Flory's Isolated-pair Hypothesis Research Articles

Exploring Nearest Neighbor Interactions and Their Influence on the Gibbs Energy Landscape of Unfolded Proteins and Peptides.

The Flory isolated pair hypothesis (IPH) is one of the corner stones of the random coil model, which is generally invoked to describe the conformational dynamics of unfolded and intrinsically disordered proteins (IDPs). It stipulates, that individual residues sample the entire sterically allowed space of the Ramachandran plot without exhibiting any correlations with the conformational dynamics of its neighbors. However, multiple lines of computational, bioinformatic and experimental evidence suggest that nearest neighbors have a significant influence on the conformational sampling of amino acid residues. This implies that the conformational entropy of unfolded polypeptides and proteins is much less than one would expect based on the Ramachandran plots of individual residues. A further implication is that the Gibbs energies of residues in unfolded proteins or polypeptides are not additive. This review provides an overview of what is currently known and what has yet to be explored regarding nearest neighbor interactions in unfolded proteins.

A new interpretation of the structure and solvent dependence of the far UV circular dichroism spectrum of short oligopeptides.

UV circular dichroism (UVCD) spectroscopy is a prominent tool for exploring secondary structures of polypeptides and proteins. In the unfolded state of these biomolecules, most of the individual residues primarily sample a conformation called polyproline II. Its CD spectrum contains a negatively biased positive couplet with a pronounced negative maximum below and a weak positive maximum above 200 nm. It is traditionally rationalized in terms of an excitonic coupling mechanism augmented by polarization effects. In this work, we carry out new time-dependent density functional theory calculations on the cationic tripeptide GAG in implicit and explicit water to determine the transitions that give rise to the observed CD signals of polyproline II and β-strand conformations. Our results reveal a plethora of electronic transitions that are governed by configurational interactions between multiple molecular orbital transitions of comparable energy. We also show that reproducing the CD spectra of polyproline II and β-strand conformations requires the explicit consideration of water molecules. The structure dependence of delocalized occupied orbitals contributes to the experimentally-observed invalidation of Flory's isolated pair hypothesis.

Molecular Simulations of the Configurational Entropy of the Trp-Cage Miniprotein

Understanding conformational entropy changes in globular protein folding is essential to both predictive models of protein structure and the development of high-affinity pharmaceuticals. The conformational entropy of the Trp-cage miniprotein is calculated using all-atom molecular dynamics simulations and the probability distributions of dihedral angles per residue. We use two force fields, Amber-99SB and Amber-94, in water and water-urea solvents in our calculations. We compute the configurational entropy using models that included correlations within individual amino acids and with nearest neighbors. We find that the entropy depends on sequence and position of the chain on the protein. Neighboring residues are shown to only have a less than 10% influence on individual residue entropies. AMBER-94 force field is shown to decrease the entropy of the alpha helical region in the unfolded state, suggesting anomalous residual helix formation in the unfolded state. Unexpectedly, the water-urea solution is shown to destabilize the alpha helical region in the folded state while stabilizing the alpha helical region in the folded state. The results of this project give new context with which to examine Flory's isolated-pair hypothesis as well as the Levinthal paradox. The results could be used to further examine the assumptions underlying the interpretation of protein NMR experiments that attempt to measure the configurational entropy. This work was done as part of an NSF REU Summer Program (Grant DMR-0850934)and MCB-0543769.

Computational basis of knowledge‐based conformational probabilities derived from local‐ and long‐range interactions in proteins

The probabilities of the various basins in Ramachandran maps are examined critically. The theoretical basis of probability calculations both from molecular computations and from protein libraries are discussed. The well-defined basins of the Ramachandran maps are treated as rotational isomeric states. Statistical independence and dependence of the states of different residues along the peptide chain are discussed. The Flory isolated pair hypothesis, near neighbor correlations, context effects, and long-range correlations are examined critically. A method of evaluating long-range correlations in helical and extended sequences is introduced in analogy with earlier polymer theory. Three different protein libraries are constructed where data is considered from residues in the (i) coiled regions, (ii) all regions, and (iii) only the helical and extended regions of proteins. Singlet and pairwise dependent probabilities calculated from these libraries are used to predict whether a given sequence is helical or extended. Predictions using pairwise dependence were not better than those using singlet probabilities. Modeling of long-range correlations improved the predictions significantly. Removal of the Chameleon sequences from the data set also improved the predictions, but to a lesser extent.

Exhaustive Metropolis Monte Carlo sampling and analysis of polyalanine conformations adopted under the influence of hydrogen bonds

We propose a novel Metropolis Monte Carlo procedure for protein modeling and analyze the influence of hydrogen bonding on the distribution of polyalanine conformations. We use an atomistic model of the polyalanine chain with rigid and planar polypeptide bonds, and elastic alpha carbon valence geometry. We adopt a simplified energy function in which only hard-sphere repulsion and hydrogen bonding interactions between the atoms are considered. Our Metropolis Monte Carlo procedure utilizes local crankshaft moves and is combined with parallel tempering to exhaustively sample the conformations of 16-mer polyalanine. We confirm that Flory's isolated-pair hypothesis (the steric independence between the dihedral angles of individual amino acids) does not hold true in long polypeptide chains. In addition to 3(10)- and alpha-helices, we identify a kink stabilized by 2 hydrogen bonds with a shared acceptor as a common structural motif. Varying the strength of hydrogen bonds, we induce the helix-coil transition in the model polypeptide chain. We compare the propensities for various hydrogen bonding patterns and determine the degree of cooperativity of hydrogen bond formation in terms of the Hill coefficient. The observed helix-coil transition is also quantified according to Zimm-Bragg theory.

