Heteropolymer Chain Research Articles

The effect of configurational complexity in hetero-polymers on the coil-globule phase transition

The coil-globule transition of hetero-polymer chains is studied here. By means of extensive Molecular Dynamics simulations, we show that the transition is directly linked to the complexity of the chain, which depends on the number of chemical species defined in the environment and the location of the binding sites along the polymer. In addition, when the number of species increases, we find that the distribution of binding sites plays an important role in triggering the transition, beyond the standard control parameters of the polymer model, i.e. binders concentration and binding affinity. Overall, our results show that by increasing the system complexity new organizational layers emerge, thus allowing a more structured control on the polymer thermodynamic state. This can be potentially applied to the study of chromatin architecture, as such polymer models have been broadly used to understand the molecular mechanisms of genome folding.

Schottky-like anomalies and phase transitions in ideal heteropolymer proteinogenic chains in terms of size and single-residue helical propensity

Proteins belong to a class of biological macromolecules capable to undergo thermodynamic phase transitions from random one-dimensional to three-dimensional non-periodic structures. For a large class of proteins, such configurational phase transitions can be directly associated with a passage from poor or non-biologically active states to highly biologically-active conformations. In this work we present a simple model suitable to study analytical and numerically thermodynamic properties for an ideal heteropolymer chain X1−X2⋯−XN composed by N aminoacid residues. This model includes as relevant parameters the single-residue helical propensity ωj associated to residue Xj and characteristic energies, ϵj and Uj corresponding to native and non-native contact energies, respectively. We derive analytical expressions for the partition function Z when two types of energy spectra E are considered. One corresponding to all-or-none transitions typically observed in protein folding and a second one which considers partial contributions to the folded state. Specific heat Cv, configurational entropy S, average energy 〈E〉 and average occupancy number N are discussed in order to analyze the onset of thermodynamic phase transitions and Schottky-like anomalies in polypeptide chains of different size.

Sequence-dependent association of alginate with sodium and calcium counterions

Molecular dynamics simulation is used to study in detail the binding of sodium and calcium ions to alginate chains, and its dependence on the content of guluronic (G) acid residues. Our previous studies showed that chains with different G content associate through different structural mechanisms due to differing degrees of rigidity of the ion-alginate chain complexes. Polymannuronate and polyguluronate chains form highly ordered structures due to their more rigid nature. Heteropolymer chains are more flexible and hence associate at higher ion and alginate concentrations, however, with association behavior that has a clear dependence on G content. The nature of interactions of sodium and calcium ions are shown to differ for poly-M, poly-G, and the heteropolymer compositions. Scattering curves of Ca2+-alginate solutions where found to have good agreement with the broken-rod SAXS model with nontrivial but clear dependence on G content, which is explained by chain flexibility and its relation to ion condensation.

Structural Characterization of Sodium Alginate and Calcium Alginate

Alginate readily aggregates and forms a physical gel in the presence of cations. The association of the chains, and ultimately gel structure and mechanics, depends not only on ion type, but also on the sequence and composition of the alginate chain that ultimately determines its stiffness. Chain flexibility is generally believed to decrease with guluronic residue content, but it is also known that both polymannuronate and polyguluronate blocks are stiffer than heteropolymeric blocks. In this work, we use atomistic molecular dynamics simulation to primarily explore the association and aggregate structure of different alginate chains under various Ca(2+) concentrations and for different alginate chain composition. We show that Ca(2+) ions in general facilitate chain aggregation and gelation. However, aggregation is predominantly affected by alginate monomer composition, which is found to correlate with chain stiffness under certain solution conditions. In general, greater fractions of mannuronic monomers are found to increase chain flexibility of heteropolymer chains. Furthermore, differences in chain guluronic acid content are shown to lead to different interchain association mechanisms, such as lateral association, zipper mechanism, and entanglement, where the mannuronic residues are shown to operate as an elasticity moderator and therefore promote chain association.

Role of single-point mutations and deletions on transition temperatures in ideal proteinogenic heteropolymer chains in the gas phase.

