MATHEMATICAL METHODS FOR SYSTEMS BIOLOGY

Prerequisites & course information

Requisites: MATH 415 and ( MATH 320 , 340 , 341 , 345 , or 375 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2025 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties in systems biology (e.g., reaction networks, reaction rate equations, mass-action kinetics models, detailed balanced and complex balanced systems, Lyapunov functions, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., reversible, weakly reversible, mass-action, detailed balanced, complex balanced, globally stable, oscillatory, persistent, permanent, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of the field (e.g., the Horn-Jackson theorem, the deficiency zero theorem, theorems on characterization of mass-action systems, theorems on persistence and permanence, theorems on dynamical equivalence, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Audience: Both Grad & Undergrad 5. Convey arguments using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Model real biological systems by means of systems of differential equations, and be able to use software (such as Matlab) for visualization of their dynamics. Example models could include: (i) Enzymes, substrates and saturating kinetics, (ii) Glycolytic oscillations, (iii) Cell cycle control, budding yeast cell cycle models, (iv) Activator-inhibitor and positive feedback systems. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties in systems biology (e.g., reaction networks, reaction rate equations, mass-action kinetics models, detailed balanced and complex balanced systems, Lyapunov functions, etc.). Audience: Both Grad & Undergrad 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., reversible, weakly reversible, mass-action, detailed balanced, complex balanced, globally stable, oscillatory, persistent, permanent, etc.). Audience: Both Grad & Undergrad 3. Recall and state the standard theorems of the field (e.g., the Horn-Jackson theorem, the deficiency zero theorem, theorems on characterization of mass-action systems, theorems on persistence and permanence, theorems on dynamical equivalence, etc.) and recall the arguments for these theorems and the underlying logic of their proofs. Audience: Both Grad & Undergrad 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Audience: Both Grad & Undergrad 5. Convey arguments using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Model real biological systems by means of systems of differential equations, and be able to use software (such as Matlab) for visualization of their dynamics. Example models could include: (i) Enzymes, substrates and saturating kinetics, (ii) Glycolytic oscillations, (iii) Cell cycle control, budding yeast cell cycle models, (iv) Activator-inhibitor and positive feedback systems. Audience: Both Grad & Undergrad 7. Identify applications of course content in current areas of research. Audience: Graduate