHz indicate that this analog binds at a site 9.1 A from the catalytic Co(II). This distance decreases to 6.9 A when NADH is bound, and a Co(II) to methyne proton distance of 6.6 A is determined indicating a conformation change leading to the formation of a second sphere enzyme-Co(II)-isobutyramide complex in which a hydroxyl or water ligand intervenes between the metal and the substrate analog. Similar behavior is observed in the enzyme-ethanol complexes. The paramagnetic effects of Co(II), at the catalytic site, on the relaxation rates of the protons of ethanol at 100 and 220 MHz, indicate that this substrate bind at a site 12-14 A distant from the catalytic Co(II) but that this distancedecreases to 6.3 A in the abortive enzyme-NADH-ethanol complex. The role of the catalytic Co(II) thus appears to be the activation of a hydroxyl or water ligand which polarizes the aldehyde carbonyl group by hydrogen bonding. The role of the structural Co(II), which is more distant from isobutyramide (9-11 A), may be that of a template for protein conformation changes. By combining the present distances with those from previous magnetic resonance studies on the liver enzyme, the arrangement of coenzyme, metal, and substrate at the active site in solution can be constructed. This arrangement is consistent with that of ADP-ribose and zinc in the crystalline complex of liver alcohol dehydrogenase as determined by X-ray crystallography (Branden et al., (1973), Proc. Natl. Acad. Sci. U.S.A.70, 2439).