Description of the kinetics of allosteric polymeric enzymes with 2 ligands based on the generalized Ising model

The two-ligand model for allosteric regulation of complex polymeric enzymes is offered. Two types of cooperative interactions are observed--the cooperative transformations inside the promoter and interactions of promoters themselves--along with the direct interaction of two ligands inside each subunit. The solution of the model is given and its kinetic properties are discussed.     

A mathematical model of the pyruvate oxidation in liver mitochondria. 1. Regulation of the Krebs cycle by adenine and pyridine nucleotides]

A mathematical model is proposed to describe the behavior of the pyruvate metabolic reactions, Krebs cycle and oxidative phosphorylation over a wide range of changes in the pyruvate influx rate and the activities of ATPase and NADH-reoxidating dehydrogenase. The role of adenine and pyridine nucleotides in various allosteric regulations of the Krebs cycle enzymes is discussed. The accumulation of ATP and NADH has been shown to proceed in definite succession, which makes the allosteric regulation of the Krebs cycle enzymes successive too. First "works" the inhibition by ATP, then by NADH. It has been shown that the properties of the model are in qualitative agreement with the experimental data (Garber A., Hanson R. [1]) on pyruvate oxidation by mitochondria from guinea pig liver, when allosteric regulation of isocitrate dehydrogenase by adenine nucleotides is taken into account.     

Changes in dynamics upon oligomerization regulate substrate binding and allostery in amino acid kinase family members

Oligomerization is a functional requirement for many proteins. The interfacial interactions and the overall packing geometry of the individual monomers are viewed as important determinants of the thermodynamic stability and allosteric regulation of oligomers. The present study focuses on the role of the interfacial interactions and overall contact topology in the dynamic features acquired in the oligomeric state. To this aim, the collective dynamics of enzymes belonging to the amino acid kinase family both in dimeric and hexameric forms are examined by means of an elastic network model, and the softest collective motions (i.e., lowest frequency or global modes of motions) favored by the overall architecture are analyzed. Notably, the lowest-frequency modes accessible to the individual subunits in the absence of multimerization are conserved to a large extent in the oligomer, suggesting that the oligomer takes advantage of the intrinsic dynamics of the individual monomers. At the same time, oligomerization stiffens the interfacial regions of the monomers and confers new cooperative modes that exploit the rigid-body translational and rotational degrees of freedom of the intact monomers. The present study sheds light on the mechanism of cooperative inhibition of hexameric N-acetyl-L-glutamate kinase by arginine and on the allosteric regulation of UMP kinases. It also highlights the significance of the particular quaternary design in selectively determining the oligomer dynamics congruent with required ligand-binding and allosteric activities.     

Ligand competition curves as a diagnostic tool for delineating the nature of site-site interactions: theory

A few molecular models have been developed in recent years to explain the mechanism of cooperative ligand binding. The concerted model of Monod, Wyman and Changeux and the sequential model of Koshland, Némethy and Filmer were formulated to account for positively cooperative binding. The pre-existent asymmetry model and the sequential model can account for negatively cooperative ligand binding. In most cases, however, it is virtually impossible to deduce the molecular mechanism of ligand binding solely from the shape of the binding isotherm. In the present study we suggest a new strategy for delineating the molecular mechanism responsible for cooperative ligand binding from binding isotherms. In this approach one examines the effect of one ligand on the cooperativity observed in the binding of another ligand, where the two ligands compete for the same set of binding sites. It is demonstrated that the cooperativity of ligand binding can be modulated when a competitive ligand is present in the protein-ligand binding mixture. A general mathematical formulation of this modulation is presented in thermodynamic terms, using model-independent parameters. The relation between the Hill coefficient at 50% ligand saturation with respect to ligand X in the absence, h(x), and in the presence of a competing ligand Z, h(x,z), is expressed in terms of the thermodynamic parameters characterizing the binding of the two ligands. Then the relationship between h(x) and h(x,z), in terms of the molecular parameters of the different allosteric models, is explored. This analysis reveals that the different allosteric models predict different relationships between h(x,z) and h(x). These differences are especially focused when Z binds non-cooperatively. Thus, it becomes possible, on the basis of ligand binding experiments alone, to decide which of the allosteric models best fits a set of experimental data.     

