It is widely accepted that insufficient insulin-stimulated activation of muscle glycogen synthesis is one of the major components of non-insulin-dependent (type 2) diabetes mellitus. Glycogen synthase, a key enzyme in muscle glycogen synthesis, is extensively regulated, both allosterically (by glucose-6-phosphate, ATP, and others) and covalently (by phosphorylation). Although glycogen synthase has been a topic of intense study for more than 50 years, its kinetic characterization has been confounded by its large number of phosphorylation states. Questions remain regarding the function of glycogen synthase regulation and the relative importance of allosteric and covalent modification in fulfilling this function. In this review, we consider both earlier kinetic studies and more recent site-directed mutagenesis and crystal structure studies in a detailed qualitative discussion of the effects of regulation on the kinetics of glycogen synthase. We propose that both allosteric and covalent modification of glycogen synthase may be described by a Monod–Wyman–Changeux model in terms of apparent changes to L, the equilibrium constant for transition between the T and R conformers. As, with the exception of L, all parameters of this model are independent of the glycogen synthase phosphorylation state, the need to determine kinetic parameters for all possible states is eliminated; only the relationship between a particular state and L must be established. We conclude by suggesting that renewed efforts to characterize the relationship between phosphorylation and the kinetics of glycogen synthase are essential in order to obtain a better quantitative understanding of the function of glycogen synthesis regulation. The model we propose may prove useful in this regard.
glucose-6-phosphate-dependent form of glycogen synthase
dual-specificity tyrosine-phosphorylated and tyrosine-regulated protein kinase
Escherichia coli glycogen synthase
glycogen synthase kinase 3
glucose-6-phosphate-independent form of glycogen synthase
mitogen-activated protein kinase
Pyrococcus abyssi glycogen synthase
Per/Arnt/Sim domain-containing protein kinase
cAMP-dependent protein kinase
protein phosphatase 1
protein phosphatase 2A
Saccharomyces cerevisiae glycogen synthase
uridine diphosphate glucose
Glycogen, a branched polymer of glucose, is used by numerous organisms as a store when glucose is abundant or as a source of glucose under conditions of metabolic depletion . The structure of glycogen has been optimized to store a large amount of glucose that is readily available without affecting cellular osmolarity . In mammals, skeletal muscle is the major site of glucose disposal [3, 4], storing significantly more glycogen than the liver . Although skeletal muscle insulin resistance is not a sufficient causative agent in non-insulin-dependent (type 2) diabetes mellitus, it is considered a primary defect in this disease . Jensen et al.  suggest that, in muscle with a high glycogen content, insulin resistance is not necessarily manifested as decreased glucose uptake, but rather as impaired activity of muscle glycogen synthase (GS, EC 220.127.116.11). GS, the enzyme that incorporates glucose from uridine diphosphate glucose (UDP-Glc) into glycogen, is extensively regulated by both allosteric and covalent modification. Glucose-6-phosphate (G6P), acting as an activator, and ATP, acting as an inhibitor, as well as many other ligands, compete for an allosteric site on GS. In addition, GS is phosphorylated at nine serine residues, resulting in marked inhibition.
Two questions regarding the regulation of glycogen synthesis are of particular interest. First, does the regulation of GS serve to control the flux of glycogen synthesis, as is traditionally believed, or does it serve to ensure metabolite homeostasis? Several in vivo NMR studies, as reviewed by Shulman et al. , suggest that it is indeed glucose uptake, not glycogen synthesis, that controls the glycogen synthetic flux. This suggests that regulation of GS is not involved in controlling the flux of glycogen synthesis, but rather serves to ensure metabolite homeostasis. Second, as GS is regulated both allosterically and covalently, and, given that insulin signalling, amongst others, use both these mechanisms to affect GS activity, what is the relative importance of allosteric and covalent regulation? Recent studies [9, 10] indicate that, in response to insulin, activation of GS is predominantly mediated through allosteric rather than covalent regulation.
The theoretical framework of metabolic control analysis [11, 12] has proven useful in obtaining quantitative insights into the possible function of regulation of GS, if not for flux control [13, 14]. It is our opinion that metabolic control analysis may also shed light on the relative importance of allosteric and covalent regulation of GS. However, as of yet, no detailed kinetic model exists that accounts for both allosteric and covalent regulation of GS. The development of such a model, which is severely complicated by the numerous phosphorylation states in which the enzyme may exist, may aid in obtaining a more nuanced understanding of the function of GS regulation and the relative importance of allosteric and covalent regulation in realizing this function.
In this review, we discuss both earlier kinetic studies and more recent site-directed mutagenesis and crystal structure studies, and show how the results from these studies may form the basis of a unifying view of the covalent and allosteric regulation of GS that largely overcomes the combinatorial explosion resulting from the numerous phosphorylation states of the enzyme. We begin with a detailed general discussion of the kinetics, structure and regulation of GS. We then proceed to formulate the kinetics of GS in terms of a phenomenological rate equation for the purpose of discussing the effects of covalent and allosteric regulation on the kinetic properties of GS. Finally, we propose a variation of the classic Monod–Wyman–Changeux model that succinctly accounts for all the apparent modifications to GS kinetic properties.
This review is not intended as a comprehensive survey of glycogen metabolism, but specifically concerns the regulation of mammalian skeletal muscle GS from a kinetic perspective. The recent publication by Roach et al.  provides a comprehensive general review of developments in glycogen metabolism research over the last decade. The present review follows what may be considered a ‘bottom-up’ approach, as we avoid discussing higher-level regulatory phenomena such as insulin signalling, but instead focus on the mechanisms underpinning GS regulation. The recent ‘top-down’ review by Jensen and Lai  provides a discussion of the effects of exercise, adrenaline and insulin stimulation on GS. Where no mammalian muscle data were available, we also considered, with due care, results from research performed on other mammalian tissues, other eukaryotes, or even prokaryotes. Unless stated otherwise, or where the context indicates otherwise, ‘GS’ refers to the muscle enzyme.
Glycogen synthase and its kinetics
Reaction and thermodynamics
Glycogen chains are readily elongated by glycogen phosphorylase (GP, EC 18.104.22.168) operating in the reverse direction, using glucose-1-phosphate as the substrate. However, Leloir et al. showed (first in liver  and then in muscle ) that the physiologically relevant synthetic pathway uses UDP–Glc as the substrate, leading to the discovery of GS. GS catalyses the bi-bi reaction in which the glucosyl (Glc) moiety of UDP-Glc is incorporated into a glycogen molecule comprising n glucose residues by means of an α(1→4) glycosidic bond, to produce UDP and a glycogen molecule comprising n + 1 glucose residues [16, 17] according to the equation
GS requires an oligosaccharide primer as a glucose acceptor and is therefore not capable of de novo glycogen synthesis. Instead, de novo glycogen synthesis is initialized in two phases by the homodimer glycogenin (EC 22.214.171.124). In the first phase, a tyrosyl residue of one subunit (Tyr194 in rabbit muscle) [18, 19] is glycosylated by its partner in an inter-subunit reaction [20, 21]. In the second phase, a further seven glucosyl residues are added successively in an intra-subunit reaction , producing a suitable primer for GS. Branches are initiated by branching enzyme (EC 126.96.36.199), which cleaves α(1→4) bonds and reintroduces them as α(1→6) bonds , thus creating new chains that may serve as primers for elongation by GS. On average, each glycogen chain branches twice and is 12–14 glucose residues long . The terminal glucosyl residues of glycogen chains are referred to as non-reducing ends.
The equilibrium constant of the GS reaction is expressed as
Although Glcn and Glcn+1 typically denote entire glycogen molecules, it is really only the non-reducing ends of a glycogen molecule that can partake in the elongation reaction. We thus define [Glcn] and [Glcn+1] as the total concentrations of all non-reducing ends that may serve as substrates and products. However, the majority of non-reducing ends may serve as both substrates and products. For sufficiently large glycogen molecules, the difference between the equilibrium values of [Glcn] and [Glcn+1] therefore becomes negligible, so that Eqn (2) simplifies to
Kornfeld and Brown  reported the formation of 0.0018 μmol UDP-Glc from 7 μmol UDP in the presence of GS and 5 mg glycogen (pH 7.5, 30 °C), from which a Keq of 3900 may be calculated using Eqn (3). Assuming that all α(1→4) glycosidic bonds in the glycogen molecule are equivalent, an assumption supported by Goldberg et al. , the Keq may also be calculated from the free energy changes of the component half-reactions. Gold  estimated a value of 400 at pH 7.0 and 25 °C. A value of 230 at pH 7.0/25 °C was estimated for the reaction with maltopentaose as the glucose acceptor using the group contribution method developed by Jankowski et al.  as implemented by the online service eQuilibrator . Adjusted for pH (7.15) and ionic strength (0.2 mm), this value increases to ∼1000. Kashiwaya et al.  report a much lower value of 37.7 (corrected for physiological pH and Mg2+ in rat heart).
The difference of more than two orders of magnitude in reported Keq values is a testament to the dependence of this value on experimental conditions. The value increases both with ionic strength and pH . The temperature dependence of the Keq is not clear. The large value calculated from the results of Kornfeld and Brown  may probably be ascribed to both the high pH and difficulties in accurately measuring the reactant concentrations. In comparison, the equilibrium ratio of ADP to ADP-glucose (ADP-Glc) for the Escherichia coli enzyme has been reported to range from 55.5 to 151 as the pH ranges from 5.27 to 6.82 at 37 °C . Considering the similarity of the ADP-Glc and UDP-Glc phosphoester bonds and the muscle pH of 6.8–7.15 , the physiologically relevant Keq for GS in muscle is probably of the order of 102. Regardless of the precise value, it is clear that the reaction does not operate in the reverse direction under physiological conditions.
Determination of the GS kinetic mechanism is complicated by glycogen's dual function as both substrate and product. In addition to the usual substrate binding terms, initial velocity equations must include product binding terms for glycogen . Moreover, if the glycogen concentration is varied, it will always vary in both its capacity as substrate and product . As a result, the interpretation of Lineweaver–Burk and other reciprocal plots in which each substrate is varied while keeping the other constant, changes significantly.
