Analysis of fractal properties of globular protein surfaces by means of small-angle x-ray scattering]

The "cube method" [M. Yu. Pavlov, B. A. Fedorov, Biopolymers, 22, 1507, 1983] has been used to calculate the intensity of the large-angle X-ray scattering from the volumes of several globular proteins. In the logarithmic plots of the scattered intensity curves from three of these proteins, there is a linear region at scattering angles corresponding to Bragg distances of from about 6.3 A to 21 A. This linear region possibly may be due to the fractal properties of the surfaces of these proteins on length scoles from 6.3 A to 21 A, and the fractal dimensions corresponding to the power-law scattering at these scattering angles have been evaluated.     

SAXSMoW 2.0: Online calculator of the molecular weight of proteins in dilute solution from experimental SAXS data measured on a relative scale

Knowledge of molecular weight, oligomeric states, and quaternary arrangements of proteins in solution is fundamental for understanding their molecular functions and activities. We describe here a program SAXSMoW 2.0 for robust and quick determination of molecular weight and oligomeric state of proteins in dilute solution, starting from a single experimental small‐angle scattering intensity curve, I(q), measured on a relative scale. The first version of this calculator has been widely used during the last decade and applied to analyze experimental SAXS data of many proteins and protein complexes. SAXSMoW 2.0 exhibits new features which allow for the direct input of experimental intensity curves and also automatic modes for quick determinations of the radius of gyration, volume, and molecular weight. The new program was extensively tested by applying it to many experimental SAXS curves downloaded from the open databases, corresponding to proteins with different shapes and molecular weights ranging from ~10 kDa up to about ~500 kDa and different shapes from globular to elongated. These tests reveal that the use of SAXSMoW 2.0 allows for determinations of molecular weights of proteins in dilute solution with a median discrepancy of about 12% for globular proteins. In case of elongated molecules, discrepancy value can be significantly higher. Our tests show discrepancies of approximately 21% for the proteins with molecular shape aspect ratios up to 18.     

Fluorescence of proteins in aqueous neutral salt solutions. II. Influence of monovalent cation chlorides, particularly cesium chloride.

The effects of varying concentrations of monovalent cation chlorides on the fluorescence of nine proteins were studied. These are discussed in terms of “direct” or “indirect” interactions with the aromatic amino acid residues. Cs⁺ is the only cation that quenches fluorescence of proteins due to “direct” interaction with aromatic amino acid residues. Quenching is due to collisional processes. An agreement with the Stern-Volmer relationship is shown and the values of [(K_Q)eff] and [(f_a)eff] are calculated. These values confirm that the fraction of fluorescence accessible to Cs⁺ belongs to the “exposed” fluorophors. The mechanism of quenching by Cs⁺ is due to the heavy-atom effect because phosphorescence enhancement is also seen at the same time. The chlorides of Na⁺, K⁺, Rb⁺, NH₄⁺, and Li⁺ do not have a similar effect on the fluorescence of all proteins. For a given protein a gradation of the same effect (i.e., quenching or dequenching) is seen. Interactions with factors that “inderectly” affect fluorescence of any protein are involved and the structural features of the protein are responsible for such “indirect” effects. The results indicate that neutral salts can act in more than one manner. The changes in fluorescence are indicative of electrostatic and lyotropic effects of ions. Only electrostatic interactions which occur in the vicinity of tryptophan in proteins are reflected. Li⁺ shows strong interactions with proteins. In 4 M LiCl, BSA, papain, and trypsin show fluorescence changes that are indicative of changes in protein structure.     

Moments of the distribution of the amino acid residues in tertiary structures of globular proteins

Moments of the distributions of the C^α and “side-chain atoms” and associated properties were examined in 22 globular proteins, considered as statistical aggregates of atoms. Although the distributions are generally anisotropic, the densities of the evaluated distributions are highly uniform in the interior of a single protein, as well as among the proteins investigated. The tertiary structure of proteins is characterized by a compact and uniform distribution of amino acids, independent of their molecular weight and hydrophobic character, and by an isotropic distribution of the virtual bond directions in the polypeptide folding. While the general uniformity of the density of distributions in the bulk of proteins can be justified by the architectural requirements of high thermodynamic stability, significant differences in the distribution of the C^α with respect to the “side-chain atoms” suggest a plausible explanation of the general anisotropic morphology of the proteins. The invariance of the density of distributions allows easy recognition of proteinlike domains in more complex proteins and suggests a practical way to predict the following path in single proteins.     

