Enzymes symmetry model

Various models have been offered to describe the mechanisms of allosteric regulation of enzyme activty, of which the symmetry model (Monod et al., 1965) is the simplest. The symmetry model has proven suitable in many cases to explain the experimentally observed characteristics of allosteric enzyme regulation. 

The symmetry model (fig. 2.4) of allostery can describe the cooperative binding of substrate to enzyme (homotropic effect), as well as the influence of effector molecules on the activity of enzymes (heterotropic effect). 

Two different enzymatically active forms of PFK could be identified which may be considered the R and T form in the framework of the symmetry model. The R form possesses a high affinity for the substrate fructose-6-P, the T form binds fructose-6-P with lower affinity. Upon binding of the inhibitor phosphoenolpyruvate, PFK converts to the T form. The enzyme is foimd in the R form upon binding the substrates (ATP or fructose-6-P) or the activator (ADP). There exist high resolution crystal structures of both forms. 

The model active transport system described by Dr. Thomas is based on an asymmetric arrangement of two enzymes. A model active transport system was also described by Blumenthal et al. several years ago based on a single enzyme immobilized between asymmetric boundaries [Blumenthal, Caplan, and Kedem, Biophys. J., 7, 735 (1967)]. In the latter case the phenomenological coefficients were measured, and it was possible to demonstrate Onsager symmetry and the correlation between the thermodynamic coefficients and the kinetic constants. 

Allosteric Enzymes Typically Exhibit a Sigmoidal Dependence on Substrate Concentration The Symmetry Model Provides a Useful Framework for Relating Conformational Transitions to Allosteric Activation or Inhibition Phosphofructokinase Allosteric Control of Glycolysis Is Consistent with the Symmetry Model Aspartate Carbamoyl Transferase Allosteric Control of Pyrimidine Biosynthesis Glycogen Phosphorylase Combined Control by Allosteric Effectors and Phosphorylation... 

Using the symmetry model, the fraction of the binding sites occupied at any given substrate concentration can be described with an expression that includes the substrate dissociation constants for the two conformations (KR and Kr) and the equilibrium constant between the T and R conformations in the absence of substrate, L = [T]/[R], Thus, the symmetry model attempts to explain the difference between Kx and K2 in equation (3) by introducing a third independent parameter. Considering that equation (3) can fit the experimental data for a dimeric enzyme with only two pa-... 

Symmetry model for allosteric transitions of a dimeric enzyme. The model assumes that the enzyme can exist in either of two different conformations (T and R), which have different dissociation constants for the substrate (KT and Kk). Structural transitions of the two subunits are assumed to be tightly coupled, so that both subunits must be in the same state. L is the equilibrium constant (T)/(R) in the absence of substrate. If the substrate binds much more tightly to R than to T (AfR [Pg.183]

The symmetry model is useful even if it does oversimplify the situation, because it provides a conceptual framework for discussing the relationships between conformational transitions and the effects of allosteric activators and inhibitors. In the following sections we consider three oligomeric enzymes that are under metabolic control and see that substrates and allosteric effectors do tend to stabilize each of these enzymes in one or the other of two distinctly different conformations. 

Phosphofructokinase was one of the first enzymes to which Monod and his colleagues applied the symmetry model of allosteric transitions. It contains four identical subunits, each of which has both an active site and an allosteric site. The cooperativity of the kinetics suggests that the enzyme can adopt two different conformations (T and R) that have similar affinities for ATP but differ in their affinity for fructose-6-phosphate. The binding for fructose-6-phosphate is calculated to be about 2,000 times tighter in the R conformation than in T. When fructose-6-phosphate binds to any one of the subunits, it appears to cause all four subunits to flip from the T conformation to the R conformation, just as the symmetry model specifies. The allosteric effectors ADP, GDP, and phosphoenolpyruvate do not alter the maximum rate of the reaction but change the dependence of the rate on the fructose-6-phosphate concentration in a manner suggesting that they change the equilibrium constant (L) between the T and R conformations. 

Figure 4-53 The concerted-symmetry model of Monod, Wyman, and Changeux. T represents a low affinity form of an oligomeric enzyme which is in equilibrium with R, a high affinity form of the enzyme. This model allows only positive coo pe rati vity.

Two theoretical models that attempt to explain the behavior of allosteric enzymes are the concerted model and the sequential model. In the concerted (or symmetry) model, it is assumed that the enzyme exists in only two states T(aut) and R(elaxed). Substrates and activators bind more easily to the R conformation, whereas inhibitors favor the T conformation. The term concerted is applied to this model because the conformations of all the protein s protomers are believed to change simultaneously when the first effector binds. (This rapid concerted change in conformation maintains the protein s overall symmmetry.) The binding of an activator shifts the equilibrium in favor of the R form. An inhibitor shifts the equilibrium toward the T conformation. 

The concerted symmetry model is much more versatile than simple sequential models described by Adair or Hill. This model is endowed by the variable values of Kr, L, and c, and therefore may provide explanations for many properties of allosteric enzymes and proteins, including... 

The MWC concerted-symmetry and KNF sequential interaction models may be considered as extreme cases of the more general model shown in Fig. 19. A general model for a four-site allosteric enzyme involves the hybrid oligomers. The first and the fourth column in Fig. 19 represent the concerted-symmetry model. The diagonal represents the sequential interaction model. As shown, there are 25 different types of enzyme forms. If the potential nonequivalent complexes are included (such as, e.g., two different T3RS2), the number raises to 44 possible enzyme forms (Hammes Wu, 1971). 

One of the questions surrounding the mechanism of tyrosinase concerns the initial site of attack. As a control, LFMD simulations of a model for the sTy active site, Meim6 (Fig. 28), give identical behavior for each Cu center consistent with its symmetry. In contrast, the LFMD simulations clearly distinguish the two copper sites in the sTy enzyme which must result from the protein environment (Fig. 29). 

In proteins with a symmetric structure, circular permutation can account for the shift of active-site residues over the course of evolution. A very good model of symmetric proteins are the (/Ja)8-barrel enzymes with their typical eightfold symmetry. Circular permutation is characterized by fusion of the N and C termini in a protein ancestor followed by cleavage of the backbone at an equivalent locus around the circular structure. Both fructose-bisphosphate aldolase class I and transaldolase belong to the aldolase superfamily of (a/J)8-symmetric barrel proteins both feature a catalytic lysine residue required to form the Schiff base intermediate with the substrate in the first step of the reaction (Chapter 9, Section 9.6.2). In most family members, the catalytic lysine residue is located on strand 6 of the barrel, but in transaldolase it is not only located on strand 4 but optimal sequence and structure alignment with aldolase class I necessitates rotation of the structure and thus circular permutation of the jS-barrel strands (Jia, 1996). 

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