Plesner et al.  ruled out all mechanisms other than the rapid equilibrium random mechanism, while others [32, 33] have obtained reciprocal plots indicative of either rapid equilibrium random or ordered sequential mechanisms. In order to overcome the pitfalls associated with reciprocal plots, Gold  studied the mechanism of the rabbit muscle enzyme by determining the equilibrium isotope exchange rates between UDP-Glc and glycogen, and UDP-Glc and UDP. Gold  concluded that the mechanism is rapid equilibrium random, but conceded that it cannot be distinguished from a rapid equilibrium ordered mechanism with dead-end binary complexes by any of the methods he employed. Although the majority of research seems to favour the random order mechanism, an ordered sequential mechanism cannot be ruled out at this point.
The rapid equilibrium random bi-bi mechanism is seemingly incompatible with the observation [25, 34, 35] that glycogen forms stable complexes with glycogen synthase . However, the kinetic mechanism only describes the rapid exchange of individual non-reducing ends and does not preclude additional interaction of the glycogen molecule as a whole with GS. It has also been suggested that GS is able to add several glucosyl residues successively to the same chain of a glycogen molecule, i.e. that elongation is processive [25, 36, 37]. However, such a pattern of elongation is incompatible with a rapid equilibrium random mechanism, which predicts that exactly one glucose residue is successively incorporated in the same chain (distributive elongation) . Baskaran et al.  found that yeast GS exhibited a distributive pattern of catalysis with maltooctaose as glucose acceptor, which suggests that deviation from distributive elongation is not necessarily linked to a change in the kinetic mechanism, but rather the result of limited access to chains.
Tertiary and quaternary structure
Glycogen synthases are members of the GT-B superfamily of glycosyltransferases . The tertiary structure of members of this family, which also includes GP, is characterized by a pair of N-terminal and C-terminal Rossmann-fold domains separated by an inter-domain cleft that houses the active site. The C-terminus typically folds back onto the N-terminal Rossmann-fold domain, such that the two domains are linked by a two-stranded hinge . Significant rotation around this narrow hinge is possible, and GT-B members differ widely with regard to the size of the inter-domain cleft. Glycogen synthases have a particularly deep fissure between the N- and C-domains , and it has been suggested that an inter-domain closure is required to bring glycogen (which binds to the N-domain) and the nucleotide sugar (which binds to the C-domain) together for catalysis . Glycogen synthases may be further classified into the ADP-Glc-utilizing non-regulated GT-3 family (including the bacterial and archaeal enzymes) and the UDP-Glc-utilizing regulated GT-5 family (including the mammalian and yeast enzymes) . The most significant structural differences between the GT-3 family (comprising ∼50 kDa protomers) and the GT-5 family (comprising ∼80 kDa protomers) are the presence of two N-terminal inserts (β2–β5 and β7–α10) and a C-terminal insert (β11–α17), of which the most prominent secondary structure is a coiled-coil formed by helices α15 and α16 in GT-5 members. Another unique feature of eukaryotic GS is the presence of a conserved arginine-rich cluster (Arg580/581/583/587/589/592 in yeast) on the regulatory R helix (helix α22), which is believed to be involved in allosteric and covalent regulation.
The only available GS crystal structures are those of the bacteria Agrobacterium tumefaciens (AtGS)  and E. coli (EcGS) , the archaeon Pyrococcus abyssi (PaGS) , and recently yeast (Saccharomyces cerevisiae) (ScGS), the first eukaryotic GS structure . The oligomerization of the known structures ranges from monomeric to tetrameric, and the secondary structures involved in inter-subunit interactions differ widely. AtGS was solved as an asymmetric dimer  in which a 10-residue C-domain insert (407–416) facilitates the primary inter-subunit contacts . PaGS lacks the AtGS dimerization insert, but terminates in an 11-residue hydrophobic tail (427–437) that is not present in bacteria . The C-terminal hydrophobic tail (folded back onto the N-domain) associates with a hydrophobic pocket (53–55, 105–115, 141–142) on the N-domain of a neighbouring subunit, resulting in a trimeric quaternary structure with threefold symmetry in which the three N-domains are tightly associated. ScGS contains both the AtGS dimerization insert and the PaGS hydrophobic tail involved in trimerization, but neither sequence is conserved and they appear not to be involved in oligomerization . Instead, ScGS [42, 44] is a dimer of a dimer, in which the subunits are numbered (based on Baskaran et al. ) from A to D (Fig. 1). The inter-subunit contacts in the A/D (and B/C) interface involve the reciprocal association of helix α16 (located in the eukaryote-specific C-terminal insert) of one subunit with the region between helix α2 and sheet β4 (located in the first of the unique N-terminal inserts) of the partner subunit. In the interface between dimer pairs (AD/BC), the main contacts comprise a reciprocal association of helix α15 from one subunit with the region between α15 and β10 of the other subunit, so that the α15/16 helix pairs of subunits A and C associate, and those of subunits B and D associate. The A/B and C/D interfaces house the allosteric sites, whereas the A/D and B/C interfaces house the active sites. It appears that GS oligomerization evolved independently in bacteria, archaea and eukaryotes.
The oligomerization state of the muscle GS isozyme (∼84 kDa) has been variously reported as dimeric [45, 46], trimeric [45, 47, 48] or tetrameric [35, 45, 49-53]. Horcajada et al.  pointed out that, in many of the earlier investigations, the oligomerization state was determined based on the sedimentation coefficient, a measure that assumes a strictly globular protein shape. Based on the presence in muscle GS of an insert analogous to the PaGS hydrophobic tail, and on the findings of Brown and Larner  using sedimentation equilibrium ultracentrifugation, a technique that is not influenced by protein shape, Horcajada et al.  favour a trimeric state for muscle GS. However, other researchers , also using sedimentation equilibrium ultracentrifugation, observed results indicative of a tetramer. The structure of eukaryotic GS is highly conserved, with only the phosphorylation sites and loops between conserved secondary structures differing . Given this high degree of conservation, and, in particular, the presence in muscle GS of secondary structures corresponding to the yeast α15–16 helices, the quaternary structure of muscle GS is probably also tetrameric.
Regulatory arginine cluster
Based on the assumption that allosteric and covalent regulation of eukaryotic GS is brought about by interaction of the negatively charged phosphorylated residues and G6P with basic amino acid residues, Pederson et al.  identified several arginine and lysine residues that are conserved in eukaryotes. They proceeded to create 23 yeast GS mutants in which these residues were systematically replaced with alanine residues, with up to three mutations per mutant enzyme. Two of the mutants, R579A/R580A/R582A (mouse muscle enzyme numbering ; initial methionine included) and R586A/R588A/R591A, were completely insensitive to activation by G6P, but still exhibited significant activity in the absence of G6P. Upon phosphorylation, the Vmax of mutant R579A/R580A/R582A, which was already very low, did not decrease much further, whereas mutant R586A/R588A/R591A, which displayed normal activity, was significantly inactivated. Hanashiro and Roach , working with the rabbit muscle enzyme, obtained essentially the same overall results, with the important difference that, in their work, the activity of the R579A/R580A/R582A mutant was decreased fourfold upon phosphorylation, whereas the R586A/R588A/R591A mutant was unaffected. The six arginine residues in these mutants constitute what is now referred to as the regulatory arginine cluster, and are located on the R helix (Fig. 2).
Noting that the mutations introduced by Hanashiro and Roach  not only abolished G6P sensitivity, but also altered the enzyme's activity in the absence of G6P, Bouskila et al. , also working with the muscle enzyme, mutated the six arginine residues singly or in pairs and found that the single point mutations R582A and R586A had no effect on GS activity, but were sufficient to abrogate G6P sensitivity. However, both mutants were still activated by dephosphorylation. These findings suggest that Arg582 and Arg586 mediate regulation by G6P, a view that is supported by the crystal structure data for the yeast enzyme, which position these residues in the G6P-binding pocket . Baskaran et al.  found that the R579A/R580A double mutant exhibited activity comparable to the wild-type enzyme, but was significantly inhibited by phosphorylation. In contrast, the R588A/R591A double mutant was significantly inactivated compared to the wild-type, but was activated to wild-type levels by addition of G6P. There were differences between the yeast triple mutant R579A/R580A/R582A and the double mutant R579A/R580A. The basal activity of the triple mutant is much lower than that of the double mutant; the triple mutant is also unresponsive to phosphorylation, whereas the double mutant is further inhibited. Similar disagreement is observed between the R586A/R588A/R591A and R588A/R591A mutants in yeast. In both cases, the results for the yeast double mutants appear to be in closer agreement with those for the muscle triple mutants reported by Hanashiro and Roach . To our knowledge the R579A/R580A and R588A/R591A double mutants have not been investigated in muscle. However, given the sequence similarity between the yeast and muscle enzymes, we speculate that the individual functions of the six arginine residues are similar in yeast and muscle. In summary (Table 1), Baskaran et al.  suggest that Arg579 and Arg580 interact with phosphorylated serine residues, thereby stabilizing an inactive conformation, whereas Arg582 and Arg586 interact with the phosphate group of G6P, thereby stabilizing an active conformation. Finally, Arg588 and Arg591 stabilize the dephosphorylated, non-activated enzyme; phosphorylation or replacement by alanine residues neutralizes the charge of these residues, leading to inactivation.
Table 1. Response of arginine cluster mutants to G6P and phosphorylation [10, 42, 55]. Amino acids are numbered based on the mouse muscle enzyme (initial methionine included) 
Inactivated by mutation
Inactivated by phosphorylation
Reactivated by G6P
a Inactivation occurs to a lesser extent than in wild-type. b Dephosphorylation activates the enzyme. c Only slight additional inactivation is observed.
As noted earlier, UDP-Glc and UDP are believed to bind to the C-terminal Rossmann-fold in the inter-domain cleft. As Rossmann-fold domains are associated with nucleoside-binding capability , the enzyme–ligand interaction probably mostly involves the UDP moiety. In agreement with this, UDP has been found to be a competitive inhibitor with regard to UDP-Glc. There is no reason to believe that either UDP-Glc or UDP binds to additional sites on the GS subunit. In the majority of kinetic studies, UDP-Glc exhibits hyperbolic saturation curves [31-33, 47, 50, 58-61], with only a few studies [60, 62-64] reporting deviations from Michaelian kinetics, mostly in the form of negative cooperativity . Sølling  argues that the observed negative cooperativity is an artefact that disappears if appropriate measures are taken to minimize UDP product inhibition.
