Showing papers in "Biopolymers in 1978"

Ellipsometry as a tool to study the adsorption behavior of synthetic and biopolymers at the air–water interface

Abstract: The application of ellipsometry of the study of the adsorption behavior of proteins and synthetic macromolecules at the air-water interface has been investigated. It is shown that for macromolecules the amount adsorbed per unit area, Γ, as determined by ellipsometry, only has a well-defined physical meaning if the refractive-index increment remains constant up to high concentrations present in the adsorbed layer. It has been found experimentally that this conditioned is fulfilled for proteins. The ellipsometric Γ values of some protein agree satisfactorily with those obtained by two independent techniques has been used to investigate the adsorption from solution of κ-casein, bovine serum albumin, and polyvinyl alcohol. For bovine serum albumin, Γ reaches a plateau value of 2.9 mg/m2 for concentrations ≥ 0.05 wt%. The thickness of the adsorbed molecules. For κ-casein, Γ steadily increases with increasing centration and multilayers are formed. The technique provides interesting information on conformational changes in adsorbed macromolecules, on the rate of the process, and on the conditions under which these occur.

Statistical mechanical deconvolution of thermal transitions in macromolecules. I. Theory and application to homogeneous systems

Abstract: The theoretical basis for the statistical mechanical deconvolution of a thermally induced macromolecular melting profile is presented. It is demonstrated that all the thermodynamic quantities characterizing a multistate macromolecular transition can be obtained from the average excess enthalpy function, 〈ΔH〉, of the system, without any assumption of the particular model or mechanism of the reaction. Experimentally, 〈ΔH〉 is obtained from scanning calorimetric data by direct integration of the excess apparent molar heat capacity function, ΦCp. Once 〈ΔH〉 is known as a continuous function of the temperature, the partition function, Q, of the system can be calculated by means of the equation From the partition function all the thermodynamic quantities of the system can be obtained. It is shown that the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.

Boundary analysis of sedimentation‐velocity experiments with monodisperse and paucidisperse solutes

Abstract: A method is presented which allows one to calculate a distribution of sedimentation coefficients from the boundries of sedimentation-velocity experiments with mono- or pauci-disperse solutes. With two solutes differences in S value as small as 20% can be resolved. In absence of heterogeneity and concentration-dependent effects, the analysis also provides values for the diffusion coefficient within an accuracy of −10 to +5%. Tests with both simulated data and ultracentrifugation experiments on short DNA fragments show the value and the limitations of the method.

Fluorescence correlation spectroscopy. III. Uniform translation and laminar flow

Abstract: We extend fluorescence correlation spectroscopy to systems that undergo translation or laminar flow in a sample cell. We include theoretical and experimental results; we consider uniform and nonuniform velocity profiles. Concentration correlation analysis extracts microscopic rate parameters from measurements of the spontaneous concentration fluctutations, which occur even at equilibrium. Fluorescence is one of the most sensitive means of monitoring these fluctuations. Analysis of flowing or translating systems (1) offers a method of measuring number concentrations of selected species, for example, of aggregates or polymers, (2) provides a nonperturbing velocity probe, (3) sometimes allows one to circumvent photolytic degradation, (4) has proved extremely helpful in testing and aliging apparatus for fluorescence correaltion measurement and in verifying theoretical analyses, and (5) may be required for interpretation of results obtained on systems in motion, even though that motion is undesired or initially unsuspected. We include both theoretical and experimental results for combined Poiseuille flow and diffusion in the geometry which is of most practical interest. Theoretical expressions for the much simpler cases of nondiffusive Poiseuille flow as well as uniform flow or translation with or without diffusion constitute limiting cases which are displayed explicitly.

Studies on protein folding, unfolding, and fluctuations by computer simulation. II. A. Three‐dimensional lattice model of lysozyme

Abstract: A three-dimensional lattice model of protein designed to assimilate lysozyme is introduced. An attractive interaction is assumed to work between preassigned specific pairs of units, when they occupy the nearest-nighbor lattice points. The behavior of this lattice lysozyme is studied by a Monte Carlo simulation method. Because of the specific interunit interactions,“native state” of the lattice lysozyme is stable at low temperatures. Conformational fluctuations in the native state are observed to occur at both termini and loop regions of the main chain existing on the surface. The process of unfolding and denatured states of this model are discussed. Complete refolding from a denatured state was not observed. However, by starting from partially folded structures, the native conformation could be attained. From these observation it is concluded that, in the process of folding of proteins as simplified in a lattice model, nulceation is a rate-limiting factor. The artificial character of this model and possible improvement are discussed.

