The branch point effect. Ultrasensitivity and subsensitivity to metabolic control

The interdependence of the activities of branch point enzymes which compete for a common substrate can yield ultrasensitivity or subsensitivity to control, even if the competing enzymes follow Michaelis-Menten kinetics. The nature of this "branch point effect" for a particular system depends on the kinetic parameters of the competing enzymes, the rate of substrate production leading into the branch point and the type of regulatory mechanism involved. With physiologically reasonable parameter values, the branch point effect can give ultrasensitivity equivalent to an allosteric enzyme with a Hill coefficient of 8 or higher. An experimental example of this ultrasensitivity was provided by the branch point between isocitrate lyase (of the glyoxylate bypass) and isocitrate dehydrogenase in Escherichia coli. The glyoxylate bypass is very active during growth on acetate but its flux decreases by a factor of approximately 150 upon addition of glucose. This inhibition is brought about by two relatively modest events: a 4-fold increase in the maximum velocity of isocitrate dehydrogenase and a factor of 5.5 decrease in the rate of isocitrate production. The mechanism which underlies this sensitivity amplification is discussed.     

Conformational spread in the flagellar motor switch: a model study

The reliable response to weak biological signals requires that they be amplified with fidelity. In E. coli, the flagellar motors that control swimming can switch direction in response to very small changes in the concentration of the signaling protein CheY-P, but how this works is not well understood. A recently proposed allosteric model based on cooperative conformational spread in a ring of identical protomers seems promising as it is able to qualitatively reproduce switching, locked state behavior and Hill coefficient values measured for the rotary motor. In this paper we undertook a comprehensive simulation study to analyze the behavior of this model in detail and made predictions on three experimentally observable quantities: switch time distribution, locked state interval distribution, Hill coefficient of the switch response. We parameterized the model using experimental measurements, finding excellent agreement with published data on motor behavior. Analysis of the simulated switching dynamics revealed a mechanism for chemotactic ultrasensitivity, in which cooperativity is indispensable for realizing both coherent switching and effective amplification. These results showed how cells can combine elements of analog and digital control to produce switches that are simultaneously sensitive and reliable.     

The dependence of flux,sensitivity and response of the flux on the concentrations of substrate and modifiers for cooperative enzymes

The sensitivity (change of flux per unit change in the concentration of substrate) and response (change of flux per unit change in the concentration of modifier) are studied for a two-site Adair model in which cooperativity arises from both binding and catalytic interactions. For positive cooperativity, the sensitivity is weakly dependent on the Hill coefficient for the binding case, but can increase without limit for the catalytic case. Negatively cooperative enzymes (binding only) give very large sensitivities compared with positively or non-interacting systems, but the sensitivity rapidly decreases as the saturation increases above 25%. Modifiers greatly enhance the sensitivity; large changes in flux can be obtained for small changes in the concentrations of substrates and modifiers. In general, increasing the degree of kinetic cooperativity decreases the degree of binding cooperativity; selective pressure to maximize the sensitivity and response of allosteric enzymes may act to optimize cooperativity of binding modifiers and kinetic cooperativity of substrate turnover. The initial velocity equations including modifiers can be extended to bi-substrate, cooperative kinetics. The kinetics of methanol dehydrogenase are discussed.     

On the relationship between the Hill coefficients for steady-state and transient kinetic data: A criterion for concerted transitions in allosteric proteins

A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.     

The molecular code for hemoglobin allostery revealed by linking the thermodynamics and kinetics of quaternary structural change. 1. Microstate linear free energy relations

A novel model linking the thermodynamics and kinetics of hemoglobin's allosteric (R --> T) and ligand binding reactions is applied to photolysis data for human HbCO. To describe hemoglobin's kinetics at the microscopic level of structural transitions and ligand-binding events for individual [ij]-ligation microstates ((ij)R --> (ij)T, (ij)R + CO --> ((i)(+1))(k)R, and (ij)T + CO --> ((i)(+1))(k)T), the model calculates activation energies, (ij)DeltaG(++), from previously measured cooperative free energies of the equilibrium microstates (Huang, Y., and Ackers, G. K. (1996) Biochemistry 35, 704-718) by using linear free energy relations ((ij)DeltaG(++) - (01)DeltaG(++) = alpha[(ij)DeltaG - (01)DeltaG], where the parameter alpha, describing the variation of activation energy with reaction energy perturbation, can depend on the natures of both the reaction and the perturbation). The alpha value measured here for the allosteric dynamics, 0.21 +/- 0.03, corresponds closely to values observed previously, strongly suggesting that the thermodynamic microstate energies directly underlie the allosteric kinetics (as opposed to the alpha((ij)DeltaG(RT)) serving merely as arbitrary fitting parameters). Besides systematizing the study of hemoglobin kinetics, the utility of the microstate linear free energy model lies in the ability to test microscopic aspects of allosteric dynamics such as the "symmetry rule" for quaternary change deduced previously from thermodynamic evidence (Ackers, G. K., et al. (1992) Science 255, 54-63). Reflecting a remarkably detailed correspondence between thermodynamics and kinetics, we find that a kinetic model that includes the large free energy splitting between doubly ligated T microstates implied by the symmetry rule fits the data significantly better than one that does not.     