A coarse-grained statistical mechanics-based model for ideal heteropolymer proteinogenic chains of non-interacting residues is presented in terms of the size K of the chain and the set of helical propensities [Formula: see text] associated with each residue j along the chain. For this model, we provide an algorithm to compute the degeneracy tensor [Formula: see text] associated with energy level [Formula: see text] where [Formula: see text] is the number of residues with a native contact in a given conformation. From these results, we calculate the equilibrium partition function [Formula: see text] and characteristic temperature [Formula: see text] at which a transition from a low to a high entropy states is observed. The formalism is applied to analyze the effect on characteristic temperatures [Formula: see text] of single-point mutations and deletions of specific amino acids [Formula: see text] along the chain. Two probe systems are considered. First, we address the case of a random heteropolymer of size K and given helical propensities [Formula: see text] on a conformational phase space. Second, we focus our attention to a particular set of neuropentapeptides, [Met-5] and [Leu-5] enkephalins whose thermodynamic stability is a key feature on their coupling to [Formula: see text] and [Formula: see text] receptors and the triggering of biochemical responses.

Conformational transitions in random heteropolymer models.

We study the conformational properties of heteropolymers containing two types of monomers A and B, modeled as self-attracting self-avoiding random walks on a regular lattice. Such a model can describe in particular the sequences of hydrophobic and hydrophilic residues in proteins [K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)] and polyampholytes with oppositely charged groups [Y. Kantor and M. Kardar, Europhys. Lett. 28, 169 (1994)]. Treating the sequences of the two types of monomers as quenched random variables, we provide a systematic analysis of possible generalizations of this model. To this end we apply the pruned-enriched Rosenbluth chain-growth algorithm, which allows us to obtain the phase diagrams of extended and compact states coexistence as function of both the temperature and fraction of A and B monomers along the heteropolymer chain.

Planar diagrams from optimization for concave potentials

We propose a toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model, the sequential intervals between neighboring monomers along a chain are considered as quenched random variables, and energies of nonlocal bonds are assumed to be concave functions of those intervals. A few factors are neglected: the contribution of loop factors to the partition function, the variation in energies of different types of complementary nucleotides, the stacking interactions, and constraints on the minimal size of loops. However, the model captures well the formation of folded structures without pseudoknots in an arbitrary sequence of nucleotides. Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we derive the local difference equation for the ground state free energy of the chain with the planar (RNA-like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale free) and demonstrate the existence of a topological crossover from sequential to essentially nested configurations of paired links.

Discontinuous Molecular Dynamics (DMD) Study of Heteropolymer Collapse in an Explicit Solvent

In this study, we employ the discontinuous molecular dynamics simulation method to investigate the collapse properties of a single heteropolymer chain in an explicit solvent. Solvent density ρ, fraction of hydrophobic monomers n H (defined as the ratio of the number of hydrophobic monomers to the total number of monomers) and a hydrophobicity parameter λ (which controls the energy mismatch between the monomers and solvent particles) were systematically varied to examine their role in polymer collapse. The average static structure factor of the polymer was used to find the so-called θ-point characterizing the state of an ideal chain. Phase diagrams of ρ versus λ for the coil-globule transition were mapped out for different values of n H. Increasing the fraction of hydrophobic monomers n H, solvent density ρ, and hydrophobicity parameter λ were all shown to aid in stabilizing the globule phase. In an effort to explore scaling behaviour of the coil-globule phase diagram as a function of n H, and to investigate whether the phase boundaries for different n H collapsed on to one universal curve, we rescaled λ by n H (δ) λ; we determined δ = 1.72, in contrast to mean-field predictions of δ = 2.0.

Statistics of noncoding RNAs: alignment and secondary structure prediction

A new statistical approach to alignment (finding the longest common subsequence) of two random RNA-type sequences is proposed. We have constructed a generalized ‘dynamic programming’ algorithm for finding the extreme value of the free energy of two noncoding RNAs. In our procedure, we take into account the binding free energy of two random heteropolymer chains which are capable of forming the cloverleaf-like spatial structures typical for RNA molecules. The algorithm is based on two observations: (i) the standard alignment problem can be considered as a zero-temperature limit of a more general statistical problem of binding of two associating heteropolymer chains; (ii) this last problem can be generalized naturally to consider sequences with hierarchical cloverleaf-like structures (i.e. of RNA type). The approach also permits us to perform a ‘secondary structure recovery’. Namely, we can predict the optimal secondary structures of interacting RNAs in a zero-temperature limit knowing only their primary sequences.

