P systems with protein rules

Abstract

Membrane computing or P-systems is a subfield of natural computing, which models living systems with mathematical tools. In classical membrane-computing, cells or organs are surrounded by a simple membrane and computational events take place in either side of the membrane. We have developed a new conceptual tool to better fit P-systems to higher-order organisms, which rely on the actual membrane structure of the cell and on the biochemical reactions (rules), which take place on the membrane of different organs in our body. 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 type-II diabetes patients. The main challenge was to prioritize the insulin-producing β-cells over other organs, i.e., once glucose has entered the body, it must first enter specifically into pancreatic β-cells in order to release the hormone Insulin. However, using classical membrane computing, we could not implement this hierarchy. Therefore, we chose to utilize the membrane actual physiology and add its properties to the current definitions of membrane computing. In particular, we use enzymes and protein-transporters (as well as channels) to apply algebraic rules. In addition, we show that the defined systems are universal, by simulating register machines. 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.