Transitions Of Biopolymers Research Articles

Thermal transitions in a one-dimensional, finite-size Ising model

We revisit the one-dimensional ferromagnetic Ising spin chain with a finite number of spins and periodic boundaries, deriving analytically and verifying numerically its various stationary and dynamical properties at different temperatures. In particular, we determine the probability distributions of magnetization, the number of domain walls, and the corresponding residence times for different chain lengths and magnetic fields. While we study finite systems at thermal equilibrium, we identify several temperatures similar to the critical temperatures for first-order phase transitions in the thermodynamic limit. We illustrate the utility of our results by their application to structural transitions in biopolymers having non-trivial intermediate equilibrium states.

Markov state models from hierarchical density-based assignment

Markov state models (MSMs) have become one of the preferred methods for the analysis and interpretation of molecular dynamics (MD) simulations of conformational transitions in biopolymers. While there is great variation in terms of implementation, a well-defined workflow involving multiple steps is often adopted. Typically, molecular coordinates are first subjected to dimensionality reduction and then clustered into small "microstates," which are subsequently lumped into "macrostates" using the information from the slowest eigenmodes. However, the microstate dynamics is often non-Markovian, and long lag times are required to converge the relevant slow dynamics in the MSM. Here, we propose a variation on this typical workflow, taking advantage of hierarchical density-based clustering. When applied to simulation data, this type of clustering separates high population regions of conformational space from others that are rarely visited. In this way, density-based clustering naturally implements assignment of the data based on transitions between metastable states, resulting in a core-set MSM. As a result, the state definition becomes more consistent with the assumption of Markovianity, and the timescales of the slow dynamics of the system are recovered more effectively. We present results of this simplified workflow for a model potential and MD simulations of the alanine dipeptide and the FiP35 WW domain.

The nature of nonfreezing water in carbohydrate polymers

In an aqueous environment, carbohydrate polymers are surrounded by hydration shells consisting of water molecules that are sometimes called “bound”. When polymer solutions are subjected to low temperatures, a part of water turns into ice, another part remains in the biopolymer phase and is called “nonfreezing water”. Thermodynamic analysis of water freezing shows that the amount of non-freezing water does not reflect the amount of bound water, neither can it be used as a measure of strength of polymer-water interactions. Upon deep cooling, crystallization of water should desiccate polymers more than is observed in experiment. The reason for existence of non-freezing water is an interplay between the crystallization of water and the glass transition in biopolymers that prevents dehydration.

Simple Approach to Generate Fluorescent Quantum Dots/Gelatin Composite with Thermo-responsive and Reversible Sol-gel Transition

Stimuli-responsive sol-gel transitions of biopolymers triggered by stimuli (e.g., temperature, pH, light, and electric field) have received tremendous attention due to their potential applications in controlled release of drugs, tissue engineering, and new functional materials. Herein, we use a simple approach to generate a fluorescent composite of quantum dots/gelatin with reversible sol-gel transition triggered by temperature stimuli. We initially prepared the aqueous CdS quantum dots with clear yellow fluorescence by a single-step process. These CdS quantum dots can reserve their fluorescence after they were combined with gelatin. Specifically, rheological measurements and vial inversion tests both confirm that CdS quantum dots/gelatin composite can undergo reversible sol-gel transition initiated by temperature stimuli near physiological temperature. Furthermore, it is shown that loading, preservation and release of CdS quantum dots in aqueous medium can be controlled by adjusting the temperature to trigger the sol-gel transition of the composite. Consequently, it can be expected that this fluorescent quantum dots/gelatin composite with thermo-responsive and reversible sol-gel transition has promising applications in biomedical fields such as bioimaging, biosensing, and drug delivery.

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.

Water Sorption and Glass Transition of Pig Gastric Mucin Studied by QCM-D

Hydration of films of pig gastric mucin was studied using a quartz crystal microbalance with dissipation monitoring (QCM-D) equipped with a humidity module. As a prerequisite, the water adsorption isotherm of a clean silica surface was determined. Atomic force microscopy was used to characterize the changes occurring on the silica surface after repeated sorption/desorption and cleaning cycles. The water sorption isotherms of several hundreds of nanometers thick mucin films were obtained in QCM-D experiments using analysis of overtone behavior. The results show that the sorption isotherms are not dependent on the film thicknesses and are in good agreement with sorption calorimetric data on mucin in the bulk phase. Moreover, hydration-induced changes of rheological properties of mucin films were investigated using a model-free approach. The ratio of G'/G″ was evaluated as a function of relative humidity. The transition from solidlike behavior to liquidlike behavior was observed in the same humidity range as in sorption calorimetric experiments. Thus, ability of QCM-D to monitor glass transition in biopolymers was demonstrated.

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).

