Monte Carlo studies on equilibrium globular protein folding. II. Beta-barrel globular protein models

In the context of dynamic Monte Carlo simulations on a model protein confined to a tetrahedral lattice, the interplay of protein size and tertiary structure, and the requirements for an all-or-none transition to a unique native state, are investigated. Small model proteins having a primary sequence consisting of a central bend neutral region flanked by two tails having an alternating hydrophobic/hydrophilic pattern of residues are seen to undergo a continuous transition to a beta-hairpin collapsed state. On increasing the length of the tails, the beta-hairpin structural motif is found to be in equilibrium with a four-member beta-barrel. Further increase of the tail length results in the shift of the structural equilibrium to the four-member beta-barrel. The random coil to beta-barrel transition is of an all-or-none character, but while the central turn is always the desired native bend, the location of the turns involving the two external strands is variable. That is, beta-barrels having the external stands that are two residues out of register are also observed in the transition region. Introduction into the primary sequence of two additional regions that are at the very least neutral toward turn formation produces an all-or-none transition to the unique, native, four-member beta-barrel. Various factors that can augment the stability of the native conformation are explored. Overall, these folding simulations strongly indicate that the general rules of globular protein folding are rather robust--namely, one requires a general pattern of hydrophobic/hydrophilic residues that allow the protein to have a well-defined interior and exterior and the presence of regions in the amino acid sequence that at the very least are locally indifferent to turn formation. Since no site-specific interactions between hydrophobic and hydrophilic residues are required to produce a unique four-member beta-barrel, these simulations strongly suggest that site specificity is involved in structural fine-tuning.     

Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions.

A lattice model of proteins is introduced. "A protein molecule" is a chain of nown-intersecting units of a given length on the two-dimensional square lattice. The copolymeric character of protein molecules is incorporated into the model in the form of specificities of inter-unit interactions. This model proved most effective for studying the statistical mechanical characteristics of protein folding, unfolding and fluctuations. The specificities of inter-unit interactions are shown to be the primary factors responsible for the all-or-none type transition from native to denatured states of globular proteins. The model has been studied by the Monte Carlo method of Metropolis et al., which is now shown applied to approximately simulating a kinetic process. In the strong limit of the specificity of the inter-unit interaction the native conformation was reached in this method by starting from an extended conformation. The possible generalization and application of this method for finding the native conformation of proteins form their amino sequence are discussed.     

Monte Carlo studies on equilibrium globular protein folding. I. Homopolymeric lattice models of beta-barrel proteins

Dynamic Monte Carlo studies have been performed on various diamond lattice models of β-proteins. Unlike previous work, no bias toward the native state is introduced; instead, the protein is allowed to freely hunt through all of phase space to find the equilibrium conformation. Thus, these systems may aid in the elucidation of the rules governing protein folding from a given primary sequence; in particular, the interplay of short- vs long-range interaction can be explored. Three distinct models (A? C) were examined. In model A, in addition to the preference for trans (t) over gauche states (g⁺ and g^?) (thereby perhaps favoring β-sheet formation), attractive interactions are allowed between all nonbonded, nearest neighbor pairs of segments. If the molecules possess a relatively large fraction of t states in the denatured form, on cooling spontaneous collapse to a well-defined β-barrel is observed. Unfortunately, in model A the denatured state exhibits too much secondary structure to correctly model the globular protein collapse transition. Thus in models B and C, the local stiffness is reduced. In model B, in the absence of long-range interactions, t and g states are equally weighted, and cooperativity is introduced by favoring formation of adjacent pairs of nonbonded (but not necessarily parallel) t states. While the denatured state of these systems behaves like a random coil, their native globular structure is poorly defined. Model C retains the cooperativity of model B but allows for a slight preference of t over g states in the short-range interactions. Here, the denatured state is indistinguishable from a random coil, and the globular state is a well-defined β-barrel. Over a range of chain lengths, the collapse is well represented by an all-or-none model. Hence, model C possesses the essential qualitative features observed in real globular proteins. These studies strongly suggest that the uniqueness of the globular conformation requires some residual secondary structure to be present in the denatured state.     