Morpheeins--a new structural paradigm for allosteric regulation

Classic models for the allosteric regulation of protein function consider an equilibrium among protein structures of constant oligomeric multiplicity. The morpheein (mor-phee'-in) concept expands this model to include a dynamic equilibrium of protein structures wherein a protein monomer can exist in more than one conformation and each monomer conformation dictates a different quaternary structure of finite multiplicity and different functionality. The morpheein concept provides a new framework for understanding allosteric regulation, kinetic cooperativity and hysteresis. Porphobilinogen synthase constitutes a prototype morpheein ensemble comprising several interconverting quaternary structure isoforms; one monomer conformation dictates assembly of a high-activity octamer, whereas an alternative monomer conformation dictates assembly of a low-activity hexamer. It is proposed here that the behavior of some other allosteric enzymes reflect dynamic morpheein equilibrium systems and six candidate proteins are enumerated.     

Direct structural evidence for a concerted allosteric transition in Escherichia coli aspartate transcarbamoylase

Regulation of protein function, often achieved by allosteric mechanisms, is central to normal physiology and cellular processes. Although numerous models have been proposed to account for the cooperative binding of ligands to allosteric proteins and enzymes, direct structural support has been lacking. Here, we used a combination of X-ray crystallography and small angle X-ray scattering in solution to provide direct structural evidence that the binding of ligand to just one of the six active sites of Escherichia coli aspartate transcarbamoylase induces a concerted structural transition from the T to the R state.     

Structure of the cooperative allosteric anthranilate synthase from Salmonella typhimurium

We have determined the X-ray crystal structure of the cooperative anthranilate synthase heterotetramer from Salmonella typhimurium at 1.9 A resolution with the allosteric inhibitor l-tryptophan bound to a regulatory site in the TrpE subunit. Tryptophan binding orders a loop that in turn stabilizes the inactive T state of the enzyme by restricting closure of the active site cleft. Comparison with the structure of the unliganded, noncooperative anthranilate synthase heterotetramer from Sulfolobus solfataricus shows that the two homologs have completely different quarternary structures, even though their functional dimer pairs are structurally similar, consistent with differences in the cooperative behavior of the enzymes. The structural model rationalizes mutational and biochemical studies of the enzyme and establishes the structural differences between cooperative and noncooperative anthranilate synthase homologs.     

Single amino acid substitution (G456A) in the vicinity of the GTP binding domain of human housekeeping glutamate dehydrogenase markedly attenuates GTP inhibition and abolishes the cooperative behavior of the enzyme

Human glutamate dehydrogenase (GDH) exists in two isoforms encoded by the GLUD1 and GLUD2 genes, respectively. Although the two enzymes share in their mature form all but 15 of their 505 amino acids, they differ markedly in their allosteric regulation. To identify the structural basis for these allosteric characteristics, we performed site-directed mutagenesis on the human GLUD1 gene at sites that differ from the GLUD2 gene using a cloned GLUD1 cDNA. Results showed that substitution of Ala for Gly-456, but not substitution of His for Arg-470 or Ser for Asn-498, renders the enzyme markedly resistant to GTP inhibition (IC(50) = 2.80 microm) as compared with the wild type GLUD1-derived GDH (IC(50) = 0.19 microm). The G456A mutation abolished the cooperative behavior of the enzyme, as revealed by the GTP inhibitory curves. The catalytic and kinetic properties of the G456A mutant and its activation by ADP were comparable with those of the wild type GDH. Gly-456 lies in a very tightly packed region of the GDH molecule, and its replacement by Ala may lead to steric clashes with neighboring amino acids. These, in turn, may affect the conformational state of the protein that is essential for the allosteric regulation of the enzyme by GTP.     

