Nonradiative energy transfer in oligopeptide chains generated by a monte-cralo mehod including long-range interactions

A Monte-Carlo method including long-range interactions is used to oligopeptide chains in random-coil state. The chains are composed of 4, 9, or 14 repeating units and are labeled with the luminopheres tyrosine or tryptophan. Interactions with a solvent (water) are taken into account in the calculations through modifications of the semiempirical potential-energy functions. The chains represent oligopeptides composed of hydrophobic or hydrophilic amino acid residues. Various properties relavent to the interpretaiton of nonradiative enrgy-transfer experiments, such as the average value of the orientation factor for dipole-dipole interaction of the luminophores, 〈k²〉, the distribution function of the distances between the luminophores f(r_l), the efficiences of energy transfer in the static and dyamic averaging regimes, 〈T〉_s amnd 〈T〉_d, as well as the fluorescence decay I(t) of the donor luminophore in various averaging conditions, are computed. It is shown that, for all chains considered, 〈k²〉 is not vary far form 0.67 and that 〈T〉_s and 〈T〉_d have completely different values. Due to the small extent of correlation between the distances r_l and the mutual orientations of the lumninophores, the decay kinetics 〈I(t)_s corresponding to a static averaging regime can be expressed in terms of distribution functions f(r_l). These results are in agrrement with those obtained previously for the unperturbed chain model.     

Calculation of the energy confinement time and power threshold for L-H transitions in a tokamak with allowance for the parameters of the transport barrier

The ASTRA-ETL code is used to simulate L-H transition scenarios and calculate the energy confinement time and the threshold power of the L-H transition as functions of the averaged electron density 〈n〉, the averaged magnetic field B, the neutral density n _n , and the neutral temperature T _n , as well as the values of T _Se , T _Si , and n _S at the separatrix. It is shown that the linear dependence of the threshold power of the L-H transition on the averaged electron density, Q _L-H∝〈n〉, is associated with an increase in the viscosity of a poloidally rotating plasma due to charge exchange and is governed exclusively by an increase in the neutral density n _n . When the averaged electron density 〈n〉 is low, the threshold power rises because T _Si and T _Se increase. The accuracy of predictions for the power threshold of the L-H transition can be improved if the scaling of Q _L-H versus 〈n〉 and B is derived by processing experimental data from discharges with close parameter values at the separatrix. The hysteresis effect during an L-H-L transition triggered by varying the input power is modeled. The global energy confinement time τ_E is shown to increase linearly with 〈n〉 in the range 〈n〉<3.6×10¹⁹ m^?3 and to saturate at higher electron densities; this behavior is found to be characteristic of the Ohmic, L-, and H-modes. The saturation is associated with the fact that losses via the ion channel (when the transport coefficients are density-independent) dominate over losses via the electron channel. The dependence of τ _E on the input power is determined from the calculated database and is found to be τ _E =0.12Q _L-H ^?0.46 at a fixed averaged electron density 〈n〉. In the simulations of the L-H transition, the energy confinement time τ _E increases by a factor of 2 only if the thermal diffusivity inside the transport barrier is lower than that in the central plasma by a factor of more than 6.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Mean-square hydrophobic moment for partially helical polypeptides

A mean-square helical hydrophobic moment, 〈h²〉, is defined for polypeptides in analogy to the mean-square dipole moment, 〈μ²〉, for polymer chains. For a freely jointed polymer chain, 〈μ²〉 is given by Σm, where m_i denotes the dipole moment associated with bond i. In the absence of any correlations in the hydrophobic moments of individual amino acid residues in the helix, 〈h²〉 is specified by ΣH, where H_i denotes the hydrophobicity of residue i. The tendency for correlations in orientations of residue hydrophobic moments in helices therefore dictates the size of 〈h²〉/〈H²〉, where 〈H²〉 denotes the average value of ΣH for all helices. The value of 〈h²〉/〈H²〉 will be greater than one in amphiphilic helices. A necessary prerequisite for this diagnostic usage of 〈h²〉/〈H²〉 is that the residue hydrophobic moment be oriented prependicular to the principal axis of the helix. Matrix-generation schemes are formulated that permit rapid evaluation of 〈h²〉 and 〈H²〉. The behavior of 〈h²〉/〈H²〉 is illustrated by calculations performed for model sequential copolypeptides.     

