Re-defining membranes in membrane-computing and its application to Diabetes Mellitus as a case study.

Membrane-computing is a subfield of natural computing, which models living systems with mathematical tools. In membrane-computing, cells or organs are surrounded with a simple membrane and computational events take place in either sides of the membrane. We have developed a new conceptual tool to be supplemented into the science of membrane-computing. This development relies on the membrane structure of the cell and on the biochemical reactions (rules), which take place on the membrane of different organs in our body, taking under consideration the true nature of membranes.

To demonstrate the power of this new concept, we modeled the process of maintaining normoglycemia in healthy individuals as well as in type-I and in type-II diabetes patients. The main challenge in membrane computing was that the rules are chosen in a non-deterministic manner, thus it occurs randomly with no predilection. However, once glucose has entered the body, it must first enter specifically into pancreatic β-cells, in order to release the hormone Insulin. However, when trying to implement this hierarchy to classical membrane computing, we were unable to prioritize β-cells over other organs (such as the liver, adipose tissue etc.). Therefore, we chose to utilize the membrane actual physiology and add its properties to the current definitions of membrane computing. Thus, allowing deterministic manner operations in a non-deterministic system by giving membrane-specific rules.

To our gratification, we succeeded to adequately describe the process of glucose homeostasis in health and disease while bringing the science of membrane-computing closer to the natural world.