The protein-protein interactions in biology have been accumulated with colossal efforts to identify a large number of proteins in several organisms. These interactions are expressed as graphs, where nodes denote proteins and edges represent physical interaction. The static network has contributed to our understanding of the cellular machinery, displaying fundamental static properties.
Clathrin-mediated endocytosis (CME) of cellular machinery is very important and has been widely investigated. In the network of CME, we can find hubs and possible pathway, but it is hard to identify their functions and importance. It is also difficult to reproduce such mechanism. Therefore we need to develop a proper method to reconcile its time dependent feature.
In this paper, we propose ‘Sudden expression-Degradation’ model that represents activation time of proteins in a CME network. Using this model, we can get several time dependent features. First, we can find many paths according to time. In previous paper, they can give just approximate time line of activation of protein by path-length. Second, we can infer the function of proteins. From the result of min-cut, we can predict that some proteins make a role of linkage which makes a connection between each of crucial stages. In this case, in different ways we had to confirm whether the proteins make a role of linkage or not. Our directed network allows us to predict the importance of accessory proteins, not hub. Third, we can change threshold of probability of activation. The threshold level is similar to interruption level of interaction. Thus we can find crucial proteins to maintain the robustness of CME.
Using this model, we can understand well how these dynamic changes operate. Furthermore, we can try to enhance the accuracy. For example, we can use dynamic threshold and explicit reaction-diffusion model.