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Ligand-binding assays: IC50, EC50 and Kd

Ligand-binding assays: IC50, EC50 and Kd


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I am reviewing several MHC-peptide binding affinity predictors trained on IEDB data. Quantitative records for MHC class I allotypes come from a lot of different assays and, by extension, have different measurement types. Here are the most common measurement type descriptions (I haven't altered them in any way):

  1. dissociation constant KD (~IC50)
  2. dissociation constant KD (~EC50)
  3. half maximal inhibitory concentration (IC50)
  4. dissociation constant KD
  5. half maximal effective concentration (EC50)

All of the predictors I've reviewed so far consider these measurement types interchangeable, which I find extremely odd. While IC50 and EC50 can indeed be similar under certain experimental circumstances, I find it hard to believe that any one of these can be approximately equal to Kd (this site already has a post on this matter). I've contacted several authors and database curators, and all of them have assured me that these values can indeed be considered more-or-less interchangeable, but I can't find any references to support these claims.


A Guide to Simple and Informative Binding Assays

The aim of binding assays is to measure interactions between two molecules, such as a protein binding another protein, a small molecule, or a nucleic acid. Hard work is required to prepare reagents, but flaws in the design of many binding experiments limit the information obtained. In particular many experiments fail to measure the affinity of the reactants for each other. This essay describes simple methods to get the most out of valuable reagents in binding experiments.


Abstract

A new web-server tool estimates Ki values from experimentally determined IC50 values for inhibitors of enzymes and of binding reactions between macromolecules (e.g. proteins, polynucleic acids) and ligands. This converter was developed to enable end users to help gauge the quality of the underlying assumptions used in these calculations which depend on the type of mechanism of inhibitor action and the concentrations of the interacting molecular species. Additional calculations are performed for nonclassical, tightly bound inhibitors of enzyme-substrate or of macromolecule-ligand systems in which free, rather than total concentrations of the reacting species are required. Required user-defined input values include the total enzyme (or another target molecule) and substrate (or ligand) concentrations, the Km of the enzyme-substrate (or the Kd of the target-ligand) reaction, and the IC50 value. Assumptions and caveats for these calculations are discussed along with examples taken from the literature. The host database for this converter contains kinetic constants and other data for inhibitors of the proteolytic clostridial neurotoxins (http://botdb.abcc.ncifcrf.gov/toxin/kiConverter.jsp).


Non-linear regression analysis

The complexity of biological systems results in a non-linear dose-response relationship requiring consideration of multiple parameters during analysis. Dose-response analysis is a type of curve-fitting analysis that uses non-linear regression&mdashan iterative mathematical model that fits your data and considers these parameters&mdashto accurately characterize the dose-response relationship.

Nonlinear regression can determine a drug&rsquos potency (EC50 or IC50), find best-fit values, compare results from different experiments and interpolate unknowns from a standard curve. For example, you can study the effect of treating cells with an agonist in the presence and absence of an antagonist (an inhibitor) as seen below.

However, this analysis has multiple assumptions and limitations.

Assumptions of non-linear regression

The exact value of X is known. Y values are the only values that have errors (scatter).

Variability of Y values at X follows Gaussian bell-shaped distribution.

Uniform variance: The amount of scatter (standard deviation) is the same along the curve. Try weighting tools in Prism to resolve non-uniform variance.

All observations (Y values) are independent (3).

Limitations

Biological systems are very complex and non-linear regression analysis may not fully characterize the dose-response relationship. For example, EC50 may be determined by both the affinity and the efficacy of the drug. Prism offers various tools to determine affinity and efficacy.

o The affinity is how well the drug binds to the receptor.

o The efficacy is the ability of the drug to evoke a response once bound. Efficacy can vary widely.

The results may vary depending on the concentration range and cell/tissue type being used.

The initial values of the parameters used also affects the analysis and may need constraining to increase analysis quality.


What is a “good” binding affinity for a drug?

If you’ve spent any time looking at biotech company presentations you’ll likely have come across a slide like the below, from cancer drug developers Mirati, which nicely summarizes the activity, potency and selectivity of their KRAS inhibitor MRTX-849 [1] .