How robust are switches in intracellular signaling cascades?

Since all-or-none decisions of the cell are controlled by extracellular signals, cells have biochemical switches within their intracellular signaling networks. Central elements of these switches are multisite phosphorylation, enzymic saturation, and amplification by cascades. Moreover, positive feedback can contribute to switch-like behavior termed also ultrasensitivity. Here we analyse the robustness of these mechanisms exemplified by models of the three-molecule MAPK-cascade and the single-molecule Goldbeter-Koshland switch. We show that the ultrasensitivity in the MAPK-cascades is more robust against changes of the kinetic parameters than the Goldbeter-Koshland switch. If multiple parameters are changed randomly, the effects of parameter changes can compensate each other in the cascade leading to a remarkable robustness of the switch-like behavior. The different degrees of robustness can be traced back to the different mechanisms of generating ultrasensitivity. While in the Goldbeter-Koshland switch the saturation of the enzymes are crucial, in the MAPK-cascade the adjustment of working ranges determines the ultrasensitivity. Our results indicate that amplification of ultrasensitivity in cascades and multisite phosphorylation might be a design principle to achieve robust switches.     

Muscle glycogenolysis. Regulation of the cyclic interconversion of phosphorylase a and phosphorylase b

Regulation of glycogenolysis in skeletal muscle is dependent on a network of interacting enzymes and effectors that determine the relative activity of the enzyme phosphorylase. That enzyme is activated by phosphorylase kinase and inactivated by protein phosphatase-1 in a cyclic process of covalent modification. We present evidence that the cyclic interconversion is subject to zero-order ultrasensitivity, and the effect is responsible for the "flash" activation of phosphorylase by Ca2+ in the presence of glycogen. The zero-order effect is observable either by varying the amounts of kinase and phosphatase or by modifying the ratio of their activities by a physiological effector, protein phosphatase inhibitor-2. The sensitivity of the system is enhanced in the presence of the phosphorylase limit dextrin of glycogen which lowers the Km of phosphorylase kinase for phosphorylase. The in vitro experimental results are examined in terms of physiological conditions in muscle, and it is shown that zero-order ultrasensitivity would be more pronounced under the highly compartmentalized conditions found in that tissue. The sensitivity of this system to effector changes is much greater than that found for allosteric enzymes. Furthermore, the sensitivity enhancement increases more rapidly than energy consumption (ATP) as the phosphorylase concentration increases. Energy effectiveness is shown to be a possible evolutionary factor in favor of the development of zero-order ultrasensitivity in compartmentalized systems.     

Ligand Depletion in vivo Modulates the Dynamic Range and Cooperativity of Signal Transduction

Biological signal transduction commonly involves cooperative interactions in the binding of ligands to their receptors. In many cases, ligand concentrations in vivo are close to the value of the dissociation constant of their receptors, resulting in the phenomenon of ligand depletion. Using examples based on rotational bias of bacterial flagellar motors and calcium binding to mammalian calmodulin, we show that ligand depletion diminishes cooperativity and broadens the dynamic range of sensitivity to the signaling ligand. As a result, the same signal transducer responds to different ranges of signal with various degrees of cooperativity according to its effective cellular concentration. Hence, results from in vitro dose-response analyses cannot be applied directly to understand signaling in vivo. Moreover, the receptor concentration is revealed to be a key element in controlling signal transduction and we propose that its modulation constitutes a new way of controlling sensitivity to signals. In addition, through an analysis of the allosteric enzyme aspartate transcarbamylase, we demonstrate that the classical Hill coefficient is not appropriate for characterizing the change in conformational state upon ligand binding to an oligomeric protein (equivalent to a dose-response curve), because it ignores the cooperativity of the conformational change for the corresponding equivalent monomers, which are generally characterized by a Hill coefficient . Therefore, we propose a new index of cooperativity based on the comparison of the properties of oligomers and their equivalent monomers.     

