Recent advances in helix-coil theory

Statistical mechanical model for helix-sheet-coil transitions in homopolypeptides

In this paper, we propose a simple statistical mechanical model to study the conformation transition between the alpha helix, beta sheet, and random coil in homopolypeptides. In our model, five parameters are introduced to obtain the partition function. There are two factors for helical propagation and initiation, which are the same as those used in the Zimm-Bragg model, and three newly introduced parameters for beta structures: the strand propagation factor for residues in beta strands and two correction factors for the initiation effect of the beta strand and beta sheet. Our model shows that the variation of these parameters may induce conformation transition from alpha helix or random coil to beta sheet. The sharpness of the transition depends on the initiation factors.

Spatial structure and pH-dependent conformational diversity of dimeric transmembrane domain of the receptor tyrosine kinase EphA1

Eph receptors are found in a wide variety of cells in developing and mature tissues and represent the largest family of receptor tyrosine kinases, regulating cell shape, movements, and attachment. The receptor tyrosine kinases conduct biochemical signals across plasma membrane via lateral dimerization in which their transmembrane domains play an important role. Structural-dynamic properties of the homodimeric transmembrane domain of the EphA1 receptor were investigated with the aid of solution NMR in lipid bicelles and molecular dynamics in explicit lipid bilayer. EphA1 transmembrane segments associate in a right-handed parallel alpha-helical bundle, region (544-569)(2), through the N-terminal glycine zipper motif A(550)X(3)G(554)X(3)G(558). Under acidic conditions, the N terminus of the transmembrane helix is stabilized by an N-capping box formed by the uncharged carboxyl group of Glu(547), whereas its deprotonation results in a rearrangement of hydrogen bonds, fractional unfolding of the helix, and a realignment of the helix-helix packing with appearance of additional minor dimer conformation utilizing seemingly the C-terminal GG4-like dimerization motif A(560)X(3)G(564). This can be interpreted as the ability of the EphA1 receptor to adjust its response to ligand binding according to extracellular pH. The dependence of the pK(a) value of Glu(547) and the dimer conformational equilibrium on the lipid head charge suggests that both local environment and membrane surface potential can modulate dimerization and activation of the receptor. This makes the EphA1 receptor unique among the Eph family, implying its possible physiological role as an "extracellular pH sensor," and can have relevant physiological implications.

Density of states for a short overlapping-bead polymer: clues to a mechanism for helix formation?

The densities of states are evaluated for very short chain molecules made up of overlapping monomers, using a model which has previously been shown to produce helical structure. The results of numerical calculations are presented for tetramers and pentamers. We show that these models demonstrate behaviors relevant to the behaviors seen in longer, helix-forming chains, particularly "magic numbers" of the overlap parameter, where the derivatives of the densities of states change discontinuously, and a region of bimodal energy probability distributions, reminiscent of a first-order phase transition in a bulk system.

Structural insights for designed alanine-rich helices: comparing NMR helicity measures and conformational ensembles from molecular dynamics simulation

The temperature dependence of helical propensities for the peptides Ac-ZGG-(KAAAA)(3)X-NH(2) (Z = Y or G, X = A, K, and D-Arg) were studied both experimentally and by MD simulations. Good agreement is observed in both the absolute helical propensities as well as relative helical content along the sequence; the global minimum on the calculated free energy landscape corresponds to a single alpha-helical conformation running from K4 to A18 with some terminal fraying, particularly at the C-terminus. Energy component analysis shows that the single helix state has favorable intramolecular electrostatic energy due to hydrogen bonds, and that less-favorable two-helix globular states have favorable solvation energy. The central lysine residues do not appear to increase helicity; however, both experimental and simulation studies show increasing helicity in the series X = Ala --> Lys --> D-Arg. This C-capping preference was also experimentally confirmed in Ac-(KAAAA)(3)X-GY-NH(2) and (KAAAA)(3)X-GY-NH(2) sequences. The roles of the C-capping groups, and of lysines throughout the sequence, in the MD-derived ensembles are analyzed in detail.