The objective of this post is to review the concepts represented in the Mirati slide above (binding affinity and how it relates to potency and selectivity) and to provide some intuition as to what “good looks like” for these parameters. I’d also like to put together a reference for people without a strong background in pharmacology who nevertheless want to understand data presentations like this one.

For those who just want the quick summary: a binding affinity of less than 10nm (in terms of Kd / Ki / EC50 / IC50) is generally considered “good”, but behind that value is a tricky balancing act that involves optimizing many other attributes of a drug like selectivity, solubility and molecular weight to ensure that patients are able to benefit from a drug that is effective, minimally toxic and without overly burdensome dosing requirements.

What is binding affinity?

Binding affinity is a measure of the strength of an interaction between a ligand molecule (i.e. a drug) and the target that it binds (often a protein a receptor, enzyme, cytokine, etc.).

In the simplistic “lock and key” model, binding affinity reflects how well a drug “key” fits into its target “lock”. Intuitively, per the model, tight binding results from a close match of the “lock” and “key” shapes, as snug complexes are more energetically favourable than loosely bound ones. In reality, proteins and other large biological molecules are floppy and dynamic structures without rigid “locks”, but the analogy is useful regardless.

Generally, binding affinity is measured in terms of the dissociation constant (Kd) and is expressed in molar concentration. The dissociation constant is a measure of the ratio of unbound (dissociated) ligands to bound ligands at equilibrium. The lower the value of Kd, the stronger the binding affinity. You may also see this ratio referred to as the inhibition constant (Ki) in the context of an inhibitory drug, which is essentially the same thing as the dissociation constant. For an overview of methods to measure Kd, see the Wikipedia article on ligand binding assays.

An equation for a general reversible chemical reaction at equilibrium involving two molecules, A and B, and a complex of the two, AB can be expressed as:

The dissociation constant is then calculated by measuring the concentrations of the various molecules at equilibrium and plugging the values into the below formula

For our purposes, A could represent a drug, B its target receptor and AB the bound drug-receptor complex. The square brackets mean concentration. x and y represent the number of molecules of A and B involved in each instance of the reaction, respectively. The lower the Kd, the more molecules of the drug (A) are bound to its target (B), and hence the tighter the binding. When measuring Kd, it is important that the reaction be given sufficient time to properly equilibrate before measuring concentrations, or the Kd may be overestimated [2] .

When x=1 and y=1 (as is often the case in biology and pharmacology, e.g. when a single molecule of a drug binds a single receptor site), Kd is equal to the concentration of A at which A has bound half the molecules of B up into the AB complex at equilibrium (i.e. the concentration of B is equal to the concentration of AB). Per the below calculation:

Another way of calculating Kd is by taking the ratio of the rate constant for the forward (binding) reaction (kon) divided by the rate constant of the backwards (dissociation) reaction (koff).

However, the values of kon and koff are rarely determined in practice and you cannot draw firm conclusions about the duration of binding from Kd alone [3] . Although in general, a higher binding affinity will result in the drug spending a higher proportion time bound to the target than not.

The binding affinity is also related to the “fractional occupancy” of a drug i.e. the percent of a target bound by a drug, calculated with the following equation:

Fractional occupancy is useful because biological activity of a drug is often dependent on its ability to bind a large percent of available targets. From the equation, you can see that the Kd is particularly important at low concentrations of a drug ([A]) a drug with a very low Kd can have high fractional occupancy even at low concentrations.

While binding affinity tells you how tightly a drug binds its target, it is not the same thing as biological “potency” or “activity”. These concepts are typically expressed using the following measures, which are more widely used in practice to screen drug compounds than Kd or Ki:

  • The half maximal inhibitory concentration (IC50), which is the concentration of a drug at which the activity of its target (e.g. an enzyme) is reduced to 50% of its maximum activity. Drugs that inhibit the activity of their target are called “antagonists”
  • The half maximal effective concentration (EC50), which is the concentration of a drug that induces a response in its target that is 50% of the maximum possible response. Response being a measure of the biological activity of the target, such as the rate of an enzymatic reaction. Drugs that activate their targets are called “agonists”. Inverse agonists are drugs that cause an opposite biological response to what an agonist would cause

While EC50 and IC50 are not formally measures of binding affinity, you may see them informally referred to as such – and it is true that a lower EC50 / IC50 implies a lower Kd / Ki, all else being equal.

