Role of coupling entropy in establishing the nature and magnitude of allosteric response

Theory vs. experiment: The rise of the dynamic view of proteins

Over the past century, the scientific conception of the protein has evolved significantly. This paper focuses on the most recent stage of this evolution, namely, the origin of the dynamic view of proteins and the challenge it posed to the static view of classical molecular biology. Philosophers and scientists have offered two hypotheses to explain the origin of the dynamic view and its slow reception by structural biologists. Some have argued that the shift from the static to the dynamic view was a Kuhnian revolution, driven by the accumulation of dynamic anomalies, while others have argued that the shift was caused by new empirical findings made possible by technological advances. I analyze this scientific episode and ultimately reject both of these empiricist accounts. I argue that focusing primarily on technological advances and empirical discoveries overlooks the important role of theory in driving this scientific change. I show how the application of general thermodynamic principles to proteins gave rise to the dynamic view, and a commitment to these principles then led early adopters to seek out the empirical examples of protein dynamics, which would eventually convince their peers. My analysis of this historical case shows that empiricist accounts of modern scientific progress-at least those that aim to explain developments in the molecular life sciences-need to be tempered in order to capture the interplay between theory and experiment.

Millisecond Timescale Motions Connect Amino Acid Interaction Networks in Alpha Tryptophan Synthase

Tryptophan synthase is a model system for understanding allosteric regulation within enzyme complexes. Amino acid interaction networks were previously delineated in the isolated alpha subunit (αTS) in the absence of the beta subunit (βTS). The amino acid interaction networks were different between the ligand-free enzyme and the enzyme actively catalyzing turnover. Previous X-ray crystallography studies indicated only minor localized changes when ligands bind αTS, and so, structural changes alone could not explain the changes to the amino acid interaction networks. We hypothesized that the network changes could instead be related to changes in conformational dynamics. As such, we conducted nuclear magnetic resonance relaxation studies on different substrate- and products-bound complexes of αTS. Specifically, we collected ¹⁵N R₂ relaxation dispersion data that reports on microsecond-to-millisecond timescale motion of backbone amide groups. These experiments indicated that there are conformational exchange events throughout αTS. Substrate and product binding change specific motional pathways throughout the enzyme, and these pathways connect the previously identified network residues. These pathways reach the αTS/βTS binding interface, suggesting that the identified dynamic networks may also be important for communication with the βTS subunit.

An engineered photoswitchable mammalian pyruvate kinase

Changes in allosteric regulation of glycolytic enzymes have been linked to metabolic reprogramming involved in cancer. Remarkably, allosteric mechanisms control enzyme function at significantly shorter time-scales compared to the long-term effects of metabolic reprogramming on cell proliferation. It remains unclear if and how the speed and reversibility afforded by rapid allosteric control of metabolic enzymes is important for cell proliferation. Tools that allow specific, dynamic modulation of enzymatic activities in mammalian cells would help address this question. Towards this goal, we have used molecular dynamics simulations to guide the design of mPKM2 internal light/oxygen/voltage-sensitive domain 2 (LOV2) fusion at position D24 (PiL[D24]), an engineered pyruvate kinase M2 (PKM2) variant that harbours an insertion of the light-sensing LOV2 domain from Avena Sativa within a region implicated in allosteric regulation by fructose 1,6-bisphosphate (FBP). The LOV2 photoreaction is preserved in the PiL[D24] chimera and causes secondary structure changes that are associated with a 30% decrease in the Km of the enzyme for phosphoenolpyruvate resulting in increased pyruvate kinase activity after light exposure. Importantly, this change in activity is reversible upon light withdrawal. Expression of PiL[D24] in cells leads to light-induced increase in labelling of pyruvate from glucose. PiL[D24] therefore could provide a means to modulate cellular glucose metabolism in a remote manner and paves the way for studying the importance of rapid allosteric phenomena in the regulation of metabolism and enzyme control.