The formation of tight enzyme–glycogen complexes [25, 34] indicates that, apart from the N-domain binding site in the catalytic cleft, glycogen probably interacts with GS at several additional sites. Díaz et al.  identified a non-catalytic glycogen-binding site on the surface of the N-domain of PaGS. Four glucose moieties of maltohexaose were found to bind at this site by curling around Tyr174. Mutation of Tyr174 to alanine decreased the acceptor affinity and specific activity with glycogen as substrate, but had no effect on specific activity with maltohexaose as acceptor. In co-sedimentation experiments, the native enzyme was found in the pellet fraction, whereas the mutant (which still had an intact catalytic glycogen-binding site) was located in the supernatant, suggesting that the non-catalytic site has a much higher affinity for glycogen than the catalytic site. Díaz et al.  also identified Tyr239 as the human muscle GS counterpart to Tyr174. Mutation of Tyr239 and the nearby Tyr242 decreased both the affinity for glycogen and the specific activity, whereas specific activities were essentially unchanged with maltohexaose as acceptor. Baskaran et al.  identified four maltodextran-binding sites, in addition to the catalytic site, on ScGS. One of these sites (site 1) corresponds roughly to the site identified for PaGS, but involves unique eukaryotic structures, and, interestingly, does not include the residue corresponding to Tyr174. The remaining three sites are located on the C-domain, with site 4 located in the catalytic cleft near the catalytic glycogen-binding site. For all four sites, mutation of key residues decreased the Vmax and affinity for glycogen.
The enhanced glycogen affinity brought about by the non-catalytic glycogen-binding sites essentially dictates that glycogen binding occurs in a positively cooperative fashion. As these additional sites have little or no effect on the affinity for oligosaccharides such as maltohexaose, this cooperativity is not expected to be the result of any conformational change, but rather an increase in the apparent concentration of chains (from the same glycogen molecule) in the vicinity of unoccupied sites on the same and possibly neighbouring subunits. It is therefore surprising that kinetic studies report non-cooperative glycogen binding [31, 32, 47] or even negative cooperativity .
Before we discuss the effects of modifiers on GS activity, a brief note on nomenclature is warranted. In line with the nomenclature used by Cornish-Bowden , we use the term ‘specific’ to refer to any modification that results in an altered substrate affinity, and the term ‘catalytic’ to refer to a modification that results in an altered maximal velocity. We adopt these terms because the more familiar terms (competitive and non-competitive) do not apply to the case of enzyme activation. The term ‘competitive’ is still used to indicate that ligands physically compete for the same site, as opposed to affecting each other's binding affinity by another mechanism.
GS is allosterically regulated by G6P, ATP and several other ligands. G6P is a potent activator of GS , and is generally recognized as the most important allosteric modifier of GS. Several studies have reported that G6P activates GS by increasing the substrate affinity, catalytic rate, or both. We discuss the nature of G6P activation in detail in a subsequent section. ATP, on the other hand, inhibits GS [30, 33, 58, 68, 69]. This inhibition is brought about by decreasing the enzyme's affinity for UDP-Glc [30, 33]. To the best of our knowledge, there is no evidence that ATP also inhibits GS catalytically, but this possibility cannot be ruled out. Regrettably, ATP inhibition is often neglected in GS kinetic studies. Kinetic studies that include both G6P and ATP indicate a competitive binding pattern [33, 58, 68]. However, contrary to what is expected for pure competition, it has been noted in a few cases that G6P saturation is unable to reverse ATP inhibition completely [33, 58]. Two explanations have been offered in this regard. First, G6P and ATP bind to different allosteric sites, but binding of either ligand significantly decreases the affinity for the other ligand . Alternatively, both ligands compete for the same allosteric site, but ATP also competes with UDP-Glc at the catalytic site . In support of the latter explanation, it has been observed that the rat muscle enzyme is able to use ADP-Glc as a glucose donor at half the rate of UDP-Glc , showing that the adenosine moiety is able to bind to the active site. Moreover, ScGS crystal structure data show that, in the G6P-binding pocket, only the amino acid residues that bind the phosphate moiety are ordered, with the remaining residues only assuming an ordered conformation upon ligand binding . The phosphate moiety is therefore probably a major determinant of ligand specificity at the allosteric site. This provides a basis on which G6P and ATP, although structurally disparate apart from the phosphate moiety, may both bind to the same site. Activation and inhibition curves of G6P and ATP have been found to be either hyperbolic or sigmoidal in various studies. Cooperative G6P binding has mostly been observed for the phosphorylated enzyme [58, 60, 63, 71], but the dephosphorylated form has also been found to exhibit mild cooperativity . ATP cooperativity has been observed for the dephosphorylated enzyme . There is also strong evidence for positive heterotropic cooperativity between G6P and ATP binding [33, 58, 60]. ATP and ADP are probably equally important GS inhibitors [30, 69], but detailed kinetic data for the latter ligand are very limited. AMP has also been reported as a weak inhibitor of GS at high concentrations [30, 69], but, given the low AMP concentration in muscle, it is unlikely that AMP is a significant effector of GS in vivo. In the remainder of this review, ATP serves as a model GS inhibitor.
Finally, GS is phosphorylated in vivo at at least nine serine residues [72, 73]. Overall, phosphorylation has a potent inhibitory effect, but not all phosphorylation sites affect the enzyme's activity. We discuss the regulation of GS by phosphorylation in detail in a later section. Briefly, inhibition by phosphorylation is the result of an altered affinity of GS for its reactants and modifiers, and possibly a decrease in the turnover number (kcat).
Phenomenological rate equation
We have reviewed the general properties and kinetics of GS. We now develop a detailed formal treatment of GS kinetics to serve as the setting within which we discuss the allosteric and covalent regulation of GS. The kinetics of most enzymes are adequately described by the familiar concepts of maximal velocity and half-saturation concentrations, quantified by the Vmax and Michaelis constants. In addition to these concepts, a formal treatment of GS kinetics must also describe cooperativity, and catalytic and specific modification. To describe these concepts, we adopt the Hill formalism as generalized by Hofmeyr and Cornish-Bowden  and Westermark et al. . It is often considered a weakness of the Hill equation that it does not have a mechanistic interpretation, i.e. it is largely independent of the kinetic mechanism and the mechanism of cooperativity, at least for non-integer values of the Hill coefficient. However, we consider this a strength when, as for GS, there is little agreement regarding these mechanisms in the first place. Moreover, although not all the Hill equation's parameters have mechanistic interpretations, they have clear operational definitions. Nevertheless, it should be mentioned that the Hill equation is unable to describe heterotropic cooperativity such as observed for GS between G6P and ATP.
Based on the properties and kinetics of GS discussed above, we make the following simplifying assumptions: (a) glycogen is saturating and binds equally well as substrate and product to GS, and is therefore left out, (b) product inhibition by UDP is significant, (c) G6P may be both a catalytic and a specific activator, (d) ATP is only a specific inhibitor, (e) ATP binds to both the catalytic and allosteric site, and (f) all other effectors are constant and their effects are absorbed in the explicit parameters. Equation (4) describes the velocity of the GS reaction as in Eqn (1) for a particular GS phosphorylation state at constant G6P and ATP concentrations :
where Vmax = kcat·[E]tot, kcat is the catalytic constant, [E]tot is the total GS concentration, σ = [UDP-Glc]/UDP-Glc0.5, π = [UDP]/UDP0.5, UDP-Glc0.5 and UDP0.5 are the UDP-Glc and UDP half-saturation concentrations in the absence of other ligands, h is the degree of reactant (UDP-Glc and UDP) binding cooperativity, Γ is the mass-action ratio, Keq is the equilibrium constant, and μcat and μspec describe catalytic and specific modification. Note that, when μcat = 1 and μspec = 1, Eqn (4) simplifies to the standard reversible Hill equation without modifier effects .
From the derivation by Westermark et al.  and considering our assumptions, the expression for μcat is given by
where ξG6P = [G6P]/G6P0.5, ξATP = [ATP]/ATP0.5, G6P0.5 and ATP0.5 are the G6P and allosteric site ATP half-saturation concentrations in the absence of other ligands, γG6P ≥ 1 is the factor by which kcat is multiplied when G6P is saturating (values > 1 indicate activation), αG6P ≥ 1 and αATP < 1 are the factors by the reactant half-saturation concentrations are divided when G6P or ATP is saturating, hG6P is the degree of G6P binding cooperativity, and hATP is the degree of ATP binding cooperativity at the allosteric site. Although we assume that ATP is not a catalytic inhibitor, it does reverse catalytic activation by G6P and must therefore appear in μcat. In the absence of G6P or if ATP is saturating, μcat = 1, thus reflecting our assumption that ATP does not affect the enzyme's catalytic capacity. In the absence of ATP, on the other hand, μcat increases from 1 to γG6P as the G6P concentration changes in the range from zero to saturation. At saturating G6P concentrations, the maximal velocity of GS is thus multiplied by the factor γG6P. Specific activation by G6P and ATP at the catalytic and allosteric sites is described by μspec :
where ξATP′ = [ATP]/ATP′0.5, ATP′0.5 is the catalytic site ATP half-saturation concentration in the absence of other ligands, and hATP′ is the degree of ATP binding cooperativity at the catalytic site. If [G6P] ≫ G6P0.5, Eqn (6) simplifies to
showing that, although G6P completely overcomes ATP inhibition at the allosteric site, ATP inhibition at the catalytic site is only abolished for a large value of αG6P. Saturation by ATP, on the other hand, causes μspec → ∞, i.e. reactant binding is completely inhibited.
The non-mathematically minded may safely ignore these equations, but should keep the operational definitions of the parameters in mind, as they form the basis for further discussion.
Measures of activity
It was initially thought that GS, like GP, is phosphorylated at only one site and that the phosphorylated form is entirely dependent on G6P for activity. This led Villar-Palasi and Larner  to introduce the activity ratio as the ratio of enzyme activity in the absence of G6P, which is proportional to the concentration of GS in the G6P-independent form (the I form), to that at saturating G6P concentrations (typically 7.2 or 10 mm), which is proportional to the concentration of total GS, i.e. the I form plus glucose-6-phosphate-dependent form (the D form).