Lysine and arginine residues do not increase the helicity of alanine-rich peptide helices

The helix-disfavoring, versus alanine, propagation values of lysine (0.8) and arginine (1.0) residues placed centrally in an (Ala)(9) unit have been measured by (13)C NMR.

Alpha-Helix folding in the presence of structural constraints

We have investigated the site-specific folding kinetics of a photoswitchable cross-linked alpha-helical peptide by using single (13)C = (18)O isotope labeling together with time-resolved IR spectroscopy. We observe that the folding times differ from site to site by a factor of eight at low temperatures (6 degrees C), whereas at high temperatures (45 degrees C), the spread is considerably smaller. The trivial sum of the site signals coincides with the overall folding signal of the unlabeled peptide, and different sites fold in a noncooperative manner. Moreover, one of the sites exhibits a decrease of hydrogen bonding upon folding, implying that the unfolded state at low temperature is not unstructured. Molecular dynamics simulations at low temperature reveal a stretched-exponential behavior which originates from parallel folding routes that start from a kinetically partitioned unfolded ensemble. Different metastable structures (i.e., traps) in the unfolded ensemble have a different ratio of loop and helical content. Control simulations of the peptide at high temperature, as well as without the cross-linker at low temperature, show faster and simpler (i.e., single-exponential) folding kinetics. The experimental and simulation results together provide strong evidence that the rate-limiting step in formation of a structurally constrained alpha-helix is the escape from heterogeneous traps rather than the nucleation rate. This conclusion has important implications for an alpha-helical segment within a protein, rather than an isolated alpha-helix, because the cross-linker is a structural constraint similar to those present during the folding of a globular protein.

Enthalpic and entropic stages in alpha-helical peptide unfolding, from laser T-jump/UV Raman spectroscopy

The alpha-helix is a ubiquitous structural element in proteins, and a number of studies have addressed the mechanism of helix formation and melting in simple peptides. However, fundamental issues remain to be resolved, particularly the temperature (T) dependence of the rate. In this work, we report application of a novel kHz repetition rate solid-state tunable NIR (pump) and deep UV Raman (probe) laser system to study the dynamics of helix unfolding in Ac-GSPEA3KA4KA4-CO-D-Arg-CONH2, a peptide designed for helix stabilization in aqueous solution. Its T-dependent UV resonance Raman (UVRR) spectra, excited at 197 nm for optimal enhancement of amide vibrations, were decomposed into variable contributions from helix and coil spectra. The helix fractions derived from the UVRR spectra and from far UV CD spectra were coincident at low T but deviated increasingly at high T, the UVRR curve giving higher helix content. This difference is consistent with the greater sensitivity of UVRR spectra to local conformation than CD. After a laser-induced T-jump, the UVRR-determined helix fractions defined monoexponential decays, with time-constants of approximately 120 ns, independent of the final T (Tf = 18-61 degrees C), provided the initial T (Ti) was held constant (6 degrees C). However, there was also a prompt loss of helicity, whose amplitude increased with increasing Tf, thereby defining an initial enthalpic phase, distinct from the subsequent entropic phase. These phases are attributed to disruption of H-bonds followed by reorientation of peptide links, as the chain is extended. When Ti was raised in parallel with Tf (10 degrees C T-jumps), the prompt phase merged into an accelerating slow phase, an effect attributable to the shifting distribution of initial helix lengths. Even greater acceleration with rising Ti has been reported in T-jump experiments monitored by IR and fluorescence spectroscopies. This difference is attributable to the longer range character of these probes, whose responses are therefore more strongly weighted toward the H-bond-breaking enthalpic process.

