Conformational studies on the enkephalin releasing peptides,Tyr-Arg and Tyr-D-Arg

Conformational energy calculations were carried out on the enkephalin releasing peptides, Tyr-Arg and Try-D-Arg. The conformations of low energy were found to result in two configurations in which the side-chains were either on opposite sides of the backbone (R1) or parallel to one another (R2). A comparison of the two molecules suggests that configuration R2 is most probably the active structure. A method for testing this hypothesis is presented.     

How proteins trigger excitation energy transfer in the FMO complex of green sulfur bacteria

A simple electrostatic method for the calculation of optical transition energies of pigments in protein environments is presented and applied to the Fenna-Matthews-Olson (FMO) complex of Prosthecochloris aestuarii and Chlorobium tepidum. The method, for the first time, allows us to reach agreement between experimental optical spectra and calculations based on transition energies of pigments that are calculated in large part independently, rather than fitted to the spectra. In this way it becomes possible to understand the molecular mechanism allowing the protein to trigger excitation energy transfer reactions. The relative shift in excitation energies of the seven bacteriochlorophyll-a pigments of the FMO complex of P. aestuarii and C. tepidum are obtained from calculations of electrochromic shifts due to charged amino acids, assuming a standard protonation pattern of the protein, and by taking into account the three different ligand types of the pigments. The calculations provide an explanation of some of the earlier results for the transition energies obtained from fits of optical spectra. In addition, those earlier fits are verified here by using a more advanced theory of optical spectra, a genetic algorithm, and excitonic couplings obtained from electrostatic calculations that take into account the influence of the dielectric protein environment. The two independent calculations of site energies strongly favor one of the two possible orientations of the FMO trimer relative to the photosynthetic membrane, which were identified by electron microscopic studies and linear dichroism experiments. Efficient transfer of excitation energy to the reaction center requires bacteriochlorophylls 3 and 4 to be the linker pigments. The temporal and spatial transfer of excitation energy through the FMO complex is calculated to proceed along two branches, with transfer times that differ by an order of magnitude.     

The Distribution of the Number of Maxima in a Cyclic Sequence

A simple statistical method is presented which tests for non-randomness in a cyclic sequence. The distribution of the statistic is tabulated for short sequences, and a large sample approximation is derived. Significant values of the statistic are given for sequences of length up to 52. Easily used computer programs to carry out appropriate calculations are presented.     

The Distribution of the Number of Maxima in a Cyclic Sequence

A simple statistical method is presented which tests for non-randomness in a cyclic sequence. The distribution of the statistic is tabulated for short sequences, and a large sample approximation is derived. Significant values of the statistic are given for sequences of length up to 52. Easily used computer programs to carry out appropriate calculations are presented.     

An analytic solution to the Förster energy transfer problem in two dimensions.

An analytic solution of the F?rster energy transfer problem in two dimensions is presented for the case in which the orientation factor is independent of the donor-acceptor distance, and both the donors and acceptors are randomly distributed in a plane. A general solution based on the method of F?rster is possible since all distances are measured in units of R0. The analytic solution is extended to the cases of donors embedded in structures that exclude acceptors, and donors that bind acceptors. The validity of the analytic solutions is demonstrated by comparison with numerical simulation calculations. Numerical approximations to the exact solutions are given for ease of computation. Specific applications to the case of fluorescence quenching of a membrane-bound donor by membrane-bound acceptors are presented.     

Automated method for modeling seven-helix transmembrane receptors from experimental data.

A rule-based automated method is presented for modeling the structures of the seven transmembrane helices of G-protein-coupled receptors. The structures are generated by using a simulated annealing Monte Carlo procedure that positions and orients rigid helices to satisfy structural restraints. The restraints are derived from analysis of experimental information from biophysical studies on native and mutant proteins, from analysis of the sequences of related proteins, and from theoretical considerations of protein structure. Calculations are presented for two systems. The method was validated through calculations using appropriate experimental information for bacteriorhodopsin, which produced a model structure with a root mean square (rms) deviation of 1.87 A from the structure determined by electron microscopy. Calculations are also presented using experimental and theoretical information available for bovine rhodopsin to assign the helices to a projection density map and to produce a model of bovine rhodopsin that can be used as a template for modeling other G-protein-coupled receptors.     

