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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Arch Biochem Biophys. Author manuscript; available in PMC Mar 15, 2013.
Published in final edited form as:
PMCID: PMC3298769
NIHMSID: NIHMS344914
Dynamic dissociating homo-oligomers and the control of protein function
Trevor Selwooda and Eileen K. Jaffea*
aFox Chase Cancer Center, 333 Cottman Avenue, Philadelphia, PA, 19111
* Corresponding author. Address: Fox Chase Cancer Center, 333 Cottman Avenue, Philadelphia, PA, 19111, Tel: 215-728-3695, Fax: 215-728-2412, Eileen.Jaffe/at/fccc.edu
Homo-oligomeric protein assemblies are known to participate in dynamic association/disassociation equilibria under native conditions, thus creating an equilibrium of assembly states. Such quaternary structure equilibria may be influenced in a physiologically significant manner either by covalent modification or by the non-covalent binding of ligands. This review follows the evolution of ideas about homo-oligomeric equilibria through the 20th and into the 21st centuries and the relationship of these equilibria to allosteric regulation by the non-covalent binding of ligands. A dynamic quaternary structure equilibria is described where the dissociated state can have alternate conformations that cannot reassociate to the original multimer; the alternate conformations dictate assembly to functionally distinct alternate multimers of finite stoichiometry. The functional distinction between different assemblies provides a mechanism for allostery. The requirement for dissociation distinguishes this morpheein model of allosteric regulation from the classical MWC concerted and KNF sequential models. These models are described alongside earlier dissociating allosteric models. The identification of proteins that exist as an equilibrium of diverse native quaternary structure assemblies has the potential to define new targets for allosteric modulation with significant consequences for further understanding and/or controlling protein structure and function. Thus, a rationale for identifying proteins that may use the morpheein model of allostery is presented and a selection of proteins for which published data suggests this mechanism may be operative are listed.
Keywords: Allostery, protein multimer, morpheein, moonlighting
Modern biophysical methods yield an enhanced appreciation of protein dynamics and the vital role these dynamics play in biochemical processes [14]. This commentary focuses on quaternary structure dynamics and strives to provide a historical perspective on the evolution of concepts and hypotheses related to quaternary structure equilibria in relation to allosteric control of protein function. It includes a historical review of protein structure dynamics, leading up to and beyond the introduction of the concept of allostery by Monod and coworkers [5, 6]. Previously established and proposed models of allostery are presented with an emphasis on the role of subunit dissociation in the allosteric process. In particular, consideration is given to the functional control of homo-oligomeric proteins that can dissociate and potentially rearrange, reversibly, under native conditions. Only proteins that change quaternary structure without covalent modification and whose quaternary structure equilibria respond to ligand binding are considered. For clarity, a glossary of important terms used in this review is included (Table 1).
Table 1
Table 1
Definitions of Terms Used.
Special emphasis is given to homo-oligomeric proteins that can reversibly come apart and change conformation in the dissociated state. The altered conformation of the dissociated state may then reassemble to a structurally and functionally distinct oligomer as illustrated in Figure 1 (a and b). We have called such proteins morpheeins and the individual oligomeric assemblies are called alternate morpheein forms [7, 8]. The unique and defining characteristics of morpheeins are 1) that different assemblies have different functions and 2) that the interchange of morpheein forms requires dissociation of higher order oligomers to allow conformational change in the dissociated state. The prototype morpheein is the enzyme porphobilinogen synthase, whose quaternary structure equilibrium includes a high activity octamer, a low activity hexamer, and a dimer whose conformation dictates assembly to one or another higher order oligomer (Figure 1c). The identification of proteins that can undergo reversible quaternary structure rearrangements has the potential to define new allosteric targets for the modulation of biologic activity with significant consequence for human health and disease. This article provides suggestions for the identification of proteins whose functional control may involve an equilibrium of morpheein forms. Based predominantly on the literature a large number of putative morpheeins, most of which remain to be verified experimentally, are listed in Table 2 along with their characteristics that are consistent with but not confirmatory that the protein is a morpheein.