Kinetic and Thermodynamic Analysis of Acetyl-CoA Activation of Staphylococcus aureus Pyruvate Carboxylase

Allosteric regulation of pyruvate carboxylase (PC) activity is pivotal to maintaining metabolic homeostasis. In contrast, dysregulated PC activity contributes to the pathogenesis of numerous diseases, rendering PC a possible target for allosteric therapeutic development. Recent research efforts have focused on demarcating the role of acetyl-CoA, one of the most potent activators of PC, in coordinating catalytic events within the multifunctional enzyme. Herein, we report a kinetic and thermodynamic analysis of acetyl-CoA activation of the Staphylococcus aureus PC (SaPC)-catalyzed carboxylation of pyruvate to identify novel means by which acetyl-CoA synchronizes catalytic events within the PC tetramer. Kinetic and linked-function analysis, or thermodynamic linkage analysis, indicates that the substrates of the biotin carboxylase and carboxyl transferase domain are energetically coupled in the presence of acetyl-CoA. In contrast, both kinetic and energetic coupling between the two domains is lost in the absence of acetyl-CoA, suggesting a functional role for acetyl-CoA in facilitating the long-range transmission of substrate-induced conformational changes within the PC tetramer. Interestingly, thermodynamic activation parameters for the SaPC-catalyzed carboxylation of pyruvate are largely independent of acetyl-CoA. Our results also reveal the possibility that global conformational changes give rise to observed species-specific thermodynamic activation parameters. Taken together, our kinetic and thermodynamic results provide a possible allosteric mechanism by which acetyl-CoA coordinates catalysis within the PC tetramer.

Entropy redistribution controls allostery in a metalloregulatory protein

Allosteric communication between two ligand-binding sites in a protein is a central aspect of biological regulation that remains mechanistically unclear. Here we show that perturbations in equilibrium picosecond-nanosecond motions impact zinc (Zn)-induced allosteric inhibition of DNA binding by the Zn efflux repressor CzrA (chromosomal zinc-regulated repressor). DNA binding leads to an unanticipated increase in methyl side-chain flexibility and thus stabilizes the complex entropically; Zn binding redistributes these motions, inhibiting formation of the DNA complex by restricting coupled fast motions and concerted slower motions. Allosterically impaired CzrA mutants are characterized by distinct nonnative fast internal dynamics "fingerprints" upon Zn binding, and DNA binding is weakly regulated. We demonstrate the predictive power of the wild-type dynamics fingerprint to identify key residues in dynamics-driven allostery. We propose that driving forces arising from dynamics can be harnessed by nature to evolve new allosteric ligand specificities in a compact molecular scaffold.

The effect of introducing small cavities on the allosteric inhibition of phosphofructokinase from Bacillus stearothermophilus

The allosteric coupling free energy between ligands fructose-6-phosphate (Fru-6-P) and phospho(enol)pyruvate (PEP) for phosphofructokinase-1 (PFK) from the moderate thermophile, Bacillus stearothermophilus (BsPFK), results from compensating enthalpy and entropy components. In BsPFK the positive coupling free energy that defines inhibition is opposite in sign from the negative enthalpy term and is therefore determined by the larger absolute value of the negative entropy term. Variants of BsPFK were made to determine the effect of adding small cavities to the structure on the allosteric function of the enzyme. The BsPFK Ile → Val (cavity containing) mutants have varied values for the coupling free energy between PEP and Fru-6-P, indicating that the modifications altered the effectiveness of PEP as an inhibitor. Notably, the mutation I153V had a substantial positive impact on the magnitude of inhibition by PEP. Van't Hoff analysis determined that this is the result of decreased entropy-enthalpy compensation with a larger change in the enthalpy term compared to the entropy term.

Pyruvate Occupancy in the Carboxyl Transferase Domain of Pyruvate Carboxylase Facilitates Product Release from the Biotin Carboxylase Domain through an Intermolecular Mechanism

Protein structure, ligand binding, and catalytic turnover contributes to the governance of catalytic events occurring at spatially distinct domains in multifunctional enzymes. Coordination of these catalytic events partially rests on the ability of spatially discrete active sites to communicate with other allosteric and active sites on the same polypeptide chain (intramolecular) or on different polypeptide chains (intermolecular) within the holoenzyme. Often, communication results in long-range effects on substrate binding or product release. For example, pyruvate binding to the carboxyl transferase (CT) domain of pyruvate carboxylase (PC) increases the rate of product release in the biotin carboxylase (BC) domain. In order to address how CT domain ligand occupancy is "sensed" by other domains, we generated functional, mixed hybrid tetramers using the E218A (inactive BC domain) and T882S (low pyruvate binding, low activity) mutant forms of PC. The apparent Ka pyruvate for the pyruvate-stimulated release of Pi catalyzed by the T882S:E218A[1:1] hybrid tetramer was comparable to the wild-type enzyme and nearly 10-fold lower than that for the T882S homotetramer. In addition, the ratio of the rates of oxaloacetate formation to Pi release for the WT:T882S[1:1] and E218A:T882S[1:1] hybrid tetramer-catalyzed reactions was 0.5 and 0.6, respectively, while the T882S homotetramer exhibited a near 1:1 coupling of the two domains, suggesting that the mechanisms coordinating catalytic events is more complicated that we initially assumed. The results presented here are consistent with an intermolecular communication mechanism, where pyruvate binding to the CT domain is "sensed" by domains on a different polypeptide chain within the tetramer.

