Mathematical modeling for immunocolloid labeling

For many biological applications, it is becoming increasingly important to extend imaging capabilities to simultaneously identify multiple molecular species in order to gain insight into the structural and functional elements of cells. A key part of this drive is the ability to rationally optimize various labeling techniques, which in turn requires an understanding of the basic physical processes operating during the labeling process, and how these processes interact. The kinetics of the immunocolloid labeling process are typically modeled using a Langmuir kinetic equation [1]. However, very different behavior which can not be explained by a Langmuir-type model has been noted in certain experiments [2], [3]. We develop a mathematical model for the labeling process which exhibits these two behaviors in different parameter limits, gives some insight into how to optimize the labeling process, and can easily be extended to more complicated situations.