The values of the EC50 / IC50 are usually higher than the Kd / Ki values, but they can be the same under certain conditions (e.g. non-competitive binding). For mathematically inclined readers, this paper is a nice overview of how the Ki relates mathematically to the IC50 under various conditions

To roughly illustrate the relationship, I’ve plotted Ki vs. IC50 for a subset of small molecule drug-like compounds in BindingDB below – clearly there’s no simple linear conversion from one to the other:

Although the graph above has some examples of drugs with a higher Ki value than IC50, theoretically, the Kd / Ki values should not be lower than the EC50 / IC50 due to a mathematical relationship known as the Cheng-Prusoff relationship. However, in practice IC50 can sometimes be lower than Ki in the case of non-steady-state reactions [4] or experimental error.

Why are EC50 / IC50 values generally larger than the binding affinity?

I previously mentioned that the values of the EC50 / IC50 are usually higher than the Kd / Ki values. So binding affinity is not the same as biological activity. This could be for a few potential reasons:

  • In cases where a drug is competing for a binding site with other molecules (such as the natural ligand of a receptor) the values of EC50 / IC50 vary depending on the concentration of the other molecules. This is because an excess of the drug is required to outcompete other molecules for the binding site [5]
  • The binding site may only become accessible under a rare or transient state of the target, and a high concentration of drug may be needed so there is enough drug “ready” to effectively bind and modulate the activity of the target in the brief periods when it is possible to do so [5]
  • Not all binding is converted into biological activity

That last point is worth expanding on, while full agonists maximally activate their target, partial agonists only elicit a sub-maximal response, regardless of their concentration. Below is a nice simple graph from Wikipedia’s article on ligands that well illustrates this concept.

Partial agonists can be desirable in instances where maximal activation of the target is associated with toxicity or would lead to receptor desensitization [6] .

Inhibitors either directly bind to the active sites of their targets and block the binding of the natural ligands (competitive inhibition) or bind elsewhere on the target and inhibit activity indirectly through inducing a change in the conformation of the target or stabilizing a particular conformation (allosteric or non-competitive inhibition). Allosteric or non-competitive inhibitors may exhibit partial inhibition despite a high binding affinity, by reducing the effectiveness of their target without eliminating activity entirely.

What target affinity do drug developers aim for?

When embarking on a drug discovery program, companies will screen libraries of compounds [7] using a particular assay and measure binding affinity/potency for each, progressing the highest potency “hits” for further development. The assays to measure potency have a variety of potential designs, depending on the biological function of the target. In the Mirati example at the beginning of this post, they measured activity (IC50) by determining the level of MRTX-849 required to half-maximally inhibit the proliferation of cancer cell lines carrying the target mutation (KRAS G12C).

As a general heuristic, small molecule drug developers want to achieve an affinity of less than 10nM for their drugs. The specific cut-off is somewhat arbitrary, but the range below 10nM Kd / Ki / EC50 / IC50 is historically where many effective drug compounds have ended up and is low enough to for drug developers to be confident that they are sufficiently engaging the desired target. To quote Derek Lowe: [8]

The lower [the IC50], the better, other things being equal. Most drugs are down in the nanomolar range – below that are the ulta-potent picomolar and femtomolar ranges, where few compounds venture. And above that, once you get up to 1000 nanomolar, is micromolar, and then 1000 micromolar is one millimolar. By traditional med-chem standards:

  • Single-digit nanomolar = good
  • Double-digit nanomolar = not bad
  • Triple-digit nanomolar or low micromolar = starting point to make something better
  • High micromolar = ignore
  • Millimolar = can do better with stuff off the bottom of your shoe

This is nicely demonstrated by the below slide from Mirati’s presentation at AACR in October 2019 [9] , where they outline the modifications made to their starter compound to increase potency and get to their eventual lead compound, MRTX849:

However, compared to small molecules, so-called “biologic” therapeutic modalities can have extremely strong binding affinities at the upper end of what is feasible with small molecules – a feature that has helped make this class of drugs so effective and generally safe. For example:

    Monoclonal antibodies typically have binding affinities in the low picomolar range, with a reported median around 70pM [10] . For example, the megablockbuster anti-TNF monoclonal antibody Humira has a measured Kd at 8.6pM [11] Kd for a perfectly matched target is

So while 10nM may be sufficient for a small molecule, antibody drug developers may expect a bit more from their lead candidates before progressing it into clinical development.

What other related metrics are potentially important apart from affinity, activity and potency?

Going from initial hit to a final drug often involves making trade-offs in the various attributes of a molecule optimizing for binding affinity over all else could result in an overall sub-optimal drug. To quote an article by J. Singh: [15]

A major challenge in drug discovery is achieving high potency and selectivity in a compound without increasing its molecular mass to the point at which beneficial pharmaceutical properties are jeopardized

I’ve picked a few additional metrics to cover in this post selectivity, ligand efficiency and covalent binding.

Selectivity:

Selectivity, the propensity of a drug to bind one target over another, is a critical attribute of a drug to manage. Drugs that are “highly selective” have a high binding affinity to the primary target, and low binding affinity with undesirable target, and this is what Mirati is illustrating on the right hand side of their slide at the beginning of the post. It may be desirable for compounds to bind multiple targets if there are multiple pathways that contribute to a disease. Many approved drugs bind multiple related proteins, such as the JAK inhibitors and other pan-kinase inhibitors.

Cranking up the binding affinity for the primary target as high as possible may also increase its propensity to bind “off-target”, resulting in toxicity. As such, there can be a sort of “Goldilocks zone” for binding affinity that is influenced by the biological context in which the drug is intended to be used. A key way in which drug developers will test their drug candidate is by counterscreening against a library of targets associated with toxicity e.g. hERG (“antitargets”) to check that their drug does not bind too well to these “antitargets”.

Ligand efficiency:

Another metric drug developers are likely to look at is ligand efficiency, a measure of the binding affinity achieved for the molecular weight of the compound. Lower molecular weights are generally preferable, as bigger drugs are less soluble and harder to get into the target cells. Lipinski’s famous “Rule of five” heuristic calls for a molecular weight of less that 500 daltons, although lately more and more big oral drugs have come to market – oral semaglutide being a particularly good example.

Covalent binding

Most drugs bind reversibly to their target. MRTX-849 is actually a targeted covalent inhibitor, meaning that it forms (potentially irreversible) chemical bonds with its target. Drug developers were historically reluctant to pursue covalent drugs systematically due to concerns over toxicity and off-target reactivity, but there has been something of a resurgence lately spurred by the success of drugs like ibrutinib. To quote J. Singh again: [15]

Inhibitors that rely on covalent bonding dramatically favour the bound form, which leads to potencies and ligand efficiencies that are either exceptionally high or, for irreversible covalent interactions, even essentially infinite. Covalent bonding thus allows high potency to be routinely achieved in compounds of low molecular mass, along with all the beneficial pharmaceutical properties that are associated with small size

Calculation of affinity for covalent inhibitors is approached differently that for non-covalent inhibitors, as the reactions are not reversible. The IC50 is theoretically of limited value because of the influence of reaction time on the value – however, Mirati has still chosen to report it.

Other considerations

When designing a drug that will bind competitively it is also important to consider the relative affinity of the natural ligand for the target versus the drug’s, as strongly binding natural ligands will be harder to displace and may require especially high binding affinities.

Other factors that may be important include the shape and steepness of the dose-response curve (related to width of the therapeutic window), cell to cell variability within a screening assay sample [16] , reaction kinetics and ligand binding thermodynamics [17] .


We deliver full biochemical and biophysical characterization of ligand-target interactions for even the most challenging drug discovery projects through the application of the RIGHT technologies and the RIGHT assays.

Proteros screening platform enables insight into various mode of inhibitions :

  • Allosteric inhibitor screening
  • Protein-Protein-Interaction inhibitors and enhancers
  • High-throughput binding affinity and residence time quantification
  • Deconvolution of non-covalent and covalent binding contribution

Proteros opens avenues towards kinetically optimized drug candidates with increased efficacy and selectivity.


HSPMdb: a computational repository of heat shock protein modulators

Heat shock proteins (Hsp) are among highly conserved proteins across all domains of life. Though originally discovered as a cellular response to stress, these proteins are also involved in a wide range of cellular functions such as protein refolding, protein trafficking and cellular signalling. A large number of potential Hsp modulators are under clinical trials against various human diseases. As the number of modulators targeting Hsps is growing, there is a need to develop a comprehensive knowledge repository of these findings which is largely scattered. We have thus developed a web-accessible database, HSPMdb, which is a first of its kind manually curated repository of experimentally validated Hsp modulators (activators and inhibitors). The data was collected from 176 research articles and current version of HSPMdb holds 10 223 entries of compounds that are known to modulate activities of five major Hsps (Hsp100, Hsp90, Hsp70, Hsp60 and Hsp40) originated from 15 different organisms (i.e. human, yeast, bacteria, virus, mouse, rat, bovine, porcine, canine, chicken, Trypanosoma brucei and Plasmodium falciparum). HSPMdb provides comprehensive information on biological activities as well as the chemical properties of Hsp modulators. The biological activities of modulators are presented as enzymatic activity and cellular activity. Under the enzymatic activity field, parameters such as IC50, EC50, DC50, Ki and KD have been provided. In the cellular activity field, complete information on cellular activities (percentage cell growth inhibition, EC50 and GI50), type of cell viability assays and cell line used has been provided. One of the important features of HSPMdb is that it allows users to screen whether or not their compound of interest has any similarity with the previously known Hsp modulators. We anticipate that HSPMdb would become a valuable resource for the broader scientific community working in the area of chaperone biology and protein misfolding diseases. HSPMdb is freely accessible at http://bioinfo.imtech.res.in/bvs/hspmdb/index.php.

© The Author(s) 2020. Published by Oxford University Press.

Figures

Schematic representation of browsing page…

Schematic representation of browsing page of HSPMdb.

Total number of entries in…

Total number of entries in HSPMdb based upon origin of Hsps ( A…

Different scaffolds/classes of modulators targeting…

Different scaffolds/classes of modulators targeting Hsp70 ( A ), Hsp90 ( B ),…


Explanation

If clinicians have not already started to encounter Ki's in the literature and product package inserts for medications, they will likely encounter them in the future.1-3 The Ki, in part, becomes important for helping to predict clinically relevant drug interactions.1,3 Simply stated, the inhibitory constant (Ki) and the half maximal inhibitory concentration (IC50) of a drug that is known to cause inhibition of a cytochrome P450 (CYP) enzyme have to do with the concentration needed to reduce the activity of that enzyme by half. More specifically the Ki is reflective of the binding affinity and the IC50 is more reflective of the functional strength of the inhibitor, but both factor in the concentration of drug present to inhibit the enzyme activity. Of note, for drugs that are noncompetitive inhibitors of CYP enzymes, the Ki of a drug is essentially the same numerical value as the IC50's numerical value, whereas for competitive and uncompetitive inhibition the Ki is about one-half that of the IC50.3 Therefore, the smaller the Ki, the smaller amount of medication needed in order to inhibit the activity of that enzyme.

If a Ki is much larger than the maximal plasma drug concentrations a patient is exposed to from typical dosing, then that drug is not likely to inhibit the activity of that enzyme. This effect can also be reflected in the [I]/Ki ratio.1 A clinically relevant example of this can be seen by evaluating the Ki for proton pump inhibitors (PPIs) on cytochrome P-450 (CYP) 3A4 enzyme.4 In this example, the Ki's are significantly higher for most PPIs (42 to 51 mM) than their respective maximum concentrations (1 to 5.2 mM) in patients who are either extensive metabolizers or poor metabolizers of 2C219.4-9 Because the Ki's for PPIs is so much greater than the maximal drug concentrations seen with typical dosing, most PPIs are not likely to inhibit the activity of CYP3A4.