Weak temporal signals can synchronize and accelerate the transition dynamics of biopolymers under tension

In addition to thermal noise, which is essential to promote conformational transitions in biopolymers, the cellular environment is replete with a spectrum of athermal fluctuations that are produced from a plethora of active processes. To understand the effect of athermal noise on biological processes, we studied how a small oscillatory force affects the thermally induced folding and unfolding transition of an RNA hairpin, whose response to constant tension had been investigated extensively in both theory and experiments. Strikingly, our molecular simulations performed under overdamped condition show that even at a high (low) tension that renders the hairpin (un)folding improbable, a weak external oscillatory force at a certain frequency can synchronously enhance the transition dynamics of RNA hairpin and increase the mean transition rate. Furthermore, the RNA dynamics can still discriminate a signal with resonance frequency even when the signal is mixed among other signals with nonresonant frequencies. In fact, our computational demonstration of thermally induced resonance in RNA hairpin dynamics is a direct realization of the phenomena called stochastic resonance and resonant activation. Our study, amenable to experimental tests using optical tweezers, is of great significance to the folding of biopolymers in vivo that are subject to the broad spectrum of cellular noises.

Transition Path Times for Nucleic Acid Folding Determined from Energy-Landscape Analysis of Single-Molecule Trajectories

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τ(TP), and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τ(TP)~10 μs and D~10(-13-14) m(2)/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.

Charged Polymers in the Attractive Regime: A First-Order Transition from Brownian Scaling to Four-Point Localization

We study a quenched charged-polymer model, introduced by Garel and Orland in 1988, that reproduces the folding/unfolding transition of biopolymers. We prove that, below the critical inverse temperature, the polymer is delocalized in the sense that: (1) The rescaled trajectory of the polymer converges to the Brownian path; and (2) The partition function remains bounded. At the critical inverse temperature, we show that the maximum time spent at points jumps discontinuously from 0 to a positive fraction of the number of monomers, in the limit as the number of monomers tends to infinity. Finally, when the critical inverse temperature is large, we prove that the polymer collapses in the sense that a large fraction of its monomers live on four adjacent positions, and its diameter grows only logarithmically with the number of the monomers. Our methods also provide some insight into the annealed phase transition and at the transition due to a pulling force; both phase transitions are shown to be discontinuous.

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.

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.

Beyond the nearest‐neighbor Zimm–Bragg model for helix‐coil transition in peptides

The nearest-neighbor (micro = 1) variant of the Zimm and Bragg (ZB) model has been extensively used to describe the helix-coil transition in biopolymers. In this work, we investigate the helix-coil transition for a 21-residue alanine peptide (AP) with the ZB model up to fourth nearest neighbor (micro = 1, 2, 3, and 4). We use a matrix approach that takes into account combinations of any number of helical stretches of any length and therefore gives the exact statistical weight of the chain within the assumptions of the ZB model. The parameters of the model are determined by fitting the temperature-dependent circular dichroism and Fourier transform infrared experimental spectra of the AP. All variants of the model fit the experimental data, thus giving similar results in terms of the macroscopic observables, such as temperature-dependent fractional helicity. However, the resulting microscopic parameters, such as distributions of the individual residue helical probabilities and free energy surfaces, vary significantly depending on the variant of the model. Overall, the mean residue enthalpy and entropy (in the absolute value) both increase with micro, but combined yield essentially the same "effective" value of the ZB propagation parameters for all micro. Greater helical probabilities for individual residues are predicted for larger micro, in particular, near the center of the sequence. The ZB nucleation parameters increase with increasing micro, which results in a lower free energy barrier to helix nucleation and lower apparent "cooperativity" of the transition. The significance of the long-range interactions for the predictions of ZB model for helix-coil transition, the calculated model parameters and the limitations of the model are discussed.

Statistical thermodynamics of helix–coil transitions in biopolymers

Helical conformations, such as the α-helix in polypeptides and the double helix in DNA, are common structural elements in biopolymers. As the temperature is raised or the pH is changed to extremes of acidity or alkalinity, the helix becomes disordered into a random coil state. The helix–coil transition has been extensively studied, both experimentally and theoretically, as a model for conformational transitions in biopolymers and as a way to obtain information about the intermolecular forces which stabilize biopolymer structure. We develop three theoretical treatments that describe the helix–coil transition with increasing degrees of detail and rigor: the all-or-none model, the zipper model, which allows initiation of the helix only once along the polymer chain, and the matrix model, which places no restrictions on helix–coil junctions. The matrix model is mathematically similar to the familiar one-dimensional Ising model.

Finite one-dimensional spin systems as models of biopolymers

New models are proposed for describing various properties of biopolymers, especially those of proteins and nucleic acids. Each model is constituted of a set of spins arranged on a chain, and each pair of spins produces an interaction. We examine the transitions of these spin systems between the ground state and the disordered state. It is found that the transitions of the present spin systems demonstrate various properties in response to values of the so-called interaction energy. If we define interaction energy parameters with no so-called frustration, the system exhibits two-state transitions, similar to the folding-unfolding transition of small proteins. The addition of frustrations to the model produces effects similar to those of mutations in proteins. On the other hand, if the interactions between two spins attenuate as a function of their separation along the chain, the transition of the system has characteristics similar to those of nucleic acids. Thus, the present spin systems can offer a unified view of the folding-unfolding transition of biopolymers in terms of differences in the pairwise interactions between spins. Based on our models, we propose a condition for two-state transition behavior for proteins.

