Polymer principles of protein calorimetric two‐state cooperativity

Abstract

The experimental calorimetric two-state criterion requires the van't Hoff enthalpy DeltaH(vH) around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy DeltaH(cal) of the entire transition. We use an analytical model with experimental parameters from chymotrypsin inhibitor 2 to elucidate the relationship among several different van't Hoff enthalpies used in calorimetric analyses. Under reasonable assumptions, the implications of these DeltaH(vH)'s being approximately equal to DeltaH(cal) are equivalent: Enthalpic variations among denatured conformations in real proteins are much narrower than some previous lattice-model estimates, suggesting that the energy landscape theory "folding to glass transition temperature ratio" T(f) /T(g) may exceed 6.0 for real calorimetrically two-state proteins. Several popular three-dimensional lattice protein models, with different numbers of residue types in their alphabets, are found to fall short of the high experimental standard for being calorimetrically two-state. Some models postulate a multiple-conformation native state with substantial pre-denaturational energetic fluctuations well below the unfolding transition temperature, or predict a significant post-denaturational continuous conformational expansion of the denatured ensemble at temperatures well above the transition point, or both. These scenarios either disagree with experiments on protein size and dynamics, or are inconsistent with conventional interpretation of calorimetric data. However, when empirical linear baseline subtractions are employed, the resulting DeltaH(vH)/DeltaH(cal)'s for some models can be increased to values closer to unity, and baseline subtractions are found to correspond roughly to an operational definition of native-state conformational diversity. These results necessitate a re-assessment of theoretical models and experimental interpretations.

Probing Possible Downhill Folding: Native Contact Topology Likely Places a Significant Constraint on the Folding Cooperativity of Proteins with ∼40 Residues

“…This condition implies a two-state-like enthalpy distribution at the transition midpoint, with a high free-energy barrier separating the folded and unfolded states of a given protein. 49 Recent analyses 56,62 showed that the ΔH vH /ΔH cal ≈ 1 condition is intimately related to a high Z score (commonly used in protein structure prediction) as well as a large T f /T g ratio between folding and glass-transition temperatures in energy landscape theories (see Eqs. (5) and (6) on pp.…”

“…The high degree of cooperativity of many barrier-limited proteins is a physically remarkable property, 49 suggesting that cooperativity itself is a consequence of stringent biological selection. [50][51][52] This recent finding from theory 49,53,54 and experiment 50 poses a serious conceptual challenge since natural two-state proteins are significantly more cooperative than coarse-grained protein chain models 55 constructed to embody common intuitive notions of pairwise additive interactions 56 (e.g., the hydrophobic-polar interaction scheme 57,58 ). Apparently, only models that explicitly 59,60 or tacitly 61 (see comment on pp.…”

“…74 Model cooperativity of a given structure depends on the interaction scheme. 40,59 Some common model interaction schemes produce cooperativity lower than that of natural proteins 53,56 whereas interaction schemes with many-body effects afford higher cooperativity. 59,75 We adopt the intuitive working assumption that the diversity in predicted behaviors of a given structure from models with different interaction schemes should be reflective of-though it is not identical with-the range of the corresponding physical properties allowed by the convergence set of amino acid sequences encoding for the structure.…”

Desolvation Barrier Effects Are a Likely Contributor to the Remarkable Diversity in the Folding Rates of Small Proteins

“…37 It was soon realized 38,39 that a likely origin for this shortcoming is that continuum Gō-like models with pairwise-additive Lennard-Jones-like potentials as well as common lattice Gō models fold less cooperatively than real two-state-like proteins. 40,41 Lattice modeling efforts inspired by this realization showed more diverse folding rates when cooperativity was enhanced by nonadditive many-body energy terms. 38,39 These studies further suggested that the remarkable diversity of experimental folding rates among two-state-like proteins is probably underpinned by specific, rather than generic, forms of many-body interactions, for there are substantial variations in folding rate diversity when different many-body interaction schemes were applied.…”

Detection and Structure Determination of an Equilibrium Unfolding Intermediate of Rd-apocytochrome b562: Native Fold with Non-native Hydrophobic Interactions

“…A series of insightful papers by Chan and co-workers have shown that all past lattice models failed to reproduce the linear dependence of the logarithm of the folding and unfolding rate constants on denaturant concentrations (linear Chevron plot) in a meaningful range of folding rates, a typical folding behavior of small apparent two-state proteins. [37][38][39][40][41] In order to reproduce the linear Chevron plot, they found that a near-flat energy landscape for the unfolded state and an additional stabilizing cooperative energy term (many-body interactions) for the native state were required. Interestingly, hidden intermediates like those observed in the native-state HX experiments in real proteins have also emerged from a new four-helix bundle lattice model when many-body interactions for the formation of the helices are added (H. Kaya & H.S.…”