CHEM 440
Biochemistry I
J. D. Cronk   Syllabus [ Previous | Next ] Pick a lecture:
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Lecture 18. Allosteric proteins

Wednesday 21 October 2009

Allosteric enzymes and other cooperative phenomena in protein function. Aspartate transcarbamoylase (ATCase), an allosteric enzyme that is subject to feedback regulation. Cooperative oxygen binding by hemoglobin (Hb). The concerted (MWC) model for cooperativity postulates two quaternary states. Quaternary structural changes associated with allosteric effects in ATCase and Hb.

Reading: BTS6 - Ch.10, pp.275-282; Ch.7, pp.183-190.

18. Summary

Lecture 18 Summary

The story of the metabolic pathway, the committed step, and feedback inhibition. Aspartate transcarbamoylase [ATCase; EC 2.1.3.2] catalyzes the reaction of aspartate and carbamoyl phosphate to form N-carbamoyl aspartate, which is the committed step for pyrimidine biosynthesis. A pyrimidine nucleotide, CTP (cytidine triphosphate) acts as a feedback inhibitor of ATCase. This inhibition involves nucleotide binding at a site distinct from the active site. Furthermore, ATP competes with CTP binding, and is an activator of ATCase activity. The biological logic of this arrangement is discussed.

ATCase is a heterododecamer consisting of two catalytic trimers bridged by three regulatory dimers. Its complex but symmetric structure is truly beautiful! The active sites in the catalytic trimers are located at the interface between monomers, and the regulatory subunits contain the CTP/ATP binding sites.

We turn to ligand binding curves and the two-state model for positive cooperativity, which leads to a sigmoidal binding (or saturation) curve. Non-cooperative binding is a hyperbolic curve, just like Michaelis-Menten enzyme kinetics. The two-state model proposes a high affinity and a low affinity state that applies to each ligand binding site or enzyme active site in the oligomeric ligand binding protein or enzyme. The high affinity and low affinity states have their separate hyperbolic saturation curves - or would have except there is an equilibrium between the high affinity state (which we'll denote as the "R" state) and the low-affinity state (we'll call it the "T" state), and this equilibrium shifts toward the R state as ligand (or substrate) concentration increases. At quite low ligand concentrations, the binding curve overlaps the T state hyperbolic curve. At very high ligand concentration, the binding curve overlaps the hyperbolic R state curve. In between, as the fraction of R state molecules increases, the binding curve traces out the steep part of the sigmoidal shape.

The structural basis for the effects we have been discussing today are allosteric effects. The positive cooperativity shown by hemoglobin, in binding oxygen, and ATCase in rate of substrate conversion, is representative of homotropic allosteric effects. The regulatory effects of CTP binding (and inhibiting) ATCase, as well as pH, [CO2], and 2,3-BPG upon the oxygen affinity of hemoglobin are prime examples of heterotropic allosteric effects.

Definitions and equations

A ligand is a molecule that is specifically bound by a protein. It can be a small or large molecule, like a a cofactor or coenzyme, or even another protein. A protein together with its ligand is termed the holoprotein, or denoted as "the complex". The protein alone is the apoprotein. In enzymology, the related terms holoenzyme and apoenzyme are commonly used.

The equilibrium between free ligand and apoprotein on the one hand, and the protein-ligand complex can be represented as
Equations for ligand (L) binding equilibrium   Ka, the association constant, is defined in terms of the free ligand concentration, [A], the concentration of the free (apoprotein) [P], and the concentration of the protein-ligand complex [P.A]. Rearranging this definition, we see that the ratio of complex to free protein is directly proportional to free ligand concentration.
An experimentally more useful quantity is the fraction y of protein with the ligand bound. Biochemists usually express binding constants in the form of dissociation constant, Kd, which is just the inverse of Ka. The form of the fractional binding relation in terms of Kd is shown. Binding of multiple ligands at multiple sites of a protein can lead to very complex behavior. Allostery is the term applied to the phenomenon in which ligands binding at sites distant from one another in a protein structure functionally interact. The most common result of this functional interaction between subunits is cooperativity. The oligomeric nature of hemoglobin (Hb), for instance, makes possible cooperative effects between subunits, where binding of the ligand to a specific ligand binding site on one subunit affects the affinity of the others for the same ligand.   Equation defining fraction y of protein with bound ligand
Expressions for the dissociation constant for ligand binding (Kd) and the fraction y of protein binding sites occupied
This is termed a homotropic effect. In Hb, the homotropic interactions between oxygen binding sites have the property that binding of one oxygen molecule at one site increases the affinity of the other sites for oxygen - that is, ligand binding in Hb shows positive cooperativity. Allosteric effects can also be heterotropic, involving interactions between different ligands. Heterotropic allosteric effects also occur in hemoglobin. Ligands such as CO2, H+, and 2,3-BPG affect the affinity of the binding sites in Hb for O2.
 