The structure of star-branched copolymers. A Monte Carlo study

Abstract A coarse-grained model of a many-arm star-branched polymer chain has been studied. The chains were flexible heteropolymers built of two kinds of united atoms (segments) – hydrophobic and hydrophilic. The positions of segments were restricted to the vertices of a [310] hybrid lattice. The force field consisted of the softened excluded volume and the long-distance potential between a pair of non-bonded segments. The properties of these macromolecular models were studied in a wide range of temperatures from random coil to dense globule states. Monte Carlo simulations were performed using an algorithm based on the chain’s local changes of conformation and employing the Replica Exchange technique. The influence of the polymer length, the sequence of segments in the chain and the temperature on the dimension and the structure of chains have been studied. It has been shown that the process of the heteropolymer chain collapse to low-temperature structures is a complicated phenomenon and a possible explanation of this behavior has been discussed.

First-Order Transition of a Nanoscale Heteropolymer Chain with Lennard-Jones Potential

First-Order Transition of a Nanoscale Heteropolymer Chain with Lennard-Jones Potential

Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

We consider a pair of random heteropolymer chains with quenched primary sequences. For this system we have analyzed the dependence of average ground state energy per monomer E on chain length n in the ensemble of chains with uniform distribution of primary sequences of monomers. Every monomer of the first (second) chain is randomly and independently chosen with the uniform probability distribution p=1/c from a set of c different types A , B , C , D ,... (A', B', C', D',...) . Monomers of the first chain could form saturating reversible bonds with monomers of the second chain. The bonds between similar monomer types (such as A-A', B-B', C-C', etc.) have the attraction energy u , while the bonds between different monomer types (such as A-B', A-D', B-D', etc.) have the attraction energy v . The main attention is paid to the computation of the normalized free energy E(n) for intermediate chain lengths n and different ratios a=v/u at sufficiently low temperatures, when the entropic contribution of the loop formation is negligible compared to direct energetic interactions between chain monomers, and when the partition function of the chains is dominated by the ground state. The performed analysis allows one to derive the force f(x) which is necessary to apply for unzipping of two random heteropolymers of equal lengths whose ends are separated by the distance x , averaged over all equally distributed primary structures at low temperatures for fixed values a and c .

Sequence effects on the forced translocation of heteropolymers through a small channel

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (lambda(A)lambda(B)) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers ( approximately lambda(A)E and approximately lambda(B)E). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=2(18) monomers (all with the same number of A and B monomers).

Computer simulation of grafted polymer chains

A model of a film formed by polymer chains was used for theoretical considerations. The linear block heteropolymer chains were constructed on a cubic lattice. The lower fragment of chain was athermal while the upper one was interacting. Chains were terminally attached (grafted) to an impenetrable surface. The computer simulation of the system was performed by means of a Monte Carlo Metropolis-like sampling algorithm basing on the micromodifications of local conformation. The size of the brush components and the structure of the polymer film were investigated and discussed for different chain lengths and for good and bad solvent conditions.

The Structure and Thermodynamics of a Heteropolymer Chain in Confinement – Computer Simulation Studies

A coarse-grained model of heteropolymer (polypeptide) chains in a slit was designed in order to study the folding process in confinement. The idealized chains represented heteropolymers consisted of hydrophobic and hydrophilic united atoms, which were restricted to vertices of a (310) lattice. The force field consisted of the excluded volume, the long-distance potential between pairs of segments and the local helical potential. Monte Carlo simulations were performed using the algorithm with micromodifications of the chain's conformation and employing the Replica Exchange technique. The influence of the size of the slit, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that a moderate confinement stabilizes folded chains while a strong confinement does not.

Recognition of complex patterned substrates by heteropolymer chains consisting of multiple monomer types

We propose a statistical mechanical model of surface pattern recognition by heteropolymers with quenched monomer sequence distribution. The chemically heterogeneous pattern consists of different adsorption sites specifically distributed on a surface. The heteropolymer sequence is complementary with respect to the pattern. The concepts of recognition probability and recognition temperature are introduced. The algorithm for calculating the recognition probability is based on efficient recurrence procedures for evaluating the single-chain partition function of a chain macromolecule consisting of multiple monomer types, which interact with multiple types of adsorption sites. The temperature dependencies of the recognition probability are discussed. We address the critical role of the commensurability between the heteropolymer sequence and the distribution of the surface adsorbing sites on the polymer adsorption. Also, we address the question of how many types of monomer units in the heteropolymer are required for unambiguous recognition of compact target patterns. It is shown that perfect pattern recognition can be achieved for the strong-adsorption regime in the case of specifically structured compact patterns with multifunctional adsorption sites and heteropolymers with multiple monomer types when the degeneracy of the ground state is suppressed. The pattern recognition ability increases with the number of different types of monomer units and complementary adsorption sites. For random heteropolymers and patterns, the free energy change associated with the recognition process decreases linearly with increasing this number. Correlated random heteropolymers are capable of recognizing related patterns on a random background.