Finding the transition state without initial guess: The growing string method for Newton trajectory to isomerization and enantiomerization reaction of alanine dipeptide and poly(15)alanine

We report a new, high-dimensional application of a method for finding a transition state (TS) between a reactant and a product on the potential energy surface: the search of a growing string along a reaction path defined by any Newton trajectory in combination with the Berny method (Quapp, J Chem Phys (2005), 122, 174106; we have provided this algorithm on a web page). Two given minima are connected by a one-dimensional, but usually curvilinear reaction coordinate. It leads to the TS region. The application of the method to alanine dipeptide finds the TS of the isomerisation C(7 ax) --> C(5), some TSs of the enantiomerisation of C(7 ax) from L-form to quasi-D-form, and it finds the TS region of a transition of a partly unfolded, bent structure which turns back into a mainly alpha-helix in the Ac(Ala)(15)NHMe polyalanine (all at the quantum mechanical level B3LYP/6-31G: the growing string calculation is interfaced with the Gaussian03 package). The formation or dissolvation of some alpha- or 3(10)-hydrogen bonds of the helix are discussed along the TS pathway, as well as the case of an enantiomer at the central residue of the helix.

Alpha-helix stabilization by alanine relative to glycine: roles of polar and apolar solvent exposures and of backbone entropy

The energetics of alpha-helix formation are fairly well understood and the helix content of a given amino acid sequence can be calculated with reasonable accuracy from helix-coil transition theories that assign to the different residues specific effects on helix stability. In internal helical positions, alanine is regarded as the most stabilizing residue, whereas glycine, after proline, is the more destabilizing. The difference in stabilization afforded by alanine and glycine has been explained by invoking various physical reasons, including the hydrophobic effect and the entropy of folding. Herein, the contribution of these two effects and that of hydrophilic area burial is evaluated by analyzing Ala and Gly mutants implemented in three helices of apoflavodoxin. These data, combined with available data for similar mutations in other proteins (22 Ala/Gly mutations in alpha-helices have been considered), allow estimation of the difference in backbone entropy between alanine and glycine and evaluation of its contribution and that of apolar and polar area burial to the helical stabilization typically associated to Gly-->Ala substitutions. Alanine consistently stabilizes the helical conformation relative to glycine because it buries more apolar area upon folding and because its backbone entropy is lower. However, the relative contribution of polar area burial (which is shown to be destabilizing) and of backbone entropy critically depends on the approximation used to model the structure of the denatured state. In this respect, the excised-peptide model of the unfolded state, proposed by Creamer and coworkers (1995), predicts a major contribution of polar area burial, which is in good agreement with recent quantitations of the relative enthalpic contribution of Ala and Gly residues to alpha-helix formation.

Fundamental processes of protein folding: measuring the energetic balance between helix formation and hydrophobic interactions

Theories of protein folding often consider contributions from three fundamental elements: loops, hydrophobic interactions, and secondary structures. The pathway of protein folding, the rate of folding, and the final folded structure should be predictable if the energetic contributions to folding of these fundamental factors were properly understood. alphatalpha is a helix-turn-helix peptide that was developed by de novo design to provide a model system for the study of these important elements of protein folding. Hydrogen exchange experiments were performed on selectively 15N-labeled alphatalpha and used to calculate the stability of hydrogen bonds within the peptide. The resulting pattern of hydrogen bond stability was analyzed using a version of Lifson-Roig model that was extended to include a statistical parameter for tertiary interactions. This parameter, x, represents the additional statistical weight conferred upon a helical state by a tertiary contact. The hydrogen exchange data is most closely fit by the XHC model with an x parameter of 9.25. Thus the statistical weight of a hydrophobic tertiary contact is approximately 5.8x the statistical weight for helix formation by alanine. The value for the x parameter derived from this study should provide a basis for the understanding of the relationship between hydrophobic cluster formation and secondary structure formation during the early stages of protein folding.

Dependence of folding dynamics and structural stability on the location of a hydrophobic pair in beta-hairpins

We study the dependence of folding time, nucleation site, and stability of a model beta-hairpin on the location of a cross-strand hydrophobic pair, using a coarse-grained off-lattice model with the aid of Monte Carlo simulations. Our simulations have produced 6500 independent folding trajectories dynamically, forming the basis for extensive statistical analysis. Four folding pathways, zipping-out, middle-out, zipping-in, and reptation, have been closely monitored and discussed in all seven sequences studied. A hydrophobic pair placed near the beta-turn or in the middle section effectively speed up folding; a hydrophobic pair placed close to the terminal ends or next to the beta-turn encourages stability of the entire chain.

