Mariusz Makowski

Potential of mean force of association of large hydrophobic particles: toward the nanoscale limit.

The potentials of mean force (PMFs) were determined, in both water with the TIP3P water model and in vacuo, for systems involving formation of nonpolar dimers composed of bicyclooctane, adamantane (both an all-atom model and a sphere with the radius of 3.4 A representing adamantane), and fullerene, respectively. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field were carried out for each pair under both environmental conditions. The PMFs were calculated by using the weighted histogram analysis method. The results were compared with our previously determined PMF for neopentane. The shape of the PMFs for dimers of all four nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule; for larger molecules they shift toward larger distances. Comparison of the PMFs of the bicyclooctane, adamantane, and fullerene dimers in water and in vacuo shows that hydrophobic interactions in each dimer are different from that for the dimer of neopentane. Interactions in the bicyclooctane, adamantane, and fullerene dimers are stronger in vacuo than in water. These dimers cannot be treated as classical, spherical, hydrophobic objects. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from that in explicit solvent. The solvent contribution to the PMFs of bicyclooctane, adamantane, and fullerene is positive, as opposed to that of neopentane. The water molecules in the first solvation sphere of both adamantane and neopentane dimers are more ordered as compared to bulk water, with their dipole moments pointing away from the surface of the dimers. The average number of hydrogen bonds per water molecule in the first hydration shell of adamantane is smaller compared to that in bulk water, but this shell is thicker for all-atom adamantane than for neopentane or a spherical model of adamantane. In the second hydration shell, the average number of hydrogen bonds is greater compared to that in bulk water only for neopentane and a spherical model of adamantane but not for the all-atom model. The strength of the hydrophobic interactions shows a linear dependence on the number of carbon atoms both in water and in vacuo. Smaller nonpolar particles interact more strongly in water than in vacuo. For larger molecules, such as bicyclooctane, adamantane and fullerene, the reversed tendency is observed.

A unified coarse-grained model of biological macromolecules based on mean-field multipole–multipole interactions

AbstractA unified coarse-grained model of three major classes of biological molecules—proteins, nucleic acids, and polysaccharides—has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site–site interactions as mean-field dipole–dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo’s cluster-cumulant series leads to the appearance of mean-field dipole–dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented. FigureComponents of the Unified Coarse Grained Model (UCGM) of biological macromolecules

Acid-base equilibria in systems involving substituted pyridines in polar aprotic protophobic media and in the amphiprotic methanol

Abstract Acid dissociation, as well as cationic homo- and heteroconjugation constants have been determined by potentiometric titration in systems involving substituted pyridines and conjugate cationic acids in the polar protophobic aprotic solvent acetone and in polar amphiprotic methanol. The values of the constant were compared with those previously determined in other polar protophobic aprotic solvents, acetonitrile, nitromethane and propylene carbonate. The p K a values of the protonated pyridine derivatives in acetone range between 2.69 and 12.69 and are on average 2–3 orders of magnitude higher than those determined in water. The p K a values in methanol vary between 1.02 and 10.37, and are only slightly higher than those in water, the difference not exceeding one order of magnitude. A comparison of the acid dissociation constants determined in all the non-aqueous solvents considered shows that the strength of the cationic acids increases on going from acetonitrile through nitromethane, propylene carbonate and acetone to methanol. In almost all systems of the type: a pyridine derivative its conjugate acid, the cationic homoconjugation equilibrium is present in acetone (1.60 K BHB + K BHB + N -bases and the conjugate cationic acids increases in the solvents studied as follows: propylene carbonate K BHB 1 + =2.13). In methanol, the tendency towards heteroconjugation in the systems studied is markedly greater. As a matter of fact, the heteroconjugation constants are lower (1.58 K BHB 1 +

Quantum-chemical studies on the favored and rare tautomers of neutral and redox adenine.