Enhancing allosteric inhibition in Thermus thermophilus Phosphofructokinase

The coupling between the binding of the substrate Fru-6-P and the inhibitor phospho(enol)pyruvate (PEP) in phosphofructokinase (PFK) from the extreme thermophile Thermus thermophilus is much weaker than that seen in a PFK from Bacillus stearothermophilus. From the crystal structures of Bacillus stearothermophilus PFK (BsPFK) the residues at positions 59, 158, and 215 in BsPFK are located on the path leading from the allosteric site to the nearest active site and are part of the intricate hydrogen-bonding network connecting the two sites. Substituting the corresponding residues in Thermus thermophilus PFK (TtPFK) with the amino acids found at these positions in BsPFK allowed us to enhance the allosteric inhibition by PEP by nearly 3 kcal mol^–1 (50-fold) to a value greater than or equal to the coupling observed in BsPFK. Interestingly, each single variant N59D, A158T, and S215H produced a roughly 1 kcal mol^–1 increase in coupling free energy of inhibition. The effects of these variants were essentially additive in the three combinations of double variants N59D/A158T, N59D/S215H, and A158T/S215H as well as in the triple variant N59D/A158T/S215H. Consequently, while the hydrogen-bonding network identified is likely involved in the inhibitory allosteric communication, a model requiring a linked chain of interactions connecting the sites is not supported by these data. Despite the fact that the allosteric activator of the bacterial PFK, MgADP, binds at the same allosteric site, the substitutions at positions 59, 158, and 215 do not have an equally dramatic effect on the binding affinity and the allosteric activation by MgADP. The effect of the S215H and N59D/A158T/S215H substitutions on the activation by MgADP could not be determined because of a dramatic drop in MgADP binding affinity that resulted from the S215H substitution. The single variants N59D and A158T supported binding but showed little change in the free energy of activation by MgADP compared to the wild type TtPFK. These results support previous suggestions that heterotropic inhibition and activation occur by different pathways prokaryotic PFK.

Allosteric regulation in phosphofructokinase from the extreme thermophile Thermus thermophilus

An investigation into the kinetics and regulatory properties of the type-1 phosphofructokinase (PFK) from the extreme thermophile Thermus thermophilus (TtPFK) reveals an enzyme that is inhibited by PEP and activated by ADP by modifying the affinity exhibited for the substrate fructose 6-phosphate (Fru-6-P) in a manner analogous to other prokaryotic PFKs. However, TtPFK binds both of these allosteric ligands significantly more tightly than other bacterial PFKs while effecting a substantially more modest extent of inhibition or activation at 25 °C, reinforcing the principle that binding affinity and effectiveness can be both independent and uncorrelated to one another. These properties have allowed us to establish rigorously that PEP only inhibits by antagonizing the binding of Fru-6-P and not by influencing turnover, a conclusion that requires kcat to be determined under conditions in which both inhibitor and substrate are saturating simultaneously. In addition, the temperature dependence of the allosteric effects on Fru-6-P binding indicate that the coupling free energies are entropy-dominated, as observed previously for PFK from Bacillus stearothermophilus but not for PFK from Escherichia coli , supporting the hypothesis that entropy-dominated allosteric effects may be a characteristic of enzymes derived from thermostable organisms. For such enzymes, the root cause of the allosteric effect may not be easily discerned from static structural information such as that obtained from X-ray crystallography.

