(262a) Mathematical Modeling of Heterogeneous Sub-Cellular Structures: Probability Models for Integrin Cluster Properties in Adherent Cells

When random variability is intrinsic to a biological system such that the traditional deterministic idealization is not possible without destroying the true essence of the problem at hand, appropriate mathematical models must explicitly account for such randomly varying phenomena. Such is the case with integrin signaling, where protein interactions are restricted to small, micron-sized protein complexes that form on the cytoplasmic tails of clustered transmembrane integrin proteins. Because integrin signaling only occurs within these complexes, the size, shape, and location of integrin clusters determine the two-dimensional properties of the control volume within which integrin signaling occurs. However, these characteristics of integrin clusters are subject to random variation, and are hence non-uniform.

The key problem associated with characterizing integrin clusters is two-fold: obtaining appropriate data, and developing appropriate mathematical models from these data. In this work, we develop and illustrate techniques for tackling this two-fold problem. For data acquisition, first we employ a protein labeling technique that specifically labels bound integrins; subsequently we use confocal microscopy and image analysis to quantify the size, shape, and location of integrin clusters. From these data, we develop probabilistic descriptions of the entire population of integrin clusters from first principles considerations of the integrin cluster characteristic in question. These models are presented in a format that is useful for computational modeling of integrin cluster characteristics in a population of adherent cells. We argue that such means of analyzing and describing heterogeneous populations of sub-cellular structures are important components of any high-fidelity spatial modeling of signal transduction on integrin scaffolds.