1. 10 Equations in Biology: Michaelis-Menten Kinetics

2. Outline 1. Brief intro to enzyme kinetics 2. From intuitive conceptions to a formal model 3. Building interactive models in Excel 4. From a mathematical model to biological insights

3. Intro to Enzyme Kinetics E + SES kfkf krkr E + P k cat Variables [E]: free enzyme molecules [S]: free substrate molecules [ES]: enzyme-substrate complexes [P]: free product molecules Parameters k f, k r, k cat : reaction rates

4. Writing “Word Equations” A word equation is a qualitative description of the system’s major processes Goal: help students express their proto- mathematical understanding of a system before introducing formal math. $ in checking account on Sept. 1st = deposits made in August – Example: Balancing a checkbook $ in checking account on Aug. 1st withdrawals made in August + ?

5. Word Equations for Enzyme Kinetics Model # of free S molecules at time t +1 = # of free S molecules at time t # of free S molecules binding to free E – # of ES complexes splitting into E + S + Write similar word equations for the other 3 variables.

6. Translate Word Equations into Formal Equations # of free S molecules at time t = [S] t # of free S molecules binding to free E = k f [E] t [S] t # of ES complexes splitting into E + S = k r [ES] t conc. of enzyme- substrate complexes conc. of free enzyme  conc. of free substrate by Law of Mass Action

7. Formal Equations for Enzyme Kinetics Model

8. Modeling in Excel Why Excel rather than more powerful tools? easily available on most campuses widely used = transferable proficiency nonthreatening to students makes students work directly with the equations: no dodges via the user interface!

9. Implementing a Model in Excel 1. Write a series of recursion equations. 2. Set up Excel sheet with time in Column A, other variables in next columns. 3. Enter and name model parameters; enter variables’ starting values. 4. Enter recursion equations for each variable. 5. Copy and paste for subsequent time steps. 6. Graph results appropriately. ✓