Figure 1
Figure 1
The morpheein model of allostery
Table 2
Table 2
Proteins with characteristics consistent with a morpheein model of allosteric regulation
Early studies of hemoglobin
Starting in 1904, when Bohr discovered the cooperative binding of oxygen to hemoglobin [9], the behavior of hemoglobin became the inspiration for hypotheses about how protein subunits communicate. Bohr’s sigmoidal curve for oxygen binding to hemoglobin suggested that the binding of one oxygen molecule increased the affinity for another. Quantification of oxygen binding to hemoglobin by Hill in 1910 was based on the premise that hemoglobin was a heterogeneous system of oligomers of different stoichiometry [10, 11]. Hill’s equation (Eqn. 1) described the sigmoidal oxygen binding curve.
equation M1
Eqn. 1
The term n represents the average stoichiometry of the oligomers; y represents the percentage saturation with O2; K is the equilibrium constant for O2 binding; and × is the O2 partial pressure. The Hill equation is valid regardless of whether the alternate oligomers are in equilibrium or if they constitute a simple non-equilibrating mixture. Hill’s “cooperativity factor” n, now known as the Hill coefficient, is most often currently interpreted to define the cooperativity that exists between subunits of a non-dissociating oligomer of fixed stoichiometry. However, the view of hemoglobin as a mixture or equilibrium of oligomers remained popular for two decades [1217].
In 1925 the pendulum swung towards a more homogeneous view of the oligomerization state of hemoglobin when Adair determined that hemoglobin was predominantly a tetramer [18]. The sigmoidal behavior was then interpreted as O2 binding to subunits of the tetramer progressively increasing the affinity of the unoccupied site(s) for O2. The homogeneous tetramer model promoted a view of hemoglobin as a protein whose function did not require dissociation. In 1936 Pauling proposed a similar model in which the heme groups were arranged in a square and that binding of O2 at one corner of the square would assist binding at adjacent corners [19]. Regardless of the details of the early models of hemoglobin function, to this day hemoglobin function is generally considered in terms of a tetrameric structure for which dissociation is not physiologically relevant [20]. With the exception of Lamprey hemoglobin, which is known to form monomers when carrying oxygen [21], there is little evidence to refute the stable tetrameric view of hemoglobin, particularly in light of the high concentration of hemoglobin in blood.
Although the function of hemoglobin was integral to the development of ideas about subunit communication (and allosteric regulation), the behavior of hemoglobin need not represent the behavior of all oligomeric allosteric proteins. Consider that hemoglobin was long believed to be a homo-oligomer, made up of one kind of subunit. It wasn’t until 1959, more than fifty years after Bohr’s first observations, that hemoglobin was established to be comprised of two different protein chains [22]. These details about the molecular heterogeneity of tetrameric hemoglobin are often downplayed when describing hemoglobin as the quintessential model for cooperativity and/or allostery. For simplicity, with the exception of hemoglobin, the focus of this review is on homo-oligomeric proteins containing subunits with one primary amino acid sequence.
Quaternary structure
The studies of Svedberg (1912–1940) [2327] suggested that many proteins are comprised of subunits. Nevertheless, Linderstrom-Lang and Schellman’s classic 1959 chapter entitled “Protein Structure and Enzyme Activity,” [28] discusses only primary, secondary, and tertiary structure. The chapter addresses molecular dynamics, but does not mention quaternary structure in either a static nor a dynamic sense. More than ten years later, in a comprehensive review of protein quaternary structure by Klotz et al., [29] the inherent symmetry of homo-oligomeric proteins is introduced with an appreciation that “all subunits in an oligomeric protein are in equivalent (or pseudo identical) environments” and that all of the interacting interfaces are saturated (or involved in a subunit interaction). This dictates that the geometries must be closed, such that if a “protein is composed of four subunits their final arrangement should be such as to make the formation of a hexamer or octamer unlikely”. When dissociation is suggested, it is uniformly seen as additive (two hexamers associating to make a dodecamer; or two tetramers associating to make an octamer). The state-of-the-art in 1970 did not consider that there might be a dissociated state with different conformations that have distinct oligomerization properties; it had not been seen and was not imagined. This additive view of homo-oligomerization has remained the common view and is implied in the most modern of works on protein subunit assembly [3032]. Thus the observation of an equilibrium of the non-additive alternate oligomers of porphobilinogen synthase as illustrated in Figure 1c and described in an accompanying article [33], was surprising, but it need not be unique [34].
