Effect of sequence-specific interactions on the stability of helical conformations in polypeptides

A modification of the Zimm–Bragg two-state model for the helix–coil transition in polypeptides, which considers the effect of charge–dipole, charge–charge, and other specific interactions on helix stability, is presented. The new model introduces a series of adjustable parameters whose values are estimated by fitting to recent spectroscopic results on medium-sized peptides. This formalism, based on traditional two-state helix–coil transition models, provides a framework in which data on the helix contents of peptides of specific sequence can be rationalized by a statistical mechanical theory.     

Validity of the "two-state" hypothesis for conformational transitions of proteins

The theory, character, and properties of cooperative transitions are developed with special reference to the abrupt changes of state which occur in protein solutions. Comparisons of helix–coil processes and protein conformational reactions show that though cooperation dominates both of these processes, there are important differences. Tests of two types for the validity of the two-state approximation are presented with specific applications to proteins. Available experimental evidence demonstrates that the thermally induced reversible transitions of ribonuclease, α-chymotrypsin, and chymotrypsinogen A under conditions thus far examined are two-state processes.     

Theory of protein secondary structure and algorithm of its prediction

A molecular theory of protein secondary structure is presented that takes account of both local interactions inside each chain region and long-range interactions between different regions, incorporating all these interactions in a single Ising-like model. Local interactions are evaluated from the stereochemical theory describing the relative stabilities of α- and β-structures for different residues in synthetic polypeptides, while long-range effects are approximated by the interaction of each chain region with the averaged hydrophobic template. Based on this theory, an algorithm of protein secondary structure prediction is proposed and examples are given of “blind” predictions made before the x-ray structural data became available.     

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.     

Contributions of Gaussian curvature and nonconstant lipid volume to protein deformation of lipid bilayers

An elastic model for membrane deformations induced by integral membrane proteins is presented. An earlier theory is extended to account for nonvanishing saddle splay modulus within lipid monolayers and perturbations to lipid volume proximal to the protein. Analytical results are derived for the deformation profile surrounding a single cylindrical protein inclusion, which compare favorably to coarse-grained simulations over a range of protein sizes. Numerical results for multi-protein systems indicate that membrane-mediated interactions between inclusions are strongly affected by Gaussian curvature and display nonpairwise additivity. Implications for the aggregation of proteins are discussed.     

Theory of protein molecule self-organization. II. A comparison of calculated thermodynamic parameters of local secondary structures with experiments

Constants of the helix–coil transition for all natural amino acid residues are evaluated on the basis of thermodynamic parameters obtained in paper I of this series. The specific effects at the termini of the helices are also considered as well as the parameters controlling the formation of β-bends in the unfolded protein chain. Evaluated s constants of the helix–coil transition agree with the experimental data on helix–coil transitions of synthetic polypeptides in water. Only a very qualitative correlation exists between s constants (both experimental and theoretical) and the occurrence of corresponding residues in internal turns of α-helices in globular proteins: residues with s > 1 occur in helices as a rule more often than residues with s < 1. At the same time a direct correlation is demonstrated between theoretical parameters of residue incorporation into α-helical termini and β-bends in an unfolded polypeptide chain and the occurrence of residues in corresponding positions of the globular protein secondary structures.     

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.     

Nonadditivity in the alpha-helix to coil transition

The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.     

Libraries of atomic multipole moments for precise modeling of electrostatic properties of amino acids

Summary Contemporary theoretical models used in describing electrostatic properties of amino acids in polypeptides rely usually on atomic point charges. Recently noted defects of such models in reproducing protein folding originate from the inadequate representation of the electrostatic term, in particular inability of atomic charges to account for local anisotropy of molecular charge distribution. Such defects could be corrected by multicenter multipole moments derived directly from any high quality quantum chemical wavefunctions. This is illustrated by comparison of monopole and multipole electrostatic interactions between some amino acids within glutathione S-transferase.High quality Point Charge Models (PCM) can be derived analytically from multipole moment databases. Preliminary results suggest that torsional potentials are controlled by electrostatic interactions of atomic multipoles.Examples illustrating various uses of multicenter multipole moment databases of protein building blocks in modeling various properties of amino acids and polypeptides have been described, including calculation of molecular electrostatic potentials, electric fields, interactions between amino acid residues, estimates of pK_a shifts and changes in catalytic activity induced by amino acid substitutions in mutated enzymes.     

