Drugs absorbed into the body are metabolized and thus removed by enzymes from several organs like the liver. The how fast the drug is cleared out of the system can be increased by other drugs that increase the amount of enzyme secretion in the body. This dramatically decreases the concentration of a drug, reducing its efficacy, often leading to the failure of having any effect at all. Therefore, accurately predicting the clearance rate in the presence of drug-drug interaction* is critical in the process of drug prescription and development of a new drug.

*Drug-drug interaction: In terms of metabolism, drug-drug interaction is a phenomenon in which one drug changes the metabolism of another drug to promote or inhibit its excretion from the body when two or more drugs are taken together. As a result, it increases the toxicity of medicines or causes loss of efficacy.

Since it is practically impossible to evaluate all interactions between new drug candidates and all marketed drugs during the development process, the FDA recommends indirect evaluation of drug interactions using a formula suggested in their guidance first published in 1997, revised in January of 2020, in order to evaluate drug interactions and minimize side effects of having to use more than one type of drugs at once.

The formula relies on the 110-year-old Michaelis-Menten (MM) model which has a fundamental limit of making a very broad and groundless assumption on the part of the presence of the enzymes that metabolizes the drug. While MM equation has been one of the most widely known equations in biochemistry used in more than 220,000 published papers, the MM equation is accurate only when the concentration of the enzyme that metabolizes the drug is almost non-existent, causing the accuracy of the equation highly unsatisfactory — only 38 percent of the predictions had less than two-fold errors.

“To make up for the gap, researcher resorted to plugging in scientifically unjustified constants into the equation,” Professor Jung-woo Chae of Chungnam National Univeristy College of Pharmacy said. “This is comparable to having to have the epicyclic orbits introduced to explain the motion of the planets back in the days in order to explain the now-defunct Ptolemaic theory, because it was THE theory back then.”

A joint research team composed of mathematicians from the Biomedical Mathematics Group within the Institute for Basic Science (IBS) and the Korea Advanced Institute of Science and Technology (KAIST) and pharmacological scientists from the Chungnam National University reported that they identified the major causes of the FDA-recommended equation’s inaccuracies and presented a solution.

When estimating the gut bioavailability (Fg), which is the key parameter of the equation, the fraction absorbed from the gut lumen (Fa) is usually assumed to be 1. However, many experiments have shown that Fa is less than 1, obviously since it can’t be expected that all of the orally taken drugs to be completely absorbed by the intestines. To solve this problem, the research team used an “estimated Fa” value based on factors such as the drug’s transit time, intestine radius, and permeability values and used it to re-calculate Fg.

Also, taking a different approach from the MM equation, the team used an alternative model they derived in a previous study back in 2020, which can more accurately predict the drug metabolism rate regardless of the enzyme concentration. Combining these changes, the modified equation with re-calculated Fg had a dramatically increased accuracy of the resulting estimate. The existing FDA formula predicted drug interactions within a 2-fold margin of error at the rate of 38%, whereas the accuracy rate of the revised formula reached 80%.

“Such drastic improvement in drug-drug interaction prediction accuracy is expected to make great contribution to increasing the success rate of new drug development and drug efficacy in clinical trials. As the results of this study were published in one of the top clinical pharmacology journal, it is expected that the FDA guidance will be revised according to the results of this study.” said Professor Sang Kyum Kim from Chungnam National University College of Pharmacy.

Furthermore, this study highlights the importance of collaborative research between research groups in vastly different disciplines, in a field that is as dynamic as drug interactions.

“Thanks to the collaborative research between mathematics and pharmacy, we were able to recify the formula that we have accepted to be the right answer for so long to finally grasp on the leads toward healthier life for mankind.,” said Professor Jae Kyung Kim. He continued, “I hope seeing a ‘K-formula’ entered into the US FDA guidance one day.”