Poisson-Boltzmann calculations versus molecular dynamics simulations for calculating the electrostatic potential of a solvated peptide

We performed a very long molecular dynamics simulation of a peptide in explicit water molecules and ions and averaged the electrostatic potential caused by peptide, water and ions at eight points in the vicinity of the peptide. These electrostatic potential values were directly compared to the potential calculated by solving the non-linear Poisson-Boltzmann equation for the system, which describes the solvent using continuum electrostatics. We analyze the contribution of dielectric constant, conformational flexibility and solvation effects on the electrostatic potential at these eight points. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Solution conformations of structured peptides: continuum electrostatics versus distance-dependent dielectric functions

To compare different implicit solvent potentials, the folding thermodynamics of the helical peptide RN24 and the β-hairpin peptide BH8 are studied by molecular dynamics simulation with adaptive umbrella sampling. As the potential energy functions, the analytical continuum solvent (ACS) potential and three simplified variants, termed EPSR₁, EPSR₄, and EPSR₁₀, are used. The ACS potential is a combination of the standard CHARMM force field for the internal energy (bonds, angles, dihedrals) and the van der Waals energy with the analytical continuum electrostatic (ACE) potential and a non-polar solvation potential. The EPSR potentials differ from the ACS potential by the use of Coulomb's law with a distance-dependent dielectric function to calculate the electrostatic energy. With the ACS potential, quantitative agreement with experiment is obtained for the helix propensity (RN24: 62% calculated vs 50–60% experiment) and the β-hairpin propensity (BH8: 33% calculated vs 19–37% experiment) of the peptides. During the simulations with the EPSR potentials, no significant formation of secondary structure is observed. It is shown that the preference for coil conformations over conformations with secondary structure by the EPSR potentials is due to an overestimation of the energy of salt bridge formation, independent of the magnitude of the Coulomb energy relative to the other energy terms. Possible improvements of the distance-dependent dielectric functions which may permit their application to the simulation of peptide folding, are discussed. Received: 11 July 1998 / Accepted: 22 September 1998 / Published online: 17 December 1998     

Molecular modelling of amphipathic basic model peptides: Interactions in aqueous solutions and in the presence of lipids

Molecular modelling calculations based on experimental data obtained in solution and in small unilamellar vesicles are used to study interactions between amphiphilic basic peptides and membranes. The behaviour of such peptides during the initial and final stages of the adsorption process is our primary interest. Primary sequences of 20 amino acid residues were designed with equal numbers of basic lysines and hydrophobic leucines in order to get an amphipathic α helix. First, in solution, aggregates with an increasing number (up to nine) of helical monomers were built up and the hydrophobic solvent accessible surface per monomer was analysed on energy minimised structures. This showed that aggregates with 5–8 of monomers should be equally probable, in reasonable accordance with experimental data. In addition, models of membranes with 21 dimyristoyl-phosphatidylcholine lipids were constructed; amphiphilic peptides were merged into these assemblies with their axes parallel to the monolayer surface and the whole lipid/peptide complex was submitted to a few steps of simulated annealing and further energy minimisation techniques in order to equilibrate alkyl chains in the vicinity of the peptide. These simulations yield an estimation of the penetration depth for the peptide in the monolayer of ∼3.2 ?, whereas experimental approaches to this question were not productive. The modification in the peptide net electrical charge by interchanging Leu in Lys residues in such systems is also examined: for low-charged peptides the penetration depth increases. Received: 20 May 1998 / Accepted : 3 September 1998 / Published online: 7 December 1998     

Stabilization centers in various proteins

Interactions among residues together with their interactions with the surrounding medium determine the unique structure of globular proteins. An algorithm was recently developed to locate residues participating in cooperative long-range interactions, called stabilization center residues, that are primarily responsible for preventing the decay of the 3D structure. While our statistical analysis showed that interactions of stabilization center residues hardly influence the formation of the various secondary structure elements, the distribution of the stabilization center residues is rather uneven among the secondary structure elements. Here we analyzed the frequency and distribution of the stabilization center residues and their interacting pairs in secondary structure classes to learn about the effect of secondary structure on the formation and properties of stabilization centers and about the types of interactions responsible for stabilization of proteins of various secondary structure classes. It was found that residues from the same secondary structure tend to interact with each other in the stabilization centers of all classes. It is also suggested that the folding-unfolding equilibrium is governed by different principles for class all-α than for the rest of the classes. Received: 24 April 1998 / Accepted: 17 September 1998 / Published online: 7 December 1998     

