Model Of Polypeptide Chain Research Articles

INTERACTION OF L-CARNOSINE WITH NICOTINIC AND ISONICOTINIC ACIDS IN AQUEOUS SOLUTIONS AT 298.15 K

Understanding the mechanism of interaction of drugs with proteins has drawn attention of numerous researchers. The thermodynamic investigations of liquid-phase systems containing peptide and drug make it possible to determine the nature and driving forces of the interaction between them. In this work, we present results of interaction study of peptide L-carnosine (Car), as model of polypeptide chains in protein, with isonicotinic and nicotinic acids, as the drug models, in aqueous solution using calorimetric method. Calorimetric measurements of the enthalpy of L-carnosine dissolution in water and aqueous solutions with two isomers of pyridine carboxylic acid additives were performed on an ampoule-type isoperibolic dissolution calorimeter at 298.15 K. The error of measuring single heat effects was below 0.2%. The relative combined uncertainty in the measurements of the enthalpies of dissolution was not more than 0.7%. Based on the obtained experimental data and the using the HEAT computer program, the thermodynamic parameters (lgKc, ΔcG, ΔcH, ΔcS) of the complex formation between the reagents were calculated. A comparison of the affinity of peptide to interaction with nicotinic acid and isonicotinic acid was carried out. It is shown that the interaction of L-carnosine with isonicotinic acid leads to the formation of a more stable complex than with nicotinic acid. This fact may be mainly explained by the changing of ionic state of the reagents in solution and the predominance of the zwitterionic forms of isonicotinic acid in compared with nicotinic acid. The data obtained reveal the presence of molecular complexes between Car and isomers of pyridine carboxylic acid with 1:2 stoichiometry in aqueous solutions. The complexes of Car with the isonicotinic acid are mainly enthalpically stabilized, while those of Car with nicotinic acid are stabilized by both enthalpic and entropic contributions to the free Gibbs energy. The main interactions in complexes stabilization are believed to be electrostatic forces and hydrogen bonds formation between peptide and pyridine monocarboxylic acids. For citation: Tyunina E.Yu., Mezhevoi I.N., Barannikov V.P. Interaction of L-carnosine with nicotinic and isonicotinic acids in aqueous solutions at 298.15 K. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2024. V. 67. N 7. P. 48-54. DOI: 10.6060/ivkkt.20246707.7010.

Prediction of Aggregation of Biologically-Active Peptides with the UNRES Coarse-Grained Model.

The UNited RESidue (UNRES) model of polypeptide chains was applied to study the association of 20 peptides with sizes ranging from 6 to 32 amino-acid residues. Twelve of those were potentially aggregating hexa- or heptapeptides excised from larger proteins, while the remaining eight contained potentially aggregating sequences, functionalized by attaching larger ends rich in charged residues. For 13 peptides, the experimental data of aggregation were used. The remaining seven were synthesized, and their properties were measured in this work. Multiplexed replica-exchange simulations of eight-chain systems were conducted at 12 temperatures from 260 to 370 K at concentrations from 0.421 to 5.78 mM, corresponding to the experimental conditions. The temperature profiles of the fractions of monomers and octamers showed a clear transition corresponding to aggregate dissociation. Low simulated transition temperatures were obtained for the peptides, which did not precipitate after incubation, as well as for the H-GNNQQNY-NH2 prion–protein fragment, which forms small fibrils. A substantial amount of inter-strand β-sheets was found in most of the systems. The results suggest that UNRES simulations can be used to assess peptide aggregation except for glutamine- and asparagine-rich peptides, for which a revision of the UNRES sidechain–sidechain interaction potentials appears necessary.

STRAIGHT CALCULATION OF HELIX–COIL TRANSITION PARAMETERS IN HETEROPOLYMERS

The main goal of this paper is the investigation of helix–coil transition in heteropolymers by means of straight calculation of partition function, free energy, helicity degree and other characteristics of transition on the bases of generalized model of polypeptide chain. Product of random matrices was applied to solve the problem for the comparison with constrained annealing method in the future.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains.

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initiopotential-energysurface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of β-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

Possible mechanism of non-monotone behavior of helix-coil transition temperature in two-component solvent

Within the frameworks of generalized model of polypeptide chain (GMPC) the concentrational behavior of helix-coil transition temperature of biopolymer in two-component solvent was observed on the simplest models. It is shown that if the solvent and the ligand interact with the biopolymer at different binding sites, and even if both components influence the helical state in the same way, the model allows one to obtain the non-monotone character of the melting temperature behavior of biopolymer depending on the ligand concentration. It is shown that changes in the regime of helical state stability is not always related with the competition of stabilizing and destabilizing interactions of blend components but can be the result of the cumulative effect of both components.

Generalized model of polypeptide chain for helix-coil transition in two-component solvent

Within the frameworks of Generalized Model ofPolypeptide Chain (GMPC) the influence of the ligands interacting by different ways in the helix-coil transition is studied. It is shown that the model is reduced to the base model by converting the energy and the entropic parameters. In contrast to the case of the pure solvent, both the competitive and the noncompetitive interactions affect to these parameters. As a result, the temperature curve of melting shows more transitions. The influence of polyethylene glycol on the helix-coil transition in the polyalanine is discussed.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations.

