GroEL Allostery Illuminated by a Relationship between the Hill Coefficient and the MWC Model

Distinguishing between concerted, sequential and barrierless conformational changes: Folding versus allostery

Characterization of transition and intermediate states of reactions provides insights into their mechanisms and is often achieved through analysis of linear free energy relationships. Such an approach has been used extensively in protein folding studies but less so for analyzing allosteric transitions. Here, we point out analogies in ways to characterize pathways and intermediates in folding and allosteric transitions. Achieving an understanding of the mechanisms by which proteins undergo allosteric switching is important in many cases for obtaining insights into how they function.

All over or overall - Do we understand allostery?

Allostery is probably the most important concept in the regulation of cellular processes. Models to explain allostery are plenty. Each sheds light on different aspects but their entirety conveys an ambiguous feeling of comprehension and disappointment. Here, I discuss the most popular allostery models, their roots, similarities, and limitations. All of them are thermodynamic models. Naturally this bears a certain degree of redundancy, which forms the center of this review. After sixty years, many questions remain unanswered, mainly because our human longing for causality as base for understanding is not satisfied by thermodynamics alone. A description of allostery in terms of pathways, i.e., as a temporal chain of events, has been-, and still is-, a missing piece of the puzzle.

Mathematical models describing oxygen binding by hemoglobin

Despite the fact that the investigation of the structural and functional properties of hemoglobin dates back more than 150 years, the topic has not lost its relevance today. The most important component of these studies is the development of mathematical models that formalize and generalize the mechanisms determining the cooperative binding of ligands based on data on the structural and functional state of the protein. In this work, we review the mathematical relationships describing oxygen binding by hemoglobin, ranging from the classical Hüfner, Hill, and Adair equations to the Szabo-Karplus and tertiary two-state mathematical models based on the Monod-Wyman-Changeux and Koshland-Némethy-Filmer concepts. The generality of the considered equations as mathematical functions, bearing in their basis a power dependence, is demonstrated. The problems and possible solutions related to approximation of experimental data by the oxygenation equations with correlated fitting parameters are noted. Attention is paid to empirical equations, extended versions of the Hill equation, where the coefficient of cooperation is modulated by Gauss and Lorentz distributions as functions of partial oxygen pressure.

Dissecting the Thermodynamics of ATP Binding to GroEL One Nucleotide at a Time

Variable-temperature electrospray ionization (vT-ESI) native mass spectrometry (nMS) is used to determine the thermodynamics for stepwise binding of up to 14 ATP molecules to the 801 kDa GroEL tetradecamer chaperonin complex. Detailed analysis reveals strong enthalpy-entropy compensation (EEC) for the ATP binding events leading to formation of GroEL-ATP₇ and GroEL-ATP₁₄ complexes. The observed variations in EEC and stepwise free energy changes of specific ATP binding are consistent with the well-established nested cooperativity model describing GroEL-ATP interactions, viz., intraring positive cooperativity and inter-ring negative cooperativity (Dyachenko A.; Proc. Natl. Acad. Sci. U.S.A.2013, 110, 7235-7239). Entropy-driven ATP binding is to be expected for ligand-induced conformational changes of the GroEL tetradecamer, though the magnitude of the entropy change suggests that reorganization of GroEL-hydrating water molecules and/or expulsion of water from the GroEL cavity may also play key roles. The capability for determining complete thermodynamic signatures (ΔG, ΔH, and -TΔS) for individual ligand binding reactions for the large, nearly megadalton GroEL complex expands our fundamental view of chaperonin functional chemistry. Moreover, this work and related studies of protein-ligand interactions illustrate important new capabilities of vT-ESI-nMS for thermodynamic studies of protein interactions with ligands and other molecules such as proteins and drugs.

Partitioning the Hill coefficient into contributions from ligand-promoted conformational changes and subunit heterogeneity

Heterooligomers that undergo ligand-promoted conformational changes are ubiquitous in nature and involved in many essential processes. Conformational switching often leads to positive cooperativity in ligand binding that is reflected in a Hill coefficient with a value greater than one. The subunits comprising heterooligomers can differ, however, in their affinity for the ligand. Such so-called site heterogeneity results in apparent negative cooperativity that is reflected by a Hill coefficient with a value less than one. Consequently, positive cooperativity due to the ligand-promoted allosteric switch can be masked, in cases of such heterooligomers, by apparent negative cooperativity owing to site heterogeneity. Here, we derived expressions for the Hill coefficient, in the case of a heterodimer, in which the contributions from the ligand-promoted allosteric switch and site heterogeneity are separated. Using these equations and simulations for higher order oligomers, we show under which conditions site heterogeneity can significantly mask the extent of observed positive cooperativity.