Conformation and stability of alpha-helical membrane proteins. 2. Influence of pH and salts on stability and unfolding of rhodopsin

We studied the stability and pH-induced denaturation of rhodopsin and its photoproducts as a model for alpha-helical membrane proteins. The increased stability of the dark state of rhodopsin as compared to its photoproduct states allows the initiation of unfolding of the protein by light-dependent isomerization of the chromophore. We could therefore characterize the transition from the native to either acid or alkaline denatured states by light-induced Fourier transform infrared difference spectroscopy, UV-visible spectroscopy, and intrinsic tryptophan fluorescence spectroscopy. The results indicate a loss of important tertiary interactions within the protein and between the protein and the retinal chromophore in the denatured state, despite that the secondary structure of the protein is almost fully retained during the transition. We therefore propose that in this denatured state the protein adopts the conformation of a loose bundle of preserved, but only weakly interacting, transmembrane helices with a largely des-oriented and partly solvent-exposed chromophore. We further characterized the influence of salts on the stability of the rhodopsin helix bundle, which was found to follow the Hofmeister series. We found that the effect of sodium chloride may be stabilizing or destabilizing, depending on the intrinsic stability of the examined protein conformation and on salt concentration. In particular, sodium chloride is shown to counteract the formation of the denatured loose bundle state presumably by increasing the lateral pressure on the helix bundle, thereby stabilizing native-like tertiary contacts within the protein.     

Mapping the interactions present in the transition state for unfolding/folding of FKBP12.

The structure of the transition state for folding/unfolding of the immunophilin FKBP12 has been characterised using a combination of protein engineering techniques, unfolding kinetics, and molecular dynamics simulations. A total of 34 mutations were made at sites throughout the protein to probe the extent of secondary and tertiary structure in the transition state. The transition state for folding is compact compared with the unfolded state, with an approximately 30 % increase in the native solvent-accessible surface area. All of the interactions are substantially weaker in the transition state, as probed by both experiment and molecular dynamics simulations. In contrast to some other proteins of this size, no element of structure is fully formed in the transition state; instead, the transition state is similar to that found for smaller, single-domain proteins, such as chymotrypsin inhibitor 2 and the SH3 domain from alpha-spectrin. For FKBP12, the central three strands of the beta-sheet, beta-strand 2, beta-strand 4 and beta-strand 5, comprise the most structured region of the transition state. In particular Val101, which is one of the most highly buried residues and located in the middle of the central beta-strand, makes approximately 60 % of its native interactions. The outer beta-strands and the ends of the central beta-strands are formed to a lesser degree. The short alpha-helix is largely unstructured in the transition state, as are the loops. The data are consistent with a nucleation-condensation model of folding, the nucleus of which is formed by side-chains within beta-strands 2, 4 and 5, and the C terminus of the alpha-helix. The precise residues involved in the nucleus differ in the two simulated transition state ensembles, but the interacting regions of the protein are conserved. These residues are distant in the primary sequence, demonstrating the importance of tertiary interactions in the transition state. The two independently derived transition state ensembles are structurally similar, which is consistent with a Bronsted analysis confirming that the transition state is an ensemble of states close in structure.     

Collapse transitions in protein-like lattice polymers: The effect of sequence patterns

The collapse transition of lattice protein-like heteropolymers has been studied by means of the Monte Carlo method. The protein model has been reduced to the α-carbon trace restricted to a high coordination lattice. The sequences of model heteropolymers contain two types of mers: hydrophobic/nonpolar (H) and hydrophilic/polar (P). Interactions of HH and PP pairs were assumed to be negative (weaker attractions of PP pairs) while the contact energy for HP pairs was equal to zero. All sequence-specific short-range interactions have been neglected in the present studies. It has been found that homopolymeric chains undergo a smooth collapse transition to a dense globular state. The globule lacks any signatures of local ordering that could be interpreted as a model of protein secondary structure. Hetero-polymers with the sequences of hydrophilic and hydrophobic residues characteristic for α- and β-type proteins undergo a somewhat sharper (though continuous) collapse transition to a dense globular state with elements of local ordering controlled by the sequence. The helical pattern induces more secondary structure than the β-type pattern. For all examined sequences the level of local ordering was lower than the average secondary structure content of globular proteins. The results are compared with other theoretical work and with known experimental facts. The implications for the reduced modeling of protein systems are briefly discussed. © 1997 John Wiley & Sons, Inc. Biopoly 42: 537–548, 1997     

Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways. I. Six-member, Greek key beta-barrel proteins

In the context of a simplified diamond lattice model of a six-member, Greek key beta-barrel protein that is closely related in topology to plastocyanin, the nature of the folding and unfolding pathways have been investigated using dynamic Monte Carlo techniques. The mechanism of Greek key assembly is best described as punctuated "on site construction". Folding typically starts at or near a beta-turn, and then the beta-strands sequentially form by using existing folded structure as a scaffold onto which subsequent tertiary structure assembles. On average, beta-strands tend to zip up from one tight bend to the next. After the four-member, beta-barrel assembles, there is a long pause as the random coil portion of the chain containing the long loop thrahes about trying to find the native state. Thus, there is an entropic barrier that must be surmounted. However, while a given piece of the protein may be folding, another section may be unfolding. A competition therefore exists to assemble a fairly stable intermediate before it dissolves. Folding may initiate at any of the tight turns, but the turn closer to the N terminus seems to be preferred due to well-known excluded volume effects. When the protein first starts to fold, there are a multiplicity of folding pathways, but the number of options is reduced as the system gets closer to the native state. In the early stages, the excluded volume effect exerted by the already assembled protein helps subsequent assembly. Then, near the native conformation, the folded parts reduce the accessible conformational space available to the remaining unfolded sections. Unfolding essentially occurs in reverse. Employing a simple statistical mechanical theory, the configurational free energy along the reaction co-ordinate for this model has been constructed. The free energy surface, in agreement with the simulations, provides the following predictions. The transition state is quite near the native state, and consists of five of the six beta-strands being fully assembled, with the remaining long loop plus sixth beta-strand in place, but only partially assembled. It is separated from the beta-barrel intermediate by a free energy barrier of mainly entropic origin and from the native state by a barrier that is primarily energetic in origin. The latter feature is in agreement with the "Cardboard Box" model described by Goldenberg and Creighton but, unlike their model, the transition state is not a high-energy distorted form of the native state.(ABSTRACT TRUNCATED AT 250 WORDS)     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

On the origin of the cooperativity of protein folding: Implications from model simulations

There is considerable experimental evidence that the cooperativity of protein folding resides in the transition from the molten globule to the native state. The objective of this study is to examine whether simplified models can reproduce this cooperativity and if so, to identify its origin. In particular, the thermodynamics of the conformational transition of a previously designed sequence (A. Kolinski, W. Galazka, and J. Skolnick, J. Chem. Phys. 103: 10286–10297, 1995), which adopts a very stable Greek-key β-barrel fold has been investigated using the entropy Monte Carlo sampling (ESMC) technique of Hao and Scheraga (M.-H. Hao and H.A. Scheraga, J. Phys. Chem. 98: 9882–9883, 1994). Here, in addition to the original potential, which includes one body and pair interactions between side chains, the force field has been supplemented by two types of multi-body potentials describing side chain interactions. These potentials facilitate the proteinlike pattern of side chain packing and consequently increase the cooperativity of the folding process. Those models that include an explicit cooperative side chain packing term exhibit a well-defined all-or-none transition from a denatured, random coil state to a high-density, well-defined, nativelike low-energy state. By contrast, models lacking such a term exhibit a conformational transition that is essentially continuous. Finally, an examination of the conformations at the free-energy barrier between the native and denatured states reveals that they contain a substantial amount of native-state secondary structure, about 50% of the native contacts, and have an average root mean square radius of gyration that is about 15% larger than native. © 1996 Wiley-Liss, Inc.     

Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding.