The effect of deuterium oxide on the stability of the collagen model peptides H‐(Pro‐Pro‐Gly)10‐OH,H‐(Gly‐Pro‐4(R)Hyp)9‐OH,and Type I collagen

The collagen triple helix has a larger accessible surface area per molecular mass than globular proteins, and therefore potentially more water interaction sites. The effect of deuterium oxide on the stability of collagen model peptides and Type I collagen molecules was analyzed by circular dichroism and differential scanning calorimetry. The transition temperatures (T_m) of the protonated peptide (Pro‐Pro‐Gly)₁₀ were 25.4 and 28.7°C in H₂O and D₂O, respectively. The increase of the T_m of (Pro‐Pro‐Gly)₁₀ measured calorimetrically at 1.0°C min^?1 in a low pH solution from the protonated to the deuterated solvent was 5.1°C. The increases of the T_m for (Gly‐Pro‐4(R)Hyp)₉ and pepsin‐extracted Type I collagen were measured as 4.2 and 2.2°C, respectively. These results indicated that the increase in the T_m in the presence of D₂O is comparable to that of globular proteins, and much less than reported previously for collagen model peptides [Gough and Bhatnagar, J Biomol Struct Dyn 1999, 17, 481–491]. These experimental results suggest that the interaction of water molecules with collagen is similar to the interaction of water with globular proteins, when the ratio of collagen to water is very small and collagen is monomerically dispersed in the solvent. © 2009 Wiley Periodicals, Inc. Biopolymers 93: 93–101, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Receptor-Agonist Interactions in Service-Theoretic Perspective,Effects of Molecular Timing on the Shape of Dose-Response Curves

Service-theoretic concepts and methods, widely used in other fields (e.g., telecommunication and operations research), are useful also in a biochemical setting because the treatment of biocatalysts (enzymes, receptors) as servers and their ligands as customers, based on the established formal methods of service or queuing theory, may lead to insights and results unobtainable by conventional, mass-action-law-based theories. In this article, we apply the service-theoretic approach to receptor-agonist systems and show how by changing the stochastic time pattern of “operationally relevant” point events (e.g., instants of agonist arrival, instants of postclimax agonist departure) a great variety of dose-response curves may be generated, even in very simple reaction schemes, which, according to mass action kinetics, invariably lead to hyperbolic r(A) curves (r and A stand for response and agonist concentration, respectively). The molecular timing inherent to a hyperbolic response system is not optimal: for instance, at the agonist concentration A₅₀, half of the agonist molecules are rejected (“lost”) because of unfortunate timing of the arrival events. The fraction of lost arrivers can be diminished considerably if the arrivals are better timed: “sub-Poisson” arrivals improve the timing and, thus, convert hyperbolic r(A) curves into “lifted” nonhyperbolic ones. Conversely, “super-Poisson” arrivals make the nonoptimal timing in hyperbolic response systems even worse and, thus, convert hyperbolic r(A) curves into “depressed” nonhyperbolic ones. Furthermore, under special timing conditions, nonhyperbolic r(A) curves can be generated, which are partly lifted, partly depressed relative to the reference hyperbola, and which resemble in shape well-known nonhyperbolic forms of enzyme and receptor kinetics (negatively cooperative, positively cooperative, and sigmoidal kinetics). In addition unusual (undulatory and sawtooth-like) r(A) curves can be generated solely by changing the temporal pattern of arrival and service completion instants. Virtually any shape of dose-response curves may be obtained by allowing for probability distributions whose characteristic shape varies with their mean; we call such distributions “variomorphic” and apply them to the arrival process of agonist molecules.     