Influence of local interactions on protein structure. I. Conformational energy studies of N‐acetyl‐N′‐methylamides of pro‐X and X‐pro dipeptides

Abstract: Conformational energy calculations using an Empirical Conformational Energy Program for Peptides (ECEPP) were carried out on the N-acetyl-N′-methylamides of Pro-X, where X = Ala, Asn, Asp, Gly, Leu, Phe, Ser, and Val, and of X-Pro, where X = Ala, Asn, Gly, and Pro. The conformational energy was minimized from starting conformations which included all combinations of low-energy single-residue minima and several standard bend structures. It was found that almost all resulting minima are combinations of low-energy single-residue minima, suggesting that intra residue interactions predominate in determining conformation. The calculations also indicate, however, that inter residue interactions can be important. In addition, librational entropy was found to influence the relative stabilities of some minima. Because of the existence of 10–100 low-energy minima for each dipeptide, the normalized statistical weight of an individual minimum rarely exceeds 0.3, suggesting that these dipeptides have considerable conformational flexibility and exist as statistical ensembles of low-energy structures. The propensity of each dipeptide to form bend conformations was calculated, and the results were compared with available experimental data. It was found that bends are favored in Pro-X dipeptides because ϕPro is fixed by the pyrrolidine ring in a conformation which is frequently found in bends, but that bends are not favored in X-Pro dipeptides because interactions between the X residue and the pyrrolidine ring restrict the X residue to conformations which are not usually found in bends.

Aromatic side-chain contributions to the far ultraviolet circular dichroism of peptides and proteins

Abstract: The rotational strength of the La transition in phenylalanine and tyrosine side chains has been calculated for dipeptides with various backbone and side-chain conformations. Similar calculations have also been performed for tripeptides in the β-turn conformation with aromatic residues at the corners of the turn. The interaction of the aromatic ring with neighboring peptides generates rotational strengths in the La transition of the order of 0.1 Debye-Bohr magneton. When the preferred backbone and side-chain conformations are considered, it is found that the most probable conformations have positive La bonds. This result accounts for the observation that the N-acyl amino acid amides of L-Tyr and LPhe have positive La bands. It also suggests that, although other interactions may affect the numerical value and even the sign, there will be a significant positive contribution to the rotational strength of aromatic residues in globular proteins from nearest-neighbor interactions. Calculations on proteins of known conformation at the nearest-neighbor level confirm the tendency toward positive La contributions for Phe and Tyr residues. This contribution can be of the order of 10% of the observed CD even in proteins with rather strong amide contributions. In some proteins, such as the gene 5 protein from bacteriophage fd and many snake-venom toxins, side-chain contributions from Tyr and Trp residues manifest themselves as positive CD bands in the 225–250-nm region. The magnitude of the nearest-neighbor contributions and the trend toward positive contributions are consistent with the observation of such CD bands in globular proteins. No special stacking interaction among aromatic side chains needs to be invoked.

Brownian motion of the ends of oligopeptide chains in solution as estimated by energy transfer between the chain ends