Molecular modeling study of an abasic DNA undecamer duplex: d(GCGTGOGTGCG) · d(CGCACTCACGC)

Molecular mechanics calculations were performed with the JUMNA program on d(GCGTGOGTGCG) · d(CGCACTCACGC) where “O” is a modified abasic site: 3-hydroxy-2-(hydroxymethyl)tetrahydrofuran. From energy minimizations, for intrahelical or extrahelical positions of the unpaired thymine, various structures with different curvatures were obtained. Dynamical properties of this abasic sequence were also investigated through the controlled studies of DNA bending. Poisson-Boltzmann calculations were used to mimic the electrostatic effect of solvent on this sequence. The lowest energy structures show an acceptable agreement with experimental data. Received: 1 June 1998 / Accepted: 17 September 1998 / Published online: 10 December 1998     

Ion channels of biological membranes: prediction of single channel conductance

The Poisson-Boltzmann equation was solved numerically for models of the pore regions of the Shaker K⁺ channel and of two glycoporins (LamB and ScrY) to yield electrostatic potential profiles along the pore axes. From these potential profiles, single-channel current-voltage (I–V) relations were calculated. The importance of a proper treatment of the ionisation state of two rings of aspartate sidechains at the mouth of the K⁺ channel pore emerged from such calculations. The calculated most likely state, in which only two of the eight aspartate sidechains were deprotonated, yielded better agreement with experimental conductance data. An approximate calculation of single-channel conductances based simply on pore geometry yielded very similar conductance values for the two glycoporins. This differed from an␣experimentally determined conductance ratio of ScrY:LamB=10:1. Preliminary electrostatics calculations appeared to reproduce the observed difference in conductance between the two glycoporins, confirming that single-channel conductance is determined by electrostatic as well as geometric considerations. Received: 25 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Transition structures and exo/endo stereoselectivities of concerted [6 + 4] cycloadditions with density functional theory

Density functional theory transition structures were located for three concerted [6 + 4] cycloaddition reactions involving cis-hexatriene and butadiene, cyclopentadiene and cycloheptatriene, and cyclopentadiene and tropone. Geometries, energies, and entropies were computed at the Becke3LYP/6-31G* level. The activation energy of the concerted [6 + 4] cycloaddition of hexatriene and butadiene is 33.3 kcal/mol, about 8 kcal/mol above the activation energy of the butadiene plus ethylene [4 + 2] cycloaddition. The endo concerted [6 + 4] transition state is 1.1 kcal/mol higher than the exo. The [6 + 4] reaction of cyclopentadiene and cycloheptatriene has a barrier of 25.9 kcal/mol, while the cyclopentadiene–tropone barrier drops to 20.7 kcal/mol. Received: 3 December 1998 / Accepted: 18 February 1999 / Published online: 7 June 1999     

The angular dependence of the multipole–multipole interaction for energy transfer

The interaction between multipoles is not isotropic even in cubic systems. This results in the introduction of geometric reduction factors in the calculation of energy-transfer rates in crystals. We derive these reduction factors for the cases of dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole couplings and present a general procedure for their derivation in other cases. For the dipole–dipole case the geometric factor is independent of the distribution of the acceptor species, but for higher-order couplings, a significant angular dependence is found. Received: 6 November 1998 / Accepted: 15 January 1999 / Published online: 7 June 1999     

A computational model of the 5-HT3 receptor extracellular domain: search for ligand binding sites

A three-dimensional model of the 5-HT₃ receptor extarcellular domain has been derived on the basis of the nicotinic acetylcholine receptor model recently published by Tsigelny et al. Maximum complementarity between the position and characteristics of mutated residues putatively involved in ligand interaction and the pharmacophoric elements derived by the indirect approach applied on several series of 5-HT₃ ligands have been exploited to gain insights into the ligand binding modalities and to speculate on the mechanistic role of the structural components. The analysis of the three-dimensional model allows one to distinguish among amino acids that exert key roles in ligand interactions, subunit architecture, receptor assembly and receptor dynamics. For some of these, alternative roles with respect to the ones hypothesized by experimentalists are assigned. Different binding modalities for agonists and antagonists are highlighted, and residues which probably play a role in the transduction of binding into a change in conformational state of the receptor are suggested. Received: 27 July 2000 / Accepted: 15 September 2000 / Published online: 21 December 2000     