Structural mapping of the coiled‐coil domain of a bacterial condensin and comparative analyses across all domains of life suggest conserved features of SMC proteins

The structural maintenance of chromosomes (SMC) proteins form the cores of multisubunit complexes that are required for the segregation and global organization of chromosomes in all domains of life. These proteins share a common domain structure in which N‐ and C‐ terminal regions pack against one another to form a globular ATPase domain. This “head” domain is connected to a central, globular, “hinge” or dimerization domain by a long, antiparallel coiled coil. To date, most efforts for structural characterization of SMC proteins have focused on the globular domains. Recently, however, we developed a method to map interstrand interactions in the 50‐nm coiled‐coil domain of MukB, the divergent SMC protein found in γ‐proteobacteria. Here, we apply that technique to map the structure of the Bacillus subtilis SMC (BsSMC) coiled‐coil domain. We find that, in contrast to the relatively complicated coiled‐coil domain of MukB, the BsSMC domain is nearly continuous, with only two detectable coiled‐coil interruptions. Near the middle of the domain is a break in coiled‐coil structure in which there are three more residues on the C‐terminal strand than on the N‐terminal strand. Close to the head domain, there is a second break with a significantly longer insertion on the same strand. These results provide an experience base that allows an informed interpretation of the output of coiled‐coil prediction algorithms for this family of proteins. A comparison of such predictions suggests that these coiled‐coil deviations are highly conserved across SMC types in a wide variety of organisms, including humans. Proteins 2015; 83:1027–1045. © 2015 Wiley Periodicals, Inc.     

Intrinsic structural disorder of mouse proNGF

The unprocessed precursor of the Nerve Growth Factor (NGF), proNGF, has additional functions, besides its initially described role as a chaperone for NGF folding. The precursor protein endows apoptotic and/or neurotrophic properties, in contrast to the mature part. The structural and molecular basis for such distinct activities are presently unknown. Aiming to gain insights into the specific molecular interactions that govern rm‐proNGF biological activities versus those of its mature counterpart, a structural study by synchrotron small angle X‐ray scattering (SAXS) in solution was carried out. The different binding properties of the two proteins were investigated by surface plasmon resonance (SPR) using, as structural probes, a panel of anti‐NGF antibodies and the soluble forms of TrkA and p75^NTR receptors. SAXS measurements revealed the rm‐proNGF to be dimeric and anisometric, with the propeptide domain being intrinsically unstructured. Ab initio reconstructions assuming twofold symmetry generated two types of structural models, a globular “crab‐like” and an elongated shape that resulted in equally good fits of the scattering data. A novel method accounting for possible coexistence of different conformations contributing to the experimental scattering pattern, with no symmetry constraints, suggests the “crab‐like” to be a more likely proNGF conformation. To exploit the potential of chemical stabilizers affecting the existing conformational protein populations, SAXS data were also collected in the presence of ammonium sulphate. An increase of the proNGF compactness was observed. SPR data pinpoints that the propeptide of proNGF may act as an intrinsically unstructured protein domain, characterized by a molecular promiscuity in the interaction/binding to multiple partners (TrkA and p75^NTR receptors and a panel of neutralizing anti‐NGF antibodies) depending on the physiological conditions of the cell. These data provide a first insight into the structural basis for the selectivity of mouse short proNGF, versus NGF, towards its binding partners. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Accessible and total molecular surfaces of unsmooth protein globules

A method for the calculation of accessible and total molecular surfaces of protein globules is proposed. It is based on consideration of structuring of protein globule surface. As a whole, the protein globule is approximated by ellipsoids. By computer imitations, the areas of accessible and total molecular surfaces as well as the volumes for 58 globular proteins were calculated. The calculation showed that the best agreement between the calculated areas and volumes and the experimental results is obtained at the radii of protein surface structures of 1-2 A.     

Learning about protein folding via potential functions

Over the last few years we have developed an empirical potential function that solves the protein structure recognition problem: given the sequence for an n-residue globular protein and a collection of plausible protein conformations, including the native conformation for that sequence, identify the correct, native conformation. Having determined this potential on the basis of only some 6500 native/nonnative pairs of structures for 58 proteins, we find it recognizes the native conformation for essentially all compact, soluble, globular proteins having known native conformations in comparisons with 10⁴ to 10⁶ reasonable alternative conformations apiece. In this sense, the potential encodes nearly all the essential features of globular protein conformational preference. In addition it “knows” about many additional factors in protein folding, such as the stabilization of multimeric proteins, quaternary structure, the role of disulfide bridges and ligands, proproteins vs. processed proteins, and minimal strand lengths in globular proteins. Comparisons are made with other sorts of protein folding problems, and applications in protein conformational determination and prediction are discussed. © 1994 Wiley-Liss, Inc.     