Abstract: The kinetics of the fluorescence decay of the energy donor in a homologous series of oligopeptides each containing at its ends a donor and an acceptor of electronic excitation energy was investigated in solvent mixtures of different viscosities. The repeating unit in the peptides was N5-(2-hydroxyethyl)-L-glutamine and the chromophores used as donor and acceptor were naphthalene and dansyl, respectively. The number of units in the peptides studied varied from four to nine. The solvents used were mixtures of glycerol and trifluoroethanol in various proportions. The decay rate of the donor fluorescence increases when the solvent viscosity decreases. This behavior is due to the disturbance of the equilibrium end-to-end distribution of distance of the excited molecules by the energy transfer process, which is more favorable foe short than for long distances. The subsequent rearrangement towards the equilibrium distribution by diffusion of the molecular ends relative to one another enhances the efficiency of the energy transfer. Assuming a modified Fick equation to describe this diffusion motion, the fluorescence decay data were analyzed in terms of a diffusion coefficient describing the Brownian motion of the molecular ends. The diffusion coefficients thus evaluated increase systematically upon decreasing the solvent viscosity. For example, for the oligopeptides studied it changes from unmeasurably small values in glycerol solution to values varying between 10−8 to 10−7 cm2/sec at room temperature in a glycerol trifluoroethanol solvent mixture of viscosity of 8 centipoise. The values obtained for the diffusion coefficient are smaller by about an order of magnitude than the values expected for the diffusion coefficients of the free chromophores in solvents of comparable viscosity. It is thus concluded that the backbone of the polymeric chains possesses appreciable internal friction which exerts resistance to the Brownian motion of the polymer chains. The diffusion coefficient of the end-to-end motion is systematically smaller for the shorter than for the longer chains. For example, at room temperature in a solvent mixture of 8 centipoise it is 3×10−8, 5×10−8, 7.6×10−8, and 8.5×10−8 cm2/sec for oligomers containing four, five, eight, and nine N5-(2-hydroxylethyl)-L-glutamine repeating units, respectively. The internal friction thus impedes the motion of the molecular ends more effectively in the shorter chains than in the longer ones. Analysis of the energy-transfer experiments in solvents spanning a wide range of viscosities shows that the orientational factor appearing in Forster's equation for energy transfer does not interfere perceptibly with the evaluation of the end-to-end distances from the fluorescence decay data when naphthalene and dansyl serve as donor and acceptor, respectively. This is due to the fact that both the donor emission and acceptor absorption in the range of spectral overlap are characterized by more than one transition dipole moment, as is evident from the corresponding polarization data.

An optimized potential function for the calculation of nucleic acid interaction energies. I - Base stacking

Abstract: An optimized potential function for base-stacking interaction is constructed. Stacking energies between the complementary pairs of a dimer are calculated as a function of the rotational angle and separation distance. Using several different sets of atomic charges, the electrostatic component in the monopole-monopole approximation (MMA) is compared to the more refined segmented multipole–multipole representation (SMMA); the general features of the stacking minima are found to be correctly reproduced with IEHT or CNDO atomic charges. The electrostatic component is observed to control the location of stacking minima. The MMA, in general, is not a reliable approximation of the SMMA in regions away from minima; however, the MMA is reliable in predicting the location and nature of stacking minima. The attractive part of the Lennard-Jones 6–12 potential is compared to and parameterized against the expression for the second-order interaction terms composed of multipole-bond polarizability for the polarization energy and transition-dipole bond polarizabilities for approximation of the dispersion energy. The repulsive part of the Lennard-Jones potential is compared to a Kitaygorodski-type repulsive function; changing the exponent from its usual value of 12 to 11.7 gives significantly better agreement with the more refined repulsive function. Stacking minima calculated with the optimized potential method are compared with various perturbation-type treatments. The optimized potential method yields results that compare as well with melting data as do any of the more recent and expensive perturbation methods.

Brownian motion of highly charged poly(L-lysine). Effects of salt and polyion concentration

Abstract: The Brownian motion of a single sample of high-molecular-weight poly(L-lysine) [(Lys)n, n = 955] has been studied by dynamic light scattering over a wide range of NaBr concentrations and at three different polyion concentrations. A substantial decrease in scattered intensity is associated with the transition from the ordinary phase to the low-salt extraordinary phase. At the salt concentration where the transition takes place the relaxations are non-exponential and appear to exhibit at all angles a rapid relaxation (τ ≅ 10 μsec) that is presumed to be a manifestation of the kinetics of the transition process. The K2 dependence of the slow relaxation rates in the extraordinary phase has been confirmed within the experimental error. The extrapolated infinite-dilution values of the diffusion coefficients in the ordinary phase are observed to decline precipitously below 10−2M salt to astonishingly small values, indicating a dramatic rise in the friction factors of the isolated polyions. An extensive discussion of these findings in relation to the theory employed here and to existing data in the literature is also given.