Improved borate method for the rapid distinction of glucosamine and galactosamine in an exopolysaccharide produced by Citrobacter sp

An improved borate method for the quantitative distinction of glucosamine (GlcN) and galactosamine (GalN) in a mixture is presented which is based on the Elson-Morgan method with addition of sodium borate to differentiate colour formation by the two hexosamines. The r2 value and maximum deviation of the method based on calculations derived in this study were 0.9979 and 5.1 %, respectively. Using this method, the GlcN/GalN ratio in an exopolysaccharide (EPS) produced by Citrobacter sp. was found to change with time during the production process, with a maximum value at 9.8:1.     

A hybrid-type approach with MD and DFT calculations for evaluation of redox potential of molecules

A simple calculation method to evaluate the redox potential of molecules by using a hybrid-type calculation with molecular dynamics (MD) and density functional theory calculations is presented with discussions of the difference of the redox potential. In our hybrid method, the standard Gibbs free energy of the molecules, acetone and 3-pentanone, in the redox reaction, is estimated from the average of ionisation free energy and the excess chemical potentials of the reduced and oxidised molecules according to the Born–Haber cycle by sampled configurations from the MD simulation. The difference of the redox potentials between the two molecules is in agreement with the experimental data within the standard deviation.     

DNA bis-intercalation: Application of theory to the binding of echinomycin to DNA

The statistical mechanical model for the binding of bifunctional intercalating ligands to duplex DNA described in the preceding paper is applied to the example of echinomycin–DNA interactions. This is the only system for which binding curves have been obtained under conditions leading to binding by both bis-intercalation and mono-intercalation simultaneously. Binding parameters and Scatchard plots are calculated for a variety of conditions. A detailed comparison of these calculations with the results from the previous analysis of the same binding data in terms of the McGhee-Von Hippel theory, assuming only one mode of binding, is presented. The results of our calculations are consistent with the model of bis-intercalation requiring the two bound chromophores of a bifunctional ligand to be separated by two base pairs. It is not necessary to assume violation of the nearest-neighbor exclusion principle, as occurred in the original analysis.     

Theory and practice of the analytical centrifugation of an active substrate-enzyme complex

The active enzyme centrifugal-ion (AEC) method presented here permits the hydrodynamic study of active enzyme–substrate(s) complexes in solutions containing micro-gram amounts of the studied enzyme, even if the enzyme preparation is very impure. The AEC method can he used only when the specific enzymatie reaction can be measured directly in a spectrophotometer. The general equations relevant to the method and their solutions are presented in detail. Their use requires some numerical calculations. A practical summary of the AEC method is given, and the precision of the measured values of the sedimentation and diffusion coefficients is discussed.     

The use of sample genealogies for studying a selectively neutral m-loci model with recombination

A selectively neutral m-loci model with recombination is studied. A general method is developed to calculate the variance of the number of segregating sites in samples of arbitrary size and the m-loci homozygosity. The method is based on properties of the genealogy of the sample rather than diffusion approximations. To demonstrate the scope of the method several calculations are presented.     

Effect of anisotropic reactivity on the rate of diffusion-controlled reactions: comparative analysis of the models of patches and hemispheres

A comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic.     

Elongation cutoff technique: low-order scaling SCF method

The elongation cutoff technique at restricted Hartree-Fock (HF) level of theory in conventional type of calculations, i.e., with two electron integrals (TEI) stored on a disc, is presented for two model systems. It is demonstrated that the number of TEI in the elongation cutoff calculations increases linearly with the system size thus, allowing to extend the conventional type of calculations to bigger systems. The step CPU (central processing unit) time in the elongation cutoff calculations is much lower than in the HF reference calculations. Such behavior reduces significantly the prefactor in the quadratic scaling relation. The total CPU time in the elongation calculation is about 40% lower than in the conventional HF calculations or comparable to direct type of calculations with the quantum fast multipoles method employed. It is shown that by introducing the interaction radius one can obtain linear scaling in the SCF calculations. Figure: The structure of density matrix and total CPU timings for polyglycine clusters in the elongation cutoff calculations. The structure of density matrix and total CPU timings for polyglycine clusters in the elongation cutoff calculations     

Evaluation of the Adaptive Umbrella Sampling Method

Abstract

The adaptive umbrella sampling technique, introduced recently to improve the probability ratio method and found to perform more reliably than the customary harmonic umbrella sampling, is tested and compared with other free energy methods. One of the tests applies the method to a transition involving a chemical change: calculation of the hydration free energy difference between acetone and dimethylamine and the other test calculates the conformational free energy difference between the C ₇ and α_R conformations of the alanide dipeptide. The dipeptide problem is also treated by two types of thermodynamic integrations and by the perturbation method. The result for the acetone-dimethylamine problem is compared with previous calculations on the same system using the perturbation method, overlap ratio method and finite difference thermodynamic integration. Enhancements to the adaptive umbrella sampling method are also presented.     