Reciprocal Regulation as a Source of Ultrasensitivity in Two-Component Systems with a Bifunctional Sensor Kinase

Two-component signal transduction systems, where the phosphorylation state of a regulator protein is modulated by a sensor kinase, are common in bacteria and other microbes. In many of these systems, the sensor kinase is bifunctional catalyzing both, the phosphorylation and the dephosphorylation of the regulator protein in response to input signals. Previous studies have shown that systems with a bifunctional enzyme can adjust the phosphorylation level of the regulator protein independently of the total protein concentrations – a property known as concentration robustness. Here, I argue that two-component systems with a bifunctional enzyme may also exhibit ultrasensitivity if the input signal reciprocally affects multiple activities of the sensor kinase. To this end, I consider the case where an allosteric effector inhibits autophosphorylation and, concomitantly, activates the enzyme''s phosphatase activity, as observed experimentally in the PhoQ/PhoP and NRII/NRI systems. A theoretical analysis reveals two operating regimes under steady state conditions depending on the effector affinity: If the affinity is low the system produces a graded response with respect to input signals and exhibits stimulus-dependent concentration robustness – consistent with previous experiments. In contrast, a high-affinity effector may generate ultrasensitivity by a similar mechanism as phosphorylation-dephosphorylation cycles with distinct converter enzymes. The occurrence of ultrasensitivity requires saturation of the sensor kinase''s phosphatase activity, but is restricted to low effector concentrations, which suggests that this mode of operation might be employed for the detection and amplification of low abundant input signals. Interestingly, the same mechanism also applies to covalent modification cycles with a bifunctional converter enzyme, which suggests that reciprocal regulation, as a mechanism to generate ultrasensitivity, is not restricted to two-component systems, but may apply more generally to bifunctional enzyme systems.     

Homotropic allosteric regulation in monomeric mammalian glucokinase

Glucokinase catalyzes the ATP-dependent phosphorylation of glucose, a chemical transformation that represents the rate-limiting step of glycolytic metabolism in the liver and pancreas. Glucokinase is a central regulator of glucose homeostasis as evidenced by its association with two disease states, maturity onset diabetes of the young (MODY) and persistent hyperinsulinemia of infancy (PHHI). Mammalian glucokinase is subject to homotropic allosteric regulation by glucose-the steady-state velocity of glucose-6-phosphate production is not hyperbolic, but instead displays a sigmoidal response to increasing glucose concentrations. The positive cooperativity displayed by glucokinase is intriguing since the enzyme functions as a monomer under physiological conditions and contains only a single binding site for glucose. Despite the existence of several models of kinetic cooperativity in monomeric enzymes, a consensus has yet to be reached regarding the mechanism of allosteric regulation in glucokinase. Experimental evidence collected over the last 45 years by a number of investigators supports a link between cooperativity and slow conformational reorganizations of the glucokinase scaffold. In this review, we summarize advances in our understanding of glucokinase allosteric regulation resulting from recent X-ray crystallographic, pre-equilibrium kinetic and high-resolution nuclear magnetic resonance investigations. We conclude with a brief discussion of unanswered questions regarding the mechanistic basis of kinetic cooperativity in mammalian glucokinase.     

Ultrasensitive synthetic protein regulatory networks using mixed decoys

Cellular protein interaction networks exhibit sigmoidal input-output relationships with thresholds and steep responses (i.e. ultrasensitivity). Although cooperativity can be a source of ultrasensitivity, we examined whether the presence of "decoy" binding sites that are not coupled to activation could also lead to this effect. To systematically vary key parameters of the system, we designed a synthetic regulatory system consisting of an autoinhibited PDZ domain coupled to an activating SH3 domain binding site. In the absence of a decoy binding site, this system is non-ultrasensitive, as predicted by modeling of this system. Addition of a high-affinity decoy site adds a threshold, but the response is not ultrasensitive. We found that sigmoidal activation profiles can be generated utilizing multiple decoys with mixtures of high and low affinities, where high affinity decoys act to set the threshold and low affinity decoys ensure a sigmoidal response. Placing the synthetic decoy system in a mitotic spindle orientation cell culture system thresholds this physiological activity. Thus, simple combinations of non-activating binding sites can lead to complex regulatory responses in protein interaction networks.     

Global conformational changes in allosteric proteins. A study of Escherichia coli cAMP receptor protein and muscle pyruvate kinase.