The activity ratio, which is often alternatively known as the −G6P/+G6P ratio or expressed as a percentage (denoted %I), may thus be interpreted as the fraction of total enzyme that is present in the I form. However, as more phosphorylation sites were discovered, it became clear that, although it provided a good measure of the effect of phosphorylation on GS kinetics, the activity ratio was no longer a mole fraction. Guinovart et al.  offered an interpretation on the basis of the Michaelis–Menten equation, assuming that G6P has no catalytic effect and increases the UDP-Glc affinity to the point of saturation for even the most phosphorylated states:
where σ = [UDP-Glc]/KUDP-Glc. It is clear from Eqn (9) that the activity ratio is independent of the affinity of GS for G6P . Fractional velocity has been proposed as a more sensitive measure of the effects of phosphorylation . It is defined as the ratio of enzyme activity in the presence of low physiological G6P concentrations to that in the presence of saturating G6P:
As G6P increases the affinity of GS for UDP-Glc, the fractional velocity reflects changes in the degree of phosphorylation even if UDP-Glc is not near its half-saturation concentration . Furthermore, it also reflects the effects of phosphorylation on G6P affinity.
In subsequent sections, we use activity ratio and fractional velocity (bearing in mind their interpretations in terms of Eqn (4)) only to examine trends in parameter values.
Regulation by phosphorylation
Rosell-Perez et al.  showed that GS may be isolated as two kinetically distinct forms: the active G6P-independent (I) form and the less active G6P-dependent (D) form. Their work was prompted by the observation that pre-incubation with insulin or G6P increased the enzyme's activity in the absence of G6P. This activation was the first indication of the covalent modification now known to be reversible phosphorylation. To date, more than 15 phosphorylation sites have been discovered, but only nine sites have so far been confirmed as in vivo targets . GS was the first enzyme in which hierarchical multi-site phosphorylation was discovered, and serves as a paradigm for this phenomenon, which is now recognized as common [73, 78].
Phosphorylation sites and clusters
Glycogen synthase is phosphorylated in vivo by a variety of kinases at at least nine phosphorylation sites (Table 2). The confirmed in vivo phosphorylation sites are grouped into four phosphorylation clusters [73, 78] (Fig. 3). Each cluster has a primary phosphorylation site that must be phosphorylated before sequential phosphorylation of the secondary sites can proceed. Phosphorylation of the primary site by the primary kinase creates the recognition motif for the secondary kinase at the second site. Phosphorylation of the secondary sites recursively creates the recognition motif for the secondary kinase as long as free sites remain in the cluster.
Table 2. In vivo phosphorylation sites in mammalian GS. Amino acids are numbered based on the rabbit muscle enzyme (initial methionine excluded) 
Sites 2 and 2a form a cluster in the N-terminal region (Ser7–Ser10). Site 2 is phosphorylated by a number of kinases, including cAMP-dependent protein kinase (PKA, EC 188.8.131.52), phosphorylase kinase (PhK, EC 184.108.40.206), calmodulin-dependent protein kinase II (CaMKII, EC 220.127.116.11) and AMP-activated protein kinase (AMPK, EC 18.104.22.168). Casein kinase 1 (CK1, EC 22.214.171.124), with a recognition motif S(P)-X-X-S, catalyses the secondary phosphorylation at site 2a [87, 93, 94]. Although phosphorylation at site 2 significantly enhances phosphorylation at site 2a, the latter may proceed in the absence of phosphorylation at site 2. Sites 5, 4, 3c, 3b and 3a form a cluster near the C-terminus. Site 5 is the primary site, and is phosphorylated by casein kinase 2 (CK2, EC 126.96.36.199). Phosphorylation of site 5 creates the glycogen synthase kinase 3 (GSK3, EC 188.8.131.52) recognition motif S-X-X-X-S(P), and is an absolute prerequisite for secondary phosphorylation by GSK3 [89, 95]. Proceeding in the N-terminal direction, GSK3 sequentially phosphorylates sites 4, 3c, 3b and 3a.
Site 1a (Ser697) and site 1b (Ser710) are technically not phosphorylation clusters. However, both are located in motifs that resemble the amino acid sequence surrounding site 2. In particular, both are phosphorylated in vivo by PKA, and are located three residues N-terminal to a serine or threonine residue . Phosphorylation of these downstream residues by CK1 has been demonstrated with synthetic peptides, but the in vivo significance of these sites is unknown . Site 1b is also phosphorylated by CaMKII .
GS dephosphorylation is catalysed by protein phosphatase 1 (PP1, EC 184.108.40.206), which is targeted to glycogen by several regulatory subunits [5, 22]. It is not known whether dephosphorylation follows a sequential pattern. There is some indication that dephosphorylation of sites 2 and 2a proceeds sequentially and in the opposite direction to phosphorylation: a phosphate at site 2a inhibits dephosphorylation of site 2 .
Despite the cluster organization of phosphorylation sites, phosphorylation does not always proceed hierarchically. Members of the dual-specificity tyrosine-phosphorylated and tyrosine-regulated protein kinase (DYRK, EC 220.127.116.11) family , as well as Per/Arnt/Sim domain-containing protein kinase kinase (PASK, EC 18.104.22.168) , and p38 mitogen-activated protein kinase (p38MAPK, EC 22.214.171.124)  do not require prior phosphorylation, i.e. their recognition motifs do not include a phosphorylated serine residue, and are thus able to circumvent hierarchical phosphorylation. DYRK1A, DYRK1B, DYRK2 and PASK directly phosphorylate site 3a. DYRK2 possibly phosphorylates site 4 , acting as a primary kinase by creating the recognition motif of GSK3 to allow secondary phosphorylation by this kinase without prior phosphorylation by CK2 at site 5. Likewise, p38MAPK phosphorylates sites 4 and 3b.
The obligate sequential phosphorylation of GS by GSK3 raises the question of whether the phosphorylation is processive (several sites are phosphorylated before the kinases dissociates from its substrate) or distributive (at most one site is phosphorylated before the kinase dissociates). Working with synthetic peptides, Fiol et al.  observed intermediate phosphorylation states, suggesting that phosphorylation is distributive. However, they also noted that some intermediate states accumulated to a lesser extent than others, indicating that phosphorylation at these sites is also processive to some degree.
Kinetic effects of phosphorylation
The majority of kinetic studies on GS have been performed using the two-state I/D model of phosphorylation. However, as the exact phosphorylation state of many of the isolated I or D forms is unknown, kinetic parameters reported in these studies are highly variable. The difficulty in isolating completely dephosphorylated GS is well-known, and has led to the adoption of bacterial expression systems . It is also unlikely that the D forms isolated by various researchers were phosphorylated to the same extent or at the same sites. Moreover, supraphysiological kinase concentrations were often used, resulting in non-specific phosphorylation and phosphorylation at sites at which it does not occur in vivo . Nevertheless, a comparison of the reported I and D kinetics provides useful information regarding the general effect of phosphorylation. In this section, we explore the general effects of phosphorylation, which is believed to be mediated by the interaction of phosphorylated serine residues with the basic residues in the arginine cluster, on the kinetic parameters of GS as defined by Eqn (4), and the contribution of individual phosphorylation sites towards these effects.
Modification of kinetic parameters
It is not clear whether phosphorylation affects the kcat of GS. Due to the low activity of phosphorylated GS, the specific activity is often determined at saturating G6P. However, by comparing specific activities obtained at saturating G6P, one may only draw conclusions about the effect of phosphorylation on the apparent kcat, which is defined as kcat,app = kcat · γG6P at saturating G6P. Interestingly, kcat,app appears to be unaffected by phosphorylation, as phosphorylated and dephosphorylated forms have similar maximal activities in the presence of G6P [62, 63, 98, 99]. This may either be interpreted to mean that phosphorylation does not alter kcat, or that both kcat and γG6P are altered such that their product remains constant. In cases where the specific activity has been determined for various phosphorylation states of GS in the absence of G6P [100, 101], the decline in this value cannot be attributed exclusively to a decline in kcat, as, in the absence of G6P, the UDP-Glc concentration (4.4 mm) used in the assays is not necessarily saturating. Roach et al.  observed essentially the same Vmax for a number of phosphorylation states; assuming similar enzyme concentrations, this suggests that phosphorylation does not affect the kcat.
As discussed below, particular phosphorylation sites target GS to specific subcellular locations. Phosphorylation at these sites does not affect the activity of GS per se, but, by targeting GS to glycogen-rich pools, it may increase the apparent local total GS concentration [E]tot, and thus the maximal velocity.
The most pronounced effect of phosphorylation is a marked decrease in UDP-Glc affinity, i.e. phosphorylation increases UDP-Glc0.5. Rosell-Perez et al. observed a fourfold higher UDP-Glc0.5 in rat muscle , a 1.5-fold higher UDP-Glc0.5 in rabbit muscle , and a fivefold higher UDP-Glc0.5 for the D form in dog muscle  than for the I form. The fold increases were much smaller in all three cases in the presence of G6P. These and other data have been interpreted to mean that, at saturating G6P, the apparent UDP-Glc0.5 is independent of phosphorylation state . At saturating G6P, the apparent UDP-Glc0.5 is defined as UDP-Glc0.5,app = UDP-Glc0.5/αG6P. In order for UDP-Glc0.5,app to remain constant despite phosphorylation, any increase in UDP-Glc0.5 must be matched by an equal increase in αG6P. Other researchers only observed a significant difference in UDP-Glc0.5 for the I and D forms in the presence of high ATP concentrations (6 mm) . Roach et al.  isolated nine samples of GS with phosphate contents ranging from 0.27 to 3.49 mol per mol subunit. In these samples, UDP-Glc0.5 increased with the phosphate content from 1.3 to 9100 mm. In the presence of 5 mm G6P, it increased from 65 to 160 μm. These high values obtained for the more phosphorylated forms are probably artefactual, as discussed by Roach et al., but the overall trend is nevertheless clear. Similarly, Guinovart et al.  recorded an increase in UDP-Glc0.5 from 1.5 to 200 mm as the number of phosphates per subunit increased from 0 to 4.3.