Ligand binding and structural changes associated with allostery in yeast NAD(+)-specific isocitrate dehydrogenase

Yeast NAD(+)-specific isocitrate dehydrogenase (IDH) is an octameric enzyme composed of four each of regulatory IDH1 and catalytic IDH2 subunits that share 42% sequence identity. IDH2 contains catalytic isocitrate/Mg2+ and NAD+ binding sites whereas IDH1 contains homologous binding sites, respectively, for cooperative binding of isocitrate and for allosteric binding of AMP. Ligand binding is highly ordered in vitro, and IDH exhibits the unusual property of half-site binding for all ligands. The structures of IDH solved in the absence or presence of ligands have shown: (a) a heterodimer to be the basic structural/functional unit of the enzyme, (b) the organization of heterodimers to form tetramer and octamer structures, (c) structural differences that may underlie cooperative and allosteric regulatory mechanisms, and (d) the possibility for formation of a disulfide bond that could reduce catalytic activity. In vivo analyses of mutant enzymes have elucidated the physiological importance of catalytic activity and allosteric regulation of this tricarboxylic acid cycle enzyme. Other studies have established the importance of a disulfide bond in regulation of IDH activity in vivo, as well as contributions of this bond to the property of half-site ligand binding exhibited by the wild-type enzyme.     

Structure of Escherichia coli UMP kinase differs from that of other nucleoside monophosphate kinases and sheds new light on enzyme regulation

Bacterial UMP kinases are essential enzymes involved in the multistep synthesis of nucleoside triphosphates. They are hexamers regulated by the allosteric activator GTP and inhibited by UTP. We solved the crystal structure of Escherichia coli UMP kinase bound to the UMP substrate (2.3 A resolution), the UDP product (2.6 A), or UTP (2.45 A). The monomer fold, unrelated to that of other nucleoside monophosphate kinases, belongs to the carbamate kinase-like superfamily. However, the phosphate acceptor binding cleft and subunit assembly are characteristic of UMP kinase. Interactions with UMP explain the high specificity for this natural substrate. UTP, previously described as an allosteric inhibitor, was unexpectedly found in the phosphate acceptor site, suggesting that it acts as a competitive inhibitor. Site-directed mutagenesis of residues Thr-138 and Asn-140, involved in both uracil recognition and active site interaction within the hexamer, decreased the activation by GTP and inhibition by UTP. These experiments suggest a cross-talk mechanism between enzyme subunits involved in cooperative binding at the phosphate acceptor site and in allosteric regulation by GTP. As bacterial UMP kinases have no counterpart in eukaryotes, the information provided here could help the design of new antibiotics.     

Multiconformational states in phosphoglycerate dehydrogenase

Phosphoglycerate dehydrogenase (PGDH) catalyzes the first step in the serine biosynthetic pathway. In lower plants and bacteria, the PGDH reaction is regulated by the end-product of the pathway, serine. The regulation occurs through a V(max) mechanism with serine binding and inhibition occurring in a cooperative manner. The three-dimensional structure of the serine inhibited enzyme, determined by previous work, showed a tetrameric enzyme with 222 symmetry and an unusual overall toroidal appearance. To characterize the allosteric, cooperative effects of serine, we identified W139G PGDH as an enzymatically active mutant responsive to serine but not in a cooperative manner. The position of W139 near a subunit interface and the active site cleft suggested that this residue is a key player in relaying allosteric effects. The 2.09 A crystal structure of W139G-PGDH, determined in the absence of serine, revealed major quaternary and tertiary structural changes. Contrary to the wildtype enzyme where residues encompassing residue 139 formed extensive intersubunit contacts, the corresponding residues in the mutant were conformationally flexible. Within each of the three-domain subunits, one domain has rotated approximately 42 degrees relative to the other two. The resulting quaternary structure is now in a novel conformation creating new subunit-to-subunit contacts and illustrates the unusual flexibility in this V(max) regulated enzyme. Although changes at the regulatory domain interface have implications in other enzymes containing a similar regulatory or ACT domain, the serine binding site in W139G PGDH is essentially unchanged from the wildtype enzyme. The structural and previous biochemical characterization of W139G PGDH suggests that the allosteric regulation of PGDH is mediated not only by changes occurring at the ACT domain interface but also by conformational changes at the interface encompassing residue W139.     