Studying the allosteric energy cycle by isothermal titration calorimetry

Isothermal titration calorimetry (ITC) is a powerful biophysical technique which allows a complete thermodynamic characterization of protein interactions with other molecules. The possibility of dissecting the Gibbs energy of interaction into its enthalpic and entropic contributions, as well as the detailed additional information experimentally accessible on the intermolecular interactions (stoichiometry, cooperativity, heat capacity changes, and coupled equilibria), make ITC a suitable technique for studying allosteric interactions in proteins. Two experimental methodologies for the characterization of allosteric heterotropic ligand interactions by ITC are described in this chapter, illustrated with two proteins with markedly different structural and functional features: a photosynthetic electron transfer protein and a drug target viral protease.

Effects of protein-ligand associations on the subunit interactions of phosphofructokinase from B. stearothermophilus

Differences between the crystal structures of inhibitor-bound and uninhibited forms of phosphofructokinase (PFK) from B. stearothermophilus have led to a structural model for allosteric inhibition by phosphoenolpyruvate (PEP) wherein a dimer-dimer interface within the tetrameric enzyme undergoes a quaternary shift. We have developed a labeling and hybridization technique to generate a tetramer with subunits simultaneously containing two different extrinsic fluorophores in known subunit orientations. This construct has been utilized in the examination of the effects of allosteric ligand and substrate binding on the subunit affinities of tetrameric PFK using several biophysical and spectroscopic techniques including 2-photon, dual-channel fluorescence correlation spectroscopy (FCS). We demonstrate that PEP-binding at the allosteric site is sufficient to reduce the affinity of the active site interface from beyond the limits of experimental detection to nanomolar affinity, while conversely strengthening the interface at which it is bound. The reduced interface affinity is specific to inhibitor binding because binding the activator ADP at the same allosteric site causes no reduction in subunit affinity. With inhibitor bound, the weakened subunit affinity has allowed the kinetics of dimer association to be elucidated.

Exact analysis of heterotropic interactions in proteins: Characterization of cooperative ligand binding by isothermal titration calorimetry

Intramolecular interaction networks in proteins are responsible for heterotropic ligand binding cooperativity, a biologically important, widespread phenomenon in nature (e.g., signaling transduction cascades, enzymatic cofactors, enzymatic allosteric activators or inhibitors, gene transcription, or repression). The cooperative binding of two (or more) different ligands to a macromolecule is the underlying principle. To date, heterotropic effects have been studied mainly kinetically in enzymatic systems. Until now, approximate approaches have been employed for studying equilibrium heterotropic ligand binding effects, except in two special cases in which an exact analysis was developed: independent binding (no cooperativity) and competitive binding (maximal negative cooperativity). The exact analysis and methodology for characterizing ligand binding cooperativity interactions in the general case (any degree of cooperativity) using isothermal titration calorimetry are presented in this work. Intramolecular interaction pathways within the allosteric macromolecule can be identified and characterized using this methodology. As an example, the thermodynamic characterization of the binding interaction between ferredoxin-NADP+ reductase and its three substrates, NADP+, ferredoxin, and flavodoxin, as well as the characterization of their binding cooperativity interaction, is presented.

The role of dynamics in allosteric regulation

The biomolecular conformational changes often associated with allostery are, by definition, dynamic processes. Recent publications have disclosed the role of pre-existing equilibria of conformational substates in this process. In addition, the role of dynamics as an entropic carrier of free energy of allostery has been investigated. Recent work thus shows that dynamics is pivotal to allostery, and that it constitutes much more than just the move from the 'T'-state to the 'R'-state. Emerging computational studies have described the actual pathways of allosteric change.

Reevaluation of the accepted allosteric mechanism of phosphofructokinase from Bacillus stearothermophilus

