Allosteric, effectors models

FIGURE 15.9 Monod-Wyman-Changeux (MWC) model for allosteric transitions. Consider a dimeric protein that can exist in either of two conformational states, R or T. Each subunit in the dimer has a binding site for substrate S and an allosteric effector site, F. The promoters are symmetrically related to one another in the protein, and symmetry is conserved regardless of the conformational state of the protein. The different states of the protein, with or without bound ligand, are linked to one another through the various equilibria. Thus, the relative population of protein molecules in the R or T state is a function of these equilibria and the concentration of the various ligands, substrate (S), and effectors (which bind at f- or Fj ). As [S] is increased, the T/R equilibrium shifts in favor of an increased proportion of R-conformers in the total population (that is, more protein molecules in the R conformational state). 

Similar to generalized mass-action models, lin-log kinetics provide a concise description of biochemical networks and are amenable to an analytic solution, albeit without sacrificing the interpretability of parameters. Note that lin-log kinetics are already written in term of a reference state v° and S°. To obtain an approximate kinetic model, it is thus sometimes suggested to choose the reference elasticities according to simple heuristic principles [85, 89]. For example, Visser et al. [85] report acceptable result also for the power-law formalism when setting the elasticities (kinetic orders) equal to the stoichiometric coefficients and fitting the values for allosteric effectors to experimental data. 

Exactly how an allosteric effector molecule (activator or inhibitor) works is explained by one of two molecular models ... 

Structural model for conformational changes in ATCase, based on the X-ray crystallographic investigations of Lipscomb and colleagues. Note that substrates are thought to enter through a channel, and allosteric effectors alter channel accessibility. 

A subset in allosteric models of cooperativity. If an allosteric effector, upon binding to a cooperative enzyme, alters the Michaelis or dissociation constants (or [S0.5] value) for the substrate(s) (but not the h"max values), then that protein is a A system enzyme. See Monod-Wyman-Changeux Model K. E. Meet (1980) Meth. Enzymol. 64, 139. 

The enzyme from B. stearothermophilus is an a4 tetramer of subunit Mr 33 900. Early kinetic studies indicated that the enzyme acts in a manner that is qualitatively consistent with an MWC two-state model. The enzyme acts as a A system i.e., both states have the same value of kcal but different affinities for the principle substrate. In the absence of ligands, the enzyme exists in the T state that binds fructose 6-phosphate more poorly than does the R state. In the absence of ADP, the binding of fructose 6-phosphate is highly cooperative, and h = 3.8. The positive homotropic interactions are lowered on the addition of the allosteric effector ADP, with h dropping to 1.4 at 0.8-mM ADP.52 ADP thus binds preferentially to the R state. The allosteric inhibitor phosphoenolpyruvate binds preferentially to the T... 

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... 

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. 

The main effect of AMP on either phosphorylase b or phosphorylase a is to decrease the Km for P,. This change can be interpreted as we have interpreted the actions of allosteric effectors on phosphofructokinase and aspartate carbamoyl transferase, on the model that the enzyme can exist in two conformational states (R and T) with different affinities for the substrate. However, phosphorylase presents the additional complexity that the equilibrium constant (L) between the two conformational states can be altered by a covalent modification of the enzyme. In the absence of substrates, [T]/[R] appears to be greater than 3,000 in phosphorylase b but to decrease to about 10 in phosphorylase a. 

The symmetry model of Monond, Wyman, and Changeux (Monad et al., 1965). This model was originally termed the allosteric model. The model is based on three postulates about the structure of an oligomeric protein (allosteric protein) capable of binding ligands (allosteric effectors) ... 

The best-characterized class I RNR is that of . coli. Excellent reviews have recently been written on this enzyme (37-39, 73). The enzyme consists of the nonidentical proteins R1 and R2, each of which is a homodimer. The holoenzyme therefore has an a2 2 structure. The crystal structures of the E. coli R1 and R2 proteins have recently been reported (18, 19, 74). Protein R1 has 2 x 761 residues and contains the substrate binding sites, as well as the binding sites for the allosteric effectors. The exact localization of the specific binding sites for the effectors and the substrate, as well as the area of subunit interaction in the active enzyme, has so far only been modeled into the R1 structure. Protein R2 has 2 x 375 residues and contains the sites for the iron center as well as the tyrosyl radical. The crystal structure is obtained for the met form, i.e., without tyrosyl free radical. There is one site for... 

The key to allosteric behavior, including cooperativity and modifications of cooperativity, is the existence of multiple forms for the quaternary structures of allosteric proteins. The word allosteric is, derived from alio, other, and stetic, shape, referring to the fact that the possible conformations affect the behavior of the protein. The binding of substrates, inhibitors, and activators changes the quaternary structure of allosteric proteins, and the changes in structure are reflected in the behavior of those proteins. A substance that modifies the quaternary structure, and thus the behavior, of an allosteric protein by binding to it is called an allosteric effector. The term effector can apply to substrates, inhibitors, or activators. Several models for the behavior of allosteric enzymes have been proposed, and it is worthwhile to compare them. 

Fig. 4.14 Plot of the results of a calculation of the steady-state concentration of frnctose 6-phosphate for the system shown in fig. 4.13. The enzyme models are either based on Michaelis-Menten formalisms or modifications of multiple allosteric effector equations. The gate exhibits a function with both AND and OR properties. At low concentrations of both inpnts, the mechanism functions similarly to an OR gate, while at simultaneously high concentrations of the inpnt species (citrate and cAMP), the output behavior more closely resembles a fuzzy logic AND gate. The mechanism satisfies the requirements for a fuzzy aggregation function. (From [7].)...

The idea of common ancestry of the different ribonucleotide reductases is difficult to test at present because protein sequencing studies have not yet begun. Exchangeability of subunits, possible among the calf thymus and mouse enzymes , has not much been tried. We have seen small but significant stimulation of enzyme activity when the separated, inactive subunits U1 of algal (Scenedesmus) ribonucleotide reductase and B 2 of E. coli were recombined, but not in the reverse combination (B1 -t- U2) . The many individual differences in enzyme structure like Mg or Ca " requirement for subunit interaction, variations in the radical environment as expressed in slightly different ESR spectra (Fig. 3), or details of allosteric effector pattern, do not in principle contradict our reductase model but will in reality severely limit its experimental verification. 

A deletion mutant (Figure 11) was constructed in which the carboxyl half of the regulatory domain in the R2 chimera was deleted. The resulting construct bound allosteric inhibitors nearly as well as the parent molecule, but the allosteric transitions were abolished. Thus, the amino half of the regulatory subdomain binds allosteric effectors, while the carboxyl half is crucial for transmitting the allosteric signal to the catalytic domain. This result is consistent with the x-ray structure of E. coli CPS and the CAD model that indicates that most of the interactions between B3 and B2 (or A2 in the case of the chimera) involve residues in the carboxyl half of the regulatory domain. 

P. J. Goodford, J. St-Louis, and R. Wootton, Br. J. Pharmacol., 68, 741 (1980). The Interaction of Human Hemoglobin with Allosteric Effectors as a Model for Drug-Receptor Interactions. 

---