Mathematical Biology seminar Alex Ginsberg University of Utah "Modeling emergent properties of death-defying networks: blood coagulation and REM sleep" Tuesday, February 3 1-2pm in LCB 215 Abstract: Blood clots are deadly. Anticoagulants, which prevent pathological clotting, are therefore vital. Protein S (PS) is an important anticoagulant implicated in pathological bleeding and clotting. PS binds with two other coagulation proteins-TFPIα and factor V short-to form the protein S complex (PSC), which enhances anticoagulant function by incompletely understood means. To investigate, we start with an experimentally validated, ODE-based model of the blood coagulation biochemical reaction network in a blood vessel with flow and platelet deposition. We extend the model to include PSC and free PS (not a part of PSC) in the plasma, as well as free PS and TFPIα in platelets. We find that PSC accumulates on platelets far more than expected, and that determining the affinity for PSC binding with clotting factor Xa is necessary to understand the anticoagulant properties of PSC. We show that deficiencies in PSC can rescue thrombin production in several bleeding disorders, including severe hemophilia A. Like blood clots, sleep deprivation is deadly. However, the need for a particular type of sleep characterized by rapid eye movements (REM sleep) is poorly understood. During sleep periods, most mammals alternate multiple times between REM and non-REM sleep. A common theory proposes that these transitions are governed by a homeostatic need to enter REM sleep that accumulates between successive REM bouts. We construct a predictive measure for the propensity to enter REM sleep precisely defined as the probability to enter REM sleep before an additional pre-specified amount of non-REM sleep has accumulated. We show that in mice, the REM propensity is correlated with REM bout duration and with the probability of the occurrence of a short REM cycle called a sequential REM cycle. These results support the theory that a homeostatic need to enter REM sleep accrues during non-REM sleep. Current work describes REM propensity across mammalian species and carries-out data analysis that helps clarify the purpose of sequential REM cycles.