The binding of phosphoenolpyruvate (PEP) to the single allosteric site on phosphofructokinase (EC ) from Bacillus stearothermophilus (BsPFK) diminishes the ability of the enzyme to bind the substrate fructose 6-phosphate (Fru-6-P). Comparisons of crystal structures with either Fru-6-P or phosphoglycolate, an analog of PEP, bound have shown that Arg-162 interacts with the negatively charged Fru-6-P. Upon the binding of phosphoglycolate, Arg-162 is virtually replaced by Glu-161, which introduces a potential coulombic repulsion between enzyme and substrate [Schirmer, T. & Evans, P. R. (1990) Nature (London) 343, 140-145]. It has previously been proposed that this structural transition explains the allosteric inhibition in BsPFK, and this explanation has appeared in textbooks to illustrate how an allosteric ligand can influence substrate binding at a distance. Site-directed mutagenesis has been employed to create three mutants of BsPFK that substitute an alanine residue for Glu-161, Arg-162, or both. The E161A mutation does not affect the inhibition of BsPFK by PEP at 25 degrees C, and while the R162A mutation decreases BsPFK's affinity for Fru-6-P by approximately 30-fold, R162A diminishes the effectiveness of PEP inhibition by only 1/3. Combining E161A and R162A produces behavior comparable to R162A alone. These and other data suggest that the movement of Glu-161 and Arg-162 does not play the central role in producing the allosteric inhibition by PEP as originally envisioned in the Schirmer and Evans mechanism.

Interactive binding to the two principal ligand binding sites of human serum albumin: effect of the neutral-to-base transition

The relationship between the two principal ligand binding sites, sites I and II, on human serum albumin (HSA) was quantitatively and qualitatively examined by equilibrium dialysis and fluorescence spectroscopy. Among the three subsite markers to site I, only the binding of dansyl-L-asparagine (DNSA), which is a subsite Ib marker (K. Yamasaki et al., Biochim. Biophys. Acta 1295 (1996) 147), was inhibited by the simultaneous binding of a site II ligand, such as ibuprofen and diazepam. This indicates that, in contrast to subsite Ib, subsites Ia and Ic do not strongly interact with site II. The thermodynamic characteristics for the coupling reaction between DNSA and ibuprofen and between DNSA and diazepam, which gave positive coupling free energies and negative values for both coupling enthalpy and entropy, indicated that the reaction process was entropically driven. Increase of pH from 6.5 to 8.2 caused an increase in coupling constant and entropy for the mutual antagonism between DNSA and the site II ligands on binding to HSA. The site II ligand-induced red-shift of lambda(max) and solvent accessibility of DNSA in subsite Ib were decreased when the albumin molecule was isomerized from the neutral (N) to the base (B) conformation in the physiological pH region. Based on these findings, we conclude that a 'competitive' like strong allosteric regulation exists for the binding of these two ligands to the N conformer, whereas for the B conformer this interaction can be classified as nearly 'independent'. Since the distance between Trp-214, which resides within the site I subdomain, and Tyr-411, which is involved in site II, is increased by 6 A during the N-B transition (N.G. Hagag et al., Fed. Proc. 41 (1982) 1189), we propose a mechanism for the pH-dependent antagonistic binding between subsite Ib and site II, which involves the transmission of ligand-induced allosteric effects from one site to another site, modified by changes in the spatial relationship of sites I and II caused by the N-B transition.

Temperature effects on the allosteric responses of native and chimeric aspartate transcarbamoylases

Although structurally very similar, the aspartate transcarbamoylases (ATCase) of Serratia marcescens and Escherichia coli have distinct allosteric regulatory patterns. It has been reported that a S. marcescens chimera, SM : rS5'ec, in which five divergent residues (r93 to r97) of the regulatory polypeptide were replaced with their Escherichia coli counterparts, possessed E. coli-like regulatory characteristics. The reverse chimera EC:rS5'sm, in which the same five residues of E. coli have been replaced with their S. marcescens counterpart, lost both heterotrophic and homotropic responses. These results indicate that the r93-r97 region is critical in defining the ATCase allosteric character. Molecular modeling of the regulatory polypeptides has suggested that the replacement of the S5' beta-strand resulted in disruption of the allosteric-zinc interface. However, the structure-function relationship could be indirect, and the disruption of the interface could influence allostery by altering the global energy of the enzyme. Studies of the temperature-sensitivity of the CTP response demonstrate that it is possible to convert CTP inhibition of the SM:rS5'ec chimera at high temperature to activation below 10 degreesC. Nonetheless, the temperature response of the native S. marcescens ATCase suggests a strong entropic effect that counteracts the CTP activation. Therefore, it is suggested that the entropy component of the coupling free energy plays a significant role in the determination of both the nature and magnitude of the allosteric effect in ATCase.

