Calibration of the angular dependence of the amide proton-C alpha proton coupling constants, 3JHN alpha, in a globular protein. Use of 3JHN alpha for identification of helical secondary structure

The vicinal amide proton-C alpha proton spin-spin coupling constants, JHN alpha, in the globular protein basic pancreatic trypsin inhibitor (BPTI) have been measured using phase-sensitive correlated spectroscopy at high digital resolution. In conjunction with the crystal structure of BPTI, these data were used to calibrate the correlation between 3JHN alpha and the dihedral angle phi. The resulting "BPTI curve" is 3JHN alpha = 6.4 cos2 theta - 1.4 cos theta + 1.9 (theta = [phi - 60 degrees]). It is further shown that measurement of the spin-spin couplings 3JHN alpha presents an independent, reliable method for identification of the location of helical structure in the amino acid sequence of proteins.     

Myocardial material mechanics: characteristic variation of the circumferential and longitudinal systolic moduli in left ventricular dysfunction

Active systolic moduli for the circumferential (E theta) and longitudinal (E phi) axes of the left ventricle were determined along with circumferential and longitudinal contractile filament stress (sigma theta and sigma phi) and circumferential and longitudinal fiber strain (epsilon theta and epsilon phi). These material property parameters were determined at four points during cardiac systole. Thirty-nine patients comprising five clinical groups were evaluated using pressure and volume data acquired from single-plane cineangiography. The results indicate that the active moduli exponentially decrease during cardiac systole. Characteristic variations from normal differentiated the various pathological groups. With compensated volume overload, E theta was significantly reduced during the latter half of systole (p less than 0.25). With decompensated volume overload, both E theta and E phi were not significantly different from the normal group throughout cardiac systole. With compensated pressure overload, both E theta and E phi were significantly lower than the normal group at end-systole (p less than 0.005; p less than 0.005). With congestive cardiomyopathy, both E theta and E phi were significantly greater during the latter half of systole compared to the normal group (p less than 0.05 and p less than or equal to 0.025).     

Protein dynamics in solution and in a crystalline environment: a molecular dynamics study

The effect of a solvent and a crystalline environment on the dynamics of proteins is investigated by the method of computer simulation. Three 25-ps molecular dynamics simulations at 300 K of the bovine pancreatic trypsin inhibitor (BPTI), consisting of 454 heavy atoms, are compared: one of BPTI in vacuo, one of BPTI in a box with 2647 spherical nonpolar solvent atoms, and one of BPTI surrounded by fixed crystal image atoms. Both average and time-dependent molecular properties are examined to determine the effect of the environment on the behavior of the protein. The dynamics of BPTI in solution or in the crystal environment are found to be very similar to that found in the vacuum calculation. The primary difference in the average properties is that the equilibrium structure in the presence of solvent or the crystal field is significantly closer to the X-ray structure than is the vacuum result; concomitantly, the more realistic environment leads to a number density closer to experiment. The presence of solvent has a negligible effect on the overall magnitude of the positional or dihedral angle fluctuations in the interior of the protein; however, there are changes in the decay times of the fluctuations of interior atoms. For surface residues, both the magnitude and the time course of the motions are significantly altered by the solvent. There tends to be an increase in the displacements of long side chains and the flexible parts of the main chain that protrude into the solvent. Further, these motions tend to have a more diffusive character with longer relaxation times than in vacuo. The crystal environment has a specific effect on a number of side chains which are held in relatively fixed positions through hydrogen-bond and electric interactions with the neighboring protein atoms. Most of the effects of the solution environment seem to be sufficiently nonspecific that it may be possible to model them by applying a mean field and stochastic dynamic methods.     

Electrostatic effects on the alpha-helix and beta-strand formation of BPTI(16-36) studied by Monte Carlo simulated annealing.