Determination of molecular size of O-(2-hydroxyethyl)cellulose (HEC) and its relationship to the mechanism of enzymatic hydrolysis by cellulases

Z-average root mean square end-to-end distance 〈r_o²〉_z^1/2 and radius of gyration 〈s_o²〉_z^1/2 for 13 samples of O-(2-hydroxyethyl)cellulose (HEC) of different molecular weights were derived from Gel Permeation Chromatography and intrinsic viscosity measurements with water as a solvent. At 40 °C and pH 4.5, contraction of chain dimensions is observed, compared with the sizes observed under neutral conditions at room temperature. The effect is lower for samples with higher molecular weights. Values of 〈r_o²〉₄₀/DP_z also indicate that chain flexibility increases at higher temperature and acidic conditions. From the analysis of molecular weight dependence of 〈s_o²〉 _z^1/2, Flory exponent υ was derived at 40 °C and pH 4.5. A value of υ = 0.70 ± 0.02 was recorded, which indicates that a relatively stiff chain is present under these conditions. Finally, different equations to calculate persistence length L_p were evaluated. Values in the range of 260-400 Å were derived for persistence length. Implications of chain conformation in the enzymatic action of cellulases are also discussed.     

Negative-polarity fast ionization wave in molecular gases: Electric field, electron density, and energy branching

The charge density per unit length, the longitudinal component of the electric field, and the electron density behind the front of a fast ionization wave initiated by a nanosecond negative voltage pulse in air, N₂, and H₂ in the 1-to 24-torr pressure range are reconstructed from the experimental data. It is shown that the electron density behind the wave front depends weakly on the sort of gas used and, at relatively high pressures (8–24 torr), is (2–3)×10¹² cm^?3. The energy deposited in the internal degrees of freedom is analyzed. It is shown that, for all gases used, most of the deposited energy (40–60%) is spent on the excitation of the electron degrees of freedom. The fraction of the energy deposited in the high-energy degrees of freedom (ionization and dissociation) monotonically decreases with increasing the pressure, whereas the fraction of the energy spent on the excitation of the low-energy degrees of freedom (rotational and vibrational) monotonically increases.     

Analysis of derivative binding isotherms. Theoretical considerations

The basic theoretical groundwork for the use of derivative binding isotherms in the analysis of ligand binding is presented. The derivative binding isotherm is defined as Γ (Y) = df/dy where f = fractional degree of saturation and y = natural logarithm of the free ligand concentration. Since Γ (y) is a positive function, which goes to zero as y → ±∞, the mean value of y, 〈y〉, and the second and third moments, μ₂ and μ₃ about 〈y〉 are well defined. For a macromolecular system consisting of N equivalent and independent binding sites, Γ (y) is a symmetrical bell-shaped function with one maximum. The maximum occurs when y = ?ln K_assoc; μ₂ = π²/3, and μ₃ = 0. For multiple sets of independent binding sites, Γ (y) is a superposition of Γ-type functions. If the sets are sufficiently well separated in binding free energy, multiple extrema may be seen at positions corresponding to the logarithms of the dissociation constants for the individual sets. In any case, 〈y〉 is equal to the mean value of the logarithms of the dissociation constants for the sets; μ₂ > π²/3 and equal to π²/3 plus the variance of the logarithms of the dissociation constants about their mean value; and μ₃ is, except by coincidence, not equal to zero and equals the third moment of the distribution of logarithms of the dissociation constants about their mean value. Analysis of Γ(y) for the case of cooperative interactions within a set of binding sites was investigated by examining (1) the Hill model (whose mathematical representation is equivalent to that used to describe antibody heterogeneity except that in the latter case the parameter a, the Sips, constant, is constrained (0 < a ≤1);(2) a common model for cooperativity in which the cooperative free energy is a linear function of the fraction bound; and (3) a general representation of cooperative interactions within a set of sites in terms of ?(f), a smooth function that gives the interaction free energy in units of RT. For the Hill model (or Sips model) Γ(y) is a symmetrical function with one maximum at y = (?1)/a)lnK, μ₂ = π²/3a²; and μ₃ = 0. For the case in which the cooperative free energy is a linear function of f [?(f) = cf], 〈y〉 = ?ln K₀ + (c/2); μ₂ = (π²/3) + c[(c/12) + 1] where c > ?4; and μ₃ = 0. General expressions for the moments in terms of ?(f) are derived. In general, μ₂ < (π²/3) for positive cooperativity and μ₂ > (π₂/3) for negative for negative cooperativity. Γ(y) will be symmetrical if and only if the cooperative free energy is introduced symmetrically about f = 0.5.     