Non-cooperative & cooperative binding curves

The equation for the fraction y of ligand bound predicts a hyperbolic binding curve when y is plotted as a function of ligand concentration. The Kd represents the concentration at which half the sites of the protein are occupied with ligand:

  
       
The graph above shows the hyperbolic binding curves for several different dissociation constants. The higher the Kd, the weaker the binding. These hyperbolic curves represent the non-cooperative binding case. The graph below shows a cooperative binding curve, and in contrast to the non-cooperative binding curve, it has a sigmoidal shape. This is what is observed for the oxygen binding curve of hemoglobin. Hemoglobin displays positive cooperativity since the binding of the first ligand increases the affinity for the next, and so on. We have encountered sigmoidal curves before - for example in the helix-coil transition of DNA. In fact, sigmoidal curves are characteristic of cooperative transitions between two distinct states that involve the making (or disruption) of numerous weak (non-covalent) interactions.
 

The graph at left shows the non-cooperative binding curve with a Kd of 1. The cooperative curve was calculated according to the Monod-Wyman-Changeux (MWC) or concerted model.

You can make your own graph for a tetrameric binding protein by input of values for the MWC parameters L and c (L = 9000, c = 0.014 models hemoglobin oxygen binding well).

Make your own graph

 

The two-state concept and model for sigmoidal (cooperative) binding curve

The simplest explanation for positive cooperativity is to postulate the existence of two states of the macromolecule, denoted T and R, with different activities. Both T and R binding curves are fully hyperbolic. If we are considering a multisubunit (oligomeric) ligand binding protein, the T state is the state in which all the ligand binding sites have relatively low affinity for the ligand. (T stands for "taut" or "tense"). The R state (R stands for "relaxed") is the state in which all the ligand binding sites have relatively high affinity for the ligand. Given two such states of differing ligand affinities, it can be shown mathematically that a sigmoidal binding curve, characteristic of positive cooperativity in ligand binding, results from a ligand-induced shift in the equilibrium between T and R state.
Sigmoidal binding can be explained as a weighted sum of two hyperbolic binding states   Left: The sigmoidal form of a binding curve, indicative of positive cooperativity, can be explained as a weighted sum of two hyperbolic binding states, a high affinity R state and a low affinity T state. The weights, fR and fT, vary between 0 and 1, with fR and fT = 1 under all conditions. In other words, all molecules are either in the R state or the T state. There is an equilibrium between T and R that greatly favors the T state in the absence of any ligand. Essentially all molecules are in the T state (fT ≈ 1) at zero or very low ligand concentration . Increasing the concentration of the ligand A shifts the equilibrium toward the R state. With continued increase of [A], the equilibrium shifts so favorably to the R state that most every molecule is an R molecule, and fR approaches 1 as the fraction Y of binding sites occupied also goes to 1.

 

Learning objectives

  • Define what is meant by the term committed step, and explain why it is typically subject to regulation.
  • Explain the metabolic logic of heterotropic effects of CTP and ATP on ATCase activity.
  • Apply the concerted (MWC) model to explain homotropic and heterotropic effects in allosteric enzymes.
  • Propose a reasonable mechanism for the reaction catalyzed by ATCase.

Page updated, 11-01-09

References
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[ E-mail: cronk@gonzaga.edu ]