A model for the coupling of alpha-helix and tertiary contact formation

Peptides corresponding to excised alpha-helical segments of natural proteins can spontaneously form helices in solution. However, peptide helices are usually substantially less stable in solution than in the structural context of a folded protein, because of the additional interactions possible between helices in a protein. Such interactions can be thought of as coupling helix formation and tertiary contact formation. The relative energetic contributions of the two processes to the total energy of the folded state of a protein is a matter of current debate. To investigate this balance, an extended helix-coil model (XHC) that incorporates both effects has been constructed. The model treats helix formation with the Lifson-Roig formalism, which describes helix initiation and propagation through cooperative local interactions. The model postulates an additional parameter representing participation of a site in a tertiary contact. In the model, greater helix stability can be achieved through combinations of these short-range and long-range interactions. For instance, stronger tertiary contacts can compensate for helices with little intrinsic stability. By varying the strength of the nonlocal interactions, the model can exhibit behavior consistent with a variety of qualitative models describing the relative importance of secondary and tertiary structure. Moreover, the model is explicit in that it can be used to fit experimental data to individual peptide sequences, providing a means to quantify the two contributions on a common energetic basis.

Comparison of the helix-coil transition of a titrating polypeptide in aqueous solutions and at the air-water interface

The transition from alpha-helix to random coil of the titrating polyamino acid co-poly-L-(lysine, phenylalanine), (p-(Lys,Phe)), has been investigated as a function of pH and ionic strength in aqueous solution and at the air-water interface by means of circular dichroism (CD) spectroscopy and the Langmuir surface film balance technique. The results strongly suggest that the helix-coil transition for peptides at the air-water interface can be determined by using the two-dimensional Flory exponent, nu, to express the pH dependent peptide surface conformation. The helix-coil titration curve of p-(Lys,Phe) shifts approximately 2.5 pH units towards lower pH at the air-water interface, as compared with the bulk solution. This finding is of relevance for the understanding of conformation and conformational changes of membrane-transporting and membrane penetrating peptides as well as for the use of peptides in molecular devices.

On the Influence of Charged Side Chains on the Folding–Unfolding Equilibrium of β-Peptides: A Molecular Dynamics Simulation Study

The influence of charged side chains on the folding-unfolding equilibrium of beta-peptides was investigated by means of molecular dynamics simulations. Four different peptides containing only negatively charged side chains, positively charged side chains, both types of charged side chains (with the ability to form stabilizing salt bridges) or no charged side chains were studied under various conditions (different simulation temperatures, starting structures and solvent environment). The NMR solution structure in methanol of one of the peptides (A) has already been published; the synthesis and NMR analysis of another peptide (B) is described here. The other peptides (C and D) studied herein have hitherto not been synthesized. All four peptides A-D are expected to adopt a left-handed 3(14)-helix in solution as well as in the simulations. The resulting ensembles of structures were analyzed in terms of conformational space sampled by the peptides, folding behavior, structural properties such as hydrogen bonding, side chain-side chain and side chain-backbone interactions and in terms of the level of agreement with the NMR data available for two of the peptides. It was found that the presence of charged side chains significantly slows down the folding process in methanol solution due to the stabilization of intermediate conformers with side chain-backbone interactions. In water, where the solvent competes with the solute-solute polar interactions, the folding process to the 3(14)-helix is faster in the simulations.