Characterization of group C meningococcal polysaccharide by light-scattering spectroscopy. III. Determination of molecular weight, radius of gyration, and translational diffusional coefficient.

Group-specific polysaccharides isolated by means of a cetavlon procedure are immunogenic in man and induce protective immunity against meningococcal meningitis. Minute quantities of the polymers in solution can act as vaccines. We now report the first characterization of a fractionated (C-1) group C polysaccharide in 0.4KM KCl and 0.05M sodium acetate by means of light-scattering spectroscopy. Independent measurements of refractive index increments, absolute scattered intensities, angular scattering intensities and line widths as a function of scattering angles and delay times at different concentrations using incident wavelengths of 632.8 nm from a He–Ne laser and of 488 nm from an argon–ion laser yield information on aggregation properties, molecular weight (M_r), radius of gyration 〈r⁰_g〉^1/2_z, translational diffusion coefficient 〈D〉⁰_z, and second virial coefficients A₂ and B₂ of C-1 polysaccharide. At relatively high ionic strength (0.04M KCl + 0.05M sodium acetate), we obtain for the C-1 polysaccharide in solution M_r = 5.15 × 10⁵, 〈r²_g〉^1/2_z = 345 Å, A₂ = 1.25 × 10^?4 ml/g, 〈D〉 = 1.16 × 10^?7 cm²/sec with a corresponding Stokes radius of 240 Å and B₂ = 4.4 ml/g. A₂ and B₂ are the second virial coefficients from intensity- and diffusion-coefficient measurements. The C-1 polysaccharide aggregates in solution and behaves hydrodynamically like random coils. Viscosity and sedimentation studies further confirm our conclusions that the fractioned C-1 polysaccharide aggregates in solution and EDTA can partially break up those aggregates. However, the system remains polydisperse even after adding an excess amount of EDTA. The weight-average molecular weight of the C-1 polysaccharide in solution depends upon ionic strength and exhibits a minimum at ～0.2M KCl. Finally, viscosity, light-scattering, and sedimentation results all show that the aggregated macromolecular system behaves like random-coiled polymers with no measurable shape factors.     

The orientation of transition moments of dye molecules used in fluorescence studies of muscle systems

Fluorescence and phosphorescence depolarization techniques can provide information on orientational order and rotational motion of crossbridges in muscle fibres. However the depolarization experiment monitors the orientation and motion of the crossbridges indirectly. The changes in depolarization arise from a change in the orientation of the transition dipoles of the dye attached to the crossbridge. In order to extract the physiologically relevant orientations from the data it is therefore necessary to characterize the orientation of the dye molecule relative to the crossbridge and the orientation of the transition moments in the frame of the dyes. The dyes 1,5-1-AEDANS and eosin-5-maleimide are commonly used for labelling the crossbridge in muscle fibres. The orientations of the absorption and fluorescence emission dipoles of these two dyes in the molecular frame were determined. Angle resolved fluorescence depolarization experiments on the dyes, macroscopically aligned in a stretched polymer matrix of poly vinyl alcohol, were carried out. The data were analyzed in terms of an orientational distribution of the dye molecules in the film and the orientations of the absorption and emission dipoles in the frame of the dye molecule. Experimental data, obtained from a given sample at different excitation wavelengths, were analyzed simultaneously in a global target approach. This leads to a reduction in the number of independent parameters optimized by the non-linear least squares procedure.Abbreviations 1,5-I-AEDANS 5-iodoacetamido-ethyl-aminonaphthalene-a-sulfonic acid - IATR iodoacetamido-tetra-methylrhodamine - E5M Eosin-5-Maleimide - ATP adenosine tri phosphate - -ATP 1:N⁶-ethano-ATP - -2-aza-ATP 1:N⁶-etheno-2-aza-ATP - ant-ATP anthraniloyl-ATP     

Solvent Effects on the Shape of a Tetramer

Abstract

The solvent effect on the shape of a tetramer with increasing temperature is analyzed. For this purpose models of an isolated chain and a chain immersed in a solvent have been simulated by Molecular Dynamics. A solvent model represented by stochastic forces has been tested against molecular dynamics results. The behaviour of the mean-square end-to-end distance 〈R ²〉 and 〈l ₁ ³ S ²〉 with increasing temperature are shown. where l ₁ is the longest eigenvalue of the moment of inertia tensor and S is the radius of gyration. All the chain models studied show different behaviour of these quantities at low temperature compared to high temperature where the shape of the tetramer is temperature insensitive. The main solvent effect is to pospone the transition to higher temperature. The stochastic solvent model qualitatively agrees with molecular dynamics results.     