Protein dynamics
Separate from hypotheses about communication between subunits of protein oligomers was the evolution of general notions about protein structure dynamics. The history of this intellectual inquiry is described from the time it was established that the chemical structure of a protein is a linear polypeptide chain and when it was generally accepted that each protein had a fixed amino acid sequence (circa 1940). Words like conformation and configuration as used in mid-twentieth century publications predated our current understanding of the protein folding process or of concepts such as a particular protein fold (e.g. the αβ-barrel). The evolution of language in a relatively rapidly changing field yields a lack of clarity as to whether the envisioned alternate configurations mentioned in mid twentieth century documents were meant to represent what are now called different protein folds (big changes), different side chain rotomer conformations (small changes), or the diverse continuum between. Early notions on the structure of proteins, particularly antibodies, included the hypothesis that at least some protein sequences can exist in many configurations with nearly the same energy [35, 36]. This hypothesis was put forth to explain how a relatively small number of antibodies could protect against the much greater number of antigens. Notable early contributions to a dynamic view of protein structure were from Linderstrom-Lang and coworkers [28]. However, during the 1950’s and 1960’s when much effort was directed at determining the one correct sequence of several proteins (e.g.) [37] and protein crystallography generated the first protein crystal structures [38, 39], the dynamic view of protein structure was undersold in favor of a more rigid view of a single, most stable conformation for a given protein sequence. The appearance of protein crystal structures, which by their very nature provide a snapshot of a single conformation of a protein, fueled static views and the bulk of the current literature continues to interpret data in terms of a single native state. Deviations from this state are often referred to as partially unfolded or misfolded. The field continues to struggle to consistently consider an equilibrium ensemble of native states as has been put forth in the concept of proteostatis [40], a modern concept that does not yet address quaternary structure dynamics.
Historical models for ligand binding also reflect the static views that derived from the first few decades of protein crystal structure determination. The lock and key hypothesis [41] illustrates a ligand binding to a rigid protein structure. The related induced fit hypothesis [42], which promoted a view of at least two distinct protein conformations, did not address alterations in terms of quaternary structure dynamics. Even by 1979, twenty years after the first solution of an X-ray crystal structure of a protein, there were crystal structures of only about fifty protein molecules [38]. Thus, although small fluctuations in protein structure were generally understood to occur, the notion of relatively fixed protein structures was generally accepted by the mid 1960’s when the classic theories of allosteric regulation of protein function were first introduced (see below).
There is an intrinsic relationship between stable protein assembly states and the probability of obtaining protein crystals that diffract to a high atomic resolution. Because the existence of a dynamic equilibrium of quaternary structure assemblies is predicted to be detrimental to the solution of a protein crystal structure, the Protein Structure Initiative avoided proteins that chromatographed as multiple peaks on a size exclusion column and focused on proteins whose size appears to be more uniform. Up until about a decade ago the Protein Data Bank provided little information on the quaternary structure of the biologically relevant assembly. Now the Protein Data Bank and related online services such as PISA, PQS, and ProtBuD provide considerable analysis of potential quaternary structure assemblies [4345]. Although determination of protein domain flexibility is a strength of NMR protein structure determination, molecular size limitations have largely prevented NMR determined structures from addressing quaternary structure. Nevertheless, Gronenborn and coworkers have recently seen evidence for alternate quaternary structure assemblies using the NMR method [4648].