It should be noted that, in order to adhere to the thermodynamic constraints of the Haldane equation, phosphorylation must have equal effects on UDP-Glc0.5 and UDP0.5. However, it has been noted in a few cases that phosphorylation strengthens UDP inhibition, i.e. it decreases UDP0.5 [69, 104]. If this is indeed the case, phosphorylation would be expected to have differential effects on the forward and reverse catalytic constants.
Piras et al. [30, 58] noted that higher G6P concentrations are necessary to reverse ATP inhibition in the D form than in the I form, and that the D form is much more strongly inhibited by ATP than the I form. As they observed no effect of G6P on UDP-Glc0.5 at pH 6.6, the higher G6P requirements suggest that G6P0.5 increases with phosphorylation, i.e. the affinity for G6P decreases while the affinity for ATP increases. Without parameter fitting, it cannot be determined whether the increase in ATP affinity is the result of decreased ATP′0.5, ATP0.5 or both. Roach et al.  showed that G6P0.5 increased by roughly three orders of magnitude as the phosphate content increased from 0.27 to 3.49 mol per mol subunit. Similarly, Nimmo et al.  observed an increase in G6P0.5 from 0.05 to 10 mm as the number of phosphates per subunit increased from 0 to 1.95. Wang and Roach  found that complete phosphorylation by GSK3 increased G6P0.5 tenfold, whereas phosphorylation by PKA and CK1 increased G6P0.5 100-fold .
As discussed above, there is evidence that γG6P and αG6P increase with phosphorylation such that the effects of phosphorylation on kcat and UDP-Glc0.5 are cancelled by saturating G6P. However, although the specific activation of GS by G6P is well-established, it is much less certain whether G6P also increases the catalytic capacity (kcat) of GS. However, if kcat · γG6P is indeed independent of the phosphorylation state, and if γG6P > 1, it is implied that phosphorylation also affects kcat. The effect of phosphorylation on αATP is not known. However, in analogy with αG6P, we speculate that αATP approaches 1 as phosphorylation increases, i.e. the presence of ATP brings about little further inhibition in GS states that are already substantially inhibited by phosphorylation.
It is generally accepted that UDP-Glc binding is non-cooperative, i.e. h =1, regardless of the phosphorylation state of GS. Hyperbolic kinetics have been reported for both the I form and the D form [32, 47, 58]. Even in cases where negative cooperativity has been reported, h appears to be unaffected by phosphorylation. Roach et al.  reported a mean h value of 0.8 for nine GS samples of varying phosphorylation degrees. In the presence of G6P, this value increased to 1 for all phosphorylation states, thus restoring hyperbolic kinetics. Roach et al.  reported an increase in sigmoidicity with regard to G6P in the presence of phosphorylation, i.e. hG6P increased with phosphorylation. In support of these findings, Piras et al.  observed steeper Hill plots for the D form than for the I form. This effect was potentiated in the presence of ATP. ATP did not seem to affect hG6P in the I form. Similar results were observed for the D form in bovine heart . However, phosphorylation of sites in the N-terminal region appears to have little effect on hG6P . Plesner et al.  observed sigmoid kinetics with regard to G6P only at low substrate concentrations.
The converse was observed with regard to hATP, i.e. sigmoidicity with respect to ATP binding decreases with phosphorylation . In the I form, G6P increased hATP, but had little effect in the D form.
Importance of individual phosphorylation sites
Studies using site-directed mutagenesis showed that no single phosphorylation site completely controls GS activity . However, by mutating two phosphorylation sites simultaneously, a dramatic increase in activity ratio is observed. This is the case if both mutated sites are in the same cluster, but more so if sites from different clusters are mutated. The experimentally determined activity ratios of GS phosphorylated at various sites are summarized in Table 3.
Table 3. Activity ratios (Eqn (8)) for various GS phosphorylation states. Unless stated otherwise, the G6P concentration, when present, was 7.2 mm. UDP-Glc was present at 4.4 mm. Lower values indicate greater inhibition
a [G6P] = 10 mm. b Sites 1a and 1b are possibly phosphorylated; mean of soluble and pellet fractions.
Brown et al.  found that phosphorylation at site 2a, using PKA as the primary kinase, had a greater effect on the activity ratio than phosphorylation at site 2. Phosphorylation at both sites did not further decrease the activity ratio significantly. In contrast, more recent findings , or studies using PhK instead of PKA , recombinant GS (in an effort to limit residual phosphorylation)  or site-directed mutagenesis  indicate that site 2 is the more important site, and that phosphorylation at only site 2a, or phosphorylation of this site in addition to phosphorylation at site 2, has a less significant effect on the activity ratio.
Incorporation of one phosphate per GS subunit by CK1 at site 5 has no effect on the activity ratio . However, phosphorylation at this site is an absolute prerequisite for phosphorylation of the secondary sites in the rest of the cluster. Using site-directed mutagenesis, Wang and Roach  showed that only phosphorylation at sites 3b and 3a has a significant effect on the activity ratio. Kuma et al.  reported that phosphorylation at site 3b had no inhibitory effect, but that subsequent phosphorylation at site 3a decreased GS activity. It thus appears that the sole function of sites 5, 4 and 3c, and to some extent 3b, is to facilitate phosphorylation at site 3a, which results in potent inhibition. The existence of kinases, such as the DYRK family, PASK and p38MAPK, that directly phosphorylate site 3a supports this possibility. It is also interesting to note that, in the C-terminal region, only sites 3a and 3b are conserved between the yeast and mammalian enzymes .
As measured by their effect on activity ratio, sites 1a and 1b do not appear to be important in terms of inhibition .
While complete phosphorylation of the clusters in the N- or C-terminal regions leads to substantial inactivation of GS, complete inactivation is only attained when both clusters are phosphorylated fully or at the important sites [94, 100].
It is becoming increasingly clear that subcellular compartmentalization and translocation are major factors in the regulation of glycogen metabolism [109, 110]. Glycogen and many enzymes associated with it have been shown to be targeted to various intracellular compartments.
Recent studies suggest a strong link between GS phosphorylation state and subcellular localization. Prats et al. , working with rabbit muscle, found that GS phosphorylated at site 1b was exclusively associated with myofibrillar cross-striations (sarcomere I-bands). This was observed under both basal and exercise-stimulated conditions. Under basal conditions,GS phosphorylated at sites 1a or 3a + 3b was found mainly in a perinuclear region and at cross-striations. However, under exercise-stimulated conditions, GS phosphorylated at these sites was associated with actinin-containing spherical structures. No association with these spherical structures was observed for GS phosphorylated at sites 1b or 2 + 2a. GS phosphorylated at sites 2 + 2a was found in inter-myofibrillar clusters, regardless of exercise stimulation. Similar results were obtained for human muscle . In summary, phosphorylation at site 1b exclusively targets GS to the intra-myofibrillar cross-striations, whereas phosphorylation at sites 2 + 2a targets GS to inter-myofibrillar clusters (Table 4). Prats et al.  propose that phosporylation at sites 2 + 2a, and the subsequent translocation, is the result of AMPK-dependent sensing of glycogen depletion in the inter-myofibrillar region. Similarly, they argue that, as intra-myofibrillar glycogen is preferentially used during exercise, phosphorylation at site 1b by PKA in response to adrenaline stimulation targets GS to this compartment to replete glycogen after exercise. Site 1b has been shown to be phosphorylated by CaMKII, suggesting a role for Ca2+ in GS translocation. From a kinetic perspective, phosphorylation at site 1b and, to a lesser extent, site 2a has little effect on GS activity. However, the above findings suggest major roles for these two sites in GS translocation, which in turn regulates GS activity.
Table 4. Phosphorylation-dependent intracellular distribution of GS [111, 112]
Sites 2, 3a, 3a + 3b, 1a
Sites 2 + 2a
Perinuclear region, cross-striations
Function of GS multi-site phosphorylation
Compared to GP, which is phosphorylated at only a single site, the multi-site phosphorylation of GS seems almost excessive. However, multi-site phosphorylation is not uncommon. Its prevalence and general function have been reviewed extensively [78, 113, 114]. Here, we discuss its function as it pertains to GS. GS has both dispersed sites and clusters, and phosphorylation within clusters is hierarchical, sequential and mostly distributive.
Multi-site phosphorylation facilitates integration of signals from various endocrine, neural and metabolic stimuli. With regard to GS, signal integration is manifested at the level of both individual phosphorylation sites and clusters. Multiple kinases phosphorylate the same sites or clusters, and many sites share the same kinase. Site 2 is a substrate for numerous kinases regulated by various signals. Similarly, site 3a may be phosphorylated directly by a number of kinases, or via hierarchical and sequential phosphorylation by GSK3. Site 1b is likewise phosphorylated both by PKA and CaMKII. The adrenaline-stimulated cAMP-dependent pathway and the insulin-stimulated phosphatidylinositol 3-kinase-dependent pathway (arguably the most prominent GS phosphorylation pathways) each affect different phosphorylation clusters.
Hierarchical phosphorylation is not a prerequisite for sequential phosphorylation. Appropriately positioned anionic amino acids are able to mimic phosphorylated primary phosphorylation sites and thus allow for sequential secondary phosphorylation . However, hierarchical phosphorylation facilitates regulation at two levels: primary phosphorylation and secondary phosphorylation . As both are catalysed by different kinases, each kinase may be regulated independently. In the N-terminal cluster of GS, it is the primary kinases that are regulated, either by the cAMP-dependent pathway (PKA) or by metabolic signals (AMPK). In the C-terminal cluster, on the other hand, the secondary kinase, GSK3, is regulated via the phosphatidylinositol 3-kinase-dependent pathway. In addition, phosphorylation may also be regulated at the phosphatase level. Both adrenaline and insulin stimulation regulate PP1 activity.