The electrostatic effects on the secondary structure forming tendencies of a peptide fragment with residues 16-36 of bovine pancreatic trypsin inhibitor, BPTI(16-36), are studied using Monte Carlo simulated annealing simulations. We consider three dielectric functions epsilon(r) of distance r: constant dielectric function (epsilon = 2; strong electrostatic interactions) and sigmoidal functions varying from epsilon(0) = 2 to epsilon(infinity) = 47 (intermediate) and to epsilon(infinity) = 78 (weak). Simulations with epsilon = 2 suggest that this peptide exhibits a significant propensity for beta-strand formations in accordance with a beta-sheet structure of the relevant segment in native BPTI. The tendency for alpha-helix formations becomes almost comparable with that of beta-strands in the simulation with epsilon(infinity) = 47, and there appears no appreciable conformational propensity for this case. Finally, the results with epsilon(infinity) = 78 generate low-energy conformations with conspicuous alpha-helices. These findings suggest the possibility that the change in electrostatic interactions can be the key factor for the conformational transitions of peptides between alpha-helix and beta-sheet that have recently been observed in experiments. These changes in electrostatic interactions can arise from those in various environmental factors such as conformations of the rest of the protein molecule and solvent conditions.     

Fast molecular shape matching using contact maps.

In this paper, we study the problem of computing the similarity of two protein structures by measuring their contact-map overlap. Contact-map overlap abstracts the problem of computing the similarity of two polygonal chains as a graph-theoretic problem. In R3, we present the first polynomial time algorithm with any guarantee on the approximation ratio for the 3-dimensional problem. More precisely, we give an algorithm for the contact-map overlap problem with an approximation ratio of sigma where sigma = min{sigma(P1), sigma(P2)} 0, is hard.     

Effects of macromolecular crowding on an intrinsically disordered protein characterized by small-angle neutron scattering with contrast matching

Small-angle neutron scattering was used to examine the effects of molecular crowding on an intrinsically disordered protein, the N protein of bacteriophage λ, in the presence of high concentrations of a small globular protein, bovine pancreatic trypsin inhibitor (BPTI). The N protein was labeled with deuterium, and the D₂O concentration of the solvent was adjusted to eliminate the scattering contrast between the solvent and unlabeled BPTI, leaving only the scattering signal from the unfolded protein. The scattering profile observed in the absence of BPTI closely matched that predicted for an ensemble of random conformations. With BPTI added to a concentration of 65 mg/mL, there was a clear change in the scattering profile representing an increase in the mass fractal dimension of the unfolded protein, from 1.7 to 1.9, as expected if crowding favors more compact conformations. The crowding protein also inhibited aggregation of the unfolded protein. At 130 mg/mL BPTI, however, the fractal dimension was not significantly different from that measured at the lower concentration, contrary to the predictions of models that treat the unfolded conformations as convex particles. These results are reminiscent of the behavior of polymers in concentrated melts, suggesting that these synthetic mixtures may provide useful insights into the properties of unfolded proteins under crowding conditions.     

Static and dynamic light scattering approach to the hydration of hemoglobin and its supertetramers in the presence of osmolites.

We used static and dynamic light scattering for comparing the mass (MW) and hydrodynamic radius (R(h)) of several hemoglobin systems, namely human hemoglobin, bovine hemoglobin, human hemoglobin cross-linked with a sebacyl residue, and bovine hemoglobin cross-linked with an adipoyl residue. We measured the MW and R(h) of these systems in 0.1M phosphate buffer at pH 7.0 in the absence and in the presence of either betaine or glycerol up to 1.7 molal concentrations. The 90 degrees scattering was measured with a photon counting machine equipped with a diode laser at 783 nm. The Rayleigh ratio [R(theta)] of the instrument was estimated using R(theta) = 7.19E-6 cm(-1) for toluene at 783 nm. The refractive index increment of hemoglobin solutions was measured using a laser beam at 750 nm. We estimated a value dn/dc = 0.210 cm3/g in the absence and dn/dc = 0.170 in the presence of 1.7 molal osmolites. For all systems both in liganded and unliganded form, the static light scattering data showed a 16% mass increase with increasing concentration of osmolites. The hydrodynamic radii of all investigated systems in the presence and absence of osmolites were close to 3.17 nm. Assuming a partial specific volume nu = 0.739 for hemoglobin, and using spherical geometry, the estimated average hydration volume of hemoglobin was 32.6 L/mole in the absence of osmolites. It decreased to 23.5 L/mole in the presence of 1.7 molal osmolites. Assuming that the density of water in the hydration volume is D = 1.0 g/cm3, the hydration of Hb was 0.51 gH2O/gHb, with a surface density of 0.20 molH2O/A2. The hydration decreased to 0.33 gH2O/gHb and 0.14 molH2O/A2 in the presence of 1.7 molal osmolites. The decreased hydration was compensated by the increased mass (i.e., decreased surface area per unit volume) so that the thickness of the water shell around these proteins remained close to a single layer of water molecules. These findings indicate that the combination of static and dynamic light scattering offer unique means for investigating the relevance of water activity on the structure and function of biological macromolecules. In the case of hemoglobin, the data suggest that the decreased oxygen affinity in the presence of osmolites reported by Colombo et al. (M. F. Colombo, D. C. Rau, and V. A. Parsegian Science, 1992, Vol. 256, pp. 655-659), as due to ligand linked water binding on hemoglobin surface, is part of a complex phenomenon involving the hydration shell of hemoglobin and the formation of low affinity supertetrameric molecules.     