How large is an alpha-helix? Studies of the radii of gyration of helical peptides by small-angle X-ray scattering and molecular dynamics

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based alpha-helix-forming peptides of the composition Ace-(AAKAA)(n)-GY-NH(2), n=2-7, in aqueous solvent at 10(+/-1) degrees C. In contrast to other techniques typically used to study alpha-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal alpha-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(+/-0.6)A, which is to be compared with the radius of gyration of an ideal 37-mer alpha-helix of 17.6A. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (< or =37 amino acid residues), these alpha-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Effect of urea on peptide conformation in water: molecular dynamics and experimental characterization

Molecular dynamics simulations of a ribonuclease A C-peptide analog and a sequence variant were performed in water at 277 and 300 K and in 8 M urea to clarify the molecular denaturation mechanism induced by urea and the early events in protein unfolding. Spectroscopic characterization of the peptides showed that the C-peptide analog had a high alpha-helical content, which was not the case for the variant. In the simulations, interdependent side-chain interactions were responsible for the high stability of the alpha-helical C-peptide analog in the different solvents. The other peptide displayed alpha-helical unwinding that propagated cooperatively toward the N-terminal. The conformations sampled by the peptides depended on their sequence and on the solvent. The ability of water molecules to form hydrogen bonds to the peptide as well as the hydrogen bond lifetimes increased in the presence of urea, whereas water mobility was reduced near the peptide. Urea accumulated in excess around the peptide, to which it formed long-lived hydrogen bonds. The unfolding mechanisms induced by thermal denaturation and by urea are of a different nature, with urea-aqueous solutions providing a better peptide solvation than pure water. Our results suggest that the effect of urea on the chemical denaturation process involves both the direct and indirect mechanisms.

Monte Carlo studies of folding, dynamics, and stability in alpha-helices

Folding simulations of polyalanine peptides were carried out using an off-lattice Monte Carlo simulation technique. The peptide was represented as a chain of residues, each of which contains two interaction sites: one corresponding to the C(alpha) atom and the other to the side chain. A statistical potential was used to describe the interaction between these sites. The preferred conformations of the peptide chain on the energy surface, starting from several initial conditions, were searched by perturbations on its generalized coordinates with the Metropolis criterion. We observed that, at low temperatures, the effective energy was low and the helix content high. The calculated helix propagation (s) and nucleation (sigma) parameters of the Zimm-Bragg model were in reasonable agreement with the empirical data. Exploration of the energy surface of the alanine-based peptides (AAQAA)(3) and AAAAA(AAARA)(3)A demonstrated that their behavior is similar to that of polyalanine, in regard to their effective energy, helix content, and the temperature-dependence of their helicity. In contrast, stable secondary structures were not observed for (Gly)(20) at similar temperatures, which is consistent with the nonfolder nature of this peptide. The fluctuations in the slowest dynamics mode, which describe the elastic behavior of the chain, showed that as the temperature decreases, the polyalanine peptides become stiffer and retain conformations with higher helix content. Clustering of conformations during the folding phase implied that polyalanine folds into a helix through fewer numbers of intermediate conformations as the temperature decreases.

The effects of individual amino acids on the fast folding dynamics of α-helical peptides

Nanosecond temperature jump experiments coupled to time-resolved infrared spectroscopy were carried out on a series of alanine-based peptides containing different guest amino acids to study the effects of residues with different helix propensities on the helix-coil dynamics.

Thermodynamics Of α‐Helix Formation

The alpha-helix was the first proposed and experimentally confirmed secondary structure. The elegant simplicity of the alpha-helical structure, stabilized by hydrogen bonding between the backbone carbonyl oxygen and the peptide amide four residues away, has captivated the scientific community. In proteins, alpha-helices are also stabilized by the so-called capping interactions that occur at both the C- and the N-termini of the helix. This chapter provides a brief historical overview of the thermodynamic studies of the energetics of helix formation, and reviews recent progress in our understanding of the thermodynamics of helix formation.