In a random phosphorylation mechanism, the number of phosphorylation states per subunit increases exponentially with the number of phosphorylation sites. A protein subunit with n phosphorylation sites has 2n phosphorylation states. In sequential phosphorylation, on the other hand, the number of phosphorylation states is a linear function (n + 1) of the number of sites. If one assumes strict sequential phosphorylation (and dephosphorylation), the number of distinct GS phosphorylation states per subunit amounts to (2 + 1) × (5 + 1) × 2 × 2 = 72. If a random mechanism were employed, the number of states would amount to 29, i.e. 512. Sequential phosphorylation therefore severely limits the number of phosphorylation states and brings about an orderly transition between different states. This is beneficial if, as in the case of GS, only specific phosphorylation sites (for example, site a) elicit a particular effect. Phosphorylation of site 3a may be achieved and reversed with precision by adjusting the ratio of kinases to phosphatases appropriately in a sequential mechanism. In a random mechanism, on the other hand, phosphorylation of a particular site cannot be achieved with precision. However, a number of kinases bypass sequential GS phosphorylation, obscuring any benefit it may confer. The number of states per cluster is therefore also likely to be significantly more than 72.
It has been argued (as discussed by Gunawardena ) that multi-site phosphorylation, particularly if it proceeds distributively and sequentially, results in an ultrasensitive response to the ratio of kinase to phosphate, such that, below a certain threshold, the protein in question is almost completely dephosphorylated, whereas, above this threshold, complete phosphorylation is rapidly attained. According to this view, more phosphorylation sites result in higher sensitivity, approaching switch-like behaviour. However, it has been demonstrated  that, although multi-site phosphorylation creates a sharp threshold, an increase in the kinase to phosphatase ratio beyond the threshold does not result in switch-like behaviour, i.e. complete phosphorylation does not rapidly attained. On the contrary, beyond the threshold, the response becomes milder as the number of phosphorylation sites increases. It thus appears feasible that a function of the sequential phosphorylation of GS is to fine-tune the threshold at which the ratio of kinase to phosphatase elicits a response. This is particularly of interest if one considers that, in addition to GS, GSK3 has numerous substrates in various signalling pathways ; regulation of GSK3 affects all these pathways, but by employing multi-site phosphorylation to different extents, each pathway may refine its response to changes in GSK3 levels.
Regulation by glucose-6-phosphate
In 1959, Leloir et al.  were the first to show that G6P activates GS. They also showed that G6P does not take part in the reaction and presumably binds to an allosteric site. This initial work was followed by kinetic studies in a variety of species [62, 102, 103, 117, 118], which showed that GS activation by G6P is a universal feature in eukaryotes. To date, five mechanisms have been described by which G6P affects GS activity: (a) as a substrate precursor, (b) as an allosteric GS activator, (c) as a GS kinase inhibitor, (d) as a GS phosphatase activator, and (e) by enhancing the export of GS from the nucleus. In this section, we discuss the binding of G6P to GS and the resulting conformational change that leads to activation (both allosteric and covalent) and possibly translocation of GS.
G6P-induced conformational change
The activation of GS by G6P must ultimately be the result of a conformational change, but little is known about such conformational changes in the muscle enzyme. However, due to the high degree of conservation between the yeast and muscle enzymes, it is useful to consider the conformational change induced in ScGS upon G6P binding, as revealed by the crystal structure of this enzyme in the presence of G6P . In ScGS, G6P binds between the R helix (α22) and helix α13. The former contains the regulatory arginine cluster and links the crossed-over C-terminus and the phosphorylation sites to the C-terminal Rossmann-fold domain. Helix α13 (together with α12) forms the main connection between the N- and C-terminal Rossmann-fold domains. The phosphate moiety of G6P binds tightly in a pocket formed by amino acid residues from both the R helix and α13, including Arg582 and Arg586, residues that have been shown to be essential for G6P activation of the yeast [42, 54] and muscle [10, 55] enzymes. The structure of this pocket is well-defined in the unbound state, and undergoes little change upon G6P binding. The G6P glucose moiety, on the other hand, forms hydrogen bonds with His280 and Gln283, which re-orders the region between residues 278 and 284, allowing Asn284 to form a hydrogen bond with the corresponding residue of the subunit across the dimerpair twofold symmetry (i.e. the A/B or C/D interface). The arginine residues therefore likely act as anchors of the G6P molecule so that the glucose moiety may bond with His280 and Gln283 . It is tempting to speculate that the phosphate of ATP is similarly anchored by Arg582 and Arg586, with the difference that the adenosine moiety stabilizes an inactive conformation.
G6P binding and the subsequent re-ordering of residues 278–284 bring about significant conformational change [42, 44] (Fig. 1D). The R helices within the A/B and C/D dimers are forced apart and the inter-subunit helices (α15 and α16) of the B/D dimer pairs are translated away from that of the A/C pair and rotated. Within subunits, the C-domain is rotated relative to the inter-subunit helix pair, and the N-domain is rotated relative to the C-domain. The overall effect of the conformational change is that the association between the N-domain insert (α2 and the loop between β4 and β5) and the C-domain insert (α16), which locks the subunits in an inactive open conformation, as well as the reciprocal inter-subunit interaction of the loops between β15 and α18 within the A/D and B/C interfaces, is abolished (Fig. 1C). In the G6P-bound form, α16 instead associates with the loop between β15 and α18 of its partner subunit in the dimer, allowing the inter-domain closure that is required for catalysis.
Effect of G6P on GS kinetics
In agreement with the extensive conformational change resulting from G6P binding, G6P affects the kinetics of GS significantly. Several researchers have observed higher apparent kcat values in the presence of G6P. Such catalytic activation is quantified by γG6P > 1. In many cases, the extent to which kcat is affected appears to depend on the degree of phosphorylation. Rosell-Perez et al. consistently found an increase in the kcat of the phosphorylated D enzyme from rat , rabbit , and dog , but observed no or little change in the kcat for the dephosphorylated I form. The effect was independent of Mg2+. However, Kornfeld and Brown  only reported an increase in kcat in the presence of Mg2+. Other researchers, working with the I form, reported no change in kcat, but did observe that contamination with the D form resulted in catalytic activation of GS . Catalytic activation was also observed for the D form from rat adipose tissue , bovine heart  and pig brain . More recently, Lai et al.  found that catalytic activation increases with glycogen content, which in turn correlates with the degree of phosphorylation. However, several studies found no increase in kcat in the presence of G6P, regardless of the phosphorylation state. Piras et al.  found no increase in kcat for both the I and D forms of the rat muscle enzyme in response to G6P. Similarly, Roach et al.  observed essentially the same Vmax, and thus kcat, in the presence and absence of G6P for a range of phosphorylation states of the rabbit muscle enzyme.
The apparent effect of G6P on UDP-Glc0.5, on the other hand, is well-established . Even for the most phosphorylated forms, G6P decreases the apparent UDP-Glc0.5 dramatically. This potent activation potential is indicative of a large αG6P value. In most cases where catalytic activation was observed, specific activation was also observed.
G6P further activates GS by suppressing ATP binding at the allosteric site. This effect is manifested as an apparent increase in ATP0.5. Several secondary effects on kcat and UDP-Glc0.5 may result, depending on the type of inactivation (specific or catalytic) that results from ATP binding. If, for instance, ATP inhibited GS by increasing the apparent UDP-Glc0.5 (i.e. αG6P < 1), then G6P would enhance substrate binding in the presence of ATP over and above its own direct activation of GS. Indeed, Piras et al.  argue that this indirect activation of GS has more physiological relevance than the direct effect of G6P on UDP-Glc0.5, as even the phosphorylated forms are often saturated with G6P at physiological concentrations, thus obscuring both the function of phosphorylation and G6P activation. In their view, ATP, which binds preferentially to the phosphorylated enzyme, restores the necessary G6P sensitivity in active GS. Moreover, G6P increases hATP, especially in the dephosphorylated enzyme, suggesting that, in addition to competing with ATP, G6P also stabilizes a conformation with a low affinity for ATP.
Finally, it is generally accepted that high G6P concentrations activate even the most phosphorylated forms of GS to the same level as the dephosphorylated enzyme [22, 76, 99]. This, as discussed above, is equivalent to stating that both kcat · γG6P and UDP-Glc0.5/αG6P are constants that are independent of the phosphorylation state. Any effect of phosphorylation on kcat or UDP-Glc0.5 is therefore reversed by G6P.
G6P-dependent covalent activation
Apart from reversing the effects of phosphorylation on the kinetics of GS, it has been demonstrated in a few cases that G6P also enhances the reversal of covalent phosphorylation itself, either by inhibiting GS kinases, or by activating GS phosphatases.
Phosphorylation by PKA at site 2 potently inactivates GS. However, it has been observed that insulin inhibits PKA in rabbit skeletal muscle in an apparently competitive fashion with respect to cAMP . At least one mechanism by which insulin inhibits PKA is by increasing the G6P concentration . PKA (or R2C2) is a tetrameric enzyme consisting of two catalytic (C) subunits, each associated with a regulatory (R) subunit . The R subunit is a pseudosubstrate that inhibits the C subunit by blocking its active site. Each R subunit has two binding sites for cAMP, which binds to it sequentially, leading to stepwise dissociation of the R and C subunits and thus activation of PKA. Several PKA substrates are able to activate PKA in a cAMP-independent fashion . These substrates compete with the R subunit for the active site. In the absence of cAMP, GS is able to stimulate PKA to a level of activity that is ∼50% of that in the presence of 2 μm cAMP. However, when G6P is bound to GS, the ability of GS to activate PKA is abolished.
G6P inhibition of phosphorylation appears to be specific to PKA and GS . No other GS kinases are inhibited by G6P, and neither is the phosphorylation of other PKA substrates affected. The possibility that G6P brings about inhibition by binding to the C or R subunits of PKA is thus ruled out, and the inactivation must be the result of G6P binding to the allosteric site on GS. As GS activates PKA by competing with the R subunit, it is expected that G6P will decrease the C subunit's affinity for GS. However, no changes in the Km or Vmax were found in the presence or absence of G6P. Thus, G6P, by causing a conformational change in GS, appears to only hinder the ability of GS to activate PKA, but does not affect the kinetics of previously activated PKA. G6P also inhibits one or more yeast GS kinases .
