In what follows I am going to attempt to answer your question using a specific example of (competitive) reversible activation, and I hope to show what a misleading parameter EC50 can be. (Rate law derivation is an area of interest, hence the long-winded answer).
It can of course give information, but IMO it needs to be used with extreme care.
I am restricting my comments to the case where A is a reversible activator and where [A] >> eo and [S] >> eo. (All constants are defined below).
In short, I am not treating irreversible activation, and I am not treating the case where A is considered a tight-binding activator (so that [A] ≈ eo). In other words, I am making the steady-state approximation (Briggs & Haldane, 1925)
Consider the following simple mechanism for activation in a single-substrate enzyme:
A Mechanism for Competitive, Reversible Activation
The substrate (S) cannot bind to the free enzyme (E) unless the activator (A) is present. That is, only the activator can bind (reversibly) to E, and the substrate binds (reversibly) to the EA complex. Reaction occurs within the EAS complex (giving EAP). Dissociation of product (P) from EAP gives EA.
The (steady-state) initial-rate law for the above mechanism is the following:
As stated, all constants are defined below and follow the usual definitions in enzyme kinetics. I'll mention just one here: KA is the dissociation constant for the activator, and has units of concentration.
I derived these equations using a computerized version of the King & Altman method (King & Altman, 1956), but it is not difficult to do. It was pure laziness that prevented a 'first principles' derivation. Rate law derivation is treated in depth in most books on enzyme kinetics and good accounts may be found in Segel (1975) and Cornish-Bowden (2004).
One can now make the following points
- There is no activity without A (as one would expect).
- When [A] >> KA, the rate law becomes identical with the Michaelis-Menten equation (as one would expect).
- The equation is similar to the case of competitive inhibition, but (note subtle change) with (1 + KA / [A]) substituted for (1 + [I] / Ki)
- One can consider this mechanism an example of competitive activation
- νiexc = the initial velocity when A is in vast excess [ie setting [A] equal to ∞ in eqn (1) ].
- EC50 = the concentration of A that gives νi equal to νiexc / 2 (half-maximal activation)
allows the following two equations to be derived:
Setting the left-hand side of the above equal to 2, and solving for [A], gives the following all-important equation
One can now draw the following conclusions
When [S] = KSm
In words, when the substrate is present at a concentration equal to the Michaelis constant the value of EC50 is half the value of KA!.
When [S] >> KSm
When [S] = 10 x KSm, for example, EC50 is one-tenth the value of KA, and when [S] = 100 x KSm the figure is one-hundreth.
When [S] << KSm
Thus, for a competitive activator, it is only when [S] << KSm
that EC50 gives a reasonable estimate of KA.
The substrate concentration in a 'normal' enzyme assay will probably be equal to or greater than the Michaelis constant (in order to 'see' activity), and thus EC50 will be an underestimate of KA.
If the substrate is present at a 'saturating' concentration (say 10 x KSm) then one is in real trouble.
However, this is not the only consideration. As well as being substrate-concentration dependent, the manner in which EC50 depends on [substrate] depends on mechanism.
As briefly discussed below, the competitive activation case is analogous to that of competitive inhibition. However for uncompetitive inhibition the Ki (inhibition constant) is only equal to IC50 (the concentration of inhibitor giving half-maximal inhibition) at high substrate concentration! (see Naqui, 1982). By analogy, one can conclude that the same is true of uncompetitive activation.
It is very difficult to see how EC50 can be of any practical use, except perhaps when the mechanism of activation is known. At the very least, conclusions drawn from EC50 data should otherwise not be considered definitive.
In addition, I have discussed the only the case of a single-substrate reaction. Two-substrate reactions have the potential for even greater complexity.
Illustrative Example (Competitive Activation)
Let's take an example, and check some conclusions:
- kfcat = 1000 s-1
- eo = 1
- KSm = 10 µM
- KA = 50 µM
It may be calculated that:
When [S] equals 10 µM (ie when [S] is equal to KSm) and when [A] is 'saturating' (for the sake of argument set equal to ∞) the velocity is 500 µM s-1 [from eqn (1) ].
From eqn (2), the concentration of A required to achieve half this value (half maximal activation) is 25 µM (EC50 equals 25 µM)
This value can be directly calculated from eqn (3)
When [S] equals 100 µM (ie [S] equals 10 x KSm) and when [A] is 'saturating' the velocity is now 909 µM s-1 [from eqn (1) ].