Experimental evidence that the membrane-spanning helix of PufX adopts a bent conformation that facilitates dimerisation of the Rhodobacter sphaeroides RC-LH1 complex through N-terminal interactions

The PufX polypeptide is an integral component of some photosynthetic bacterial reaction center-light harvesting 1 (RC-LH1) core complexes. Many aspects of the structure of PufX are unresolved, including the conformation of its long membrane-spanning helix and whether C-terminal processing occurs. In the present report, NMR data recorded on the Rhodobacter sphaeroides PufX in a detergent micelle confirmed previous conclusions derived from equivalent data obtained in organic solvent, that the α-helix of PufX adopts a bent conformation that would allow the entire helix to reside in the membrane interior or at its surface. In support of this, it was found through the use of site-directed mutagenesis that increasing the size of a conserved glycine on the inside of the bend in the helix was not tolerated. Possible consequences of this bent helical structure were explored using a series of N-terminal deletions. The N-terminal sequence ADKTIFNDHLN on the cytoplasmic face of the membrane was found to be critical for the formation of dimers of the RC-LH1 complex. It was further shown that the C-terminus of PufX is processed at an early stage in the development of the photosynthetic membrane. A model in which two bent PufX polypeptides stabilise a dimeric RC-LH1 complex is presented, and it is proposed that the N-terminus of PufX from one half of the dimer engages in electrostatic interactions with charged residues on the cytoplasmic surface of the LH1α and β polypeptides on the other half of the dimer.     

Helix propensities of the amino acids measured in alanine-based peptides without helix-stabilizing side-chain interactions.

Helix propensities of the amino acids have been measured in alanine-based peptides in the absence of helix-stabilizing side-chain interactions. Fifty-eight peptides have been studied. A modified form of the Lifson-Roig theory for the helix-coil transition, which includes helix capping (Doig AJ, Chakrabartty A, Klingler TM, Baldwin RL, 1994, Biochemistry 33:3396-3403), was used to analyze the results. Substitutions were made at various positions of homologous helical peptides. Helix-capping interactions were found to contribute to helix stability, even when the substitution site was not at the end of the peptide. Analysis of our data with the original Lifson-Roig theory, which neglects capping effects, does not produce as good a fit to the experimental data as does analysis with the modified Lifson-Roig theory. At 0 degrees C, Ala is a strong helix former, Leu and Arg are helix-indifferent, and all other amino acids are helix breakers of varying severity. Because Ala has a small side chain that cannot interact significantly with other side chains, helix formation by Ala is stabilized predominantly by the backbone ("peptide H-bonds"). The implication for protein folding is that formation of peptide H-bonds can largely offset the unfavorable entropy change caused by fixing the peptide backbone. The helix propensities of most amino acids oppose folding; consequently, the majority of isolated helices derived from proteins are unstable, unless specific side-chain interactions stabilize them.     

Design of stable α‐helices using global sequence optimization

The rational design of peptide and protein helices is not only of practical importance for protein engineering but also is a useful approach in attempts to improve our understanding of protein folding. Recent modifications of theoretical models of helix‐coil transitions allow accurate predictions of the helix stability of monomeric peptides in water and provide new possibilities for protein design. We report here a new method for the design of α‐helices in peptides and proteins using AGADIR, the statistical mechanical theory for helix‐coil transitions in monomeric peptides and the tunneling algorithm of global optimization of multidimensional functions for optimization of amino acid sequences. CD measurements of helical content of peptides with optimized sequences indicate that the helical potential of protein amino acids is high enough to allow formation of stable α‐helices in peptides as short as of 10 residues in length. The results show the maximum achievable helix content (HC) of short peptides with fully optimized sequences at 5 °C is expected to be ～70–75%. Under certain conditions the method can be a powerful practical tool for protein engineering. Unlike traditional approaches that are often used to increase protein stability by adding a few favorable interactions to the protein structure, this method deals with all possible sequences of protein helices and selects the best one from them. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.     

Correlation between computed conformational properties of cytochrome c peptides and their antigenicity in a T-lymphocyte proliferation assay

By means of conformational energy calculations, we previously showed that the antigenic strength of a series of oligopeptides (derived from the carboxyl terminal sequence of cytochrome c) in a T-lymphocyte proliferation assay depends on their ability to adopt the α-helix conformation. Using experimentally determined statistical weights (within the framework of the Zimm–Bragg theory for the helix–coil transition), here we present a simple free energy analysis of the ability of these peptides to adopt the α-helix conformation in water. The experimental statistical weights have been modified to include the effect of long-range charge–dipole interactions on helix stability. We find that there is a close correlation between the tendency of a peptide to adopt the α-helix conformation and its ability to stimulate antigen-primed T cells. The shortest peptide with a tendency to adopt the α-helix conformation is also the shortest one that exhibits antigenic activity. The rapid and simple method presented here can thus be used to predict relative antigenicities for different peptides derived from cytochrome c.     

The thermal denaturation of nonpolymerizable alpha alpha-tropomyosin and its segments as a function of ionic strength

Nonpolymerizable tropomyosin (NPTm) is found to unfold thermally at high ionic strength almost exactly as the parent protein, but it does not aggregate at low ionic strength. Thus, NPTm can be used as a tropomyosin surrogate whose coiled-coil structural stability can be probed by varying the ionic strength. Studies of NPTm by CD show that increasing ionic strength stabilizes the coiled-coil structure. CD spectra over a wide range of helix content, obtained by varying either temperature or ionic strength, show an isodichroic point at 203 nm, suggesting a local, residue-level, two-state model. At given temperature, such a local helix in equilibrium random equilibrium suggests ln [phi h/(1-phi h)] = A1 + A2In, wherein phi h is the fraction helix, and A1, A2, and n are constants. In the low ionic strength region, theoretical limiting laws for ionic strength mediated charge-charge, dipole-dipole, and apolar-apolar (salting out) interactions give, respectively, n = 0.5, 1.0, and 1.0. Our experimental values for 40 degrees C, where the data span a wide range of helix content, show n = 1.0, suggesting that ionic strength stabilizes either by reducing dipole-dipole repulsions or by enhancing hydrophobic interactions, both probably interhelix in nature. Two segments of tropomyosin, 11Tm127 and 142Tm281, neither of which aggregate at low ionic strength, give results similar to those for NPTm, i.e., n = 0.96 and 0.84, respectively.     

Long timestep dynamics of peptides by the dynamics driver approach

Previous experience with the Langevin/implicit-Euler scheme for dynamics (“LI”) on model systems (butane, water) has shown that LI is numerically stable for timesteps in the 5–20 fs range but quenches high-frequency modes. To explore applications to polypeptides, we apply LI to model systems (several dipeptides, a tetrapeptide, and a 13-residue oligoalanine) and also develop a new dynamics driver approach (“DA”). The DA scheme, based on LI, addresses the important issue of proper sampling, which is unlikely to be solved by small-time step integration methods or implicit methods with intrinsic damping at room temperature, such as LI. Equilibrium averages, time-dependent molecular properties, and sampling trends at room temperature are reported for both LI and DA dynamics simulations, which are then compared to those generated by a standard explicit discretization of the Langevin equation with a 1 fs timestep. We find that LI's quenching effects are severe on both the fast and slow (due to vibrational coupling) frequency modes of all-atom polypeptides and lead to more restricted dynamics at moderate timesteps (40 fs). The DA approach empirically counteracts these damping effects by adding random atomic perturbations to the coordinates at each step (before the minimization of a dynamics function). By restricting the energetic fluctuations and controlling the kinetic energy, we are able with a 60 fs timestep to generate continuous trajectories that sample more of the relevant conformational space and also reproduce reasonably Boltzmann statistics. Although the timescale for transition may be accelerated by the DA approach, the transitional. information obtained for the alanine dipeptide and the tetrapeptide is consistent with that obtained by several other theoretical approaches that focus specifically on the determination of pathways. While the trajectory for oligoalanine by the explicit scheme over the nanosecond timeframe remains in the vicinity of the full α_R-helix starting structure, and a high-temperature (6000°K) MD trajectory departs slowly from the a helical structure, the DA-generated trajectory for the same CPU time exhibits unfolding and refolding and reveals a range of conformations with an intermediate helix content. Significantly, this range of states is more consistent with spectroscopic experiments on small peptides, as well as the cooperative two-state model for helix–coil transition. The good, near-Boltzmann statistics reported for the smaller systems above, in combination with the interesting oligoalanine results, suggest that DA is a promising tool for efficiently exploring conformational spaces of biomolecules and exploring folding/unfolding processes of polypeptides. © 1995 Wiley-Liss, Inc.     

Co-operative regulation mechanism of muscle contraction: Inter-tropomyosin co-operation model

A new model is presented on the basis of our experimental data and the “tropomyosin-blocking theory” of muscle relaxation to explain the regulation of certain characteristics of muscle contraction, namely that the relation of contraction to pCa is co-operative while calcium-binding is essentially non-cooperative. Our experiments show that end-to-end interactions between adjacent tropomyosin molecules in the groove of the actin helix are essential for the co-operative regulation. The blocking theory says that the tropomyosin molecule in relaxed muscle sterically blocks the myosin attachment site on actin, whereas in contracting muscle it moves to a position away from the attachment site. In this model a concerted movement of tropomyosin molecules, brought about by their end-to-end interactions, is considered to be the essential mechanism of co-operative regulation, and it is assumed that the positional changes of tropomyosin occur primarily when the four calcium binding sites of troponin on the tropomyosin are saturated with calcium. Theoretical analysis of the model, based upon the two-state allosteric model, leads to a Michaelis-Menten equation for the Ca-binding function together with a co-operative equation for the state function, proportional to the contraction or ATPase activity. These two functions fit well the experimental data. With cardiac muscle the slope of the contraction versus pCa curve is slightly less steep than that obtained with skeletal muscle. This difference can be explained by the difference in the number of Ca-binding sites of troponins.     

A statistical mechanical study of helix-coil transition in concentrated solutions of polypeptides and proteins

The helix–coil transition in polypeptides was studied by methods of statistical mechanics, taking account of interaction between “melted” amide groups through hydrogen bonds. The statistical sums are calculated in the explicit form for two limit cases: (1) the dilute solution when the main contribution is given by collisions of two particles; (2) “condensation” when contacting macromolecules form a united aggregate. In the first case the transition enthalpy was shown to decrease linearly when the concentration increases, while at the appropriate choice of theoretical parameters, melting temperature and range are almost independent of the concentration. In the second case the structural transition parameters were shown to be independent of the concentration (the saturation effect). These results agree with the experimental data on synthetic polypeptides reported by other authors and with data on some globular proteins (serum and egg albumin) reported in this paper.