Sol ‐ gel transition in biopolymers

AbstractRheological measurements have been performed on pectin biopolymers close to the sol‐gel transition. From these measurements scaling exponents were determined independently for the viscosity, s = 0.82(5), for the elastic modulus, t = 1.93(8), for the frequency‐dependent modulus, Δ = 0.71(2), and for the relaxation times below and above the transition, vz = 2.67(12) and vz' = 2.65(9). The exponents satisfy the scaling relations predicted by the theory and their numerical values agree with those from scalar elasticity percolation.

Phase transitions in sequence matches and nucleic acid structure.

Analyses of phase transitions in biopolymers have previously been restricted to studies of average behavior along macromolecules. Extremal properties, such as longest helical region, can now be studied with a new family of probability distributions [Arratia, R., Gordon, L. & Waterman, M. S. (1986) Ann. Stat. 14, 971-993]. Not only is such extremal behavior analyzed with great precision, but new phase transitions are determined. One phase transition occurs when behavior of the free energy of the longest helical region abruptly changes from proportional to sequence length. The annealing of two single-stranded molecules and the melting of a double helix are both considered. These results, initially suggested by studies of optimal matching of random DNA sequences [Smith, T. F., Waterman, M. S. & Burks, C. (1985) Nucleic Acids Res. 13, 645-656], also have importance for significance tests in comparison of nucleic acid or protein sequences.

Characterization of cooperative conformational transitions by Fourier transform infrared spectroscopy: application to phospholipid binary mixtures

Temperature-induced cooperative conformational transitions in biopolymers may be examined in aqueous solution by the use of Fourier transform infrared spectroscopy. The transition is described in terms of a two-state model with a fractional population parameter (which describes the degree of transition at various values intermediate between the two limiting cases) that can be generated by a least-squares technique. This procedure allows for calculation of a conformational index without assuming a linear dependence of the infrared parameter on the extent of transition. Calculations based on the Zimm–Bragg theory of cooperative conformational transitions allow thermodynamic quantities to be derived using the conformational index in conjunction with calorimetric measurements.The method is illustrated with data from the gel/liquid-crystalline phase transitions of binary phospholipid vesicles where the use of isotopic substitution allows the conformation of each component of the binary mixture to be independently monitored. The data suggest the coexistence of well-defined structural domains of phospholipid as well as the preferential clustering of one of the lipid components at the interface between the two phases.

Energetics of structural transitions in biopolymers

Of all structural transitions in biopolymers the helix coil transition of DNA as prerequisition of replication and transcription is considered. The theoretical concept of weak bonds and the experimental procedure of measurements of cooperative processes is outlined. As result we present the complete thermodynamic state functions ΔH, ΔG and ΔS for any DNA sequence.

Statistical thermodynamic analysis of the excess heat capacity function of macromolecular systems

The deconvolution theory of thermal transitions has proven to be a powerful method with which to analyze the heat capacity function of macromolecular systems. In this article, the basic results of the theory will be presented and their application to multistate transitions and general cooperative transitions of biopolymers and phospholipid membranes will be discussed. INTRODUCTION The development of highly precise differential scanning calorimeters has made possible the accurate definition of the heat capacity function associated with thermally-induced transitions of proteins, polypeptides, nucleic acids, lipid bilayers and other macromolecular systems. The importance of having experimental access to the exact shape of this function is that it contains all the information necessary to develop a complete thermodynamic description of a thermally-induced transition. In fact, it has been demonstrated that the excess heat capacity function can be appropriately transformed to yield the partition function of such a system and that this partition function can be used to deduce the microscopic mechanism of the transition (Refs. 1-6). In this article the analytical methods directed to obtaining a detailed statistical thermodynamic description of complex macromolecular systems will be presented. These methods constitute the basis of the deconvolution theory of thermal-transitions in macromolecules and, thus f.ar, have been applied to the study of protein unfolding reactions, helix-coil transitions in polynucleotides, thermal-transitions of transfer ribonucleic acids (tRNA) and biomembrane phase transitions. MACROMOLECULAR CONFORMATIONAL TRANSITIONS Most theories directed toward describing the molecular basis of function and modulation of biochemical systems include structural variations of the relevant macromolecules. Thus important questions relate to what are the characteristics of the equilibrium and dynamic fluctuations within an ensemble of such states. In general, the accessible structural states of a macromolecular system can be represented by the following reaction scheme: A+A A A (1) 0+ 1+ 2 n where the indexing of states is such that the enthalpy of state i (H.) is greater than the i-l state. (i.e. H>H.,). Thus as temperature i increased the population distribution mohotonically progresses toward state n. A normalized partition function for this system can be written in terms of the Gibbs energy differences as: