The Science Snail
  • Home
  • Science
  • Philosophy
  • About
  • Contact
  • Privacy Policy

The difference between Ki, Kd, IC50, and EC50 values

12/31/2019

10 Comments

 
In biochemistry and pharmacology, a variety of parameters are reported as measures of the potency of enzyme inhibitors/drugs, including Ki, Kd, IC50, and EC50. Though related, their definitions greatly differ. In this article, I highlight the meaning and significance of each term, with emphasis on their disambiguation and appropriate usage.

Ki vs Kd

Ki refers to inhibition constant, while Kd means dissociation constant. Both terms are used to describe the binding affinity that a small molecule or macromolecule has for an enzyme or receptor. The difference is that Kd is a more general, all-encompassing term. As discussed in my article on the difference between Km and Kd, Kd measures the equilibrium between the ligand-protein complex and the dissociated components.
Definition of dissociation constant, Kd
Where [P] is the free protein concentration, [L] is the free ligand concentration, [PL] is the protein-ligand complex, k-1 is the dissociation rate constant for the complex and k1 is the association rate constant.

The Ki inhibition constant also represents a dissociation constant, but more narrowly for the binding of an inhibitor to an enzyme. That is, a ligand whose binding reduces the catalytic activity of the enzyme. The binding equilibrium described by the Ki value depends on the kinetic mechanism of inhibition. Common options include competitive, uncompetitive, non-competitive, and mixed inhibition. I define the equilibria for each below. 
Kinetic schemes for enzyme inhibition: competitive, uncompetitive, non-compeptitive, and mixed
In competitive inhibition, the inhibitor binds only to free enzyme (E), not to the enzyme-substrate complex (ES). In uncompetitive inhibition, the inhibitor binds only to the enzyme-substrate complex. Mixed inhibition involves inhibitor binding to both free enzyme and enzyme-substrate complex with different binding constants (Ki and αKi). Lastly, non-competitive inhibition is a special case of mixed inhibition where substrate binding has no effect on inhibitor binding (α = 1).

Importantly, Ki values only accurately report a binding constant when the kinetic mechanism is correctly identified. The term ‘Ki’ is used whenever this binding constant is measured through inhibition kinetics, while ‘Kd’ is preferred when the binding is measured more directly (e.g. by fluorescence quenching, isothermal titration calorimetry, or surface plasmon resonance). 

ARTICLE CONTINUES BELOW ADVERTISEMENT

IC50 vs Ki

​IC50 stands for inhibitory concentration 50%. That is, the concentration of inhibitor required to reduce the biological activity of interest to half of the uninhibited value. Because it does not directly measure a binding equilibrium, IC50 is less precise than Ki or Kd. Importantly, the values obtained are highly dependent on the measurement conditions and the mechanism of inhibition. The simplicity and lack of assumptions required to generate these data make them useful. They are particularly convenient for characterizing the in vivo activity of a drug/inhibitor, where the various factors contributing to its potency cannot easily be independently accessed. For instance, the drug's in vivo distribution, cell wall permeability, target engagement, and clearance rate are all contributing factors. To measure IC50 values, dose-response curves are measured and fit to the following equation:
IC50 dose response equation
Where R is the response (fraction of the biological activity that has been inhibited), [I] is the inhibitor concentration and n is the Hill coefficient (a parameter which describes how steep the curve is).

IC50 values are also used for quick comparison of the in vitro activity of enzyme inhibitors. Despite their ease of measurement, this use case carries certain limitations and caveats. Meaningful comparison of IC50 values can be challenging, especially when an inhibitor’s mechanism is unknown or the experimental details are not reported in sufficient detail. IC50 values are highly dependent on the substrate concentration, with the nature of this dependence being determined by the inhibition mechanism. To demonstrate this, I show how IC50 and Ki are related for related for the common inhibition types.
 
First, I review how IC50 equations are derived from initial velocity equations, taking competitive inhibition as an example. An enzymatic reaction’s initial velocity under competitive inhibition (vi) is given by:
Initial velocity equation for competitive inhibition
Where Vmax is the maximum velocity ([E]T*kcat), [S] is the substrate concentration, and Km is the Michaelis constant. Without any competitive inhibitor, the initial velocity (v0) simplifies to typical Michaelis-Menten kinetics: 
Michaelis-Menten equation
The IC50 concentration is reached when the ratio of the inhibited to the uninhibited reaction rate is 50%:
Deriving IC50 equation for competitive inhibition
Solving for IC50, we obtain:
IC50 equation for competitive inhibition
Using this strategy, it is possible to derive IC50 equations for any kinetic scheme of enzyme inhibition. I show the results of this for the common types of enzyme inhibition in the table below.
IC50 equations for competitive, uncompetitive, non-competitive, and mixed inhibitors
To view these relations graphically, I plot them supposing Km = Ki = 1 and α = 0.1:
IC50 values as a function of substrate concentration for each inhibition mechanism
Interestingly, non-competitive inhibition yields an IC50 value independent of substrate concentration. However, competitive inhibition IC50 values increase with increasing substrate concentration, while uncompetitive and mixed inhibition IC50 values decrease. Based on these dependencies, it is important to consider the substrate concentration and likely mechanism of inhibition when interpreting IC50 values. Where possible, this information should be reported alongside such data.
 
As a final caveat, another complication with IC50 values comes in the case of “tight binding” inhibitors, where the enzyme concentration affects the apparent value. This problem arises when the formation of enzyme-inhibitor complex appreciably depletes the concentration of free inhibitor (specifically, when Ki < [E]T).  In these situations, a correction can be applied to account for the effect of this on the IC50 value.

IC50 vs EC50

I conclude with a discussion of EC50, effective concentration 50%. This refers to the concentration of drug at which 50% of its maximum effect is achieved. The term is quite general, applying regardless of whether the drug enhances or diminishes the biological parameter. Its equation is a modified version of the IC50 equation, taking the ratio of the response (R) to the maximum response (Rmax):
EC50 equation
In cases where a drug completely inhibits a biological activity at high dose, the values of EC50 and IC50 are identical (where Rmax = 100%). However, some drugs give only partial attenuation of a biological activity, even at high concentrations. In this case, IC50 values may be misleading about the potency of the drug. For instance, suppose an inhibitor reduces an enzyme’s activity to, at most, 60%. Here the IC50 value would be undefined, as 50% inhibition is never reached. Using EC50 values allows the dose-response of such drugs to be quantified and reported. In pharmacology, the concepts of drug potency and efficacy are worth examining in relation to IC50 and EC50 values. Potency refers to how much drug it takes to have maximum biological effect, while efficacy describes how large the effect size is. Therefore, potent drugs have low EC50 values but not necessarily low IC50 values. Furthermore, efficacious drugs have more similar IC50 and EC50 values than less efficacious drugs.

EC50 values are commonly used for in vivo measurements made on cells or animals; incomplete inhibition of a phenotype is often seen in complex biological systems. In principle though, this nomenclature can also be used for comparing the in vitro activity of partial enzyme inhibitors. As an example, consider a partial non-competitive inhibitor. 
Partial non-competitive inhibitor kinetic scheme
In this inhibition mechanism, binding of the inhibitor results in a decreased, but non-zero turnover rate of enzyme-substrate complex (0 < k’cat < kcat). To illustrate the difference between EC50 and IC50, I derive equations for both. For this kinetic scheme, the ratio of the inhibited to the uninhibited initial rate is:
Partial non-competitive inhibition equation
The IC50 value is the concentration at which this ratio is reduced to 50%:
Deriving IC50 equation for partial enzyme inhibitor
IC50 is not only a function of inhibitor binding affinity (Ki), but also on the relative amount of residual turnover rate of the ESI complex (k’cat). To visually illustrate this, I plot the IC50 equation assuming Ki = 1:
IC50 values increase with the residual activity of enzyme-inhibitor complex
Progressively higher residual activity of the ESI complex (k’cat/kcat ratio) increases the IC50 value. It approaches infinity toward 50% residual activity, above which IC50 is undefined.

​In contrast to IC50 values, EC50 reports on the binding affinity of the inhibitor, regardless of its efficacy. The fraction of enzyme (f) bound by inhibitor is given by:
Langmuir isotherm
The effective concentration 50% is achieved when half of the enzyme is bound:
EC50 equation for partial enzyme inhibitor
Though I’ve only derived equations for the non-competitive partial inhibition case, these trends hold for other inhibition mechanisms. The EC50 values are useful for comparing the relative binding affinities of partial enzyme inhibitors. Furthermore, EC50s are essential where IC50 values can’t be reported due to >50% of the biological activity being retained at maximum response. The main limitation of this parameter is that it offers no information about the efficacy of the drug/inhibitor. Overall, Kd, Ki, IC50, and EC50 values all have important roles in characterizing the biological activity of drugs and enzyme inhibitors. I hope that their differences, uses, and advantages/disadvantages are now clear.


10 Comments
광영
8/3/2020 04:15:50 am

thank you for your article.

Reply
joth ethan link
1/5/2021 04:42:41 am

Journal of Pharmacokinetics & Experimental Therapeutics is an open access journal that focuses on pharmacokinetic properties of drugs, including Absorption, Distribution, Metabolism and Excretion (ADME) while underlining the importance of experimental therapeutics in pharmacokinetic research. Journal of Pharmacokinetics & Experimental Therapeutics accepts manuscripts in clinical pharmacokinetics, population pharmacokinetics, antibody pharmacokinetics, pharmacokinetics review, vancomycin pharmacokinetics, tacrolimus pharmacokinetics, pharmacokinetic drugs, pharmacokinetics intravenous, pharmacokinetics oral, pharmacokinetics renal, pharmacokinetics human, pharmacokinetics rat, pharmacokinetics mice, pharmacokinetics for children, pharmacokinetics research to promote healthy life are welcome.
If your interested can submit your manuscript.
That manuscript should not publish in any other journal pages.
You can submit your manuscript, to the below email id.
Email id: [email protected]
Journal url:
https://www.omicsonline.org/pharmacokinetics-and-experimental-therapeutics.php

Reply
Rea Kalampaliki
1/27/2021 02:15:33 pm

Thank you so much, it is a very clear article.

Reply
Helen
2/16/2021 11:20:30 pm

Does EC50 also work for activators?

Reply
Joh
5/4/2022 04:39:13 pm

Excellent article, very clear the explanation. I am going to use it for my classes. Thanks A LOT!

Reply
Zai
1/23/2023 05:49:06 pm

Thank you so much! I was very confused by all of the these. This is very well written and a tremendous help in my MCAT prep!

Reply
Real Life Pharmacologist
10/24/2023 06:00:39 pm

This is a great article and appreciate the time and effort it took to create it! As a PhD Pharmacologist, I've come across multiple examples of confusion between binding affinity (or Ki value) versus IC50 or EC50 values. I have a few suggestions to help Readers:
First, it would be most helpful if the article stated at the beginning the discussion and equations relate to Enzymes + Inhibitory Substrates.
- This is because 'binding affinity' and 'Ki values' are also reported for ligand and receptor assays, not just enzymes & substrates.
Next, the binding affinity (Ki) is NOT always an 'inhibitory constant'. I recently came across an example where someone took this article to define Ki as an 'inhibitory constant' when in fact they were referring to the binding affinity of an agonist to a GPCR (G-protein coupled receptor)! It would be more correct to state Ki = equilibrium disassociation constant then to try and connect it to the IC50. Read on for explanation.....

Briefly, the difference can be summarized as:
- Ki or binding affinity of a ligand to a receptor is determined from Receptor Binding Assays and calculated from semi-logarithmic plots of ligand concentration versus Percent (%) Receptors Bound.

- EC50 or IC50 values are determined from Dose-Response assays and semi-logarithmic plots of ligand concentration versus % Response, where the 'response' is a predetermined variable that is typically easily measured and an agonist measured up to 100% and an antagonist measured from 100% to 0.

Note this would apply to enzymes and substrates. Determining the affinity or response (activate or inhibit) of an enzyme by a substrate follows the same principles and 2 separate experiments are required.

Pharmacology Example:
A given ligand (L) can act as an Agonist at Receptor A (stimulates a response) and an antagonist at Receptor B (inhibits a response).
The Ki value is the 'equilibrium dissociation constant' of the ligand and receptor A or B in this example, and represents the dissociation constant between the ligand (L) and the receptor (R) *at equilibrium*. A lower Ki value indicates that the ligand (L) is bound to the receptor (R) as the L-R complex for a longer period of time than the ligand is unbound as (L) from (R). The reverse is true with a higher Ki value (e.g. more time spend unbound versus bound to receptor).
In pharmacology, Competition Binding experiments report Ki values, and use a constant concentration of radioactive ligand in the presence increasing concentrations of non-radioactive ligand. In comparison, Saturation Binding experiments report Kd, which also represents the dissociation constant determined at equilibrium between a ligand and receptor, and differ by use of increasing concentrations of the radioactively labeled ligand.