As crystal structures began to appear, other studies were emerging that supported the rigid protein view. Based on work started in the 1950’s [49], Anfinsen and coworkers had established by the early 1970’s that protein sequence alone can provide all the information necessary to specify the native three-dimensional structure of at least some proteins [50, 51]. Implicit in Anfinsen’s principle is the assumption that there is only one physiologically relevant native structure, and presumably one native quaternary assembly. Despite Anfinson’s demonstration that denatured ribonuclease refolded to only one structure [50, 51], not all proteins were found to be so well behaved. The molecular chaperones later (1980s and beyond) found to assist protein folding had not yet been described. Thus, in the late 1960’s several groups considered metastable structural states. Nickerson and Day proposed metastable structures of a given protein with alternate functions [52]. Epstein and Schechter considered the possibility of “conformational isozymes” as one protein with more than one structure, each structure having different kinetic properties [53]. Recently revealed interdomain chain swapping is one example of such a conformational variant whose physiologic significance has yet to be addressed [54]. Leventhal considered the problem of multiple structures for one protein in the context of computational structure prediction [55]. These, and related papers on multistable proteins [56], protein conformers [57], and conformational isomers [58] were largely overlooked in favor of a one amino acid sequence, one structure paradigm. Conformational drift, introduced by Weber in 1986 to describe the slow recovery of homo-oligomeric proteins following high pressure treatment [59], was the first consideration of alternate oligomers in equilibrium through alternate conformations of a dissociated state (two different dimers interconverting through alternate monomer conformations). The recent NMR studies of Gronenborn and coworkers have indeed revealed alternate quaternary structure assemblies for what was originally considered a small monomeric protein [46]. The potential for physiologically relevant interchange of these forms is not yet documented.
The overwhelming data in favor of a dynamic protein structure is reflected by the “new view” of protein dynamics [60] in which proteins exist as an ensemble of conformations. Concepts such as conformational diversity [3] and intrinsically disordered (or naturally unfolded) proteins [2, 4, 61] are now readily accepted. Intrinsically disordered proteins which are thought to be unfolded in the absence of a ligand template are a prime example of the dynamics of proteins in solution.
The evolution of models for allostery
The focus of this section is to discuss the evolution of allostery in the context of the evolving views of protein quaternary structure dynamics. While it is not a requirement, most allosteric proteins are oligomeric and the significance of their dissociation/association to allosteric control is a focus of this review. Key observations revealing allostery were made in the 1950’s; metabolic products, chemically distinct from an enzyme substrate, were found to modulate enzyme activity [62, 63]. Thus arose the idea that protein function could be governed by binding of a ligand at a site other than the active site, and that such functional control could be physiologically significant [62, 6466]. In 1963 the word allostery was introduced to describe the modulation of enzyme activity by effector molecules that were not sterically analogous to the substrate [6]. Monod and coworkers considered the complication of dissociating oligomers in the formulation of their model of allostery [32] and the 1965 introduction of the MWC concerted model for allostery explicitly made the simplifying assumption that the two distinct allosteric states of the protein (R and T) had the same fixed quaternary structure (e.g. both were tetrameric [5]). This assumption rapidly became an established view of allosteric oligomers, which has been perpetuated in texts for decades. In the concerted or “two state” model (Figure 2a) there are two conformations of the subunits. To maintain symmetry, all four subunits transform concertedly from one conformation to another. Both conformations were postulated to be accessible in the absence of allosteric effectors; with effectors stabilizing one form over the other. In this model, subunit dissociation was not considered essential to the interconversion between states. The KNF sequential model of allostery, introduced by Koshland, Nemanthy, and Filmer continued the assumption of a fixed oligomer [67]. The sequential model (Figure 2b) proposed that individual subunits in the oligomer were able to change conformation independent of their partner subunits. In this case the conformational change was mediated by an induced fit of the ligand. The introduction of the classic MWC or KNF model downplayed the possibility that quaternary structure assembly could be a dynamic component of the allosteric phenomenon. Oligomer dissociation was not promoted as part of the equation.
Figure 2
Figure 2
Models of allostery
Immediately after the concerted and sequential models were formulated others invoked subunit dissociation as part of allosteric control. In 1967 Frieden’s study of glutamate dehydrogenase led him to extend the concerted model to account for a dissociating/associating system (Figure 2c), i.e., the two conformations of the model have different quaternary structures and each conformation is limited to only one quaternary structure [68]. In the same year, Kurganov [69, 70] and Nichol, Jackson and Winzor [71] also proposed mathematical models for the allosteric control of a dissociating/associating oligomer whose different quaternary forms have different functionality. One model proposed by Nichol, Jackson and Winzor [71] and later extended by Drozdov-Tikhomirov [72] accounted for allostery without invoking conformational change in a subunit (Figure 2d). Notably, in 1970 Koshland described dissociation in an allosteric system as means to attenuate the allosteric response [73]. One of the theoretical models proposed therein is shown in Figure 2e. This model represents the phenomenon that has come to be known as auto-inhibition, as in the action of the epidermal growth factor receptor [74], and is prescient of the minimal description of a morpheein, described below.