Carbon‐13 NMR chemical shifts of the common amino acid residues measured in aqueous solutions of the linear tetrapeptides H‐Gly‐Gly‐ X‐L‐ Ala‐OH

Abstract: The 13C nmr chemical shifts of the common amino acid residues were measured in D2O solutions of the linear tetrapeptides H-Gly-Gly-X-L-Ala-OH. For Asp, Glu, Lys, Tyr and His, the titration shifts arising from the ionization of te amino acid side chains were also obtained. These data are compared with the corresponding 13C chemical shifts in the protected tetrapeptides CF3CO-Gly-Gly-X-L-Ala-OCH3, the linear pentapeptides H-Gly-Gly-X-Gly-Gly-OH, and the free amino acids. On this basism the selection of suitable “random coil” 13C chemical shifts for conformational studies of polypeptides chain is discussed.

Packaging of DNA in bacteriophage Heads: Some considerations on energetics

Abstract: We have made quantitative estimates of some of the energetic factors to be considered in packaging of double-stranded DNA in virus particles. Numerical calculations were made using parameters appropriate for T4 bacteriophage. The unfavorable factors, and the Gibbs free energies per mole virus at 20°C associated with them, are bending, 1.5 × 103 kcal/mol; conformational restriction upon condensation, 5.1 × 102 kcal/mol; polyelectrolyte repulsion, 2.1 × 105kcal/mol; and melting or kinking, 6.9 × 103 kcal/mol. These must be counterbalanced in the assembled phage by noncovalent bonding interactions between protein subunits in the phage-head shell; by interactions between the DNA and polyvalent cations, especially putrescine and spermidine; nad perhaps by repulsive excluded volume and electrostatic interaction between the DNA and acidic polypeptides. Indeed, a rough estimate of the standard free energey of interaction between T4 DNA and the putrescine and spermidine contained in the head is --2.1 × 105 kcal/mol. In the absence of the other two sources of stabilization, each head protein subunit must contribute about 210 kcal/mol of binding energy.

Analysis of the 1H‐NMR spectra of ferrichrome peptides. I. The non‐amide protons

Abstract: The thus far unexplored aliphatic region of the proton magnetic resonance spectra of ferrichrome peptides was investigated at 360 MHz. Six isomorphic diamagnetic analogues of the ferric cyclohexapeptide differing in the coordinated cation (AL3+ or Ga3+) and the amino acid composition were studied in d6-DMSO solution. By use of a novel resolution enhancement technique which applies a sinusoidal half-wave window to the free induction decay combined with multiplication by an increasing exponential, the proton chemical shifts and spin-spin couplings were accurately measured. Homonuclear decoupling combined with Fourier difference spectroscopy was used to selectively extract resonances out of crowded spectral regions. The spectra revealed unique features of fine structure in the proton resonance lines. Thus, the conformation-dependent geminal coupling constants of glycyl α-protons were found to be constant throughout the suite of analogue peptides. A similar invariance was observed for the vicinal coupling constants between α-, β-, γ-, and δ-protons in the ornithyl side chains. Comparison of the proton spin–spin coupling constants with the crstallographic dihedral angles led to a unique stereochemical assignment of the side-chain resonances. The combined data sets of x-ray atomic coordinates and 1H-nmr spin-spin coupling parameters have been used to calibrate the coefficients for a Karplus curve related to the torsional x angles in amino acid side chains: Structurial information was also obtained for the seryl residues, where the multiplet structures of the OH resonances indicate preferred spatial arrangements of the side chains.

Hydrophobic interaction and a model for the elasticity of elastin.

Abstract: The thermodynamics of the elastic process in the rubberlike protein elastin have been investigated by microcalorimetery. The results indicate that the reversible heat liberated upon the extension of water-swollen elastin at room temperature is much largerthan the stored elastic energy, indicating a large than the stored elastic energy, indicating a large, negative internal energy change for stretching. The ratio of the measured internal energy change to the stored energy varies inversely wiht extension, and at 22° C it is −91 for 2% extension and −3 for 70% extension. The interanl energy change also varies dramatically with temperature over the range of 2–65° C it is zero. The temperature dependence for internal energy change is virtually identical to the temperature dependence for internal energy changes associated with the breaking of hydrophobic interactions, and it is suggested that the measured internal energy change can be attributed entirely to hte absorption of water onto nonpolar groups in the elastin network. Calculatons based on this assumption indicate that the free-energy change associated with this solvent–polymer process is large and positive. It is concluded that the absorption of water onto hydrophobic groups contributes to the elasticity of elastin, particularly at extensions of less than about 70%. The implications of this elastic mechanism are discussed in terms of the random-network model for elastin structure.

