Mathematical Modeling of Cellular Pharmacokinetics: Cell-Based Molecular Transport Simulators

Every single protein encoded bya genome -human or otherwise- is localized to some microccopic subcellular compartment or organelle. In the case of the malaria parasite, the parasite generally inhibits the red blood cells in theciruclation. Within the red blood cells, the parasite thrives by feeding on hemoglobin, which constitutesthe bulk of theprotein mass of the red blood cell.Todigest thehemoglobin, the parasite relies on lysosomes, a digestive organelle that contains proteases that chop thelarge hemoglobin molecules into smaller peptides and ultimately amno acids that can beincorporated into the parasite's own metabolismto help it grow, reproduce and infect other cells. So, how does one design a small molecule that is absorbed by the body, enters the blood without being metabolized, ultimately accumulating in the parasites lysosome without accumulating in other parts of the body?

To enable design of such a drug, one of the graduate students in my lab -Xinyuan Zhang- has developed a new type of computational tool referred to as a cell based molecular transport simulator. Her work was recently published in a peer-reviewed research journal:

Xinyuan Zhang, Kerby Shedden, Gus Rosania. (2006). A cell-based molecular transport simulator for pharmacokinetic prediction and cheminformatic exploration. Molecular Pharmaceutics; 3(6) pp 704 - 716.

For orally administered drug products, dissolution of drug molecules in the gastrointestinal tract followed by transport across the epithelial cell monolayer lining the lumen of the intestine can exert a major influence on systemic drug concentration and activity. This research project will involve building computational models to simulate biochemical reactions and diffusion of small drug-like molecules inside and across intestinal epithelial cells. These cells form the barrier between the lumen of the intestine and the inside of the human body. Acting as a gateway, intestinal epithelial cells exert a major influence on drug absorption into the body, and are a key determinant of drug concentration in the blood.

For mathematical modeling, passive and active transport of drug molecules can be described in fundamental biophysical terms, using several well-known differential equations. For example, Ficks equation and Nernst-Planck equation can be used to calculate the rate of transmembrane drug transport based on the pKa of functional groups on the drug molecule, and the octanol:water partition coefficients of the different ionic species that the drug molecule can exist in, as a function of the local pH microenvironment. Michaelis-Mentens equation can be used to capture the effect of transmembrane transport proteins (such as P-glycoprotein) as well as the effect of drug metabolizing enzymes, on local drug concentrations and distributions within any given subcellular compartment.

To model drug transport within and across cells, we consider the individual subcellular compartments that are delimited by membranes (ie. apical and basolateral compartment; cytosolic compartment; mitochondrial compartment; lysosomal compartments; etc). Each compartment has a characteristic pH, and the membrane delimiting each compartment possesses its own transmembrane electrical potential. Accordingly, we will use coupled sets of the aforementioned differential equations to describe how the different subcellular compartments selectively accumulate different drug concentrations through time, as well as the rate at which drug molecules are transported across cells (the drugs transcellular permeability) “all in the presence of a transcellular drug concentration gradient to mimic intestinal absorption. To test and improve the model, the computational resultsare beingrelated to published experimental measurements, as well as measurementswe performin the lab.

Complementary to in vivo and in vitro models used in drug discovery today, the cell-based molecular transport simulations we aim to develop are promising new tools to facilitate pharmaceutical discovery and development. Nevertheless, computational models are inexpensive, flexible and scalable, and they can be continually improved upon by future generation of scientists. Indeed, with the aid of computational simulations of drug transport such as the one we are developing, we expect that one day, drugs may be designed, optimized and ultimately approved for clinical use computationally - in terms of their site of action- as much as the drugs today are designed, optimized and approved experimentally, in terms of their mechanism of action.