Ab initio MO study of ethylene insertion into the Sm–C bond of H2SiCp2SmCH3

Ethylene insertion into the Sm–C bond of H₂SiCp₂SmCH₃, a model reaction of an olefin polymerization propagation step, has been studied by ab initio molecular orbital methods. The small electronegativity of the Sm atom makes the Sm–C bond ionic, the methyl group being negatively charged by −0.75. The reaction passes through a loose ethylene complex with a binding energy of 15 kcal/mol and then a tight four-centered transition state with an agostic interaction between the Sm atom and one of the methyl CH bonds. A small activation energy of 14 kcal/mol is required to pass through this transition state, indicating that this is an easy reaction. Compared with the reactions with group 4 cationic silylene-bridged metallocenes the activation energy is higher and the reaction is less exothermic. The origin of these differences is discussed. The results of molecular mechanics calculations on regio- and stereoselectivities in the insertion reaction of propylene are also reported. Received: 13 July 1998 / Accepted: 28 August 1998 / Published online: 2 November 1998     

Ab initio studies on the mechanism of dimerization reactions of ketene imine and bis(trifluoromethyl)ketene imine

The dimerization reactions of ketene imine and bis(trifluoromethyl)ketene imine were studied theoretically. All the dimerization processes take place in a concerted but asynchronous manner, each proceeding through a four-membered ring transition state. For the ketene imine dimerization reactions, three different processes have almost equal activation barriers, while for the three bis(trifluoromethyl)ketene imine dimerization processes the reaction giving symmetrical a four-membered heterocyclic product has the lowest activation barrier. Received: 15 July 1998 / Accepted 3 September 1998 / Published online: 17 December 1998     

Theoretical study on decomposition of γ-halo allylalkoxide and β-halo acrylate ions

β, γ-Substituted γ-halo allylalkoxide ions decompose to form a halogen ion, formaldehyde, and an alkyne under mild conditions, for example at room temperature. The E isomer does not differ from the Z isomer in terms of activation energy. We attempted to shed light on the mechanism of the reaction by using ab initio molecular orbital calculations. The observed propensity was confirmed by the present calculation on model molecules, γ-chloro allylalkoxide ions. We conducted further calculations and compared the alkoxide results with a similar reaction of β-haloacrylate ions that release carbon dioxide instead of formaldehyde. This similar reaction needs heating as high as 150°C. The activation energy of the acrylate ions (36–39 kcal mol⁻¹) was calculated to be about 10 kcal mol⁻¹ higher than that of the alkoxide ions. The activation energy of the E acrylate ion is smaller by 0.8 kcal mol⁻¹ than that of the Z isomer at the MP2/6-31+G**//RHF/6-31+G* level of theory. This is consistent with experimental results. While the ready deprotonation from the carboxylic group does not activate the acrylate ion very much, the alkoxide ion is destabilized to a great degree in the process of anion formation. The difficulty in deprotonation that proceeds from the neutral molecule is seen in the difference in the activation energies for the decomposition of the corresponding anions. Therefore, the pK _a of a hydroxy or a carboxylic group plays the leading role in determining the magnitude of activation energies of allyl halides with a negatively charged fragment. Received: 2 July 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Prediction of stability changes upon single-site mutations using database-derived potentials

One of the purposes of studying protein stability changes upon mutations is to get information about the dominating interactions that drive folding and stabilise the native structure. With this in mind, we present a method that predicts folding free-energy variations caused by point mutations using combinations of two types of database-derived potentials, i.e. backbone torsion-angle potentials and distance potentials, describing local and non-local interactions along the chain, respectively. The method is applied to evaluate the folding free-energy changes of 344 single-site mutations introduced in six different proteins and a synthetic peptide. We found that the relative importance of local versus non-local interactions along the chain is essentially a function of the solvent accessibility of the mutated residues. For the subset of totally buried residues, the optimal potential is the sum of a distance potential and a torsion potential weighted by a factor of 0.4. This combination yields a correlation coefficient between measured and computed changes in folding free energy of 0.80. For mutations of partially buried residues, the best potential is the sum of a torsion potential and a distance potential weighted by 0.7. For fully accessible residues, the torsion potentials taken alone perform best, reaching correlation coefficients of 0.87 on all but 10 mutations; the excluded mutations seem to modify the backbone structure or to involve interactions that are atypical for the surface. These results show that the relative weight of non-local interactions along the sequence decreases as the solvent accessibility of the mutated residue increases, and vanishes at the protein surface. On the contrary, the weight of local interactions increases with solvent accessibility. The latter interactions are nevertheless never negligible, even for the most buried residues. Received: 20 May 1998 / Accepted: 3 September 1998 / Published online: 7 December 1998     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 1998     

