Hi Ryan, I applaud your efforts to simplify kinetic analysis. As for your question, in my experience there are a lot of challenges facing attempts to develop drugs, to put it mildly, and improper enzyme kinetic models are probably not among the most important. (Even so, that doesn't excuse drug discovery scientists from applying enzyme kinetics incorrectly.)

HI Adam 

The use of incorrectly applied kinetic equations has lead to the acceptance of ic50 values by funding institutions, regulatory bodies and industry.  While there are a lot of additional things to deal with in the development of drug candidates the assumption that all biology functions in an on off ic50 is both detrimental to our understanding of biology and our ability to develop interventions in disease.  

Disregarding the complexity of enzyme kinetic interactions at the molecular, cellular or physiological level is is hindering our ability to generate rational models of disease processes and wasting huge amounts research funding. 

So I would have to disagree with your statement that improper kinetic models are not among the most important problems facing drug development.  

I'm assume AstraZeneca only asks you to look to generate ic50s as thats all the FDA requires?

Hi Ryan,

One thing I can definitely agree with you about is that the IC50 is often an inappropriate measurement of compound potency. You bring up some deep reasons for it, but I would like to focus only on one relatively straightforward problem in the application of IC50s to in vitro assays.

The use of an IC50 (as a proxy for Ki) as a measurement of inhibitor potency is based on the assumption that the system is in equilibrium on the time scale of the measurement. Unfortunately, this is not always true. Non-covalent inhibitors may be slow binding and take minutes to hours to reach equilibrium. Covalent inhibitors are never at equilibrium. The potencies of such compounds depend upon the length of time with which they have been in contact with the target. Of course, one can standardize the amount of time in order to be able to rank-order compound potencies, but the IC50s themselves will bear an unknown relationship to the affinities of the compounds.

There are many drugs that are covalent inhibitors, and the mathematical treatment of them is well-established: their potencies can be expressed in terms of second-order inactivation rate constants. There is also a well-known treatment of slow-binding inhibitors. The throughput of IC50 measurements is a lot higher than the throughput of measurements of inactivation rate constants or slow-binding kinetic constants, which is probably why people prefer to make IC50 measurements, but the IC50 is not the right tool for the job.

To put this into perspective, however, biochemical measurements of potency play their most active role early in the discovery phase (target validation and lead generation). Once sufficiently potent inhibitors are identified, cellular assays of potency and validation of in vivo, ex vivo, or cellular mode of action; physical properties (solubility, plasma protein binding); and pharmacokinetic considerations outweigh IC50s as drivers of project progression. 

Hi Adam

To refocus this as we are in agreement that ic50s are bad.

The complexity associated with biology that ic50s obscure in their application to in vitro molecular studies or cellular based studies does not disappear in the the full organism. If anything it becomes more complex.

While you may want to avoid my question about ic50 use at AstraZeneca with reference to covalent inhibition  which isn't the focus of this post, but if you read my book chapter I would have to disagree with your assessment that the mathematical treatment of covalent inhibitors is well-established as well.  

So back to your perspective I agree measurement of biochemical potency is the most important at early stages as it has to be based on understanding of the biological processes.  However this process has turned into an ic50 based hunt for inhibitors with "sufficient potency" because the tools for assessing the molecular interactions are missing, the point of this post. 

But since these tools are missing pharmaceutical companies are chasing down poor drug candidates like secretase inhibitors in Alzheimer's disease which when evaluated with ic50s and found to have "sufficient potency" have wasted years of research and not produced one viable drug in Alzheimer's disease. How is BACE inhibitor AZD3293 working out for AstraZeneca?

Hi Ryan, do your equations distinguish covalent inhibition of an enzyme from competitive inhibition of an enzyme?

Hi Steingrimur

As most of the noncovalent inhibitor equations are representations of steady state approximations, (ie not incorporating time course kinetics), the usual way data is gathered to fit noncovalent inhibition equations discards time course information focusing on initial rates.  

This sort of treatment of the data is related to the work that produced the initial understandings of how enzymes worked which was done without computers.  So most fitting was achieved using linear transformations of initial enzymatic reaction rates (LWB plots).  The initial enzymatic rates themselves were usually generated by choosing concentrations of substrate that produced rates of change over the observed time periods. The rates of change that were being measured then and are still measured today are not linear however they are exponential, as any decrease of a compound in a fixed volume has to be exponential if more of the compound is not added to replace what is being consumed.  

Therefore the MM equation does not describe steady state approximations but the rates associated with the exponential decrease of substrate in a fixed volume.  This means that the MM equation can be used as is to describe the time course decrease of substrate during a reaction.  

That is the regular exponential decay equation  

[S]t = [S]o  e^-kt

can be rewritten to combined the constants "e" and "-k" to make an equation where these values are represented by one constant (i'll use big K). 

[S]t = [S]o K^t

Where K is a number less than 1 because the substrate is being used up and it is equal to the fraction of the substrate left after the first time interval of the reaction t=1.

The amount of substrate converted into product by the enzyme is defined by the MM equation so K can easily be replaced with the MM equation once the amount of substrate consumed by the MM equation is equated to the initial substrate concentration.

K =(1-(MM/[S]o))

So using this line of reasoning all of my equations can be inserted into the K term and modeled using full time coarse analysis.  Working on this allowed me to determine that imidazole in addition to being a noncovalent inhibitor also acts as a weak covalent inhibitor of beta-galactasidase (section 4, of the book chapter).

So while the equations I mention above do not need full time course data for analysis they can be adapted to it and the use of full time course data allows the detection and characterization of covalent interactions that may be missed using just initial rates.

However most covalent interactions are quite blunt and are described using Ka values that are generated at one substrate concentration because the reactions are fast occurring at speeds comparable or faster than substrate catalysis so noncovalent components are generally ignored in those cases.