Solvent exchange of buried water and hydrogen exchange of peptide NH groups hydrogen bonded to buried waters in bovine pancreatic trypsin inhibitor

Solvent exchange of 18O-labeled buried water in bovine pancreatic trypsin inhibitor (BPTI), trypsin, and trypsin-BPTI complex is measured by high-precision isotope ratio mass spectrometry. Buried water is labeled by equilibration of the protein in 18O-enriched water. Protein samples are then rapidly dialyzed against water of normal isotope composition by gel filtration and stored. The exchangeable 18O label eluting with the protein in 10-300 s is determined by an H2O-CO2 equilibration technique. Exchange of buried waters with solvent water is complete before 10-15 s in BPTI, trypsin, and BPTI-trypsin, as well as in lysozyme and carboxypeptidase measured as controls. When in-exchange dialysis and storage are carried out at pH greater than or equal to 2.5, trypsin-BPTI and trypsin, but not free BPTI, have the equivalent of one 18O atom that exchanges slowly (after 300 s and before several days). This oxygen is probably covalently bound to a specific site in trypsin. When in-exchange dialysis and storage are carried out at pH 1.1, the equivalent of three to seven 18O atoms per molecule is associated with the trypsin-BPTI complex, apparently due to nonspecific covalent 18O labeling of carboxyl groups at low pH. In addition to 18O exchange of buried waters, the hydrogen isotope exchange of buried NH groups H bonded to buried waters was also measured. Their base-catalyzed exchange rate constants are on the order of NH groups that in the crystal are exposed to solvent (static accessibility greater than 0) and hydrogen-bonded main chain O, and their pH min is similar to that for model compounds. The pH dependence of their exchange rate constants suggests that direct exchange with water may significantly contribute to their observed exchange rate.     

Characterization of the IgE Fc receptors on monocytes and macrophages

Subpopulations of human monocytes (15%) and alveolar macrophages (AM phi, 8%) and rat and mouse AM phi (89%) and peritoneal M phi (57%) bear Fc receptors for IgE (Fc epsilon R) as shown by IgE-specific rosette formation. Cells from M phi-like cell lines of human, rat, and mouse origins also express Fc epsilon R. Monomeric IgE binds to Fc epsilon R on M phi with an equilibrium association constant Ka congruent to 10(7) M-1. The Fc epsilon R on human monocytes and M phi are antigenically similar to Fc epsilon R on lymphocytes but differ from Fc epsilon R on basophilic granulocytes. The Fc epsilon R on human and mouse M phi promote phagocytosis and lysis of IgE-coated erythrocytes. Patients with active IgE-mediated allergic diseases have elevated percentages of Fc epsilon R(+) monocytes (56%) that show allergic increased lytic activity against IgE-coated erythrocytes as compared to monocytes from normal humans. M phi from rats infested with Nippostrongylus brasiliensis parasites express more Fc epsilon R than normal M phi. The data indicate that Fc epsilon R expressed on M phi differ from those on mast cells and basophils, increase in number during IgE immune responses, and are likely to play an important role in the host's defense against parasites and in the pathogenesis of allergic diseases.     