Muscle acylphosphatase (AcP) is a small protein that folds very slowly with two-state behavior. The conformational stability and the rates of folding and unfolding have been determined for a number of mutants of AcP in order to characterize the structure of the folding transition state. The results show that the transition state is an expanded version of the native protein, where most of the native interactions are partially established. The transition state of AcP turns out to be remarkably similar in structure to that of the activation domain of procarboxypeptidase A2 (ADA2h), a protein having the same overall topology but sharing only 13% sequence identity with AcP. This suggests that transition states are conserved between proteins with the same native fold. Comparison of the rates of folding of AcP and four other proteins with the same topology, including ADA2h, supports the concept that the average distance in sequence between interacting residues (that is, the contact order) is an important determinant of the rate of protein folding.     

De novo protein design. I. In search of stability and specificity.

We have developed a fully automated protein design strategy that works on the entire sequence of the protein and uses a full atom representation. At each step of the procedure, an all-atom model of the protein is built using the template protein structure and the current designed sequence. The energy of the model is used to drive a Monte Carlo optimization in sequence space: random moves are either accepted or rejected based on the Metropolis criterion. We rely on the physical forces that stabilize native protein structures to choose the optimum sequence. Our energy function includes van der Waals interactions, electrostatics and an environment free energy. Successful protein design should be specific and generate a sequence compatible with the template fold and incompatible with competing folds. We impose specificity by maintaining the amino acid composition constant, based on the random energy model. The specificity of the optimized sequence is tested by fold recognition techniques. Successful sequence designs for the B1 domain of protein G, for the lambda repressor and for sperm whale myoglobin are presented. We show that each additional term of the energy function improves the performance of our design procedure: the van der Waals term ensures correct packing, the electrostatics term increases the specificity for the correct native fold, and the environment solvation term ensures a correct pattern of buried hydrophobic and exposed hydrophilic residues. For the globin family, we show that we can design a protein sequence that is stable in the myoglobin fold, yet incompatible with the very similar hemoglobin fold.     

Correlation between mutational destabilization of phage T4 lysozyme and increased unfolding rates

The thermodynamics and kinetics of unfolding of 28 bacteriophage T4 lysozyme variants were compared by using urea gradient gel electrophoresis. The mutations studied cause a variety of sequence changes at different residues throughout the polypeptide chain and result in a wide range of thermodynamic stabilities. A striking relationship was observed between the thermodynamic and kinetic effects of the amino acid replacements: All the substitutions that destabilized the native protein by 2 kcal/mol or more also increased the rate of unfolding. The observed increases in unfolding rate corresponded to a decrease in the activation energy of unfolding (delta Gu) at least 35% as large as the decrease in thermodynamic stability (delta Gu). Thus, the destabilizing lesions bring the free energy of the native state closer to that of both the unfolded state and the transition state for folding and unfolding. Since a large fraction of the mutational destabilization is expressed between the transition state and the native conformation, the changes in folding energetics cannot be accounted for by effects on the unfolded state alone. The results also suggest that interactions throughout much of the folded structure are altered in the formation of the transition state during unfolding.     

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.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

A heuristic approach to predicting the tertiary structure of bovine somatotropin

A combination of a heuristic approach and energy minimization was used to predict the three-dimensional structure of bovine somatotropin (bSt), also known as bovine growth hormone, a protein of 191 amino acids. The starting points for energy minimizations were generated from the following two types of inputs: (a) the amino acid sequence and (b) the heuristic inputs, which were derived according to physical, chemical, and biological principles by piecing together all useful information available. The predicted 3-D structure of the bSt molecule has all the features observed in four-helix bundle proteins. The four alpha-helices in bSt are intimately packed to form an assembly with an approximately square cross section. All the adjacent alpha-helices are antiparallel, with a somewhat tilted angle between each of the adjacent pairs so that the assembly of the four helices looks like a left-handed twisted bundle. There are two disulfide bonds in the bSt structure: one "hooking" the middle of a long loop with helix 4 so as to pull the long loop onto the surface of the helix bundle and the other "hooking" the C-terminal segment with the same helix so as to force the C-terminal segment to bend toward the helix bundle. As a consequence, a considerable part of the surface of the four-helix bundle is closely packed or intimately embraced by the loop segments. The predicted bSt structure has a hydrophobic core and a hydrophilic exterior surface. The energetic analysis of the predicted bSt structure indicates that the interaction between helices and loops plays a dominant role in stabilizing the four-helix bundle structure from the viewpoint of both electrostatic and nonbonded interactions. A technique called FOLD was meanwhile developed, by which one can fold a polypeptide chain into any shape as desired. This tool proved to be very useful during the heuristic model-building process.     