Effect of chain length on coiled-coil stability: Decreasing stability with increasing chain length

The de novo design and biophysical characterization of three series of two-stranded alpha-helical coiled coils with different chain lengths are described. Our goal was to examine how increasing chain length would affect protein folding and stability when one or more heptad repeat(s) of K-A-E-A-L-E-G (gabcdef) was inserted into the central region of different coiled-coil host proteins. This heptad was designed to maintain the continuous 3-4 hydrophobic repeat of the coiled-coil host and introduce an Ala and Leu residue in the hydrophobic core at the a and d position, respectively, and a pair of stabilizing interchain ionic i to i' + 5 (g to e') interactions per heptad inserted. The secondary structures of the three series of disulfide-bridged polypeptides were studied by CD spectroscopy and their stabilities determined by chemical and thermal denaturation. The results showed that successive insertions of this heptad systematically decreased the stability of all the coiled coils studied regardless of the overall initial stability of the host coiled coil. These observations are in contrast to the generally accepted implication that the folding and stability of coiled coils are enhanced with increasing chain length. Our results imply that, in these examples where an Ala and Leu hydrophobic residue were introduced into the coiled-coil core per inserted heptad, there was still insufficient stability to overcome unfavorable entropy associated with chain length extension, even though the inserted heptad contained the most stabilizing hydrophobic residue (Leu) at position d and stabilizing ionic attractions.

Length Dependent Helix-Coil Transition Kinetics of Nine Alanine-Based Peptides

It is well-known that end caps and the peptide length can dramatically influence the thermodynamics of the helix-coil transition. However, their roles in determining the kinetics of the helix-coil transition have not been studied extensively and are less well understood. Kinetic Ising models and sequential kinetic models involving barrier crossing via diffusion all predict that the helix formation time depends monotonically on the peptide length with the relaxation time increasing with respect to increasing chain length. Here, we have studied the helix-coil transition kinetics of a series of Ala-based α-helical peptides of different length (19-39 residues), with and without end caps, using time-resolved infrared spectroscopy coupled with laser-induced temperature jump (T-jump) initiation method. The helical content of these peptides was kinetically monitored by probing the amide carbonyl stretching frequencies (i.e., the amide I' band) of the peptide backbone. We found that the relaxation rates for peptides with efficient end caps are more rapid than those of the corresponding peptides without good end caps. These results indicate that efficient end-capping sequences can not only stabilize preexisting helices but also promote helix formation through initiation. Furthermore, we found that the relaxation times of these peptides, following a T-jump of 1-11 °C, show rather complex behaviors as a function of the peptide length, in disagreement with theoretical predications. Theses results are not readily explained by theories in which Ala is taken to have a single helical propensity (s). However, recent studies have suggested that s depends on chain length; when this factor is considered, the mean first-passage times of the coil-to-helix transition show similar dependence on the peptide length as those observed experimentally.

Understanding the alpha-helix to coil transition in polypeptides using network rigidity: predicting heat and cold denaturation in mixed solvent conditions

Thermodynamic stability in polypeptides is described using a novel Distance Constraint Model (DCM). Here, microscopic interactions are represented as constraints. A topological arrangement of constraints define a mechanical framework. Each constraint in the framework is associated with an enthalpic and entropic contribution. All accessible topological arrangements of distance constraints form an ensemble of mechanical frameworks, each representing a microstate of the polypeptide. A partition function is calculated exactly using a transfer matrix approach, where in many respects the DCM is similar to the Lifson-Roig model. The crucial difference is that the effect of network rigidity is explicitly calculated for each mechanical framework in the ensemble. Network rigidity is a mechanical interaction that provides a mechanism for long-range molecular cooperativity and enables a proper treatment of the nonadditivity of a microscopic free energy decomposition. Accounting for (1) helix <--> coil conformation changes along the backbone similar to the Lifson-Roig model, (2) i to i + 4 hydrogen-bond formation <--> breaking similar to the Zimm-Bragg model, and (3) structured <--> unstructured solvent interaction (hydration effects), a six-parameter DCM describes normal and inverted helix-coil transitions in polypeptides. Under suitable mixed solvent conditions heat and cold denaturation is predicted. Model parameters are fitted to experimental data showing different degrees of cold denaturation in monomeric polypeptides in aqueous hexafluoroisopropanol (HFIP) solution at various HFIP concentrations. By assuming a linear HFIP concentration dependence (up to 6% by mole fraction) on model parameters, all essential experimentally observed features are captured.