Polarization of fluorescence of an oriented solution of rodlike particles bearing a fluorescent label

The variation of the polarized components of fluorescence of a rodlike particle bearing a fluorescent label upon partial orientation is calculated for some special geometry of the dye macromolecules complexes. Explicit expressions are given for the case where the energy of the molecule in the field depends only on one angle θ, showing that the result is a function of both 〈sin²θ〉 and 〈sin⁴θ〉. For the case of orientation in an electric field through an anisotropic induced moment, the expressions allow the calculation of this anisotropy of polarizability. The method is applied to the measurement of the polarizability of rodlike fragments of DNA labeled by intercalated molecules of Acridine Orange.     

Measurement of diffusion coefficients of meningococcal polysaccharide by optical mixing spectroscopy. I. A preliminary characterization on the aggregation of the group C polysaccharide

The angular distribution of scattered intensity and decay times of concentration fluctuations have been measured by means of digital photon counting and single-clipped photon correlation for solutions of Group C meningococcal polysaccharides at 31°C. The z-average diffusion coefficient 〈D〉_z and its second moment 〈D²〉_z have been determined from the time-dependent correlation function using the cumulant expansion technique. Very low observed values of 〈D〉_z and the tremendous width of the polydispersity index, which is the z-average normalized variance, suggest a higher degree of aggregation than the monomer–dimer type self-association at finite concentrations.     

Solution properties of synthetic polypeptides. V. Helix–coil transition in poly(β-benzyl L-aspartate)

Simple approximate expressions have been derived from the theory of Zimm and Bragg for use in the analysis of experimental data on the helix-coil transition in polypeptide. On the basis of the resulting expressions practical procedures are proposed to determine two basic parameters characterizing a thermally induced transition, i.e., helix initiation parameter σ and enthalpy change for helix formation, ΔH. They have been applied to the data for poly(β-benzyl L -aspartate) (PBLA) with the result: σ = 1.6 × 10^?4 and ΔH = ?450 cal/mole for PBLA in m-cresol; σ = 0.6 × 10^?4 and ΔH = 260 cal/mole for PBLA in chloroform containing 5.7 vol-% of dichloroacetic acid. This result gives evidence that σ may change not only from one polypeptide to another but also for a given polypeptide in different solvents. The change in limiting viscosity number [η] accompanying the transition was measured in the same solvents. The curve of [η] versus helical content had a relatively monotonic shape for the chloroformdichloroacetic acid solutions as compared with that for the m-cresol solutions, indicating that [η] depended largely on σ. Provided that [η] is a direct measure of the mean-square radius of gyration, 〈S²〉, the results are consistent with the theoretical predictions of Nagai and of Miller and Flory for 〈S²〉.     

Mean-square helical hydrophobic moments in partially ordered proteins

Helical hydrophobic moment ratios, 〈h²〉/〈H²〉, have been evaluated for 34 polypeptides under conditions where the helix content is dictated solely by the short-range interactions operative in aqueous media. The mean-square helical hydrophobic moment is denoted by 〈h²〉, and 〈H²〉 is the averaged of the squared hydrophobicites. This ratio would be one in absence of any correlation in the hydrophobicities of amino acid residues in helices. The 〈h²〉/〈H²〉 tend to be substantially larger than values of the analogous ratio formulated for the mean-square dipole moments of typical synthetic polymers. For 24 of the 34 polypeptide chains considered, 〈h²〉/〈H²〉 is found to be greater than one, indicating a tendency to form helices with amphiphilic character. The ratio is exceptionally large in the case of the δ-hemolysins. It is also large for two other surface-active peptides, for two of the four apolipoproteins examined, and for myohemerythrin. A much smaller 〈h²〉/〈H²〉 is found for melittins. If melittins is to form helices with large 〈h²〉/〈H²〉, the configurational statistics must be governed by effects in addition to those short-range interactions that occur when water is the solvent.     

