| Description |
Ubiquitin is a small protein which interacts with other proteins as a post-translational modification and as a binding partner for proteins which contain a ubiquitin binding domain (UBD). Proteins modified with ubiquitin are often targeted for degradation. Ubiquitin regulates both soluble and membrane-bound proteins in cells of nearly all tissues. Here we use mathematical models to study three distinct regulatory systems involving ubiquitin: regulation of the yeast uracil transporter, Fur4, protein sorting mediated by the endosomal sorting complexes required for transport (ESCRTs), and regulation of Rad18 in the DNA damage tolerance pathway. Using a differential equation model of Fur4 regulation, we demonstrate that deubiquitination and retention are essential roles of the Rsp5/Ubp2 complex localized to the endosome. We also predict a nearly constant pool of endosomal Fur4 independent of extracellular conditions. ESCRTs are responsible for sorting ubiquitinated proteins (cargo) on the endosomal membrane prior to formation of intralumenal vesicles. However, the mechanisms of sorting remain unclear. Motivated by recent experimental data, we present a cellular automata model of ESCRT sorting which demonstrates that a flexible network of ESCRTs and cargoes is sufficient for high efficiency sorting under specified rules. ESCRT-cargo networks exist on membranes while all ESCRT binding studies consider ESCRT interactions in solution. We present novel results on the dimensional dependence of dissociation constants for general protein-protein interactions using stochastic methods. We present a conversion for transforming three-dimensional dissociation constants to two-dimensional dissociation constants and demonstrate that ESCRT-cargo interactions are more stable on membranes than in solution. Using our computed two-dimensional reaction rates, we present an ODE model for the evolution of the size of ESCRT-cargo networks. Our results suggest that ESCRT-mediated sorting can be achieved on the order of seconds. Lastly, we examine ubiquitin-dependent regulation of Rad18 in the DNA damage tolerance pathway, a system of strictly soluble proteins which does not rely on ubiquitin-dependent degradation. Results of ODE models suggest that the dissociation constants for Rad18 binding events must be measured in order to better understand the mechanisms behind damage-specific responses. |