The original concerted and sequential models of allostery, promoting the view of stable oligomers, remain the most often considered. Since 1970, the relationship between dissociation/association and allostery has been rarely invoked; there have been only five reviews [7578], the most recent of which was more than fifteen years ago, and two books [79, 80], which consider this relationship. However, throughout the past decade we have characterized a protein for which allostery involves oligomer dissociation, conformational change in the dissociated state, and reassembly to a structurally and functionally distinct oligomer [7, 8, 34, 8189]. Our initial unwillingness to embrace the possibility for this particular type of quaternary structure dynamic was seated in our general appreciation for the one sequence → one structure paradigm, which we, like most, considered to be applicable on the level of quaternary structure. This enlightening system, which is described in detail in an accompanying article [33], is introduced below along with consideration of whether other proteins may behave in a similar fashion. The homooligomeric protein is porphobilinogen synthase (PBGS), which catalyzes the first common step in the synthesis of the tetrapyrrole pigments (heme, chlorophyll, vitamin B12). PBGS can exist as a high activity octamer that can dissociate to dimers; the dimers can populate alternate conformations; and one alternate dimer conformation can assemble into a low activity hexamer (Figure 1c) [34, 8185]. In some species there is an allosteric activator that stabilizes a subunit interface present in the octamer and absent in the hexamer [34]. These findings led to a new dissociating model for allosteric regulation termed the morpheein model [7, 8, 81]; this is described in more detail below.
Morpheein model of allosteric regulation
The morpheein model of allosteric regulation [7] marries conformational diversity with quaternary structure dynamics and establishes a physiological relevance to the pressure induced quaternary structure rearrangements described as conformational drift. In the context of the morpheein model, homo-oligomer assemblies readily associate and dissociate under physiologic conditions and there is sufficient conformational flexibility in the dissociated state to dictate formation of more than one kind of oligomeric assembly. A morpheein is defined to be a protein that exists as an equilibrium of quaternary structure assemblies such as is illustrated in Figure 1 by both a three-dimensional dice analogy (Figure 1a) and a two-dimensional geometric (Figure 1b) analogy. The assembled higher order oligomers are of finite multiplicity and different functionality. The individual states (morpheein forms) are linked by dynamic equilibria such that interchange between higher order oligomers must involve dissociation. The dissociated form has conformational flexibility and the specific conformation of this form determines which higher order oligomer is assembled. The change in conformation involves a small number of peptide backbone angles, such as hinge motion between domains; it does not involve protein unfolding/refolding. Assembly of oligomers is such that symmetrical contacts are maintained between the subunits in each oligomer (one dot to four dots for the dice; dashed line to thick line for the geometric shapes). The morpheein forms are all relatively close in energy, e.g. the low population states are present at some, albeit small, mole fraction. In this way the interconversion of morpheein forms can be accomplished under normal physiologic (native) conditions. The equilibrium can be drawn in one direction or the other through non-covalent ligand binding (Figure 1b); such allosteric ligands exert their effect on protein function by stabilizing one or another of the functionally distinct morpheein forms.
In the morpheein allosteric model, all forms are accessible in the presence and absence of allosteric effector molecules; the dynamic equilibria are merely shifted through binding of effectors. This is emphasized in Figure 1b by the position of the equilibria in the presence or absence of appropriately shaped allosteric effector molecules. While stable alternate conformations (or quaternary assemblies) are often associated with post-translational modifications, interchange between morpheein forms occurs without such modification. Without chemical modification, the ready interchange of morpheein forms demands that they be of similar energy, as has been demonstrated for the morpheein forms of PBGS [34, 8185]. There may however be a substantial kinetic barrier to the interconversion process.
What rules might dictate how identical subunits can rearrange?