Effect of magnitude and variability of energy of activation in multisite ultrasensitive biochemical processes

Protein activity is often regulated by ligand binding or by post-translational modifications such as phosphorylation. Moreover, proteins that are regulated in this way often contain multiple ligand binding sites or modification sites, which can operate to create an ultrasensitive dose response. Here, we consider the contribution of the individual modification/binding sites to the activation process, and how their individual values affect the ultrasensitive behavior of the overall system. We use a generalized Monod-Wyman-Changeux (MWC) model that allows for variable conformational free energy contributions from distinct sites, and associate a so-called activation parameter to each site. Our analysis shows that the ultrasensitivity generally increases as the conformational free energy contribution from one or more sites is strengthened. Furthermore, ultrasensitivity depends on the mean of the activation parameters and not on their variability. In some cases, we find that the best way to maximize ultrasensitivity is to make the contribution from all sites as strong as possible. These results provide insights into the performance objectives of multiple modification/binding sites and thus help gain a greater understanding of signaling and its role in diseases.

Population Distributions from Native Mass Spectrometry Titrations Reveal Nearest-Neighbor Cooperativity in the Ring-Shaped Oligomeric Protein TRAP

Allostery pervades macromolecular function and drives cooperative binding of ligands to macromolecules. To decipher the mechanisms of cooperative ligand binding, it is necessary to define, at a microscopic level, the thermodynamic consequences of binding of each ligand to its energetically coupled site(s). However, extracting these microscopic constants is difficult for macromolecules with more than two binding sites, because the observable [e.g., nuclear magnetic resonance (NMR) chemical shift changes, fluorescence, and enthalpy] can be altered by allostery, thereby distorting its proportionality to site occupancy. Native mass spectrometry (MS) can directly quantify the populations of homo-oligomeric protein species with different numbers of bound ligands, provided the populations are proportional to ion counts and that MS-compatible electrolytes do not alter the overall thermodynamics. These measurements can help decipher allosteric mechanisms by providing unparalleled access to the statistical thermodynamic partition function. We used native MS (nMS) to study the cooperative binding of tryptophan (Trp) to Bacillus stearothermophilus trp RNA binding attenuation protein (TRAP), a ring-shaped homo-oligomeric protein complex with 11 identical binding sites. MS-compatible solutions did not significantly perturb protein structure or thermodynamics as assessed by isothermal titration calorimetry and NMR spectroscopy. Populations of Trpn-TRAP11 states were quantified as a function of Trp concentration by nMS. The population distributions could not be explained by a noncooperative binding model but were described well by a mechanistic nearest-neighbor cooperative model. Nonlinear least-squares fitting yielded microscopic thermodynamic constants that define the interactions between neighboring binding sites. This approach may be applied to quantify thermodynamic cooperativity in other ring-shaped proteins.

Evolutionary and functional insights into the mechanism underlying body-size-related adaptation of mammalian hemoglobin

Hemoglobin (Hb) represents a model protein to study molecular adaptation in vertebrates. Although both affinity and cooperativity of oxygen binding to Hb affect tissue oxygen delivery, only the former was thought to determine molecular adaptations of Hb. Here, we suggest that Hb affinity and cooperativity reflect evolutionary and physiological adaptions that optimized tissue oxygen delivery. To test this hypothesis, we derived the relationship between the Hill coefficient and the relative affinity and conformational changes parameters of the Monod-Wymann-Changeux allosteric model and graphed the 'biophysical Hill landscape' describing this relation. We found that mammalian Hb cooperativity values all reside on a ridge of maximum cooperativity along this landscape that allows for both gross- and fine-tuning of tissue oxygen unloading to meet the distinct metabolic requirements of mammalian tissues for oxygen. Our findings reveal the mechanism underlying body size-related adaptation of mammalian Hb. The generality and implications of our findings are discussed.