1. A Mathematical Model of Metabolism for Diabetes Dayu Lv dlv@nd.edu Advisor: Dr. Goodwine

2. Metabolism Biochemical reactions and processes In a cell, a tissue, an organ, … Anabolism + Catabolism

4. Diabetes Mellitus A disease in which the body does not produce or properly use insulin --- from American Diabetes Association Insulin: a hormone to regulate carbohydrate metabolism, fat metabolism –Plasma glucose –Fatty acids –Liver –Kidney –Muscle

5. Diabetes Mellitus 20.8 million (children and adults) in the United States Health issues –Heart disease, Stroke –Renal failure –Vascular disease –High blood pressure and cholesterol level –Nerve systems

6. Diabetes Mellitus Type 1 –Cannot produce insulin Type 2 –Insulin resistance –Insulin deficiency Gestational diabetes Pre-diabetes

8. NameTissue distribution Approximate Km (for inward transport of glucose or a glucose analogue) GLUT1 Erythrocytes, fetal tissue, placenta, brain blood vessels 5-7 mmol/l GLUT2 Liver, kidney, intestine, pancreatic – cell High (7-20 mmol/l) GLUT3Brain (neuronal cells)Low (1.6 mmol/l) GLUT4Muscle, adipose tissue5 mmol/l GLUT5Jejunum5 mmol/l for fructose SGLT-1Duodenum, jejunum, renal tubules SGLT-2,3Renal tubules

10. Sorensen Model Gut Liver Brain Peripheral Kidney Heart uptake Reabsorb/excretion Glycogen break down/ synthesis insulin Fatty acids glucose

11. Blood flow balance Utilize; Uptake Systems –Glucose –Insulin –Fatty Acids –Glucagon –… Subsystems – -cell secretion – -cell dysfunction –… Controlling equations

12. -cell variables -cell variables -cell mass HbA1c: glycated hemoglobin Lipotoxity

13. -cell characteristics -cell characteristics Glucose Effectiveness –Slope of the glucose production & uptake vs. glucose levels Insulin sensitivity –Slope of the glucose effectiveness vs. insulin curve Pulse Oscillation Early phase response

18. Thank you!