It is important to note that:
- Ki values are typically compared...either between receptors for a given ligand, or between different ligands at the same receptor. Thus when comparing 2 Ki values, the lower Ki value (e.g., Receptor A, Ki = 0.005nM) represents a higher or stronger binding affinity of the ligand for the receptor in question versus a higher Ki value (e.g., Receptor B, Ki = 0.08nM) >> in this example the ligand has a higher affinity for receptor A than receptor B. Note this has nothing to do with the ligand acting as an Agonist or Antagonist!
- The Ki value for a ligand and a receptor is determined from a receptor binding assay and calculated from a semi-logarithmic plot of ligand concentration versus % receptors bound.

The EC50, or Effective Concentration of ligand required to elicit a 50% Response (vs 100%), is determined from a Dose-Response curve generated by an assay that measures the 0-100% response elicited by the ligand acting on Receptor A (agonist).

The IC50, or Inhibitory Concentration of ligand that inhibits 50% of the Response, is determined by an assay that measures the decrease in response when the ligand acts on Receptor B (antagonist) in the presence of a positive control (known to stimulate 100% response), and calculated from the resulting Dose-response curve (another semi-logarithmic graph).

Hopes this helps those who were a bit confused....like the person who thought Ki = inhibitory constant, always. Happy studying!

Reply
Vlad
7/8/2024 01:10:34 pm

The plot too dramatizes the difference for a uncompetitive case: usually [S] >> K_m and IC50 = K_i (1 + 0) = K_i

Hyperbolic relationship between IC50 and K_i is not pronounced in most cases.

Reply
Tori R link
7/29/2024 06:40:22 am

Great post thaankyou

Reply
Syed Jamal
11/2/2024 01:55:15 pm

Very nice article.

Reply



Leave a Reply.

    Archives

    April 2024
    February 2024
    July 2023
    December 2022
    April 2022
    December 2021
    December 2020
    September 2020
    August 2020
    December 2019
    June 2019
    February 2019
    January 2019
    December 2018
    October 2018
    August 2018
    July 2018
    February 2018
    December 2017
    December 2016
    April 2016
    January 2016
    August 2015
    July 2015
    February 2015
    December 2014
    August 2013

    Categories

    All
    Biochemistry
    Biology
    Enzymology
    Finance
    Health
    Mathematics
    Organic Chemistry
    Physical Chemistry

    RSS Feed

    List of all articles

    The Tollens condensation

    How long it takes chemical reactions to reach completion

    Benzocaine synthesis

    Mathematics of compound interest

    Dynamic nuclear polarization in solid state NMR 

    Modelling a multi-state G protein signalling pathway

    Organic synthesis of Aspirin

    Distinguishing enzyme inhibition mechanisms


    ​Metformin total synthesis
    ​
    ​Ki, Kd, IC50, and EC50 values

    ​
    AZT: mechanism and synthesis


    Forecasting website ad revenue

    Km vs Kd

    The relationship between TV screen size and price

    ​Health benefits of green tea

    Synthesis of ibuprofen from benzene

    ​The mechanism of action of Eflornithine
    ​
    Synthesis of sucralose from sucrose


    Diluting a solution to Avogadro's limit
    ​
    The affect of mutation rate on evolutionary equilibrium

    ​
    Organic synthesis of indomethacin


    Probing protein-protein interactions in the yeast glycolytic metabolon

    Time course enzyme kinetics

    A generalized​ model for enzymatic substrate inhibition
    ​
    ​The basis of high thermostability in thermophilic proteins
    ​

    First order drug elimination kinetics
    ​
    Improving the efficiency of protein dialysis: constant dialysate replacement


    Mathematical modelling of evolution

    Calculating the optimum ddNTP:dNTP ratio in Sanger sequencing

    A mathematical model of hair growth

    Life does not violate the second law of thermodynamics


    Collagen and the importance of vitamin C

    Temperatures below absolute zero are surprisingly hot

    The molecular difference between heat and work

    Want to keep up to date with new articles? Subscribe to the monthly newsletter! ​

Subscribe to Newsletter

​© 2024 Copyright The Science Snail. All rights reserved.