One of the basic features in allosteric regulation involves long range transduction of information. Based on crystallographic data on protein systems that are regulated by allosteric mechanisms, a global conformational change has always been observed. It is, therefore, important and useful to correlate the cooperativity of global structural change with the mode of binding of the regulatory ligand. Two systems were chosen for study, namely Escherichia coli cAMP receptor protein and muscle pyruvate kinase, which show negative and positive cooperativity in the binding of allosteric ligands, respectively. Quantitative titration of the global structural change, monitored by a high precision analytical gel chromatography technique, was conducted as a function of allosteric effector concentration. The results obtained for cAMP receptor protein show that the protein undergoes contraction upon binding of cAMP. The decreases in Stokes radius associated with complex formation are 0.1 +/- 0.1 and 0.7 +/- 0.1 A when one and two cAMP-binding sites are filled, respectively. The results for the pyruvate kinase system show a concerted structural change that quantitatively match the predicted behavior based on equilibrium constants derived from the analysis of steady state kinetic data by a two-state model. Hence, for these two systems, these results show that negative and positive cooperativity are correlated with sequential and concerted modes of structural change, respectively.     

Robust spindle alignment in Drosophila neuroblasts by ultrasensitive activation of pins

Cellular signaling pathways exhibit complex response profiles with features such as thresholds and steep activation (i.e., ultrasensitivity). In a reconstituted mitotic spindle orientation pathway, activation of Drosophila Pins (LGN in mammals) by Gαi is ultrasensitive (apparent Hill coefficient of 3.1), such that Pins recruitment of the microtubule binding protein Mud (NuMA) occurs over a very narrow Gαi concentration range. Ultrasensitivity is required for Pins function in neuroblasts as a nonultrasensitive Pins mutant fails to robustly couple spindle position to cell polarity. Pins contains three Gαi binding GoLoco domains (GLs); Gαi binding to GL3 activates Pins, whereas GLs 1 and 2 shape the response profile. Although cooperative binding is one mechanism for generating ultrasensitivity, we find GLs 1 and 2 act as "decoys" that compete against activation at GL3. Many signaling proteins contain multiple protein interaction domains, and the decoy mechanism may be a common method for generating ultrasensitivity in regulatory pathways.     

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.     

Kinetic cooperativity in the concerted model for allosteric enzymes.

The cooperativity of enzyme-substrate interactions is investigated in the concerted allosteric model of Monod, Wyman and Changeux. The general case of K-V systems is considered, in which the two protomer conformational states R and T postulated in the theory differ in catalytic and binding properties. An expression for the Hill coefficient nH defined with respect to the asymptotic velocity V infinity to is analyzed in conditions which exclude substrate inhibition. Kinetic cooperativity is always positive (nH greater than 1) in the case of a dimer enzyme, and in the case of an inactive T state. Slight kinetic negative cooperativity (nH less than 1) occurs under restrictive conditions for larger numbers of protomers when the substrate binds significantly to the less active state of the enzyme, but the phenomenon remains negligible for trimers and tetramers. These conclusions differ from those obtained [A. Goldbeter, J. Mol.Biol.90 (1974) 185] with the Hill coefficient based on the absolute maximum velocity, which may exceed the experimental value V infinity to in K-V systems. The results extend those of Paulus and DeRiel [J. Mol. Biol. 97 (1975) 667] and support the view that in most cases, negative cooperativity is not compatible with a mechanism based on a concerted and conservative allosteric transition. The Hill coefficients for binding and catalysis are compared in K-V systems.     

Relation between Mg2+ activation and AMP inhibition of fructose-1,6-diphosphatase from rabbit skeletal muscles

It was shown that AMP, an allosteric inhibitor of fructose-1.6-bisphosphatase, decreases the apparent affinity of the enzyme for the activating cation, Mg2+, which is accompanied by a decrease of the kinetic cooperativity between the Mg2+-binding sites. In its turn, the Mg2+ increase diminishes the enzyme sensitivity to the inhibiting effect of AMP and decreases the cooperativity of the inhibitor binding. The heterotropic interactions between the allosteric inhibitor and activator binding centers are consistent with the predictions of the Monod-Wyman-Changeux model which involves two conformational states of the enzyme (of which one is catalytically inactive) differing in their affinity for the ligands. An increase in pH from 7.4 to 9.0 increases the enzyme affinity for Mg2+ and causes an equilibrium shift towards the catalytically active state of the enzyme.     

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.     

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.