Cooperative response of chemically excitable membrane. II. Two-state models and their limitations

Various types of two-state models, classified by the type of direct receptorionophore coupling, were formulated based on the previously presented generalized two-state model of cooperativity (Kijima &; Kijima, 1978) and their dose-response relationships were examined. Hill coefficient at the mid-point of dose-response curve n_H^o the measure of the cooperativity of curves, is restricted for partial agonists in any two-state models because n_H^o is expressed by the product of two terms, one of which decreases when the other increases. In the independent gating unit model in which the channel opens only when the independent gating units are all in the activated state, the restriction of n_H^o is the most stringent: it never exceeds 2. In 2 ÷ 1·39 even for full agonist. It appears to be incompatible with most of the cooperative responses observed on chemically excitable membrane. In the basic model or one protomer-one channel model, n_H^o never exceeds 2·0 when 〈p〉_∞, the maximum fraction of open-channel, is less than $\text{2}\text{3}$. In the cooperative gating unit model, n_H^o is the least restricted, which is less than 2·8 when 〈p〉_∞ ≤ 0·5, but if the number of gating units, N in a receptor is practically reasonably small (N ≤ 12), n_H^o ≤ 2·0 when 〈p〉_∞ ≤ 0·58. It is discussed whether or not several representative drug-receptive membranes can be accounted for by two-state models. Response of the insect sugar receptor is out of the above limitations of two-state models and can be accounted for by three-state model. The origin of cooperative interaction can be inferred by the shapes of dose-response curves. Cooperative dose-response curves of two dimensional lattices or oligomerc systems with large number of protomers weakly interacting by long range forces bend upward more markedly at lower region than the curves of strongly interacting oligomers, when curves with the same n_H^o are compared.     

Base sequence effects in double-helical DNA. II. Configurational statistics of rodlike chains

Matrix generator techniques have been adapted to account for precise structural features of the nucleotide repeating unit and to translate the primary sequence of DNA base pairs into three-dimensional structures. Chains have been constructed to reflect the local sequence-dependent differences of bending and twisting of adjacent residues and various overall chain properties, including the average unperturbed moments of the end-to-end vector r and the mean angular orientation (〈γ〉 between base pair normals, 〈?₁〉 between long axes, and 〈?₂〉 between short axes) of terminal chain residues, have been computed. The chain backbone is treated implicitly in terms of the spatial fluctuations of successive base pairs. Motions are limited to low-energy perturbations of the standard B-DNA helix. Approximate potential energy schemes are used to represent the rules governing the patterns of local base–base morphology and flexibility. Theoretical predictions are compared with experimental observations at both the local and the macro-molecular level. Initial applications are limited to the rodlike poly(dA) · poly(dT) and poly(dG) · poly(dC) helices. The former duplex is found to be more compressed and the latter more extended than random-sequence DNA of the same chain length. The flexibility of the duplexes as a whole is described in terms of the average higher moments of the displacement vector ρ = r - 〈r〉 and the likelihood of chain cyclization is estimated from the three-dimensional Hermite series expansions of the displacement tensors. Emphasis is placed on theoretical methodology and the practical relevance of the calculated chain moments to observed physical properties.     

The kinetics of protein-protein recognition

We examine a simple kinetic model for association that incorporates the basic features of protein-protein recognition within the rigid body approximation, that is, when no large conformation change occurs. Association starts with random collision at the rate k_coll predicted by the Einstein-Smoluchowski equation. This creates an encounter pair that can evolve into a stable complex if and only if the two molecules are correctly oriented and positioned, which has a probability p_r. In the absence of long-range interactions, the bimolecular rate of association is p_r k_coll. Long-range electrostatic interactions affect both k_coll and p_r. The collision rate is multiplied by q_t, a factor larger than 1 when the molecules carry net charges of opposite sign as coulombic attraction makes collisions more frequent, and less than 1 in the opposite case. The probability p_r is multiplied by a factor q_r that represents the steering effect of electric dipoles, which preorient the molecules before they collide. The model is applied to experimental data obtained by Schreiber and Fersht (Nat. Struct. Biol. 3:427–431, 1996) on the kinetics of barnase-barstar association. When long-range electrostatic interactions are fully screened or mutated away, q_tq_r ≈1, and the observed rate of productive collision is p_r k_coll ≈10⁵ M⁻¹ · s⁻¹. Under these conditions, p_r ≈1.5 · 10⁻⁵ is determined by geometric constraints corresponding to a loss of rotational freedom. Its value is compatible with computer docking simulations and implies a rotational entropy loss ΔS_rot ≈ 22 e.u. in the transition state. At low ionic strength, long-range electrostatic interactions accelerate barnase-barstar association by a factor q_tq_rof up to 10⁵ as favorable charge-charge and charge-dipole interactions work together to make it much faster than free diffusion would allow. Proteins 28:153–161, 1997. © 1997 Wiley-Liss Inc.     