From eqn (2), the concentration of A required to achieve half this value is now only ~4.5 µM
This value can be directly calculated from eqn (3) [EC50 equals (50 / 11) µM]
When [S] equals 1 µM (ie [S] equal to one-tenth the Michaelis constant) and when [A] is 'saturating' the velocity is now only ~91 µM s-1 [from eqn (1) ].
From eqn (2), the concentration of A required to achieve half this value is ~45.5 µM (now almost equal to KA)
This value can be directly calculated from eqn (3) [EC50 equals (500 / 11) µM]
Reversible Inhibition & IC50. A Brief Comment
There is nothing much new in any of the above. In the field of enzyme inhibition, the inadequecies of IC50 (the concentration of inhibitor giving 50% inhibition) and the relationship to the Inhibition constant are well-known [see, for example, Chou (1974), Segel (1975), Naqui (1982) & Tsou (1987)], but (it seems to me) often ignored.
The paper of Naqui gives a very succinct analysis of the situation and the pdf is freely available to all.
Reversible inhibitors may be divided into four classes, depending on the pattern of inhibition: competitive, uncompetitive, non-competitive and 'mixed' (see Naqui, 1982, and references therein).
In all cases except non-competitive inhibition, Ki ≠ IC50, and IC50 is substrate- dependent.
(Non-competitive inhibition is the 'fluky' one where it just so happens that the catalytic constant and the specificity constant (kfcat / KSm) are changed to the same extent or, to put it another way, the slope and intercept of a Lineweaver-Burk plot (it just so happens) are changed to the same extent)
For an uncompetitive inhibitor (as stated) the IC50 only equals Ki at high substrate concentration (see Naqui, 1982).
Like the case of competitive activation, IC50 equals Ki for a competitive inhibitor only at low susbstrate concentrations (see Naqui, 1982).
'Mixed' inhibition is even more complex, and the inhibition constant may be greater than or less than IC50 depending on experimental conditons (see Naqui, 1982).
Great question, BTW.
As I have derived the full form of the rate law (as opposed to the initial-rate law), it is probably worth posting it. The initial-rate law is obtained from this equation by setting [P] equal to zero.
Kinetic Constants defined in terms of Rate Contants
Rate constants are numbered (as subscripts) from species, to species, with numbering as in diagram.
Thus the rate constant k1,2 is that from E (species 1) to EA (species 2).
Kinetic Constant Definition
νi the initial velocity
KSm the Michaelis Constant for S
KPm the Michaelis Constant for P
kfcat the catalytic constant (in the forward direction)
krcat the catalytic constant (in the reverse direction)
Vmax the maximum velocity, equal to kfcat eo
eo the total enzyme concentration
KA the dissociation constant for (activator), equal to k2,1 / k1,2, with units of concentration (Molarity, say) [rate constants are numbered from species, to species, numbering as in diagram].
νiexc the initial velocity when A is in excess ([A] = ∞).
EC50 the concencentration of A that gives νi equal to νiexc / 2 (half-maximal activation)
[A] The initial concentration of activator.
- [S] The initial concentration of substrate.
The rate law and the diagrams were obtained using Mathematica. For Matematica at SE see here
Briggs, G. E. & Haldane, J. B. S. (1925). A note on the kinetics of enzyme action. Biochem. J. 19, 338 - 339.[pdf]
Chou, T.C. (1974) Relationships between inhibition constants and fractional inhibition in enzyme-catalyzed reactions with different numbers of reactants, different reaction mechanisms, and different types and mechanisms of inhibition. Mol. Pharmacol., 10, 235-247 [pubmed]
Cornish-Bowden, A. (2004). Fundamentals of Enzyme Kinetics. 3rd edn. Portland Press Ltd, London.
King, E. L. & Altman, C. (1956). A schematic method of deriving the rate laws for enzyme-catalyzed reactions. J. Phys. Chem. 60, 1375 - 1378. [ACS site]
Naqui, A. (1982). What does I50 mean? (1983) Biochem. J. 215, 429-430 [pdf]
Segel, I. H. (1975). Enzyme Kinetics. Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. John Wiley & Sons, Inc., New York.
Tsou, C. L. (1987) The screening of enzyme-targeted drugs. Bioessays, 6, 237-238. [pubmed]