Kinetic consequences of native state optimization of surface-exposed electrostatic interactions in the Fyn SH3 domain

Optimization of surface exposed charge-charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge-charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge-charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture.     

Direct analysis of backbone-backbone hydrogen bond formation in protein folding transition states

Here we investigate the role of backbone-backbone hydrogen bonding interactions in stabilizing the protein folding transition states of two model protein systems, the B1 domain of protein L (ProtL) and the P22 Arc repressor. A backbone modified analogue of ProtL containing an amide-to-ester bond substitution between residues 105 and 106 was prepared by total chemical synthesis, and the thermodynamic and kinetic parameters associated with its folding reaction were evaluated. Ultimately, these parameters were used in a Phi-value analysis to determine if the native backbone-backbone hydrogen bonding interaction perturbed in this analogue (i.e. a hydrogen bond in the first beta-turn of ProtL's beta-beta-alpha-beta-beta fold) was formed in the transition state of ProtL's folding reaction. Also determined were the kinetic parameters associated with the folding reactions of two Arc repressor analogues, each containing an amide-to-ester bond substitution in the backbone of their polypeptide chains. These parameters were used together with previously established thermodynamic parameters for the folding of these analogues in Phi-value analyses to determine if the native backbone-backbone hydrogen bonding interactions perturbed in these analogues (i.e. a hydrogen bond at the end of the intersubunit beta-sheet interface and hydrogen bonds at the beginning of the second alpha-helix in Arc repressor's beta-alpha-alpha structure) were formed in the transition state of Arc repressor's folding reaction. Our results reveal that backbone-backbone hydrogen bonding interactions are formed in the beta-turn and alpha-helical transition state structures of ProtL and Arc repressor, respectively; and they were not formed in the intersubunit beta-sheet interface of Arc repressor, a region of Arc repressor's polypeptide chain previously shown to have other non-native-like conformations in Arc's protein folding transition state.     

Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.     

Hydrogen Bonds,Hydrophobicity Forces and the Character of the Collapse Transition

We study the thermodynamic behavior of a model protein with 54 amino acidsthat is designed to form a three-helix bundle in its native state. The model contains three types of amino acids and five to six atoms per amino acid, and has the Ramachandran torsion angles as its only degrees of freedom.The force field is based on hydrogen bonds and effective hydrophobicity forces. We study how the character of the collapse transition depends on the strengths of these forces. For a suitable choice of these two parameters, it is found that the collapse transition is first-order-like and coincides with the folding transition. Also shown is that the corresponding one- and two-helix segments make less stable secondary structure than the three-helix sequence.     

Amino acid sequence pattern in the regulatory peptides.

The essential properties of the primary structure of regulatory peptides, i.e. amino acid residues and their combinations, which are characteristic of the whole population of regulatory peptides, have been revealed using statistical methodology. These properties are as follows: increased content of certain residues (Gly, Pro, Phe, Arg, Tyr, Met and Trp) as well as an increased rate of occurrence of certain pairs of residue as compared with proteins, a random sequence of residues and "nonregulatory" peptides. By representing regulatory peptides as a sequence of hydrophobic (2 types) and hydrophilic (3 types) segments, the pattern for alternation of these segments in regulatory peptides has been determined. The segments were classified into 5 types according to the peculiarities of mutual localization of hydrophobic and hydrophilic residues within the primary structure of regulatory peptides. As compared with proteins, "nonregulatory" peptides and a random sequence of segments, regulatory peptides were characterized by an increased frequency of 4 particular pairs of segments among 12 theoretically possible pairs. These 4 pairs are fragments of the periodic segment sequence with periods of 4 segments. The revealed pattern indicates that there exists a general principle of the regulatory peptide primary structure organization and possibly a common type of the regulatory peptides flexible peptide chain folding at the ligand-receptor complex formation.