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Helix-coil transition in biopolymers with multicomponent heterogeneity of energy and number of conformations

We consider the theory of helix-coil transition in heteropolymeric biopolymers with an arbitrary number of components in cases of heterogeneity with respect to both energy and number of conformations. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with employing the constrained annealing method. Expression for the free energy of heteropolymer is derived using averaged transfer-matrix of homopolymer GMPC with redefined energy and conformation parameters. We obtain an algorithm of calculation of the melting curve of a heteropolymeric system and compare that with the homopolymeric curve. We show that bimodal heterogeneity determines qualitatively the basic properties of melting of a random heteropolymer. We also show that heterogeneity with respect to energy and heterogeneity with respect to number of conformations provide essentially the same characteristics of melting curves.

On the theory of helix-coil transition in heterogeneous biopolymers. Constrained annealing method

A theory of helix-coil transition in DNA, heteropolymeric with respect to energies of H-bond formation, is considered. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with employing the constrained annealing method. Expression for the free energy of heteropolymer is derived using transfer-matrix of homopolymer with redefined energy parameter. The technique of calculation of broadening of melting interval depending on the GC-composition and hydrogen bonding energy of AT and GC pairs is developed. Two maxima are revealed on the differential melting curve of heteropolymer. The temperature dependence of the correlation length is considered as well.

Helix-coil transition in terms of Potts-like spins

In the spin model of a helix-coil transition in polypeptides a preferred value of spin has to be assigned to the helical conformation, in order to account for different symmetries of the helical vs. the coil states, leading thus to the Generalized Model of Polypeptide Chain (GMPC) Hamiltonian as opposed to the Potts model Hamiltonian, both with many-body interactions. Comparison of explicit transfer matrix secular equations of the Potts model and the GMPC model reveals that the largest eigenvalue of the Potts model with Δ many-body interactions coincides with the largest eigenvalue of the GMPC model with Δ - 1 many-body interactions, indicating the identity of both free energies. In distinction, the second largest eigenvalues in both models do not coincide, indicating a different behavior for the spatial correlation length that in its turn defines the width of the helix-coil transition interval. We explore in detail the thermodynamic consequences, resulting from spin models with and without the built-in spin anisotropy, that should indicate which model to favour as a more appropriate description of the equilibrium physical properties pertaining to the helix-coil transition.

170 GMPC model and the helix–coil transition in biopolymers

The Hamiltonian of the generalized model of polypeptide chain (GMPC) is introduced to describe the system in which the conformations are correlated over some dimensional range Δ. The Hamiltonian does not contain any parameter designed especially for helix–coil transition and uses pure molecular microscopic parameters (the energy of hydrogen bond formation, reduced partition function of repeated unit, the number of repeated units fixed by one hydrogen bond, the flexibility of chain, the energies of interaction between the repeated units and the solvent molecules) (Badasyan et al., 2005, 2004). We evaluate the partition function using transfer-matrix approach. We describe the influence of solvent interaction with biopolymer, both with competing and noncompeting for hydrogen bond formation ways. On handling the problem of solvent influence on helix–coil transition, we obtained dependence on energy of solvent–macromolecule interaction, how solvents change correlation length, transition temperature, and interval. We obtained that two type interaction of solvent results in low temperature coil–helix transition, which we connect with cold denaturation. A consistent inclusion of osmotic pressure effects in a description of helix–coil transition for poly(L-glutamic acid) in solution with polyethylene glycol can offer an explanation of the experimentally observed linear dependence of transition temperature on osmotic pressure as well as the concurrent changes in the cooperativity of the transition (Badasyan et al., 2012). We also took into account two biopolymers’ side-by-side interactions. In the case of effective repulsion; the shape of the melting curve is two-phase with high and wide correlation length in a plateau on denaturation curve (Badasyan et al., 2009). We also took into account structural heterogeneity of biopolymers using constrained annealing approximation (Serva & Paladin, 1993).

Two-scale generalized model of polypeptide chain in combined solvent

The Hamiltonian of the two-scale generalized model of the polypeptide chain is constructed for the case of combined solvent. It is shown that the partition function for the model with solvent equals to within unessential factor the partition function without solvent with redefinition of the reduced energy of interaction, for competitive interaction between solvents and biopolymer, and of the number of conformations, for non-competitive interactions. Behavior of the correlation length at changes in contributions from different types of interaction is considered.

Helix-coil transition of biopolymers in solvents interacting in competitive and non-competitive ways

Within the framework of generalized model of polypeptide chain, on the basis of the Hamiltonian of model of solvent, which interacts with a biopolymer in both competitive and noncompetitive ways, introduced earlier, analytical expressions are obtained and thermodynamic and other averaged parameters are calculated for both the repeating units of the biopolymer and the solvent molecules. Different cases of relations between parameters of competitive and non-competitive bonding are considered and processes of melting and alignment are studied. It is shown that these processes are accompanied by changes in solvation and redistribution of solvent molecules between the helical and coiled portions of the chain.