All possible twenty-three prototropic tautomers of neutral and redox adenine (nine amine and fourteen imine forms, including geometric isomerism of the exo ═NH group) were examined in vacuo {DFT(B3LYP)/6-311+G(d,p)}. The NH → NH conversions as well as those usually omitted, NH → CH and CH → CH, were considered. An interesting change of the tautomeric preference occurs when proceeding from neutral to reduced adenine. One-electron reduction favors the nonaromatic amine C8H-N10H tautomer. This tautomeric preference is similar to that (C2H) for reduced imidazole. Water molecules (PCM model) seem to not change this trend. They influence solely the relative energies. The DFT vertical detachment energy in the gas phase is positive for each tautomer, e.g., 0.03 eV for N9H-N10H and 1.84 eV for C8H-N10H. The DFT adiabatic electron affinity for the favored process, neutral N9H-N10H → reduced C8H-N10H (ground states), is equal to 0.18 eV at 0 K (ZPE included). One-electron oxidation does not change the tautomeric preference in the gas phase. The aromatic amine N9H-N10H tautomer is favored for the oxidized molecule similarly as for the neutral one. The DFT adiabatic ionization potential for the favored process, neutral N9H-N10H → oxidized N9H-N10H (ground states), is equal to 8.12 eV at 0 K (ZPE included). Water molecules (PCM model) seem to influence solely the composition of the tautomeric mixture and the relative energies. They change the energies of the oxidation and reduction processes by ca. 2 eV.

Acid–base and hydrogen-bonding equilibria in aliphatic amine and carboxylic acid systems in non-aqueous solutions

Abstract Acid–base and hydrogen-bonding equilibria in acetic acid – acetate, n-butylammonium cation – n-butylamine and acetic acid (acetate) – n-butylamine (n-butylammonium cation) systems were studied in five polar non-aqueous solvents with varying prototropic and dielectric properties: acetonitrile, acetone, dimethyl sulfoxide, methanol, and propylene carbonate using the potentiometric-titration technique. These systems were designed to model the acid–base and hydrogen-bonding phenomena that involve acid and basic amino-acid side chains in proteins. The obtained order of p K a values of acetic acid and n-butylamine is consistent with the variation of prototropic, basic, dielectric, and hydrogen-bonding properties of the solvents used. The homoconjugation and heteroconjugation constant values decrease with increasing basicity of the solvents; they turn out to be indeterminable in dimethyl sulfoxide (the most basic solvent) for cationic homoconjugation and in methanol (the second most basic solvent) for anionic homoconjugation and heteroconjugation.

Simple physics-based analytical formulas for the potentials of mean force of the interaction of amino-acid side chains in water. VI. Oppositely charged side chains.

The two-site coarse-grained model for the interactions of charged side chains, to be used with our coarse-grained UNRES force field for protein simulations proposed in the accompanying paper, has been extended to pairs of oppositely charged side chains. The potentials of mean force of four pairs of molecules modeling charged amino-acid side chains, i.e., propionate-n-pentylamine cation (for aspartic acid-lysine), butyrate-n-pentylamine cation (for glutamic acid-lysine), propionate-1-butylguanidine (for aspartic acid-arginine), and butyrate-1-butylguanidine (for glutamic acid-arginine) pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expression was fitted to the potentials of mean force. Compared to pairs of like-charged side chains discussed in the accompanying paper, an average quadrupole-quadrupole interaction term had to be introduced to reproduce the Coulombic interactions, and a multistate model of charge distribution had to be introduced to fit the potentials of mean force of all oppositely charged pairs well. The model reproduces all salt-bridge minima and, consequently, is likely to improve the performance of the UNRES force field.

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. IV. Pairs of different hydrophobic side chains.