The structural basis for allosteric inhibition of a threonine-sensitive aspartokinase

The commitment step to the aspartate pathway of amino acid biosynthesis is the phosphorylation of aspartic acid catalyzed by aspartokinase (AK). Most microorganisms and plants have multiple forms of this enzyme, and many of these isofunctional enzymes are subject to feedback regulation by the end products of the pathway. However, the archeal species Methanococcus jannaschii has only a single, monofunctional form of AK. The substrate l-aspartate binds to this recombinant enzyme in two different orientations, providing the first structural evidence supporting the relaxed regiospecificity previously observed with several alternative substrates of Escherichia coli AK ( Angeles, T. S., Hunsley, J. R., and Viola, R. E. (1992) Biochemistry 31, 799-805 ). Binding of the nucleotide substrate triggers significant domain movements that result in a more compact quaternary structure. In contrast, the highly cooperative binding of the allosteric regulator l-threonine to multiple sites on this dimer of dimers leads to an open enzyme structure. A comparison of these structures supports a mechanism for allosteric regulation in which the domain movements induced by threonine binding causes displacement of the substrates from the enzyme, resulting in a relaxed, inactive conformation.     

Functional linkage of adenine nucleotide binding sites in mammalian muscle 6-phosphofructokinase

6-Phosphofructokinases (Pfk) are homo- and heterooligomeric, allosteric enzymes that catalyze one of the rate-limiting steps of the glycolysis: the phosphorylation of fructose 6-phosphate at position 1. Pfk activity is modulated by a number of regulators including adenine nucleotides. Recent crystal structures from eukaryotic Pfk revealed several adenine nucleotide binding sites. Herein, we determined the functional relevance of two adenine nucleotide binding sites through site-directed mutagenesis and enzyme kinetic studies. Subsequent characterization of Pfk mutants allowed the identification of the activating (AMP, ADP) and inhibitory (ATP, ADP) allosteric binding sites. Mutation of one binding site reciprocally influenced the allosteric regulation through nucleotides interacting with the other binding site. Such reciprocal linkage between the activating and inhibitory binding sites is in agreement with current models of allosteric enzyme regulation. Because the allosteric nucleotide binding sites in eukaryotic Pfk did not evolve from prokaryotic ancestors, reciprocal linkage of functionally opposed allosteric binding sites must have developed independently in prokaryotic and eukaryotic Pfk (convergent evolution).     

Time-dependent model for hemoglobin and allosteric enzymes. I. General formulation

A previous equilibrium model is generalized to study time-dependent behavior of hemoglobin and allosteric enzymes. An exact solution for two interacting subunits (e.g., diheme) is given, and a general method for solving the resulting set of differential equations is outlined. At half saturation (equilibrium) concentration, the model takes a particularly simple form which suggests an experiment to determine the number of subunits of an allosteric enzyme, or in particular to distinguish diheme from ordinary hemoglobin. The relation between the present model and other kinetic models is also discussed.     

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate kinase I-homoserine dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves the way for a more generalized prediction of the behavior of bifunctional enzymes.     