Water--collagen interactions: calorimetric and mechanical experiments.

Abstract: The influence of hydration of rat-tail tendons has been studied by measuring the heat involved in the water fixation deplending on the degree of hydration. The modulus and damping dependences have been measured when changing the temperature for different water uptakes. In situ hydrations have been realized. Evidence of several states of water absorption has been dervied from both calorimetic and dynamic mechanical experiments. A model has been proposed taking into account the energies corresponding to the different regimes of fixation.

A semiempirical extension of polyelectrolyte theory to the treatment of oligoelectrolytes: Application to oligonucleotide helix‐coil transitions

Abstract: The interaction of counterions with a suitably long, charged oligomer appears susceptible to treatment in the context of polyelectrolyte theory by the introduction of an end-effect parameter that reflects the reduced association of counterions with the terminal regions of the oligo-ion. Use of a physically reasonable value for the end-effect parameter provides excellent agreement between theory and the experimental data of Elson, Scheffler, and Baldwin [J. Mol. Biol.54, 401–415 (1970)] on the dependences of melting temperature on salt concentration and chain length for a series of hairpin helices formed by d(TA) oligomers. The differences in behavior expected for hairpin, dimer, and oligomer-polymer helices are discussed. The salt dependence of the end-joining equilibrium investigated for λ DNA by Wang and Davidson [Cold Spring Harbor Symp. Quant. Biol.33, 409–415 (1968)] is treated as an oligomer–polymer interconversion. The dependence of equilibrium constant for this reaction on counterion concentration is in good agreement with that predicted by theory for an end-region totalling 24 nucleotides, the known length of the λ ends.

A Monte Carlo study of the amylosic chain conformation

Abstract: Monte Carlo studies of the unperturbed amylosic chain conformation have been carried out in the approximation of separable chain configuration energies. Sample chains of arbitrary chain length have been generated so as to be distributed consistent with refined estimates of the configuration energy and thus suitable for evaluation of averages of the desired configuration-dependent properties. Perspective drawings of representative chains from the Monte Carlo sample have been made for comparison with standard idealizations of amylosic chain conformation. He molecular model employed generates a randomly coiling chain possessing perceptible regions of left-handed pseudohelical backbone trajectory. Distribution functions for the end-to-end distance of short amylosic chains disclose some propensity for the chain to suffer self-intersections at sort range in the chain sequence, which may vitiate the usual amylosic chain models based on the assumed independence of sets of glycosidic linkage torsion angles. The amylosic persistence vector and persistence length have been calculated as a function of chain length for the chain model employed.

Interaction of alcohols with proteins

Abstract: The kinetics of denaturation of egg albumin have been determined for methanol, ethanol, propanol, and butanol. The reactions are first order in respect to protein but between 11th and 18th order for the alcohols. The denaturation reaction is characterized by a large temperature coefficient with little or no dependence on pH. There is a marked change of pH when proteins are denatured. A series of eight proteins has been studied. There is surprisingly little difference in susceptibility to alcohol denaturation between the various proteins. Methanol, ethanol, propanol, and butanol are strongly bound to egg albumin—butanol being the most strongly bound. The binding of alcohol is probably accompanied by protein dehydration. The polyhydric alcohols' behavior is much different. These alcohols do not denature proteins and the protein is hydrated. Sucrose produces the greatest degree of hydration.

Analysis of the 1H‐NMR spectra of ferrichrome peptides. II. The amide resonances

Abstract: The high-resolution 1H-nmr study of the ferrichrome cyclohexapeptides, in d6-DMSO solutions, has been extended to the amide NH spectral region. A total of ten diamagnetic analogues of ferrichrome that differ in the coordinated metal ion (Al3+, Ga3+ or Co3+), the primary structure, the nature of the bidentate hydroxamate moiety, or the isotope compositions (14N, 15N) have been investigated. The 3JαNH values reflect regiorous conformational isomorphism throughout the complete suite of analogues, quite independent of the residue occupancy of each site. Totally resolved amide multiplets have been obtained in most cases and the four-line (doublet of doublets) appearances of glycyl NH resonances has been observed for the first times; these data enabled stereospecific assignment and accurate analysis of the NH-CαH proton spin systems. The high resolution was made possible by the use of a suitable spectral deconvolution shceme at 360 MHz. The fine structure, extraordinarily well displayed in the 15N-peptide spectra, provides a series of parameter values whose consistency has been checked by computer simulation. Since the crystallographic structure for two of the ferric peptides is known to 0.002-A resolution, a 3J vs θ correspondence could be confidently established. A Karplus curve was derived from the combined x-ray and nmr data: It is suggested that seriously nonplanar amides can exhibit 3JαNH values higher than predicted by the ferrichrome curve.