Traut and Lipmann  observed that incubation with G6P increased the activity of lamb muscle GS in the absence of G6P. GS activated in this way retained the activation after several days in cold storage. The activation by G6P was reversed by incubation with ATP. Therefore, apart from allosterically activating GS, it also activated the enzyme in a presumably covalent fashion. Kinase inhibition by G6P, as discussed above, does not appear to have contributed significantly to the results obtained by Traut and Lipmann, as their preparations were already extensively phosphorylated, as indicated by the activity ratio. This suggests that G6P also has the potential to enhance dephosphorylation of GS. These findings have subsequently been verified by various other researchers. Kato and Bishop  showed that G6P enhances the I to D form conversion of rabbit muscle GS by a protein phosphatase. This effect of G6P was not observed in the absence of the phosphatase. G6P analogues such as glucosamine-6-phosphate and galactose-6-phosphate, which also activate GS, had a similar effect on the dephosphorylation of GS. No effect was seen for the dephosphorylation of histone by the same phosphatase in the presence of G6P, suggesting that activation of the phosphatase by G6P is mediated by the binding of G6P to GS. Other studies have shown that activation of the phosphatase reaction by G6P is inhibited by inorganic phosphate and sulfate , and ATP . ATP was also shown to inhibit dephosphorylation of GS in human muscle .
More recently, Villar-Palasi  found that, in rabbit muscle, G6P activates the D form of GS covalently by promoting dephosphorylation. This effect was observed for both PP1 and protein phosphatase 2A (PP2A, EC 126.96.36.199). Except for a slight activation of GP dephosphorylation by PP1 at low G6P concentrations, G6P did not enhance dephosphorylation of any other tested PP1 or PP2A substrates. This suggests that G6P does not directly activate the phosphatases in question, but rather causes a conformational change in GS, rendering it a better substrate. G6P activated dephosphorylation by PP1 and PP2A to the same degree. The G6P phosphatase activation was observed by measuring both the change in GS activity ratio and phosphate release. By both methods, a Ka of 0.2 mm was calculated for phosphatase activation. This coincided with the Ka for GS activation as determined for the preparation used in the study, strengthening the argument that the activation is caused by G6P binding to GS. Intriguingly, the affinity of the phosphatases for GS was not altered by G6P. Instead, the activation appears to involve an increase in the Vmax and thus presumably the catalytic constant kcat. Note that even though PP2A is not generally considered a major in vivo GS phosphatase, we include it here to better illustrate that the reported activation of GS dephosphorylation by G6P is substrate-specific, i.e. independent of the particular phosphatase.
There is mounting evidence that the subcellular distribution of GS in both liver and muscle is regulated by glucose. In liver, incubation with glucose results in the translocation of GS from the cytosol to a region near the cell membrane [128, 129]. Similarly, Cid et al.  have shown that muscle GS translocates from the nucleus to the cytosol when incubated with glucose. Under conditions of glycogen and glucose depletion, GS conversely translocates to the nucleus. In addition to mediating the allosteric and covalent regulation of GS, the arginine cluster also functions as a nuclear localization sequence. Arginine cluster mutants, in which G6P sensitivity and presumably nuclear localization are abolished, exhibited little or no nuclear accumulation. Systematic mutation of the GS phosphorylation sites indicated that phosphorylation does not affect nucleocytosolic GS translocation, suggesting that only G6P stimulates translocation to the cytosol. Moreover, based on the observation that 6-deoxyglucose does not stimulate translocation to the cytosol, Cid et al.  suggest that it is in fact G6P, and not glucose, that elicits the translocation. If this is indeed the case, G6P-stimulated translocation of GS to the cytosol would effectively increase the total GS concentration, [E]tot, in the cytosol.
As G6P stimulates net dephosphorylation of GS, it is expected that it will also influence the sub-cytosolic distribution of GS by promoting the dephosphorylation of sites, such as 2a and 1b, that are associated with targeting GS to various fractions in the cytosol.
Function of G6P feedforward activation
G6P is a precursor of UDP-Glc, one of the GS substrates. Activation of GS by G6P therefore constitutes a feedforward activation loop. Hofmeyr and Cornish-Bowden  have demonstrated that a similar regulatory mechanism, the feedback inhibition loop, does not function to control the flux through the regulated enzyme, but rather to maintain the concentration of the regulatory metabolite within a narrow range. In terms of GS, supposing a function of feedforward activation that is similar to that of feedback inhibition, the function of G6P activation is not to regulate the flux through GS, but rather to enhance G6P homeostasis. However, we argue  that, unlike the situation in feedback inhibition, the type of activation, whether by increasing kcat or decreasing Km, has important consequences for the effectiveness of the mechanism in maintaining the concentration of the regulatory metabolite. We only briefly consider these consequences here. A thorough mathematical exposition is provided elsewhere .
In the minimal feedforward activation loop shown in Fig. 4, enzyme 2, the regulated enzyme, is activated allosterically by metabolite X, the regulatory metabolite. In order for the feedforward loop to be effective, i.e. for activation of enzyme 2 to have any significant effect on the pathway, enzyme 2 must control the flux through the isolated sub-pathway (that part of the pathway that excludes the supply enzyme). One way in which complete flux control by enzyme 2 may be achieved is if it is saturated by its immediate substrate, S. However, in such a scenario, any increase in the affinity of enzyme 2 for S resulting from activation by X is clearly futile, as enzyme 2 is already saturated by S and cannot bind more substrate in order to operate faster, i.e. enzyme 2 has reached its maximal velocity. Alternatively, if the action of X is to increase the catalytic rate, kcat, of enzyme 2 (and, by extension, Vmax), the enzyme may operate faster despite being saturated by its substrate. We thus argue that catalytic activation (increase in kcat) is expected to be the dominant type of activation in feedforward mechanisms .
Thus, in terms of GS, it is expected that G6P is a catalytic but not necessarily a specific activator of GS, i.e. γG6P > 1 should hold. This is indeed the case for the major yeast GS . However, it is much less certain whether this is also the case for the mammalian muscle enzyme. As discussed, many earlier studies found catalytic activation for the D form and specific activation for the I form. There are two solutions that were not previously considered explicitly , in which pure specific activation may still result in efficient feedforward activation. First, GS is a bi-substrate enzyme. In bi-substrate kinetics, specific activation (and catalytic activation) with regard to one substrate, say glycogen, manifests as catalytic activation with regard to the other, say UDP-Glc, with the condition that the first substrate is not saturating. Therefore, if G6P enhances glycogen binding, which is probably the case, it would appear to increase the apparent kcat if considered with respect to UDP-Glc, even if, kinetically, G6P is only a specific activator. However, it is not clear to what extent such a situation is relevant physiologically, as GS is probably saturated by glycogen in vivo. Second, saturation by UDP-Glc is not the only means by which flux control can be retained by GS; the same outcome would be achieved if the enzyme preceding GS operated near equilibrium. As GS need no longer be saturated by UDP-Glc, a G6P-induced increase in the affinity for UDP-Glc becomes an effective form of activation.
However, we must not only consider the direct effects of G6P on GS. As mentioned, G6P also activates GS by reversing inhibition by ATP and phosphorylation. If either ATP or phosphorylation decreases the apparent kcat, then, by reversing this decrease, G6P would appear to be a catalytic activator, even if it exhibits no such activation in the absence of ATP or phosphorylation. The observation that G6P is a catalytic activator of the D form probably indicates a reversal of inhibition by phosphorylation, but there is no definitive evidence that either ATP or phosphorylation decreases the apparent kcat. Finally, G6P increases the total cytosolic concentration of GS by inducing its translocation from the nucleus. Such a G6P-dependent increase in the cytosolic GS is kinetically equivalent to catalytic activation (an apparent increase in the kcat). However, as glycogen depletion is a requirement for nuclear retention of GS, this mechanism of activation is probably only relevant during the onset of glycogen re-synthesis after exercise.
The effectiveness of G6P feedforward activation, whether specific or catalytic, appears to depend strongly on such cellular conditions as the concentrations of UDP-Glc and ATP, the degree of GS phosphorylation, and glycogen content. In order to understand the function of GS feedforward regulation by G6P, it must be established definitively whether G6P is a catalytic or specific activator of GS, to what extent GS is saturated by its substrate in vivo, and to what extent ATP and phosphorylation affect the apparent catalytic capacity of GS.
A unifying view of covalent and allosteric regulation
The complex kinetics and regulation of GS, as discussed in the previous sections, continue to evade description by a succinct mechanistic model. The sheer number of phosphorylation states and an incomplete understanding of how GS kinetics are altered by phosphorylation makes it almost impossible to capture the enzyme's behaviour with conventional enzyme kinetic rate equations. In this section, we argue that, without deriving any form of rate equation, the Monod–Wyman–Changeux (MWC) model may provide an adequate description of the nuances of GS kinetics and regulation, both allosteric and covalent, as reviewed in this paper.
Let us briefly summarize the interplay between G6P, ATP and phosphorylation. In many respects, the effects of regulation by G6P and phosphorylation are reciprocal (Fig. 5A). G6P binding activates GS (a) in a cooperative fashion (b). It not only reverses the inhibitory effects of phosphorylation, but also reverses phosphorylation itself (c). Phosphorylation, on the other hand, inhibits GS (e). It also inhibits G6P binding (g), but enhances G6P binding cooperativity (h). Conversely, the effects of ATP and phosphorylation on GS and each other appear to be qualitatively identical (Fig. 5B). Both inhibit GS (a, e). ATP enhances phosphorylation (c) and phosphorylation enhances ATP binding (g). In addition, phosphorylation decreases ATP binding cooperativity (h). Finally, G6P binding affects ATP binding and phosphorylation similarly, and ATP binding and phosphorylation affect G6P binding in similar ways (Fig. 5C). G6P and ATP decrease each other's binding affinity (c, g), but enhance each other's binding cooperativity (h, d).