The potentials of mean force of 21 heterodimers of the molecules modeling hydrophobic amino acid side chains: ethane (for alanine), propane (for proline), isobutane (for valine), isopentane (for leucine and isoleucine), ethylbenzene (for phenylalanine), methyl propyl sulfide (for methionine), and indole (for tryptophane) were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation. Analytical expressions consisting of the Gay-Berne term to represent effective van der Waals interactions and the cavity term proposed in our earlier work were fitted to the potentials of mean force. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules, are well represented by the analytical expressions for all systems; large deviations between the MD-determined PMF and the analytical approximations are observed for pairs involving the least spheroidal solutes: ethylbenzene, indole, and methyl propyl sulfide at short distances at which the PMF is high and, consequently, these regions are rarely visited. When data from the PMF within only 10 kcal/mol above the global minimum are considered, the standard deviation between the MD-determined and the fitted PMF is from 0.25 to 0.55 kcal/mol (the relative standard deviation being from 4% to 8%); it is larger for pairs involving nonspherical solute molecules. The free energies of contact computed from the PMF surfaces are well correlated with those determined from protein-crystal data with a slope close to that relating the free energies of transfer of amino acids (from water to n-octanol) to the average contact free energies determined from protein-crystal data. These observations justify future use of the determined potentials in coarse-grained protein-folding simulations.

Geometric and energetic consequences of prototropy for adenine and its structural models – a review

Heterocycles containing one or more amidine moieties {–NH–C(R) N–} such as adenine and its building blocks, imidazole, 4-aminopyrimidine, and purine, are excellent examples of tautomeric systems for which changes of position(s) of labile proton(s) cause parallel changes of geometric and energetic parameters for prototropic tautomers. One-electron oxidation has a slight effect on this relationship. The amino-imine conversions within the amidine group(s) are favored. Well delocalized (aromatic) tautomers, containing labile proton(s) at heteroatom(s), are major, minor, or rare forms. Non-aromatic tautomers with a labile proton at the C atom can be considered as very rare isomers. Dramatic changes take place for reduced heterocycles. Electron delocalization is not the main factor that dictates tautomeric preferences. The HOMED/ΔE relationship seems to be more complex. The enamino-imine conversions predominate and some very rare forms have the lowest energies. This clearly shows the importance of very rare tautomers, often neglected in proton-transfer, electron-transfer, and ion–radical reactions.

Towards temperature-dependent coarse-grained potentials of side-chain interactions for protein folding simulations. I: Molecular dynamics study of a pair of methane molecules in water at various temperatures

By means of molecular dynamics simulations of a pair of methane molecules in a TIP3P periodic water box with the NVT scheme at six temperatures and, additionally, the NPT scheme at three temperatures ranging from T = 283 to 373 K, we determined the potential of mean force (PMF) of pairs of interacting methane molecules in water as functions of distance between the methane molecules. The PMFs converge to a single baseline only for r> 11 A at all temperatures. The curves of the dimensionless PMF obtained at different temperatures with the NVT scheme overlap almost perfectly in the region of the contact minimum and still very well in the regions of the desolvation maximum and the solvent-separated minimum, which suggests that the temperature-dependent hydrophobic interaction potentials at constant volume in united-residue force fields can be obtained by scaling the respective dimensionless potentials by RT, R being the universal gas constant. For the dimensionless potentials of mean force obtained with the NPT scheme, the depth of the contact minimum increases, whereas the height of the desolvation maximum and the depth of the solvent-separated minimum decrease with temperature, in agreement with results reported in the literature.

Potentiometric investigation of acid dissociation and anionic homoconjugation equilibria of substituted phenols in dimethyl sulfoxide

Abstract Standard acidity constants, K a DMSO (HA), expressed as p K a DMSO (HA) values, and anionic homoconjugation constants, K DMSO AHA − , (in the form of lg K DMSO AHA − values) have been determined for 11 substituted phenol–phenolate systems a polar protophilic aprotic solvent, dimethyl sulfoxide (DMSO) with a potentiometric titration. A linear relationship has been determined between lg K DMSO AHA − and p K a DMSO (HA). The tendency towards anionic homoconjugation in these systems increases with increasing p K a DMSO (HA) that is with declining phenol acidity. The p K a DMSO (HA) are correlated with both p K a W (HA) water and other polar non-aqeous solvents.