Polyelectroyte behavior of a bacterial polysaccharide from Xanthomonas campestris: Comparison with carboxymethylcellulose

Abstract: The main physicochemical properties of the polysaccharide called Xanthan produced by Xanthomonas compestris are discussed: the activity coefficient of the counter-ion, the pK(α), and the ionic selectivity are investigated and compared to those of a carboxymetholcellulose. The weight-average molecular weight (Mw = 2 × 106), the intrinsic viscosity and the constant of sedimentation are determined as a function of the ionic strength. It is proved that in dilute solution, there is no intermolecular association, whatever the ionic strength. The conformation is proposed to be a rigid rodlike molecule whose length is 6000 A, independent of ionic strength > 10−2N.

Solid-phase synthesis of somatostatin and glucagon-selective analogs in gram quantities

Abstract: Somatostatin (SS) and two glucagon selective analogs [D-Cysl4]-SS and [D-Trp8, D-Cys14]-SS have been synthesized in gram quantities by the solid-phase procedure. A general modification of Monahan and Gilon's procedure for esterification of the first protected amino acid onto the chloromethylated resin as well as a general protocol for solid-phase peptide synthesis on Beckman 990 automatic synthesizer are described. A new general procedure for disulfide formation, which involves the adaptation of the “high-dilution” principle to the ferricyanide oxidation and the optimization of the sequence of purification steps as applied to somatostatin and its analogs, yields highly purified peptides (≥ 199% pure) as checked by reverse-phase high-pressure liquid chromatography—which is shown to be a highly sensitive, resolutive, and quantitative analytical tool for evaluation of the homogeneity of peptides.

Opticohydrodynamic properties of high‐molecular‐weight DNA. III. The effects of NaCl concentration

Abstract: Excluded volume and persistence length of high-molecular-weight DNA from T2 bacteriophage have been evaluated over a range of NaCl concentrations from 0.005 to 2.0M using low-shear flow-birefringence and intrinsic-viscosity data. Uncertainty in persistence length due to ambiguity in the assignment of intrinsic birefringence has been avoided by calibrating the data at 0.2M NaCl using a recently reported persistence-length value based upon photon correlation spectroscopy [Jolly, D. & Eisenberg, H. (1976) Biopolymers15, 61]. Results at high salt concertrations are in satisfactory agreement with other estimates of excluded volume and chain flexibility in the literature, but at very low salt concentrations they reflect greater chain expansion than has heretofore been reported. The extinction-angle data imply a transition from a nondraining chain with excluded volume at 0.1M NaCl to an almost freely draining chain at 0.005M NaCl. Over this same salt range, the experimental persistencelength data agree very well with Flory's thermodynamic chain-expansion theory [Flory, P. J. (1953) J. Chem. Phys. 21, 162], but are in generally poor agreement with other theoretical treatments. A detailed comparison of the results with other data in the literature suggests that the combined flow-birefringence-intrinsic-viscosity technique employed here may be more sensitive to the distribution of chain stiffness and excluded volume in polyelectroytechain expansion of DNA than are othe rhydrodynamic methods such as sedimentation or intrinsic viscosity alone.