Determination of local conformation of proteins from 1H-NMR spectroscopy data

A method is proposed to determine conformations of amino acid residues of the protein and effective correlation time tau c from cross-peak intensities in two-dimensional nuclear Overhauser enhancement (NOESY) spectra. The method consists in fitting complete relaxation matrix of dipeptide unit protons to experimental cross-peak intensities by varying phi, psi, chi torsional angles and tau c. To verify the method, NOESY spectra of basic pancreatic trypsin inhibitor (BPTI) were theoretically generated at mixing times tau m = 25-300 ms and tau c = 4 ns and used for local structure determination. The method works well with optimum for measurement of NOE intensities tau m 100-200 ms. As a result, the backbone phi, psi torsion angles were unambiguously determined at tau m = 100 ms for all but Gly residues of BPTI, and chi 1 angles were determined for the majority of side chains. The obtained dipeptide unit conformations are very close to the BPTI crystallographic structure: root mean square deviation (RMSD) of interproton distances within dipeptide units, on the average, is 0.08 A (maximal deviation 0.44 A), and RMSD of phi and psi angles are 18 and 9 degrees, respectively (maximal deviations are 44 and 22 degrees).     

Distributions of Potential in Cylindrical Coordinates and Time Constants for a Membrane Cylinder

A mathematical problem relating to membrane cylinders is stated and solved; its implications are illustrated and discussed. The problem concerns the volume distribution, in cylindrical coordinates, of the electric potential inside and outside a membrane cylinder of finite length (with sealed ends), during passive decay of an initially nonuniform membrane potential. The time constants for equalization with respect to the angle, theta, are shown to be typically about ten thousand times smaller than the time constant, tau(m) = R(m)C(m), for uniform passive membrane potential decay. The time constants for equalization with respect to length are shown to agree with those from one-dimensional cable theory; typically, they are smaller than tau(m) by a factor between 2 and 10. The relation of the membrane current density, I(m)(theta, x, t), to the values (at the outer membrane surface) of the extracellular potential phi(e)(r, theta, x, t) and of partial differential(2)phi(e)/ partial differentialx(2), is examined and it is shown that these quantities are not proportional to each other, in general; however, under certain specified conditions, all three of these quantities are proportional with each other and with phi(i)(r, theta, x, t) and partial differential(2)phi(i)/ partial differentialx(2) (at the inner membrane surface). The relation of these results to those of one-dimensional cable theory is discussed.     

Using Molecular Markers to Estimate Quantitative Trait Locus Parameters: Power and Genetic Variances for Unreplicated and Replicated Progeny

Many of the progeny types used to estimate quantitative trait locus (QTL) parameters can be replicated, e.g., recombinant inbred, doubled haploid, and F3 lines. These parameters are estimated using molecular markers or QTL genotypes estimated from molecular markers as independent variables. Experiment designs for replicated progeny are functions of the number of replications per line (r) and the number of replications per QTL genotype (n). The value of n is determined by the size of the progeny population (N), the progeny type, and the number of simultaneously estimated QTL parameters (q - 1). Power for testing hypotheses about means of QTL genotypes is increased by increasing r and n, but the effects of these factors have not been quantified. In this paper, we describe how power is affected by r, n, and other factors. The genetic variance between lines nested in QTL genotypes (sigma 2n:q) is the fraction of the genetic variance between lines (sigma 2n) which is not explained by simultaneously estimated intralocus and interlocus QTL parameters (phi 2Q); thus, sigma 2n:q = sigma 2n - phi 2Q. If sigma 2n:q not equal to 0, then power is not efficiently increased by increasing r and is maximized by maximizing n and using r = 1; however, if sigma 2n:q = 0, then r and n affect power equally and power is efficiently increased by increasing r and is maximized by maximizing N.r. Increasing n efficiently increases power for a wide range of values of sigma 2n:q.sigma 2n:q = 0 when the genetic variance between lines is fully explained by QTL parameters (sigma 2n = phi 2Q).(ABSTRACT TRUNCATED AT 250 WORDS)     

Conformation of a cyclic decapeptide analog of a repeat pentapeptide sequence of elastin: cyclo-bis(valyl-prolyl-alanyl-valyl-glycyl)