It is also important to recognize when interpreting or when reviewing the Ki for a particular medication that a few factors are known to influence the value obtained from a study. Those factors include specificity of the substrate, the binding components in the incubation system and any substrate or inhibitor depletion.1 As it relates to the incubation system, depending on the biologic system used, the Ki can fluctuate resulting in a range for the Ki.4,10

Therefore, the use of the Ki is helpful in designating the likelihood that a particular medication is going to inhibit a particular enzyme and result in a clinically relevant drug interaction with a substrate for the enzyme. In many cases, the evaluation of the Ki in relation to the concentration of the inhibitor present in the body has already been done and is used as the basis for programs or certain drug information sources to report a particular medication as an inhibitor or not. It is equally important for clinicians to also recognize that all medications may or may not have been fully evaluated depending upon their arrival into the market. In such cases or situations, when trying to discern the likelihood of a drug interaction occurring between coadministered medications, clinicians may need to resort to this method of evaluation.


Ligand-binding assays: IC50, EC50 and Kd - Biology

Background A key barrier to effective immunotherapy for cancer is the immunosuppressive tumor microenvironment (TME) characterized by infiltrating regulatory T cells (Tregs) and myeloid-derived suppressor cells (MDSC). While depletion of immune-suppressive cells is a promising cancer immunotherapy strategy, current approaches are ineffective due to lack of specificity and safety concerns. Tumor Necrosis Factor Receptor 2 (TNFR2) is emerging as a novel, selective target to overcome immunosuppression in TME. TNFR2 expression is generally restricted to highly immunosuppressive cell populations in the TME and the TNFR2-TNF-α pathway plays an important role in the generation and survival of these cells. TNFR2 is also an oncogene upregulated on certain tumors and can enhance tumor cell survival. Thus, targeting TNFR2 is a promising therapeutic approach with multiple potential mechanisms of action.

Methods A diverse panel of antibodies to TNFR2 was created using APXiMAB™, Apexigen’s proprietary rabbit monoclonal antibody technology. A robust assessment of over 100 antibody candidates for TNFR2 binding, TNF-α blockade and functional assays yielded APX601, a humanized IgG1 antibody, as the lead therapeutic candidate. The ability of APX601 to reverse immune suppression was assessed in Treg and MDSC suppression assays. In addition, the ability of APX601 to deplete TNFR2-expressing Treg and tumor cells was assessed both in vitro and in vivo using the mouse Colo205 xenograft model.

Results APX601 binds specifically to human TNFR2 with high affinity (Kd = 47 pM) and recognizes a unique epitope in the CRD1 domain of TNFR2. APX601 is a potent antagonist that blocks the TNFR2-TNF-α interaction in cell-based ligand binding assays (IC50 = 0.149 nM). APX601 is capable of reversing immune suppression via two mechanisms: 1) significant blockade of the immunosuppressive functions of both Tregs and MDSCs by inhibiting the binding of TNFR2 to its ligand TNF-α and 2) depletion of TNFR2-expressing Tregs, MDSC and tumor cells via antibody-dependent cell cytotoxicity (ADCC) (EC50 = 1.14 nM) and ADCP (EC50 = 0.71 nM) effector functions.

Conclusions APX601 is a potent TNFR2 antagonist antibody that reverses immune suppression by targeting TNFR2-expressing Treg and MDSC, and induces killing of tumor cells. Our data support the further development of APX601, a promising immunotherapeutic antibody with multiple potential mechanisms of action, for the treatment of a variety of solid tumors.

Ethics Approval Healthy human blood samples were obtained from Stanford Blood Center (Palo Alto, CA) from consenting donors under an approved protocol.


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Watch the video: Example of non linear regression dose response data in GraphPad Prism (July 2022).


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