Determination of the number of cross‐links in a protein gel from its mechanical and swelling properties

Abstract: The relation between the chemical structure of a protein and the physical properties of a heat-set gel of that protein has been investigated. The physical properties of the gel are determined by means of mechanical experiments in which the viscoelastic properties of the gel are determined in terms of the storage shear modulus, the loss modulus and the stress-strain curve. The storage shear modulus defined the solid (elastic) character of the gel. The chemical structure of the protein and the nature of the solvent determine the nature and number of cross-links in the gel. The cross-links in gels formed by heating concentrated solutions of ovalbumin in 6M urea solutions were found to be disulfide bridges and the mechanical properties of these ovalbumin/urea gels approximated those of an ideal rubber. The latter finding enables one to calculate the number of cross-links per ovalbumin molecule from the value of the storage modulus, using the classical theory of rubber elasticity. This theory, together with the Flory-Huggins lattice model, can also be used to calculate the number of cros-links per ovalbumin molecule from the swelling behavior of ovalbumin/urea gels. The number of cross-links per ovalbumin molecule calculated from these two types of experiments are in mutual agreement and correspond with the number of thiol groups in ovalbumin. We conclude, thereforee, that theories of polymer physics can be used to relate the chemical structure of a protein to the physical properties of its gel.

Different families of double‐stranded conformations of DNA as revealed by computer calculations

Abstract: An algorithm has been developed that permits one to find all possible conformations of the sugar-phosphate backbone for any given disposition of DNA base pairs. For each of the conformations thus obtained, the energy of the helix was calculated by the method of atom-atom potentials. Several isolated regions in the space of the bases′ parameters (Arnott's parameters) have been found for energetically favorable helical structures. Two parameters, the distance of a base pair from the helix axis, D, and the windling angle, τ, allow one to subdivide possible conformations into the families of closely related forms. Two regions (ravines) on the (D, τ) map correspond to the know A and B families. In the B family a continuous transition has been obtained in which the double helix undergoes increasing winding, while the base pairs are moving toward the major (nonglycosidic) groove. Interrelationships between the variables, characterizing the spatial structure of the double helix, D, τ, TL and χ, when going along the bottom of the B ravine, were also obtained. Besides the Known A and B families, several new ones were found to be energetically possible. Among these the strongly underwound helices with the negative D values, as well as the forms with the C4-C5 angle in a trans position, should be mentioned. Biological roles of the different double-stranded conformations, in particular, in protein-nuclei acid interaction are discussed.

Collagen fibrils and elastic fibers in rat-tail tendon: an electron microscopic investigation.

Abstract: Earlier studies by the authors showed that the collagen fibrils in rat-tail tendon have a bi-modal distribution of fibril diameters from a time shortly after birth through to the onset of maturity at about 3–4 months. Present work has extended those observations for rats up to the age of 2 years. Histograms of the fibril diameter distributions for mature tail tendon and direct electron microscope observations show that the fibrils break down as the tendon ages. Further work on the constant diameter subfibrils of diameter 140 A described previously, has confirmed that these are part of the elastic fibers present in tendon at all ages. It has been shown that there is relatively little variation in the collagen fibril diameter distribution as a function of the position of the specimen in the tail, and as the measured percentage of the area taken by the collagen fibrils present at any particular point. Estimation of the fibrillar collagen content of rat-tail tendon as a function of age indicates that it increases steadily from birth and reaches a maximum at the onset of maturity, beyond which the fibrillar collagen content appears to remain constant.

Dynamic light‐scattering studies of internal motions in DNA. I. Applicability of the rouse‐zimm model

Abstract: The intermediate scattering function G(K,t) for any polymer model obeying a linear separable Langevin equation can be expressed in terms of the eigenvalues and eigenvectors of its normal coordinate transformation. An algorithm for the extract numerical evaluation of G(K,t) for linear Rouse-Zimm chains in the presence of hydrodynamic interaction has been developed. The computed G(K,t)2 were fit to C(t) = A exp(−t/τA) + B, and apparent diffusion coefficients calculated according to Dapp ≡ 1/(2τAK2). G(K,t)2 was surprisingly well-fit by single-exponential decays, especially at both small and large values of Kb, where K is the scattering vector and b the root-mean-squared subunit extension. Plots of Dapp vs K2 in-variably showed a sigmoidal rise from D0 at K2 = O up to a constant plateau value at large K2b2. Analytical expression for G(K,t), exact in the limit of short times, were obtained for circular Rouse-Zimm chains with and without hydrodynamic interaction, and also for free-draining linear chains, and in addition for the independent-segment-mean-force (ISMF) model. The predicted behaviors for G(K,t) at large Kb (or KRG) was found in all cases to be single-exponential with 1/τ ∝ K2 at large Kb, in agreement with the computational results. A simple procedure for estamating all parameter of the Rouse-Zimm model from a plot of Dapp vs K2 is proposed. Experimental data for both native and pH-denatured calf-thymus DNA in 1.0M Nacl with and without EDTA clearly plateau behavior of Dapp at large values of K, in harmony with the present Rouse-Zimm and ISMF theories, and in sharp contrast to previous predictions based on the Rouse-Zimm model.