The conformation of a cyclic decapeptide analog of a repeat sequence of elastin has been determined in the crystalline state using X-ray crystallographic techniques. Tetragonal crystals were grown from a solution of the decapeptide in water; space group P4(2)2(1)2, a = 19.439(2) & c = 13.602(1) A, with four formula units (C40H66N10O10.4H2O) per unit cell. The cyclic decapeptide in the crystal exhibits exact twofold symmetry. The asymmetric unit contains one pentapeptide and two water molecules for a total of 32 nonhydrogen atoms. The structure has been determined by the application of direct methods and refined by full-matrix least squares to an R index of 0.053 for 2272 reflections with intensities greater than 2 sigma(I). The backbone conformation of the asymmetric pentapeptide can be described as consisting of a double beta bend of Type III-I. The Type III turn has Pro (phi = -59.3 degrees, psi = -26.8 degrees) and Ala (phi = -65.9 degrees, psi = -23.1 degrees) at the corners while Type I turn has Ala (phi = -65.9 degrees, psi = -23.1 degrees) and Val (phi = -98.9 degrees, psi = 8.3 degrees) as the corner residues. The cyclic decapeptide has two such double bends linked together by Gly-Val bridges.     

Two new species of Isospora (Apicomplexa: Eimeriidae) from passeriform birds of South America

Summary Two new species of Isospora (Apicomplexa: Eimeriidae) are described from the faeces of passeriform birds of South America. I. cyanocoracis n. sp. is described from Cyanocorax chrysops (Passeriformes: Corvidae) and I. paroariae n. sp. from Paroaria coronata (Passeriformes: Emberizidae). I. cyanocoracis oocysts are spherical or subspherical, 28.7×26.8 m (25.0–30.5×24.5–29.0), with bi-layered wall about 2.0 m thick. Micropyle and oocyst residuum are absent; large polar granule present. Sporocysts are ovoid, 19.3×11.4 m (17.0–21.0×10.5–12.2), with smooth, single-layered wall about 0.8 m thick. Stieda and substiedal bodies and sporocyst residuum are present. Sporozoites 12.2×4.2 m (10.5–15.0×3.5–4.5), possess spherical anterior and posterior refractile bodies. I. paroariae oocysts are spherical or subspherical, 22.3×21.4 m (19.5–25.5×18.5–24.0), and have bi-layered wall about 1.8 m thick. Micropyle, polar granule, and oocyst residuum are absent. Sporocysts ovoid, 15.2×10.0 m (14.0–16.5×8.0–11.5), possess smooth, single-layered wall about 0.7 m thick. Stieda and substiedal bodies and sporocyst residuum are present. Sporozoites elongate, 11.3×3.4 m (10.0–13.5×3.2–4.0), have single, large, posterior refractile body. ac]19840712     

Energetics of charge-charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson-Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate of rhodanese is analyzed, with attention to the influence of alpha-helices. Finally, relationships between electrostatic potential and charge-charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance-dependent dielectric constant (epsilon = R) and a fixed dielectric constant (epsilon = 2), and Tanford-Kirkwood theory. The primary conclusions are as follows: 1) The Poisson-Boltzmann model agrees with the subtilisin data over a range of ionic strengths; 2) two alpha-helices generate a large potential in the active site of rhodanese; 3) epsilon = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; 4) Tanford-Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson-Boltzmann equation in globular proteins; and 5) the modified Tanford-Kirkwood theory over-screens the measured electrostatic interactions in subtilisin.     

The determination of the three-dimensional structure of barley serine proteinase inhibitor 2 by nuclear magnetic resonance, distance geometry and restrained molecular dynamics

The solution structure of the 64 residue structured domain (residues 20-83) of barley serine proteinase inhibitor 2 (BSPI-2) is determined on the basis of 403 interproton distance, 34 phi backbone torsion angle and 26 hydrogen bonding restraints derived from n.m.r. measurements. A total of 11 converged structures were computed using a metric matrix distance geometry algorithm and refined by restrained molecular dynamics. The average rms difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.2 A for the backbone atoms and 2.1 +/- 0.1 A for all atoms. The overall structure, which is almost identical to that found by X-ray crystallography, is disc shaped and consists of a central four component mixed parallel and antiparallel beta-sheet flanked by a 13 residue alpha-helix on one side and the reactive site loop on the other.     

