







Fig 1. Representation of increasing enzyme activity (food vender business) with increasing substrate (potential customers)









To illustrate how our law of customer density is going to work let's make 100 potential customers, the number of people needed to make half the vendors busy (#50% business = 100). When the street has 100 potential customer hanging around you would divide 100 potential customers by 100 potential customers added to the #50% business value (100). That gives you 100/200 or 50%, very easy stuff.



If you had 1 potential customer on the street there would be very little likelihood (1/101 = less than 1%) of seeing any the food venders doing business and if you had a million potential customers it would be unlikely to see a vender without a customer (1,000,000/1,000,100 = almost 100%) setting the limits of business the food venders can engage in between 0 where no one has a customer and 100% where everyone has a customer.



The curve this equation produces can describe the majority of molecular interactions going on in your body and attempts to modulate this relationship have formed the basis of most medical drug based interventions.



Drugs are generally things that interfere with the job of the enzyme they are targeted to. For the street venders example, let’s use a bus load of tourist as our substitute drug. The tourists in this example are not hungry, but they are looking for directions or information about the area. Not all of the tourists will stop to talk with a food vender but just like customers the higher the density of tourists on the street the better the chance one will be chatting with a food vender, preventing a customer from buying food.



This can be modeled with the exact same relationship used to defining customer and vendor interactions.



To characterize how much the tourists are disrupting buisness it is common practice and easiest to quantify the affect when the venders are busiest (this is also due to the fact researchers are measuring the disappearance of substrate or appearance of product rather than directly measuring the activity of the enzyme).



That is if the bus releases the tourists at lunch time when there are the most potential customers rather than when there are fewer customers, it’s easier to see the disruption they create (Let’s call this the “lunch time rush”). The number of tourists required to slow down business at lunch time by half is then used to quantify the interaction of the tourists with the food venders. This is basically the way IC50 values (inhibition constant 50%) for drug studies are produced. For this example, we could call the interference caused by the touriststhe “interference constant 50%” so IC50 still works.



These values are based on the assumptions that all the venders (enzymes) deal with one customer at a time and the tourists (inhibitors) completely stop the food venders from serving customers while they are talking with the tourist.







Fig 2. Decrease in Enzyme activity (food vender business) produced by increasing the concentration of a potential drug candidate (tourist).







These assumptions might be appropriate and provide all the information that is needed to understand most drug studies but, unfortunately, that’s not all of them. For example, a tourist talking with a food vendor may not completely stop him from serving customers. The presence of the tourist may not be completely negative either.



Say the tourist are celebrities this might increase the appeal of the food carts drawing more customers (in the example above the “#50% business” value of 100 may decrease to 50). Conversely if the tourists are very unpleasant they may repel potential customers causing the “#50% business” value to increase. These complexities are stripped away by IC50 values which assume a simple on/off model of drug interactions.



So what’s the point?



Let’s look at how the use of IC50s is affecting Alzheimer’s disease research.



In Alzheimer’s disease, there is an overproduction of a peptide known as beta-amyloid which forms plaques in the brains of people afflicted by the disorder. Whether this causes the disease or is just a byproduct of the disease is debatable but none-the-less there is a lot of interest in stopping the production of this peptide. Lots of money and research hours have been devoted to looking for the perfect molecule to stop beta-amyloid production.



It was discovered that an enzyme called gamma-secretase produces beta-amyloid so naturally there has been a hunt for inhibitors of this enzyme using IC50s to characterize the interactions. That is a company hired a researcher to develop a test to see if their compounds interfere with the production of beta-amyloid. Setting up the test, the researcher looked for the amount of substrate that produced the most enzymatic activity (the “lunch time rush” in the example above).



Once this concentration of substrate was determined they made this the standard way for screening their compounds. This was based on the assumption that gamma-secretase follows the simple model of how enzymes work, processing one substrate molecule at a time and the inhibitors would completely stop it from working once bound, but surprise it hasn't worked out quite that way.



To use the food vender analogy again, gamma-secretase doesn't act like the food venders described above, serving every customer individually. It does at low customer (substrate) densities, but if a second customer comes to the stand, it speeds up its activity, like a versatile food vendor, cooking both orders at once. This makes gamma-secretase quite fast when 2 customers are there but if more customers show up the shop shuts down.





Fig 3. Representation of gamma-secretase activity in response to substrate. The top line represents the observed activity of the enzyme over changing concentrations of its substrate. The lower lines represent transitions between these substrate induced states. On the left when the enzyme encounters one substrate it has a certain rate of activity (represented by the single customer). As it transitions to dealing with two substrate its activity increases, followed by shut down when the crowd becomes too much.



So to generalize when most researchers set up their experiments to look for things that interfered with gamma-secretase activity they choose to work where the enzyme was most active. For gamma-secretase, this happened to be the region where the enzyme works on two substrate molecules. This, of course, ignored conditions where only one substrate molecule is present and what happened at very high substrate concentrations.