Scaling Behavior and Structure of Denatured Proteins

An ensemble of random-coil conformations with no persistent structures has long been accepted as the classical model of denatured proteins due to its consistency with the experimentally determined scaling of protein sizes. However, recent NMR spectroscopy studies on proteins at high chemical denaturant concentrations suggest the presence of significant amounts of native-like structures, in contrast to the classical random-coil picture. To reconcile these seemingly controversial observations, we examine thermally denatured states of experimentally characterized proteins by using molecular dynamics simulations. For all studied proteins, we find that denatured states indeed have strong local conformational bias toward native states while a random-coil power law scaling of protein sizes is preserved. In addition, we explain why experimentally determined size of the protein creatine kinase does not follow general scaling. In simulations, we observe that this protein exhibits a stable intermediate state, the size of which is consistent with the reported experimental observation.

Neighbor Effect on PPII Conformation in Alanine Peptides

The polyproline II (PPII) conformation is dominant in short alanine oligomers. The noncooperativity of PPII structure in alanine peptides indicates that PPII in water is locally determined and that alanine neighbors are consistent with Flory's isolated pair hypothesis. However, neighbor effects from beta-branched or bulky aromatic residues tend to increase the Phi angle of the nearest neighbor as observed in coil library data. Here we demonstrate directly the neighbor effect using short alanine model peptides GGAAAGG, GGLnALnGG (Ln is norleucine), GGIAAGG, and GGIAIGG. The far-UV CD spectra, NMR 3JalphaN coupling constant, and H-D hydrogen exchange measurements reveal that Ile reduces the PPII content of the probe Ala side chain relative to Ala or norLeu. The free energy differences are consistent with predictions from electrostatic solvation free energy (ESF) calculations. The results indicate that prediction of PPII propensities or scales requires including the neighbor effect.

Preferred peptide backbone conformations in the unfolded state revealed by the structure analysis of alanine-based (AXA) tripeptides in aqueous solution.

We have combined Fourier transform IR, polarized Raman spectroscopy, and vibrational CD measurements of the amide I' band profile of alanyl-X-alanine tripeptides in (2)H(2)O to obtain the dihedral angles of their central amino acid residue. X represents glycine, valine, methionine, histidine, serine, proline, lysine, leucine, tryptophan, tyrosine, and phenylalanine. The experimental data were analyzed by means of a recently developed algorithm, which exploits the excitonic coupling between the amide modes of the two peptide groups. The results were checked by measuring the respective electronic CD spectra. The investigated peptides can be sorted into three classes. Valine, phenylalanine, tryptophan, histidine, and serine predominantly adopt an extended beta-strand conformation. Cationic lysine and proline prefer a polyproline II-like structure. Alanine, methionine, glycine, and leucine populate these two conformations with comparable probability. Our results are in variance with the prediction of the random-coil model, but supportive of Flory's isolated-pair hypothesis. We combined the obtained structural propensities of the investigated residues and similar information about other residues in the literature (i.e., glutamate, aspartate, isoleucine, and glutamine) to predict possible conformations of the monomeric amyloid beta peptide A beta(1-42) in aqueous solution, which reproduces results from most recent spectroscopic studies. Thus, it is demonstrated that the unfolded state of peptides can be understood in terms of the intrinsic structural propensities of their amino acid residues.

Exploring Flory's isolated-pair hypothesis: statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A.

To evaluate Flory's isolated-pair hypothesis in the context of helical peptides, we explore equilibrium conformations of alpha-helix-forming polypeptides as a function of temperature by means of replica exchange molecular dynamics in conjunction with the CHARMM/GB implicit solvent force field and the weighted histogram analysis method. From these simulations, Zimm-Bragg parameters, s and sigma, of Ac-Alan-NMe are computed as a function of temperature. The values obtained for s(T) and sigma(T) remain unchanged along the length of the polypeptide except for very short chains and yield results consistent with measurements based on short helix-forming peptides but suggest larger s values than anticipated from polymer-based measurements. From direct estimates of the density of states for Ac-Alan-NMe (n = 3-20) and peptide constructs based on the C peptide from RNase A, the conformational entropy is calculated versus temperature. The calculated S(T) shows a clear proportionality to the chain length over a wide range of temperature. This is observed in polypeptides with both significantly branched and simple methyl (alanine) side chains. These results provide evidence for the validity of Flory's isolated pair hypothesis, at least in the context of helical peptides and helix-to-coil transitions in these peptides.

The Flory isolated-pair hypothesis is not valid for polypeptide chains: implications for protein folding.

Using an all-atom representation, we exhaustively enumerate all sterically allowed conformations for short polyalanyl chains. Only intrachain interactions are considered, including one adjustable parameter, a favorable backbone energy (e.g., a peptide hydrogen bond). The counting is used to reevaluate Flory's isolated-pair hypothesis, the simplifying assumption that each phi,psi pair is sterically independent. This hypothesis is a conceptual linchpin in helix-coil theories and protein folding. Contrary to the hypothesis, we find that systematic local steric effects can extend beyond nearest-chain neighbors and can restrict the size of accessible conformational space significantly. As a result, the entropy price that must be paid to adopt any specific conformation is far less than previously thought.