Effects of temperature and pH on the helicity of a peptide adsorbed to colloidal silica

The conformation of a cationic alpha-helical peptide (DDDDAAAARRRRR) adsorbed to anionic colloidal silica has been investigated by circular dichroism (CD) spectroscopy as a function of temperature and pH in order to examine how the structure of an adsorbed molecule responds to two simultaneous perturbations. Increased temperature destabilizes the helicity of the peptide in solution, while pH changes alter the substrate surface charge and the corresponding strength of the interaction with the peptide. Near neutral pH, the helicity of the adsorbed peptide, which is determined from the intensity of the CD signal at 222 nm, decreases with increasing temperature, similarly to the temperature-dependent behavior observed for the peptide in aqueous solution. By contrast, at basic pH and a strongly negative surface charge, the helicity of the adsorbed peptide increases with temperature. In order to elucidate the origin of the reversal of the temperature dependence of helicity, a statistical model for the conformation of the adsorbed peptide has been formulated based on the Lifson-Roig model for the helix-coil transition of the peptide in solution. The model provides insight into the trends in fractional helicity and reveals that the temperature dependence of the helicity of the adsorbed peptide results from a competition between the intramolecular interactions that promote helicity and the intermolecular interactions with the surface. The statistical model also enables estimation of the free energy contributions from specific aspects of the adsorption process. Through identification of a connection between the conformation of adsorbed peptide and the interactions of the peptide with the surface, this work suggests a route for the control of adsorbate conformation through peptide and surface engineering.

Network rigidity at finite temperature: relationships between thermodynamic stability, the nonadditivity of entropy, and cooperativity in molecular systems

A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free-energy functions. Topological rearrangements of thermally fluctuating constraints are permitted. The partition function is obtained by combining microscopic free energies of individual constraints using network rigidity as an underlying long-range mechanical interaction, giving a quantitative explanation for the nonadditivity in component entropies exhibited in molecular systems. Two exactly solved two-dimensional toy models representing flexible molecules that can undergo conformational change are presented to elucidate concepts, and to outline a DCM calculation scheme applicable to many types of physical systems. It is proposed that network rigidity plays a central role in balancing the energetic and entropic contributions to the free energy of biopolymers, such as proteins. As a demonstration, the distance constraint model is solved exactly for the alpha-helix to coil transition in homogeneous peptides. Temperature and size independent model parameters are fitted to Monte Carlo simulation data, which includes peptides of length 10 for gas phase, and lengths 10, 15, 20, and 30 in water. The DCM is compared to the Lifson-Roig model. It is found that network rigidity provides a mechanism for cooperativity in molecular structures including their ability to spontaneously self-organize. In particular, the formation of a characteristic topological arrangement of constraints is associated with the most probable microstates changing under different thermodynamic conditions.

Noncharged amino acid residues at the solvent-exposed positions in the middle and at the C terminus of the alpha-helix have the same helical propensity

It was established previously that helical propensities of different amino acid residues in the middle of alpha-helix in peptides and in proteins are very similar. The statistical analysis of the protein helices from the known three-dimensional structures shows no difference in the frequency of noncharged residues in the middle and at the C terminus. Yet, experimental studies show distinctive differences for the helical propensities of noncharged residues in the middle and in the C terminus in model peptides. Is this a general effect, and is it applicable to protein helices or is it specific to the model alanine-based peptides? To answer this question, the effects of substitutions at positions 28 (middle residue) and 32 (C2 position at the C terminus) of the alpha-helix of ubiquitin on the stability of this protein are measured by using differential scanning calorimetry. The two data sets produce similar values for intrinsic helix propensity, leading to a conclusion that noncharged amino acid residues at the solvent-exposed positions in the middle and at the C terminus of the alpha-helix have the same helical propensity. This conclusion is further supported with an excellent correlation between the helix propensity scale obtained for the two positions in ubiquitin with the experimental helix propensity scale established previously and with the statistical distribution of the residues in protein helices.