In general, protein subunits assemble with themselves (homomeric assembly) such that they retain an element of symmetry wherein equivalent surfaces of equivalent monomers are in equivalent environments (see Figure 1). If one monomer has, for instance, residue X in a hydrogen bond with residue Y of another subunit, then it is preferred that all residues X of each subunit are in a hydrogen bond with all residues Y of a neighboring subunit. Complete dissociation of an oligomer (Figure 1) releases all these interactions simultaneously, retaining the equivalence of the protein surfaces, one subunit to the next. But removal of one subunit from the trimer or tetramer would result in a loss of this equivalence and establish an asymmetric structure. In a given environment (pH, temperature, ionic strength), the physical chemical forces governing association of the subunits are equivalent for all subunits and the system will strive to retain symmetry. Thus, there are many oligomeric assemblies larger than a dimer where partial dissociation creates asymmetry. For the PBGS octameric assembly, illustrated in Figure 3, loss of one subunit or one dimer would result in such asymmetry; splitting the octamer in half by removing two pro-octamer dimers also results in asymmetry. However, separating the octamer into two halves in a process that cleaves each pro-octamer dimer (along the barrel-to-barrel interface) would retain symmetry. The resulting tetramers would each contain four dangling N-terminal arms. Although there are valid arguments against this latter example, such as the significance of the pulled apart arms to the structural integrity barrel-barrel contacts, symmetry is retained. However, one way that PBGS could dissociate and still retain both symmetry and two out of the three surface-to-surface contacts would be to simultaneously dissociate to four dimmers (Figure 1c). As described above, it is the need to maintain symmetry and the orientation of the Nterminal arm that drives formation of the hexamer and/or octamer of PBGS. For an in depth discussion of oligomeric assembly, the reader is referred to a review article by Goodsell and Olson [90].
Figure 3
Figure 3
Generation of protein asymmetry during multimer disassembly
Morpheeins expand our understanding of disease and drug action
Inborn errors of metabolism often result from mutations that alter the function of essential proteins. If the natural function of a particular protein relies on its ability to equilibrate between morpheein forms, then single amino acid variations that alter the equilibrium of such forms can result in a disregulation of said protein function and cause or contribute to a disease state. This is indeed the case for human PBGS in relation to the disease of ALAD porphyria; all of the naturally occurring mutations of human PBGS that are associated with the disease ALAD porphyria have been shown to shift the quaternary structural equlibria toward the low activity hexameric assembly [83]. Such diseases can be considered among the conformational diseases. Hence, identification of proteins that function as morpheeins can improve our understanding of the structural basis of human diseases associated with the function of these protein and/or variations in disease susceptibility. Several of the putative morpheeins in Table 2 are associated with inborn errors of metabolism. These are 1) alpha-galactosidaseA, which is associated with Fabry disease, 2) the ATPase of the ABCA1 transporter, which is mutated in Tangier’s disease and familial high-density lipoprotein deficiency, 3) cystathionine-β-synthase, for which some mutations cause a form of homocystinuria, 4) dihydrolipoamide dehydrogenase, associated with E3-deficient maple syrup urine disease and lipoamide dehydrogenase deficiency, 5) NAD(+)-dependent mitochondrial malic enzyme, where mutations are related to certain hereditary forms of epilepsy, 6) phenylalanine hydroxylase deficiency, which causes phenylketonuria, and 7) pyruvate kinase, whose deficiency is the most common cause of hemolytic anemia. For each of these proteins, there are one or more publications that justify a model of functional control via equilibrium of alternate protein assemblies (see Table 2).
Just as understanding disease mechanism may be improved by considering that certain proteins function as morpheeins, so too can our understanding of the mechanism of action of effective therapeutics whose mechanism is not otherwise explained. In proof of this concept small molecule allosteric inhibitors of PBGS, which function by stabilizing the inactive hexameric assembly, have been identified [84, 88, 89]. Following the identification of the morpheein character of medically relevant proteins, comes the possibility of designing or discovering allosteric inhibitors or activators of these proteins. The literature suggests that small molecule allosteric stabilization of alternative quaternary structures may be the an effective approach to finding inhibitors directed against prominent drug targets such as tumor necrosis factor α [91] or HIV integrase [92]. To this end the characteristics of a morpheein as these may aid in the identification of such proteins are discussed.
Characteristics that suggest a protein functions as a morpheein
There are myriad characteristics that suggest, but do not prove, that a particular protein may function as a morpheein. Table 2 provides a list of proteins that exhibit one or more of these characteristics and are thus suspect of being able to exist as an equilibrium of functionally distinct, non-additive quaternary structure assemblies or morpheein forms. Each entry in Table 2 includes at least one reference which the reader can use to begin exploring the putative morpheein nature of this protein. Some suggestive characteristics are illustrated in Figure 4.