Structural principles of the globular organization of protein chains. A stereochemical theory of globular protein secondary structure

The paper reveals the types of amino acid sequences of polypeptide chain regions of globular protein which form a regular (α or β) or irregular conformation in the native globule. The study was made taking into account general “architectural” principles of packing of polypeptide chains in globular proteins and considering the interactions of proteins with water molecules. An a priori theory is developed which permits the identification, in good agreement with experiment, of α-helical and β-structural regions in globular proteins from their primary structure.     

Protein Structures and Neutral Theory of Evolution

Abstract

The neutral theory of evolution is extended to the origin of protein molecules. Arguments are presented which suggest that the amino acid sequences of many globular proteins mainly represent “memorized” random sequences while biological evolution reduces to the “editing” these random sequences. Physical requirements for a functional globular protein are formulated and it is shown that many of these requirements do not involve strategical selection of amino acid sequences during biological evolution but are inherent also for typical random sequences. In particular, it is shown that random sequences of polar and unpolar amino acid residues can form α-helices and β-strands with lengths and arrangement along the chain similar to those in real globular proteins. These α- and β-regions in random sequences can form three-dimensional folding patterns also similar to those in real proteins. The arguments are presented suggesting that even the tight packing of side groups inside protein core do not require very strong biological selection of amino acid sequences either. Thus many structural features of real proteins can exist also in random sequences and the biological selection is needed mainly for the creation of active sites of proteins and for their stability under physiological conditions.     

Multistep Brownian dynamics: application to short wormlike chains

Brownian dynamics simulations of short wormlike chains are carried out using the method of Ermak and McCammon [(1978) J. Chem. Phys. 69 , 1352–1360]. Following Hagerman and Zimm [(1981) Biopolymers 20 , 1481–1502], the wormlike chain is modeled as a string of beads. In each simulation, the dynamic evolution of an ensemble of 100 randomly generated chains is calculated for a period of from 3 to 200 ns. Two different “experiments,” fluorescence depolarization and dynamic light scattering, were performed in these simulations. Since we are primarily interested in the bending motions and not the torsional motions in this work, we have placed the transition moments along the local symmetry axis of the wormlike chain in the fluorescence depolarization “experiment.” As predicted by the Barkley and Zimm theory [(1979) J. Chem. Phys. 70 , 2991–3008], a considerable amount of rapid bending motion was detected by fluorescence depolarization, though not as much as predicted by theory. We conclude that these differences are primarily due to differences between the model used in the theory and the simulations. The light-scattering experiment was found to be insensitive to internal motion in the low scattering angle limit.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

Determination of the accessible surface of globular proteins by means of tritium planigraphy

Results are presented for proteins with known three-dimensional structure (lysozyme, myoglobin, ribonuclease), which show that the probability of label incorporation upon bombardment by hot tritium atoms may be quantitatively linked with the surface area of the protein accessible to water molecules. Possible deviations from simple linear dependency caused by particular mechanisms of label introduction are discussed. The data obtained in experiments with model systems were used to determine the accessible surface area of human serum albumin, for which structural data is not sufficiently accurate to allow estimation of accessible surface area. Experimental data correlate reasonably well with estimations based on conventional concepts of the relationship between accessible surface area and molecular weight for globular proteins. Correspondence to: A. V. Volynskaya     