Crystal structure of form II of cholesteryl palmitelaidate at 295 K

Form II for cholesteryl palmitelaidate (trans-9-hexadecenoate) (C43H74O2) is monoclinic P2(1) with a = 12.745(3), b = 9.006(2), c = 18.153(4) A, beta = 96.63 (2) degrees, Z = 2. The X-ray crystal structure of form II has been determined from 2506 reflections of which 2126 gave (F greater than 2 sigma). The data up to sin theta/lambda = 0.44A-1 (Dmin = 1.14 A) were measured with CuK alpha radiation from a sealed tube. These were supplemented up to sin theta/lambda = 0.52 A-1 (Dmin = 0.96 A) by measurements on the same crystal using a rotating anode X-ray source. The electron density was diffuse in the ester chain and the atoms of the cholesteryl tail were found to be disordered. The tail and the chain atoms were refined by restrained least squares methods to give R = 0.087 and Rw = 0.10 for reflections with F greater than 2 sigma. Crystal forms I and II represent two standard structure types already characterized for fatty acid esters of cholesterol. In form II, the ester chain is almost fully extended as is also the case for one of the two independent molecules (A) in form I. In form II, the chains pack loosely together for most of their length. M.s. amplitudes of thermal vibration for the chain C-atoms are almost uniform along the entire chain (approximately 0.25 A2 at 295 K). In form I, the proximal part of the A chain is surrounded by rigid cholesteryl groups. In this region, C-atom m.s. amplitudes are much reduced (approximately 0.10 A2) but they increase to about 0.5 A2 at the distal end of the chain where packing is very loose.     

Inelastic neutron scattering analysis of picosecond internal protein dynamics. Comparison of harmonic theory with experiment

The experimental inelastic neutron scattering spectrum of a protein, the bovine pancreatic trypsin inhibitor (BPTI), in a powder sample is presented together with the generalized density of states, G(omega), as a function of the frequency, omega, derived from the scattering data. The experimental results are compared with calculations from two different normal mode analyses of BPTI. One of these, based on an improved model, gives a calculated spectrum and density of states in general agreement with those obtained experimentally; the other, based on an earlier model, shows considerable disagreement. The important improvements in the newer normal mode analysis are the explicit treatment of all atoms (non-polar as well as polar hydrogens are included) and a modified truncation scheme for the long-range electrostatic interactions. The fact that the inelastic neutron scattering measurements can distinguish between the two theoretical models makes clear their utility for the analysis of protein dynamics.     

Solvation parameters for predicting the structure of surface loops in proteins: transferability and entropic effects

A new procedure for optimizing parameters of implicit solvation models introduced by us has been applied successfully first to cyclic peptides and more recently to three surface loops of ribonuclease A (Das and Meirovitch, Proteins 2001;43:303-314) using the simplified model E(tot) = E(FF)(epsilon = nr) + Sigma(i) sigma(i)A(i), where sigma(i) are atomic solvation parameters (ASPs) to be optimized, A(i) is the solvent accessible surface area of atom i, E(FF)(epsilon = nr) is the AMBER force-field energy of the loop-loop and loop-template interactions with a distance-dependent dielectric constant, epsilon = nr, where n is a parameter. The loop is free to move while the protein template is held fixed in its X-ray structure; an extensive conformational search for energy minimized loop structures is carried out with our local torsional deformation method. The optimal ASPs and n are those for which the structure with the lowest minimized energy [E(tot)(n,sigma(i))] becomes the experimental X-ray structure, or less strictly, the energy gap between these structures is within 2-3 kcal/mol. To check if a set of ASPs can be defined, which is transferable to a large number of loops, we optimize individual sets of ASPs (based on n = 2) for 12 surface loops from which an "averaged" best-fit set is defined. This set is then applied to the 12 loops and an independent "test" group of 8 loops leading in most cases to very small RMSD values; thus, this set can be useful for structure prediction of loops in homology modeling. For three loops we also calculate the free energy gaps to find that they are only slightly smaller than their energy counterparts, indicating that only larger n will enable reducing too large gaps. Because of its simplicity, this model allowed carrying out an extensive application of our methodology, providing thereby a large number of benchmark results for comparison with future calculations based on n > 2 as well as on more sophisticated solvation models with as yet unknown performance for loops.