Statistical mechanical deconvolution of thermal transitions in macromolecules. II. General treatment of cooperative phenomena

Abstract: In the preceding article1 we demonstrated that the partition function of a system is experimentally accessible from scanning calorimetric data. In this article the general results of the deconvolution theory are applied to the general case of cooperative transitions in macromolecules. It is demonstrated that, in the limit of very large systems, all the relevant molecular averages and molecular distribution functions can be directly obtained from the experiment. In doing this, the method of the grand partition function is used. It is shown that in the case of homopolymers, only one parameter, the stability constant, needs to be explicitly specified for a complete description of the system. Since the partition function is directly evaluated from the experiment, no special assumptions or artificial constraints directed to obtain a mathematically solvable model are required. This result offers the unique opportunity of having direct experimental access to statistical averages of systems in which the partition function cannot analytically be solved. Consequently, the theory can be extended to cooperative transitions occurring in two and three dimensions by introducing cluster distribution functions.

Hydrodynamic properties of macromolecular complexes. IV. Intrinsic viscosity theory, with applications to once‐broken rods and multisubunit proteins

Abstract: We have extended our previous theories of the translational and rotational frictional properties of multisubunit complexes to calculate the intrinsic viscosity of such structures. Our theory is similar to those recently construced by McCammon and Deutch, and by Nakajima and Wada, in that it uses a modified hydrodynamic interaction tensor and solves the system of simultaneous interaction equations by digital computation rather than by successive approximations. However, there are some differences in the formulation and averaging of these equations. Extensive numerical comparison is made between this theory and others that are available—associated with the names of Hearst and Tagami, Abdel-Khalik and Bird, and Tsuda—using as a basis exact results for prolate ellipsoids of revolution. For large axial ratios, only our theory asymptotically approaches the correct limit; but for small axial ratios, only the Tsuda “shell-model” theory is adequate, because the other theories neglect the preponderant influence of the sphere located at the center of rotation. Intrinsic viscosities, translational frictional coefficients, and Scheraga-Mandelkern β parameters, are tabulated for a large number of polygonal and polyhedral subunit structures, with up to eight elements, using both our theory and Tsuda's. Particular application is made to hemerythrin and aspartate transcarbamylase. Finally, the viscosities and friction coefficients o once-broken rods are calculated and compared with an approximate theory by Wilenski.

1H‐15N Spin–spin couplings in alumichrome

Abstract: We report the determination of two- and three-bond 1H-15N spin–spin couplings in the nmr spectra of a polypeptide. The 1H- and 15N-nmr spectra of 99.2% 15N-enriched alumichrome have been studied at 360 MHz and 10.1 MHz, repectively. While some 2J and 3J coupling are of the order of 5 Hz, most splitting resulting from the heteronuclear interaction are ≲2 Hz, which introduces strigent requirements of spectral resolution. In the 1H spectra these requirements were met by digital deconvolution with a sine bell routine combined with positive exponential filtering. Although the 15N spectra clearly exhibit features of fine structure, mainly because of the intrinsic higher nmir sensitivity of protons, observation of 1H-15N spin–spin couplings was found to be more practical in the 1H than in the 15N spectra. We find that the alumichrome data do not satisfy a simple cyclic relationship linking the heteronuclear couplings to the crystallographic ψ dihedral angles. It is suggested that a formal treatment of the ψ-related interresidue 1H-15N coupling might have to take into account a more complex dependence of the intervening 3J on the overall local electronic structure, which is dependent on ϕ,ψ, and ω simultaneoulsy. In contrast, our analysis indicates that χ1 can be readily determined from the measurement of the corresponding heteronuclear 3J coupling in the 1Hβ or in the amide 15N resonances. Karplus relationships are proposed that relate this heteronuclear 3J to the corresponding dihedral angle θ and which, on average, yield