Three-Dimensional Lattice Monte Carlo Simulations of Model Proteins. IV. Proteins at an Oil−Water Interface

Lattice Monte Carlo simulations describe the adsorption of protein-like heteropolymer chains at an oil/water interface. The heteropolymers are designed sequences of 27 and 64 amino acid-type lattice sites taken from a 20-letter alphabet. We use our recently suggested energy scale to model oil and water. We investigate the effect of the oil parameters on adsorption properties of a single chain and on the aggregation of adsorbed chains while keeping the water parameters fixed to their optimum values found previously. By varying the oil parameters, we can cause a large range of adsorption behavior: from no adsorption to reversible adsorption to irreversible adsorption. We compare adsorption at a liquid/solid interface to that at a liquid/liquid interface. A liquid interface leads to stronger adsorption and denaturation than a solid interface with the same water and oil interaction parameters. We propose "optimal" oil parameters and use them to study multichain adsorption at a liquid interface.

A Quadratic Programming Formulation for the Design of Reduced Protein Models in Continuous Sequence Space

The notion of optimization is inherent in the design of a sequence of amino acid monomer types in a long heteropolymer chain of a protein that should fold to a desired conformation. Building upon our previous work wherein continuous parametrization and deterministic optimization approach were introduced for protein sequence design, in this paper we present an alternative formulation that leads to a quadratic programming problem in the first stage of a two-stage design procedure. The new quadratic formulation, which uses the linear interpolation of the states of the monomers in Stage I could be solved to identify the globally optimal sequence(s). Furthermore, the global minimum solution of the quadratic programming problem gives a lower bound on the energy for a given conformation in the sequence space. In practice, even a local optimization algorithm often gives sequences with global minimum, as demonstrated in the examples considered in this paper. The solutions of the first stage are then used to provide an appropriate initial guess for the second stage, where a rescaled Gaussian probability distribution function-based interpolation is used to refine the states to their original discrete states. The performance of this method is demonstrated with HP (hydrophobic and polar) lattice models of proteins. The results of this method are compared with the results of exhaustive enumeration as well as our earlier method that uses a graph-spectral method in Stage I. The computational efficiency of the new method is also demonstrated by designing HP models of real proteins. The method outlined in this paper is applicable to very large chains and can be extended to the case of multiple monomer types.

Thermodynamical properties of simple models of protein-like heteropolymers.

The lattice approximation of a heteropolymer chain as a model of a single polypeptide was used in the computer simulation. The residues of a model polypeptide were represented by the chain of alpha-carbons located on a very flexible [310] lattice. The force field that mimic the intramolecular interactions contained the long-range contact potential between the residues and the local preferences in forming helical structures. The chain consisted of two types of residues that had different hydrophobicity. The simulations were performed by means of the Replica Exchange Monte Carlo method combined with the Histogram method. The series of simulations were carried out to investigate the influence of both components of the force field on the transition temperature and the characteristics of the coil-to-globule transition. The properties of low-temperature ordered structures were determined. The thermodynamical description of the model chain was also given. The phase transition was found to be sharp and cooperative for longer chains and strong helical potential. The collapsed globule contained the strongly hydrophobic residues inside the globule while the remaining residues were mainly located close to the globule surface.

Monte Carlo simulation on thermodynamic properties of a heteropolymer chain

The equilibrium thermodynamic properties of a heteropolymer chain of 4 hydrophobic and 26 hydrophilic segments with Lennard-Jones interaction among segments were studied by multicanonical Monte Carlo methods in a three-dimensional off-lattice model. It is approved that the multicanonical algorithms provide us a practical way to accurately calculate thermodynamic properties of the chain at lower temperature. The collapse transition of a heteropolymer chain cooled from higher temperature is able to be separated in three steps: First, the hydrophobic segments associate together to form a hydrophobic core; then, the hydrophilic segments collapse on the surface of the core; finally, the heteropolymer chain reorganizes into its lowest energy state.