The nucleic acid distribution function: evaluation of the loop closure probability

We present a detailed theoretical study of nucleic acid distance distribution functions for chain lengths up to thirty-five nucleotides. The distribution functions were found by the Monte Carlo techniques described previously and, where they are symmetric, by reconstruction from their even moments. A comparison of the two approaches allows an assessment of the utility of expansion procedures for stiff chains (C_∞ ≈ 17), as a function of length and extension. It was found that for chains with fewer than fourteen nucleotides over seventy even moments were required to obtain a reliable function for extensions R ≥ (〈R²〉)^1/2. On the other hand at thirty-five nucleotides the first ten even moments were sufficient to reconstruct the distribution for all but extreme extensions. The other feature of the calculation is the prediction of a loop weighting function. It was found that for a thirty-five nucleotide chain, the form of the distribution function is very nearly gaussian for R < (〈R²〉)^1/2. Consequently a loop weighting function based on detailed crystallographic data is now known for all values of N. The first derivative of the function is within 8% of the Jacobson-Stockmayer value at 170 nucleotides, but differs severely from the latter for chains with less than twenty nucleotides.     

Monte Carlo simulations of structure and entanglements in polymer melts

Atomistic models of short chain branched (SCB) polyethylene melts have been equilibrated at 450 K using a connectivity altering Monte Carlo method. Quantities related to the chain dimensions and entanglements have been determined. The simulated tube diameters, 〈a_pp〉, of SCB melts are found to scale with the backbone weight fraction, ?, as 〈a_pp〉～?^? 0.46, close to the scaling predicted by the binary contact model, 〈a_pp〉～?^? 0.5. Similar relationships are observed experimentally for polymer solutions, and reproduced by the present methods.     

NMR study of the structure of short-chain peptides in solution.

The electron-mediated spin–spin coupling constant J between the amide NH and the α-CH protons in the dipeptide fragment C^α? CO(NH? C^αH)R? C′ONH? C^α is dependent on the dihedral angle of rotation (Φ) around the N? C bond. Measurement of J in a series of zwitterionic dipeptides H₃N⁺? CHR₁? CONH? CHR₂? CO₂^? (which is conformationally similar to the dipeptide fragment) in TFA solution shows that J is independent of R₁, but dependent on the steric bulk of R₂. The data are interpreted in terms of a model that assumes that what we measure is an average value of J? a thermal average over all the possible rotamers. The groups R₁ and R₂ are, in most cases, sterically kept apart by the trans and planar amide bonds, and hence the independence of J of R₁. This model is consistent with the theoretical calculations done on the dipeptide fragment. The effect of the structural characteristics of the side chains (e.g., the effect of lengthening and branching the side chains) on the J values in dipeptides is discussed in the light of the existing results of theoretical calculations. Study of 〈J〉 values in tripeptides (C₆H₅CH₂OCONH? CHR₁? CONH? CHR₂? CO₂CH₃, essentially three linked peptide units) shows that electrostatic interaction between the two amide bonds modifies the potential energy surface and the 〈J〉 value of a dipeptide subunit in the tripeptides. Also in some cases, direct steric interaction between the two side chains in the two adjacent dipeptide subunits in the tripeptide affects the potential energy surfaces of the individual dipeptide subunits and hence the 〈J〉 values. The influence of the structural characteristics of the side chains of individual amino acids on structure formation at or beyond the dipeptide level is discussed at various points. The J(NH? ^αCH) values of CH₃CONH? CHR? CONH₂ and CH₃CONH? CHR? CO₂CH₃ with the same R are quite different for R = valine, leucine, phenylalanine, methionine, but equal for R = glycine. This, coupled with the fact that one of the carboxamide NH resonances has a chemical shift different from its counterpart in simple amides like CH₃CONH₂ and the other carboxamide NH has the same chemical shift as its counterpart in CH₃CONH₂, suggest the presence of a hydrogen bond in dipeptide CH₃CONH? CHR? CONH₂ with carboxamide NH as the donor. Theoretical evidence for two seven-membered hydrogen-bonded rings with the carboxamide NH as donor and the acetyl oxygen as acceptor is summarized. Our data cannot suggest the number of such hydrogen-bonded rings, nor can they conclude the relative proportion of these rings in a particular dipeptide. A discussion of the difficulty of interpretation is presented and the data are discussed under certain simplifying assumptions.