Piras et al.  offered an explanation of this interplay between G6P, ATP and phosphorylation using the MWC model. Noting that phosphorylation enhanced G6P cooperativity but decreased ATP cooperativity, they suggested that the covalent modification of GS exerts its effects in exactly the same way as classic MWC-type allosteric modification does: by altering the equilibrium constant L between an active R conformation and an inactive T conformation. In the MWC model, cooperativity arises due to simultaneous or concerted conformational change of all subunits of the enzyme. By binding preferentially to a particular conformation, modifiers shift the equilibrium of all subunits, regardless of whether they are occupied, towards that conformation, and thus enhance subsequent modifier binding. However, cooperativity is only observed if the majority of the enzyme is in the conformation that is not favoured by the modifier in question. The results obtained by Piras et al.  are thus explained if the majority of the dephosphorylated I form is already in the active form, such that G6P binding is only mildly cooperative. Phosphorylation, which favours the T conformation, would thus enhance G6P cooperativity. The converse would be true with regard to ATP cooperativity. This model is shown in Fig. 6. Sølling  also described the kinetics of GS by employing two enzyme conformations, and suggested that the MWC model may account for his findings. However, as he worked with the I form, which shows little G6P cooperativity, normal Michaelian kinetics for each conformation provided an adequate description. Kinetic  and crystal structure  studies of the yeast enzyme lend further support to a discrete-state model such as the MWC model. A three-state model has been suggested in which the enzyme is normally present in a basal I conformation (not to be confused with the I form of the I/D nomenclature). Phosphorylation would then stabilize an inactive T conformation, whereas G6P would stabilize an active R conformation. Conformational change, particularly involving the inter-domain closure of subunits, is a recurring theme in results from various GS crystal structure studies.
A few objections have been levelled against the MWC model as a model for GS regulation. First, Piras et al.  argued that non-cooperative substrate binding is seemingly incompatible with this model. However, non-cooperative substrate binding may be achieved by making the usual assumption that only the R conformation is catalytically active, as well as the assumption that the UDP-Glc substrate binds with equal (or only slightly different) affinity to the R conformation and the T conformation. These assumptions lead to no, or very mild, substrate binding cooperativity for both the dephosphorylated and phosphorylated states (comparable to that seen for G6P in the dephosphorylated form), but also necessitate catalytic activation by G6P. Modifier binding cooperativity is retained, as modifiers bind with vastly different affinities to the two conformations. This mechanism is predicted to exhibit positive substrate cooperativity if the apparent affinity of the two conformations for UDP-Glc is affected to different extents by a competitive inhibitor. This has indeed been observed for the bovine heart enzyme, in which UTP elicited positive cooperativity with respect to UDP-Glc binding . These assumptions are also supported by Sølling , who was unable to detect significant conformational change induced by UDP-Glc or UDP.
In a further objection, Plesner et al.  argue that G6P cooperativity is an artefact that disappears at high substrate concentrations, and they thus reject the MWC model. However, their observation is in agreement with the model proposed here. UDP-Glc is expected to bind preferentially to the R conformation (at least in the presence of ATP). High substrate concentrations would therefore stabilize the R conformation and so abrogate G6P cooperativity. The disappearance of G6P cooperativity is thus not an artefact but a characteristic of the model.
Perhaps the strongest argument in favour of the MWC-type model proposed here is that it predicts the observed inhibition of phosphorylation as manifested by G6P-induced kinase inhibition and phosphatase activation. If, as proposed, phosphorylation stabilizes the inactive T conformation, then, by extension, the T conformation is more readily phosphorylated. Hence, all modifiers that stabilize the R conformation not only activate GS kinetically, but also promote its covalent activation by stabilizing the conformation that is less readily phosphorylated. Similarly, ATP is predicted to enhance GS phosphorylation over and above its contribution as kinase co-substrate (c in Fig. 5B). Such activation, if present, is not readily observed in the kinase reaction, but inhibition of PP1 by ATP, in a manner reversible by G6P, is well established [123, 126, 133-135].
The MWC model proposed here makes a few predictions that have, to our knowledge, not been tested experimentally. First, it predicts that phosphorylation is cooperative (f in Fig. 5A), i.e. phosphorylation of, say, site 2 on one subunit must enhance phosphorylation of site 2 on the next subunit. And, more generally, phosphorylation of any site that increases L should enhance subsequent phosphorylation of any other phosphorylation site, on the same or other subunits of the oligomeric enzyme, that also increases L. Not all phosphorylation sites affect the activity of GS, and thus the equilibrium constant L between the T and R conformations. Phosphorylation sites such as 1a, 1b, 5, 4, and 3c have little if any effect on GS activity, and thus no cooperative phosphorylation of these sites is expected. Hierarchical sequential phosphorylation is not equivalent to cooperative phosphorylation; however, in an MWC model, these two mechanisms may be difficult to tell apart in phosphorylation assays. For example, if phosphorylation at both sites 2 and 2a stabilizes the T conformation, phosphorylation of site 2a will then be enhanced by prior phosphorylation at site 2 by virtue of the recognition motif of CK1 containing a phosphorylated serine residue, but also because phosphorylation at site 2 stabilizes the same conformation that is favoured by phosphorylation at site 2a. It has been noted that phosphorylation of sites2 and 2a is synergistic : prior phosphorylation at site 2 greatly enhances, but is not a requirement for, phosphorylation at site 2a. If regulation of GS is indeed adequately described by an MWC-type model, this enhanced phosphorylation at site 2a cannot purely be the result of hierarchical sequential phosphorylation.
Second, it is predicted that G6P enhances the degree of cooperative phosphorylation by stabilizing the conformation that is not favoured by phosphorylation (d in Fig. 5A). ATP, on the other hand, decreases the degree of cooperativity of phosphorylation (d in Fig. 5B), despite the fact that it enhances phosphorylation itself (c in Fig. 5B).
The kinetics and regulation of GS appear to be adequately described by an MWC model in which phosphorylation acts like a classic allosteric modifier. However, the sequential or Koshland–Némethy–Filmer model  is expected to provide an equally adequate, although more complicated, description. It is also likely that more than two conformations are required to fully describe all the aspects of GS activity and regulation. In particular, the findings of Piras et al.  suggest the presence of an additional pH-dependent conformational change. The MWC-type model proposed here is almost certainly a gross over-simplification of the true regulation of GS, but is nevertheless a useful working model.
Discussion and Conclusions
In this review, we have discussed the general kinetic properties of GS and how these properties are affected by allosteric and covalent regulation. The covalent regulation of GS is particularly elaborate, allowing the enzyme to be sensitive to multiple regulatory signals. However, only a few of the phosphorylation sites have direct effects on the enzyme's activity. The majority appear to fulfil auxiliary roles, such as targeting the enzyme to appropriate subcellular compartments or to facilitate phosphorylation of those sites that do directly affect activity. In this regard, the sites phosphorylated by GSK3 are of particular interest, as this kinase may be considered a focal point in signal transduction, regulating several downstream processes. We postulate that the multiple GSK3 sites on GS calibrate the response of GS to changes in the activity of GSK3. The allosteric regulation of GS also appears to be multi-faceted. Not only is the enzyme's activity directly influenced by its allosteric modifiers, its subcellular and nucleocytoplasmic distribution is also affected. Moreover, the allosteric and covalent regulation of GS are tightly inter-linked. It is clear that no discussion of the covalent regulation of GS is complete without mention of its effect on G6P activation, and no treatment of its allosteric regulation is complete without also considering its effect on phosphorylation. It appears that part of the function of either regulatory mechanism is to regulate the other.
There is no a priori reason why covalent and allosteric modification of an enzyme should be considered to be qualitatively different. In fact, both kinds of interaction are allosteric; in either case, the enzyme's activity is affected by binding of modifiers (whether covalently, or through ionic or hydrophobic interactions) to a site other than the catalytic site. Notwithstanding, earlier studies on GS kinetics were usually entirely devoted to either the I or D form, with little attempt to provide an integrated view. In an effort to remedy this situation, we here propose a unifying view of GS regulation in which covalent modification is considered to be qualitatively identical to classic allosteric modification as per the MWC model. This is indeed the standard depiction of the regulation of GS in textbooks: phosphorylation favours an inactive T conformation, whereas G6P favours the active R conformation. However, to our knowledge, this model has never been applied in a kinetic treatment of GS, and its implications for the function of the extensive phosphorylation of GS have not been considered. Our own endeavours in this regard will be reported elsewhere. A major advantage of this model is that it eliminates the need to determine the kinetic parameters for glycogen synthase in all its possible phosphorylation states, leaving only the requirement to establish the relationship between a particular phosphorylation state and the equilibrium constant between the T and R conformers in the absence of ligands.
We have discussed the function of G6P as a feedforward activator of GS, and suggested that this feedforward mechanism plays a role in G6P homeostasis in that it increases the response to G6P of the flux local to the glycogen synthesis pathway. One reason for this elevated response is the fact that G6P binds cooperatively to GS. In the unifying model of GS regulation that we propose here, both ATP (h in Fig. 5C) and phosphorylation (h in Fig. 5A) increase the degree of G6P binding cooperativity and are thus expected to enhance the response of the glycogen synthesis pathway to G6P. If the feedforward loop is indeed a mechanism of G6P homeostasis, then physiological concentrations of ATP, as demonstrated by Piras et al. , and phosphorylation are expected to enhance G6P homeostasis.
The model we propose here has interesting implications regarding the relative importance of allosteric and covalent regulation. Using knock-in mice in which GS was desensitized to G6P, Bouskila et al.  recently reported that allosteric, and not covalent, regulation is the major mechanism by which insulin activates glycogen synthesis. From Fig. 5A, it is clear that if GS is desensitized to activation by G6P, i.e. if ‘a’ is removed, some functions of phosphorylation are also removed (h, g), leading to a possible underestimation of the importance of phosphorylation. In particular, only the direct effect of phosphorylation on the activity of GS would be observed, and its role in increasing the sensitivity of GS towards G6P would be neglected. Similarly, if the phosphorylation sites on GS are removed, the function of G6P as promoter of net GS dephosphorylation becomes irrelevant. It is our opinion that metabolic control analysis [11, 12] may provide insights into the relative contributions of allosteric and covalent regulation to activation of GS, if indeed these contributions may be considered in isolation. It may also provide valuable insights into the regulatory design of muscle glycogen metabolism and its involvement in the onset of insulin resistance. One of the central aims of metabolic control analysis is to relate properties of individual enzymes to global pathway responses. It is therefore essential to obtain a quantitative understanding of the precise effects of regulation on the kinetics of GS, an understanding that may only be obtained by returning to enzyme kinetics. We thus echo the call by Jensen and Lai  for a detailed quantitative investigation of the effects of allosteric and covalent regulation on the kinetic properties of GS.
The research of D.C.P. is supported by the National Research Foundation of South Africa and the University of Stellenbosch. The authors wish to thank the referees of this manuscript for their invaluable suggestions.