Is there a toxicological advantage for non-hyperbolic kinetics in cytochrome P450 catalysis? Functional allostery from "distributive catalysis"

The cytochrome P450s (CYPs) are the major enzymatic detoxification and drug metabolism system. Recently, it has become clear that several CYP isoforms exhibit positive and negative homotropic cooperativity. However, the toxicological implications of allosteric kinetics have not been considered, nor understood. The allosteric kinetics are particularly enigmatic in several respects. In many cases, CYPs bioactivate substrates to more toxic products, thus making it difficult to rationalize a functional advantage for positive cooperativity. Also, CYPs exhibit cooperativity with many structurally diverse ligands, in marked contrast to the specificity observed with other allosteric systems. Here, kinetic simulations are used to compare the probabilistic time- and concentration-dependent integrated toxicity function during conversion of substrate to product for CYP models exhibiting Michaelis-Menten (non-cooperative) kinetics, positive cooperativity, or negative cooperativity. The results demonstrate that, at low substrate concentrations, the slower substrate turnover afforded by cooperative CYPs compared with Michaelis-Menten enzymes can be a significant toxicological advantage, when toxic thresholds exist. When present, the advantage results from enhanced "distribution" of toxin in two pools, substrate and product, for an extended period, thus minimizing the chance that either exceeds its toxic threshold. At intermediate concentrations, the allosteric kinetics can be a modest advantage or modest disadvantage, depending on the kinetic parameters. However, at high substrate concentrations associated with a high probability of toxicity, fast turnover is desirable, and this advantage is provided also by the cooperative enzymes. For the positive homotropic cooperativity, the allosteric kinetics minimize the probability of toxicity over the widest range of system parameters. Furthermore, this apparent functional cooperativity is achieved without specific molecular recognition that is the hallmark of "traditional" allostery.     

Prediction and confirmation of a switch-like region within the N-terminal domain of hSIRT1

Many proteins display conformational changes resulting from allosteric regulation. Often only a few residues are crucial in conveying these structural and functional allosteric changes. These regions that undergo a significant change in structure upon receiving an input signal, such as molecular recognition, are defined as switch-like regions. Identifying these key residues within switch-like regions can help elucidate the mechanism of allosteric regulation and provide guidance for synthetic regulation. In this study, we combine a novel computational workflow with biochemical methods to identify a switch-like region in the N-terminal domain of human SIRT1 (hSIRT1), a lysine deacetylase that plays important roles in regulating cellular pathways. Based on primary sequence, computational methods predicted a region between residues 186–193 in hSIRT1 to exhibit switch-like behavior. Mutations were then introduced in this region and the resulting mutants were tested for allosteric reactions to resveratrol, a known hSIRT1 allosteric regulator. After fine-tuning the mutations based on comparison of known secondary structures, we were able to pinpoint M193 as the residue essential for allosteric regulation, likely by communicating the allosteric signal. Mutation of this residue maintained enzyme activity but abolished allosteric regulation by resveratrol. Our findings suggest a method to predict switch-like regions in allosterically regulated enzymes based on the primary sequence. If further validated, this could be an efficient way to identify key residues in enzymes for therapeutic drug targeting and other applications.     

Dynamic dissociating homo-oligomers and the control of protein function

Homo-oligomeric protein assemblies are known to participate in dynamic association/disassociation equilibria under native conditions, thus creating an equilibrium of assembly states. Such quaternary structure equilibria may be influenced in a physiologically significant manner either by covalent modification or by the non-covalent binding of ligands. This review follows the evolution of ideas about homo-oligomeric equilibria through the 20th and into the 21st centuries and the relationship of these equilibria to allosteric regulation by the non-covalent binding of ligands. A dynamic quaternary structure equilibria is described where the dissociated state can have alternate conformations that cannot reassociate to the original multimer; the alternate conformations dictate assembly to functionally distinct alternate multimers of finite stoichiometry. The functional distinction between different assemblies provides a mechanism for allostery. The requirement for dissociation distinguishes this morpheein model of allosteric regulation from the classical MWC concerted and KNF sequential models. These models are described alongside earlier dissociating allosteric models. The identification of proteins that exist as an equilibrium of diverse native quaternary structure assemblies has the potential to define new targets for allosteric modulation with significant consequences for further understanding and/or controlling protein structure and function. Thus, a rationale for identifying proteins that may use the morpheein model of allostery is presented and a selection of proteins for which published data suggests this mechanism may be operative are listed.