QUANTITATIVE METHOD FOR DETERMINING A REPRESENTATIVE ALGAL SAMPLE COUNT1

A method for determining a representative count of a sample dependent on number of species is presented for application to various algal communities. Constant species curves are calculated as efficiency = (number of individuals–number of species)/number of individuals and diagrammed on a plot of efficiency versus number of individuals counted. Efficiency is defined as the probability that a new species encountered is minimal. That is, as the ratio of number of species to number of individuals approaches 1, more individuals will need to be counted in order to achieve a representative count. Data and calculations of efficiency from two algal communities are presented for illustration.     

The conformation of dehydroalanine in short homopeptides: molecular dynamics simulations of a 6-residue chain

A molecular dynamics study about the conformational preferences in a chloroform solution of a homo-oligomer constituted by six residues of dehydroalanine is presented. For this purpose, two sets of force-field parameters and explicit solvent molecules have been used. Furthermore, ab initio calculations have been performed in order to estimate 1[H]-NMR chemical shifts. Results have been compared with experimental data.     

The adjustment for a natural response rate in probit analysis

A revised scheme of computation is suggested for the fitting of a probit regression line to quantal response data which have to be adjusted because of the occurrence of natural responses not caused by the stimulus under test. The calculations lead to the same results as those proposed when the method was first introduced, but have the advantages of close similarity with multiple regression calculations and of simplifying the test of heterogeneity. The new scheme is illustrated on the example used in the earlier paper.
A table of weighting coefficients for use with high natural response rates is presented.     

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size.     

Electrostatic calculations for an ion channel. II. Kinetic behavior of the gramicidin A channel.

A theoretical model of the gramicidin A channel is presented and the kinetic behavior of the model is derived and compared with previous experimental results. The major assumption of the model is that the only interaction between ions in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate that there will be potential wells at each end of the channel and, at high concentrations, that both wells can be occupied. The kinetics are based on two reaction steps: movement of the ion from the bulk solution to the well and movement between the two wells. The kinetics for this reaction rate approach are identical to those based on the Nernst-Planck equation in the limit where the movement between the two wells is rate limiting. The experimental results for sodium and potassium are consistent with a maximum of two ions per channel. To explain the thallium results it is necessary to allow three ions per channel. It is shown that this case is compatible with the electrostatic calculations if the presence of an anion is included. The theoretical kinetics are in reasonable quantitative agreement with the following experimental measurements: single channel conductance of sodium, potassium, and thallium; bi-ionic potential and permeability ratio between sodium-potassium and potassium-thallium; the limiting conductance of potassium and thallium at high applied voltages; current-voltage curves for sodium and potassium at low (but not high) concentrations; and the inhibition of sodium conductance by thallium. The results suggest that the potential well is located close to the channel mouth and that the conductance is partially limited by the rate going from the bulk solution to the well. For thallium, this entrance rate is probably diffusion limited.     

A quantum chemical investigation of structures,vibrational spectra and electron affinities of the radicals of quinone model compounds

In the present study, the first quantum chemical calculations of structures and vibrational spectra of radicals of 1,4-naphthoquinone and 2-methoxy-1,4-benzoquinone that account for electron correlation are presented. In the case of 1,4-naphthoquinone a good agreement between calculated vibrational frequencies and ¹⁸O-shifts of the 1,4-naphthoquinone radical (protonated radical anion) with experimental data of a species detected after irradiation of vitamin K₁ in solution is found. Our calculations, thus, support the previous assignment. In the case of 2-methoxy-1,4-benzoquinone we have localized the stable conformations with respect to the orientation of the methoxy group and we have determine the harmonic force fields for these structures. Our calculation suggest that, while the frequencies of the two conformers are similar, the ¹⁸O-shift of the most intensive absorptions in the spectral region between 1400 and 1700 cm^–1 of the two conformers differ significantly and might serve as a tool to distinguish between the two conformers. The applied DFT method is shown to predict electron affinities which are systematically underestimated by 10%.