Figure 4
Figure 4
Some characteristics of a morpheein ensemble
Protein concentration dependent specific activity (Figure 4a)
Specific activity (units of enzyme activity per protein mass) is a value often used during protein purification to assess protein purity. In the case of monomeric enzymes, or stable enzyme oligomers, specific activity is expected to be independent of the concentration of the enzyme used in the assay. However, for an equilibrium of morpheeins forms, if rapid interchange of oligomeric assemblies is occurring during the assay, the observed specific activity may be dependent upon the concentration of the enzyme in the assay mixture. This relationship derives from the law of mass action, which favors the largest oligomer as the protein concentration is increased in the range of its inherent dissociation constant. The illustration in Figure 4a refers to a situation where the largest oligomer is the most active. In the case where a smaller oligomer is most active, there will be an inverse relationship between protein concentration and specific activity, as has been reported for purine nucleoside phosphorylase [93]. However, it is important to note that one may only recognize such a protein concentration dependent specific activity if one is varying the protein concentration within the range (+/− one order of magnitude) of the apparent K0.5. Outside that range the effect will be too small to discriminate from experimental error.
Kinetic hysteresis
One is classically taught that initial rates of enzyme catalyzed reactions should display a linear increase in the concentration of product. However, in the case of an enzyme that functions as a morpheein, this may not be so. Upon dilution into assay buffer, a lag (shown in Figure 4b) or a burst in activity may be apparent as the equilibrium of morpheein forms adjusts to assay conditions. In the example in Figure 4b the assay conditions promote a shift to a more active morpheein form and the rate of product production increases with time. A shift to a less active form would have the opposite with a decrease in the rate of product production occurring with time. The term hysteresis was coined by Frieden in 1970 to describe non-linear kinetics [94]. Subsequently Kurganov presented mathematical models to explain various hysteretic behavior [79]. While the early work on kinetic hysteresis did not have the luxury of the structural insight gained from a decade of work on the PBGS quaternary structure equilibrium, one explanation for hysteretic behavior is a switch in the distribution of morpheein forms. The work of Frieden and Kurganov also points to the fact that kinetic hysteresis is a possible characteristic of an enzyme that functions as a morpheein, but it is not a diagnostic tool by itself.
Non-traditional Michaelis Menten kinetics
The existence of multiple forms of an enzyme may be reflected by non-traditional Michaelis-Menten plots. Generally it is expected that a Michaelis-Menten plot will be hyperbolic unless there is some phenomenon such as product inhibition to perturb this trend. In the case of a morpheein it is possible that two or more catalytically active forms may be present. Provided that the affinities of the various forms for the substrate are sufficiently different, a nontraditional Michaelis-Menten plot will be produced that consists of more than one hyperbola, the number of which corresponds to the number of active forms present in the assay. For example, the predominant forms of human PBGS are the octamer and the hexamer. These two forms have vastly different Km values and the result is a double hyperbolic relationship between substrate concentration and activity. However, to see this relationship, it is necessary that experimental substrate concentrations cover the range of the two Km values [85].
Multiple quaternary structures
Often multiple quaternary structural forms that are visualized by gel filtration chromatography or native-PAGE are viewed as representing an impure sample. This is especially true if one or more of the separated forms are found to be inactive. However, if a protein functions as a morpheein, the multiple quaternary structures may be functionally distinct forms of the same protein. Rechromatography under different conditions may produce a different distribution of quaternary structural forms and even more confounding is the fact that these forms may have vastly different functions (see moonlighting proteins below). In addition to separation by traditional sizing methods the surface charge differences between the different quaternary structural forms may allow separation by ion-exchange chromatography. For example, the octameric, hexameric, and dimeric forms of PBGS can be separated by anion exchange chromatography [34, 81, 85].
pH profile effects
pH profiles also may depend on the conditions under which they are obtained. For example, the alkaline limb of the human PBGS pH-activity profile is due at least in part to the pH dependence of the quaternary structure equilibrium. High pH favors the less active hexamer compared to the more active octamer [85].