Dilute solution properties of proteoglycan fractions from bovine nasal cartilage

Fresh proteogycans (adult bovine nasal cartilage) isolated from the densest portion of a dissociative density gradient had a weight-average molecular weight of ca. 10⁶ in 4M guanidine hydrochloride (GdnHCI) by light scattering. Fractions of such material obtained by elution with 4M GdnHCI from 2% agarose gel, both normal and cross-linkd, has proteoglycan subunit molecular weights ranging from 0.8 to 2.6 × 10⁶ and root-mean-square radii ranging from 35 to 52 nm in the same solvent. The protein molecular weight per proteoglycan subunit was about 1.2 × 10⁵ and that of keratan sulfate about 1.8 × 10⁵, both independent of total molecular weight. A random-flight “graft copolymer” model having uniform side chains of chondroitin sulfate (40 disaccharides) and keratan sulfate (15 disaccharides) and a random-coil polypeptide back bone was used to estimate the unperturbed radius, whihc was about 19 nm for a mol wt of 1.5 × 10⁶. Experimental light-scattering data for fractions were fitted very well by theoretical curves for the particale scattering factor for both linear and appropriate branched polymers. Examination of coil expansion on the basis of perturbation calculations for branched polymer models suggested that expansion did not account for the experimentally observed radii in terms of unperturbed radii calculated from the model. A possible explanation is that substantial local stiffening of the polypeptide chain due to substitution of side-chain clusters increases the unperturbed radii. The intrinsic viscosity [η] is 4M GdnHCI ranged from 120 to 180 ml/g, and could be interpreted in terms of th eequivalent sphere model; the Flory number has approximately its normal value for flexible linear polymers. The treatment of the sedimentation coefficient by this is less successful, since the Man delkern-Flory parameter β apparently increases with increasing molecular weight; average value are similar to those for flexible polymers, but the variation in β makes this method useful only for rough estimation of molecular weight of proteoglycans. Molecular weights of purified proteoglycans are the same in 0.2M NaCI as in 4M GdnHCI, while crude preparations gave higher molecular weights in 0.2M NaCI, probably because of association due to incomplete removel of “linking” proteins.     

Effect of the fluctuations in electron density within a globular protein on the excess small-angle X-ray scattering

Excess small angle X-ray scattering in solvents of differing electron density has been calculated from the crystal structures obtained for rubredoxin, trypsin inhibitor, myogen, ferricytochrome c₂, ribonuclease S, lysozyme, nuclease, myoglobin, α-chymotrypsin, elastase, subtilisin, carboxypeptidase A, thermolysin, methemoglobin, deoxyhemoglobin, and a single polypeptide chain of M₄ lactate dehydrogenase. The scattering curves for each protein can be reproduced by the sum of three curves, with the weighting of the three curves depending on the electron density of the solvent. The radius of gyration obtained from the small angle X-ray scattering by globular proteins in aqueous solution will usually exceed the values defined by the shape of the macromolecule. Deviations for certain of the proteins cited are calculated to be as large as 6%. These deviations arise from the tendency for the amino acid residues with low electron density to be situated closer to the center of the protein than the amino acid residues of high electron density. An upper limit of 19% is obtained for the discrepancy between the radius of gyration defined by the shape of a spherical globular protein of typical amino acid composition and the apparent radius of gyration measured for that protein in water by small angle X-ray scattering.     

Distribution of amino acid residues and residue-residue contacts in molecular chaperones.

The amino acid distribution and residue-residue contacts in molecular chaperones are different when compared to normal globular proteins. The study of molecular chaperones reveals a different surrounding environment to exist for the residues Cys, Trp, and His which may play an important role in determining the chaperone structures. Unlike globular proteins, it has been observed that a one-to-one correspondence between the amino acid distribution in a sequence and the structures of molecular chaperones. The preference of amino acid residues surrounding all 20 types of residues in secondary structures and their accessible surface areas have been analysed.     

The "block" approach in x-ray diffusion dispersion as a method of studying the packing of secondary structure elements in globular proteins

To calculate large angle scattering intensity of biopolymers in solution a "block" method of modeling the globular proteins structures is suggested: conformation of protein alpha-helical and beta-structural parts are described in detail, whereas the remaining part of the macromolecule is substituted by a continuum with homogeneous electron density. A comparison of large-angle scattering curves on the basis of the "block" method and the exact structure was made for a number of alpha-helical and beta-structural globular proteins. It is shown that there is a qualitative agreement between the "exact" and model curves.