MODEL

The Pharmacological Model
- Introduction
- Mathematical Model
References

The Pharmacological Model

Introduction

We present a model to approximate the steady state concentration of PFOA in the bloodstream based on various parameters, including the initial concentrations of proteins and PFOA, the relative binding efficiencies, e.g. they can be associated together a complex or dissociated and the concentration sin dynamic equilibrium. However, once we introduce our binder into the system, it competes with albumin for PFOA and also exists in dynamic equilibrium with the PFOA complex. However, the binder + PFOA complex is capable of undergoing transcytosis out of the bloodstream, resulting in a net decrease of PFOA in the bloodstream. We assume that albumin only has one pocket that actively binds to PFOA despite it having four pockets total because the other three pockets have a negligible binding affinity for PFOA. We additionally assume that no PFOA is added to the bloodstream during the duration of treatment and we only introduce the binder to the bloodstream once. Our full system is shown below:

Figure 1. Competition System of Albumin and Binder (Engineered Protein). Solid white arrows indicate association of compounds while dashed white arrows indicate dissociation. Transcytosis (solid black arrow) removes the binder-PFOA complex from the bloodstream.

Mathematical Model

To model the system, we employ a simple system of ordinary differential equations that tracks the concentrations of the various components of the systems. The system is described below, with A(t) = [Albumin], P(t) = [PFOA], B(t) = [Binder], CA(t) = [Albumin-PFOA Complex], and CB(t)= [Albumin-Binder Complex]. Initial concentration of albumin (63.9 uM) was derived from literature (Moman et al, 2022) and initial PFOA concentration was set to 1 uM, which is roughly between highly exposed populations and occupational exposure (CDC, 2024). Rate constants were not derived experimentally in literature, but we estimate them as the dissociation constants of complexes. While this removes the time component of our system (e.g. the system can not accurately give a time scale for the dynamics), we are still able to accurately measure the steady state due to the ratios between values since they predominate the dynamics of the system. We report the literature values (Maso et al., 2021) and other values in the following table:

Without experimentally determined values the dissociation constants of our engineered protein, we approximate them relative to that of albumin with the scalar S. Additionally, due to the system lacking a hard time scale, we test discreet rates of transcytosis on a logarithmic scale to see how such changes affect the system. Our mathematical set up is described as below:

The change in binder concentration is dependent on the rate of dissociation of the binder-PFOA complex (k0CB) and the rate of association of the binder and PFOA (k1BP).

The change in albumin concentration is dependent on the rate of dissociation of the albumin-PFOA complex (k2CA) and the rate of association of albumin and PFOA (k3AP).

The change in PFOA concentration is dependent on the rate of dissociation of the albumin-PFOA complex (k2CA) and the binder-PFOA complex (k0CB) and the rate of association of albumin and PFOA (k3AP) and binder and PFOA (k1BP).

The change in albumin-PFOA complex concentration is dependent on the rate of dissociation of the albumin-PFOA complex (k2CA) and the rate of association of albumin and PFOA (k3AP).

The change in binder-PFOA complex concentration is dependent on the rate of dissociation of the binder-PFOA complex (k0CB), the rate of association of binder and PFOA (k1BP), and the rate of transcytosis of the complex (k4CB).

See the results page for modeling results and analysis.

MODEL

Contents

The Pharmacological Model

Introduction

Mathematical Model

REFERENCES