Order of addition effects
Incubation conditions prior to addition of the reaction initiating compound can influence the distribution of morpheein forms of a protein. GDP-mannose dehydrogenase (GMD) provides a striking example of order of addition effects [95]. The substrates for GMD are GDP-mannose and NAD+, and both phosphate and GMP act as allosteric effectors [95]. As shown in Figure 4d the four very different reaction rate curves are produced when the assays were carried out using four different orders of addition of reactants and/or allosteric effectors. Similar phenomena have also been referred to as enzyme memory [96].
Moonlighting proteins
It has become common to find that one protein has multiple unrelated functions; these proteins are said to moonlight [97]. One notable example is the glycolytic enzyme glyceraldehydes-3-phosphate dehydrogenase which has been reported to have many activities unrelated to glycolysis [98–104]. It is possible that proteins that moonlight may not always do so as the same quaternary structure assembly. It is not clear if glyceraldehyde-3-phosphate dehydrogenase (GAPDH) performs all of its activities as the tetramer believed to be functional in glycolysis. It may be possible to modulate a preferred function of multimeric moonlighting proteins with small molecules that modulate an equilibrium of morpheein forms.
Morpheeins in relation to other oligomerizing proteins
Morpheeins represent a subset of oligomerizing proteins. The features that distinguish morpheeins from other oligomerizing proteins are that they are homo-oligomeric, of finite stoichiometry, must dissociate/associate to interchange between functionally distinct multimers, and assembly of oligomers is autonomous, i.e., that is oligomer assembly occurs without the need for covalent modification or the presence of a template/scaffold. We have chosen to limit the definition of morpheeins to homo-oligomeric proteins because the archetypical morpheein PBGS is such a protein. There is no direct evidence for or against hetero-oligomers existing in dynamic equilibria such that they dissociate, change shape and come back together differently to regulate function. However, on the simplest level hetero-oligomers can be viewed as one protein being regulated by interaction with another; a scenario that does not require morpheein-like behavior.
Among homo-oligomeric proteins, morpheeins represent a distinct category. Conformational flexibility is evident in many homo-oligomers that do not follow the morpheein model. For example, prions adopt at least two conformations; one that does not oligomerize and one that does [105]. In terms of the morpheein model these could be viewed as conformations of a fundamental unit. However, oligomerization of prions differs markedly from that of morpheeins. The symmetry of oligomerization does not dictate a size limit for the oligomer such that large fibrils may be formed. Furthermore the thermodynamics of fibril formation is generally not amenable to a physiologically relevant and readily reversible mechanism for allostery.
Virus coat proteins also bear similarities to, but are not, morpheeins. These proteins must assemble to form a capsid around the virus genome to protect it from damage but upon invading a cell the coat must disassemble to allow infection by release of the genome. These properties imply that there are two conformations of the protein only one of which is capable of oligomerization. To form the capsid the proteins assemble with either a helical or an icosahedral symmetry in which the subunits may lie in quasi-equivalent environments [106, 107]. However, the requirement to form a stable barrier necessitates that the oligomer is not in dynamic equilibrium, but that the oligomer forming conformation is a metastable state that remains until some trigger removes a barrier to a conformational change that favors dissociation. Further distinctions are that, this conformational change must occur in the oligomer, not all capsids are homo-oligomeric, and the genome or some scaffold protein generally forms a template for the capsid.
Summary
Herein the morpheein model of allosteric regulation (Figure 1) and the history of thought on protein quaternary structure, dynamics and allostery that preceded it are detailed. In this model, subunits of an oligomer must dissociate to allow conformational change. The conformation of the dissociated protein dictates the symmetry of assembly of higher order oligomers. Consideration that a homo-oligomeric protein may be a morpheein opens up many new avenues for the understanding of protein function and the basis for and the treatment of disease. The insight gained into these facets of PBGS that are detailed in an accompanying review testify to this.
Acknowledgement
The authors would like to thank Dr. Sarah Lawrence for useful discussion.
This work was supported by the National Institutes of Health grants R01E5003654 (EKJ) and CA06927 and an Appropriation from the Commonwealth of PA
Abbreviations used
PBGSPorphobilinogen synthase

Footnotes
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