Generalized extended empirical bond-order dependent force fields including nonbond interactions

We present a general approach for describing chemical processes (bond breaking and bond formation) in materials using force fields (FF) that properly describe multiple bonds at small distances while describing nonbond (Coulomb and van der Waals) interactions at long distances. This approach is referred to as the generalized extended empirical bond-order dependent FF. In this paper we use the Brenner empirical bond-order dependent FF for the short-range interactions and report applications on the energetics and structures of graphite crystal, dynamics of molecular crystals, and distortions of bucky tubes. Received: 7 August 1998 / Accepted: 26 October 1998 / Published online: 16 March 1999     

Temperature dependency of the intrinsic carrier density of hydrogenated amorphous silicon in MOS structures

The admittance versus frequency of a hydrogenated amorphous silicon metal oxide semiconductor capacitor is measured at a fixed bias in inversion and for temperatures in the range of 20–50 °C. The data are fitted to theoretical capacitance and conductance curves where the time constant of inversion is the result of the fit. In turn, the time constant can be converted to the (minority) carrier lifetime so that a lifetime value for each measurement temperature is available. The conversion from the time constant to the minority carrier lifetime requires the knowledge of the temperature-dependent intrinsic carrier density or rather its activation energy. The criterion for the correct choice is a temperature-independent carrier lifetime. Three published room temperature values of the intrinsic carrier density have been tested. The carrier lifetime activation energy is E _a = 0.70 ± 0.03 eV. Received: 17 June 1998 / Accepted: 23 October 1998     

How possible is the detection of correlated mutations?

The remarkable conservation of protein structure, compared to that of sequences, suggests that, in the course of evolution, residue substitutions which tend to destabilise a particular structure must be compensated by other substitutions that confer greater stability on that structure. Given the compactness of proteins, spatially close residues are expected to undergo the compensatory process. Surprisingly, approaches designed to detect such correlated changes have led, until now, only to limited success in detecting pairs of residues adjacent in the three-dimensional structures. We have undertaken, by simulating the evolution of DNA sequences including sites mutating in a correlated manner, to analyse whether such poor results can be attributed to the detection methods or if this failure could result from a compensatory process more complex than that implicitly underlying the different approaches. Present results show that only methods taking into account the phylogenetic reconstruction can lead to correct detection. Received: 24 April 1998 / Accepted: 8 August 1998 / Published online: 11 November 1998     

Stabilization centers and protein stability

The well-balanced stability of protein structures allows large-scale fluctuations, which are indispensable in many biochemical functions, ensures the long-term persistence of the equilibrium structure and it regulates the degradation of proteins to provide amino acids for biosynthesis. This balance is studied in the present work with two sets of proteins by analyzing stabilization centers, defined as certain clusters of residues involved in cooperative long-range interactions. One data set contains 56 proteins, which belong to 16 families of homologous proteins, derived from organisms of various physiological temperatures. The other set is composed of 31 major histocompatibility complex (MHC)–peptide complexes, which represent peptide transporters complexed with peptide ligands that apparently contribute to the stabilization of the MHC proteins themselves. We show here that stabilization centers, which had been identified as special clusters of residues that protect the protein structure, evolved to serve also as regulators of function – related degradation of useless protein as part of protein housekeeping. Received: 25 August 2000 / Accepted: 6 September 2000 / Published online: 21 December 2000     

Mechanism of activation of glassy carbon electrodes by cathodic pretreatment

The performance of carbon electrodes depends on the surface pretreatment methods. An exclusively cathodically pretreated glassy carbon electrode (GCE) shows very good activity towards monomeric molybdate(VI) ion adsorption and its reduction. X-ray photoelectron spectroscopy studies reveal the creation of >C–O– surface groups on cathodisation. A strong interaction between the Mo(VI) ion and these >C–O– surface groups with the formation of Mo(V) is responsible for the activation of the cathodically pretreated GCE surface. Received: 5 January 1998 / Accepted: 10 January 1999