Competitive and non-competitive interaction of solvent with biopolymers at the helix-coil transition

On the basis of generalized model of polypeptide chain (GMPC) as a microscopic theory of the helix-coil transition applicable to both polypeptides and DNA, the Hamiltonian of the model of solvent, which interacts with a biopolymer in both competitive and non-competitive ways, is introduced. It is shown that the partition function of this model is reduced to multipliers to the model without solvent. In this case thermal and entropic parameters of the theory are redefined. Based on calculation of the helicity degree and correlation length different cases of relation between parameters of competitive and non-competitive interaction are discussed.

Intersegment interactions and helix-coil transition within the generalized model of polypeptide chains approach

The generalized model of polypeptide chains is extended to describe the helix-coil transition in a system comprised of two chains interacting side-by-side. The Hamiltonian of the model takes into account four possible types of interactions between repeated units of the two chains, i.e., helix-helix, helix-coil, coil-helix, and coil-coil. Analysis reveals when the energy I(hh)+I(cc) of (h-h, c-c) interactions overwhelms the energy I(hc)+I(ch) of mixed (h-c, c-h) interactions, the correlation length rises substantially, resulting in narrowing of the transition interval. In the opposite case, when I(hh)+I(cc)<I(hc)+I(ch), nontrivial behavior of the system is predicted where an intermediate plateau appears on the denaturation curve. For the latter case, calculations of the number of junctions and the average length of helical segments indicate rearrangement of helical segments at the transition point. Conceptual links are established with experimentally oriented theories of Ghosh and Dill [J. Am. Chem. Soc. 131, 2306 (2009)] and Skolnick and Holtzer [Biochemistry 25, 6192 (1986)], providing a potential explanation for both favorable helix formation and disfavored intersegment interactions from the same theoretical perspective.

Hamiltonian and partition function of the generalized model of polypeptide chain in competing and non-competing solvents in the presence of interchain interactions

For the generalized model of polypeptide chain in competing and non-competing solvents, the Hamiltonian is constructed with allowance for interchain interactions. It is shown that the partition function for the model in a solvent coincides to inessential factor with the partition function without solvent, if redefinition is made of the reduced interaction energy J for a competing solvent and of the number of conformations Q for a non-competing solvent.

Helix-coil transition in the case of interaction between two chains

Based on the generalized model of polypeptide chain the helix-coil transition in two chains, which are interacting abreast, is studied. There are four types of interaction (hh, hc, ch, cc). The Hamiltonian of system includes the basic Hamiltonian for two chains and the term which is responsible for interactions. It is shown that, when the energy of one type interaction (hh, cc) is more than the energy of mixed-type interaction (hc, ch), the correlation length grows sharply and melting interval becomes narrower. The system has a nontrivial behavior when the energy of mixed-type interactions (hc, ch) is higher than that of the one-type interaction (hh, cc). In this case one can observe the growth of the correlation length, and the melting curve has a two-stage character. The portion of junctions and the average length of helical fractions show that the merging and breakup of helical fractions take place.

Generalized model of polypeptide chain with limitations on the length of helical fractions

A model is proposed described by a Hamiltonian consisting of two terms corresponding to Hamiltonians of the generalized model of polypeptide chain (GMPC) with different scales of interaction. We consider a case where the long-scale interaction corresponds to attraction, while the short-scale interaction corresponds to repulsion; this case models the melting of the system in compact packing conditions (globularized polypeptide or DNA in capsid). In the framework of the transfer-matrix approach we calculate the correlation length and the helicity degree. It is shown that the temperature dependence of the correlation length is determined by the complex second eigenvalue of the transfer-matrix. In this regime the system displays a new type of correlations when the melting interval cannot be a measure of the system cooperativity.

Generalized Model of Polypeptide Chain with two-scale interactions

On the basis of the Generalized Model of Polypeptide Chain (GMPC) introduced earlier, which describes the helix-coil transition in both polypeptides and polynucleotides, a Hamiltonian is proposed consisting of two different-scale GMPC Hamiltonians. Within the framework of the transfer-matrix approach the degree of helicity and the correlation length are calculated. It is shown that the two-scale-interaction model may be reduced to a single-scale model with redefined parameter of the hydrogen bond closure.

Computer simulation of polypeptides in a confinement

A coarse-grained model of polypeptide chains confined in a slit formed by two parallel impenetrable surfaces was studied. The chains were flexible heteropolymers (polypeptides) built of two kinds of united atoms-hydrophobic and hydrophilic. The positions of the united atoms were restricted to the vertices of a [310] lattice. The force field consisted of a rigorous excluded volume, a long-distance potential between a pair of amino-acid residues and a local preference for forming secondary structure (helices). The properties of the chains were studied at a wide range of temperatures from good to bad solvent conditions. Monte-Carlo simulations were carried out using the algorithm based on the chain's local changes of conformation and employing the Replica Exchange technique. The influence of the chain length, the distances between the confining surfaces, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that the presence of the confinement chain complicates the process of the chain collapse to low-temperature structures. For some conditions, one can find a rapid decrease of chain size and a second transition indicated by the rapid decrease of the total energy of the system.