Obfuscation of allosteric structure-function relationships by enthalpy-entropy compensation

The pH and temperature dependence of the allosteric properties of phosphofructokinase (PFK) from Bacillus stearothermophilus have been studied from 5 to 9 and 6 to 40 degrees C, respectively. Throughout this pH and temperature range the allosteric ligands MgADP and phospho(enol)pyruvate (PEP) have no effect on kcat. The dissociation constants of the substrate, fructose 6-phosphate, and the allosteric ligands, as well as the absolute value of the coupling free energies between these ligands, all increase when the pH is raised, indicating that the inhibition by PEP and the activation by MgADP increase despite each ligand's somewhat lower affinity. However, the constituent coupling enthalpies and entropies substantially diminish in absolute value as pH is increased, suggesting that the magnitudes of molecular perturbations engendered by the binding of allosteric ligands do not correlate with the magnitudes of the functional consequences of those perturbations. Temperature and pH exert their influence on the observed allosteric behavior by changing the relative contributions made by the largely compensating DeltaH and TDeltaS terms to the coupling free energy.

Cold denaturation of a repressor-operator complex: the role of entropy in protein-DNA recognition

The mechanisms by which regulatory proteins recognize specific DNA sequences are not fully understood. Here we examine the basis for the stability of a protein-DNA complex, using hydrostatic pressure and low temperature. Pressure converts the DNA-binding Arc repressor protein from a native state to a denatured, molten-globule state. Our data show that the folding and dimerization of Arc repressor in the temperature range 0-20 degrees C are favored by a large positive entropy value, so that the reaction proceeds in spite of an unfavorable positive enthalpy. On binding operator DNA, Arc repressor becomes extremely stable against denaturation. However, the Arc repressor-operator DNA complex is cold-denatured at subzero temperatures under pressure, demonstrating that the favorable entropy increases greatly when Arc repressor binds tightly to its operator sequence but not a nonspecific sequence. We show how an increase in entropy may operate to provide the protein with a mechanism to distinguish between a specific and a nonspecific DNA sequence. It is postulated that the formation of the Arc-operator DNA complex is followed by an increase in apolar interactions and release of solvent which would explain its entropy-driven character, whereas this solvent would not be displaced in nonspecific complexes.

Energy coupling between DNA binding and subunit association is responsible for the specificity of DNA-Arc interaction

The effects of several DNA molecules on the free energy of subunit association of Arc repressor were measured. The association studies under equilibrium conditions were performed by the dissociating perturbation of hydrostatic pressure. The magnitude of stabilization of the subunit interaction was determined by the specificity of the protein-DNA interaction. Operator DNA stabilized the free energy of association by about 2.2 kcal/mol of monomeric unit, whereas poly(dG-dC) stabilized the subunit interaction by only 0.26 kcal. Measurements of the stabilizing free energy at different DNA concentrations revealed a stoichiometry of two dimers per 21 bp for the operator DNA sequence and for the nonspecific DNA poly(dA-dT). However, the maximum stabilization was much larger for operator sequence (delta p = 1,750 bar) as compared for poly(dA-dT) (delta p = 750 bar). The importance of the free-energy linkage for the recognition process was corroborated by its absence in a mutant Arc protein (PL8) that binds to operator and nonspecific DNA sequences with equal, low affinity. We conclude that the coupling accounts for the high specificity of the Arc-operator DNA interaction. We hypothesize a mutual coupling between the protein subunits and the two DNA strands, in which the much higher persistency of the associated form when Arc is bound to operator would stabilize the interactions between the two DNA strands.

Unique and independent parameters (UIP) formulation for thermodynamic models of complex protein-ligand systems

A method for reformulating the thermodynamic (delta G) description of complex equilibria is presented. The purpose of this reformulation is to take a system of N complexes which is completely defined by N delta Gs, and recast it in terms of a new set of N delta Gs. This reformulation is an extension of the concept of interaction energy (J. Wyman, Adv. Protein Chem. 19 (1964) 223-286). The new delta Gs obtained by this reformulation reflect the intrinsic properties of the binding sites and the hierarchical nature of potential interactions between them. A simple set of rules are developed which allow for the description of complex protein-ligand binding schemes and these rules are used to derive schemes for hemoglobin O2 binding. This reformulation represents the foundation for the theoretical description of the coupling of energy in protein-ligand systems as illustrated by the theoretical analysis of allosterism in a dimeric protein presented in the following paper. This reformulation also provides the foundation for the analysis of data pertaining to complex equilibria.