A specific example of this is the compound known as DAPT ( I like how it is labeled as a γ-secretase inhibitor in the product information ). It was found that very little of it was needed to disrupt gamma-secretase activity, a good quality for a potential drug. But because it was improperly characterized with an IC50 value, that didn't examine what happened at high and low concentrations of substrate it was a total failure.



To describe how DAPT interacts with gamma-secretase it might be useful to think of DAPT as one of the food venders family members. It turns out that if DAPT shows up when the food vender is busiest, with two customers, it is a distraction and business shuts down, which was the goal. Unfortunately, if it shows up when the vender has one customer it actually helps out, speeding up business, comparable to the rate the vender works at when two customers are present.



Probably not a good thing when you are trying to shut down the enzyme.



This was initially missed based on the characterization of DAPT with IC50s ( Figure 2 and 3 ) and you might think well how long could it have taken for this interesting bit of information to be worked out? A guess of 10 years would get you in the right ballpark ( ~600 articles found on Pubmed last time I looked for this compound ). But to put this in perspective the use of IC50s to characterize DAPT is not an isolated case where this one compound was improperly characterized, slipped through the cracks and resulted in 10 years of wasted research funding, IC50s are still the standard for characterizing potential drugs targeting secretases .



The regulation of beta-amyloid production is a major focus for research into therapeutic intervention in Alzheimer’s disease, yet the fact that gamma secretase is dynamically regulated by its own substrate and that each of the states produced by these substrate interactions react to compounds differently is obscured by the use of IC50 values.





To keep the bad news coming this isn't the only example of this problem in Alzheimer`s disease research. The class of drugs known as cholinesterases inhibitors, the only known compounds that provide some clinical benefit in the treatment of Alzheimer’s disease, are also usually characterized using IC50s . This is in spite of the fact that these enzymes have been known to be dynamically regulated by their substrate since the 60`s .



I don’t believe a more thorough characterizing of these compounds will cure Alzheimer’s disease as both cholinesterase inhibitors and gamma-secretase inhibitors have already been extensively studied. However, I do believe developing models that that move away from the oversimplified view of how biological systems work, provided by IC50s, can only produce a better understanding of the disease than what exists right now.



Just based on the confusion caused by DAPT interactions with gamma-secretase, one can only speculate how IC50s may be contributing to the problems of reproducibility in the biological sciences. So taking the pessimistic point of view one has to wonder, if such problems exist in the research infrastructure of such an important and well-funded disease as Alzheimer`s disease, whats going on in other fields?



Well still much to get into with the problems associated with classical inhibition equations and I’ll try to get to it next post now that I have sort of covered IC50s.

Decrease in Enzyme activity (food vender business) produced by increasing the concentration of a potential drug candidate (tourist). Representation of increasing enzyme activity (food vender business) with increasing substrate (potential customers)

have to warn everyone that there is going to be a little math at the start, but not much, only one easy equation that you need to have a sense of if you are going to understand what drugs that inhibit enzymes do.This equation is universal and can be easily expanded to describe most molecular interactions. Actually the most basic form of it is the IC50 equation which has been used as a crutch for describing drug interactions for years. So if nothing else you might get a sense of what researchers are referring to when they get excited about IC50 values.Okay, so, an easy way to conceptualize how drugs that inhibit enzymes work is to think of enzymes as food venders on a busy street corner. Any enzyme in your body is doing a job converting one substance into another (usually referred to as a conversion of substrate to product), likewise food venders are doing a job providing food to hungry customers. How busy the food venders are relates to the density of people on the street and how appealing the food stands are to the potential customers.For an enzyme how busy it is relates to the amount of substrate around and how much affinity the substrate has for the enzyme, how appealing the enzyme is to the substrate.Based solely on the number of people on the street corner you can describe how busy the food venders are. For example, right before lunch the street might be almost empty. Therefore, it is a lot less likely to see a customer buying food from a vender. As the density of people increases the chance of seeing customers at the food stands increases and at lunch time it wouldn't be unlikely for you to see multiple customers at some of the food stands possibly even lines forming. So as a group, how busy the food vendors are, is a function of the density of potential customers.This can be described using the mass action relationship but let’s refer to it as the law of customer density here. If you watched the street for a while, you would observe that at times the number of people on the street corner gets high enough that half of the venders are serving customers. This is an important value and can be used to define how busy the venders will be relative to the number of potential customers on the street corner.Let's make this number a constant for our system, the number of potential customers needed to engage half the food venders in transactions (#50% business) and really this constant and the number of people on the street corner are the only values we need to model how busy the venders are. To determine the amount of business being done by the food venders we would divide the number of potential customers by the number of potential customers plus our “#50% business value”.