10 Equations in Biology: Michaelis-Menten Kinetics.

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10 Equations in Biology: Michaelis-Menten Kinetics

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

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

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 + ?

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.

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

Formal Equations for Enzyme Kinetics Model

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!

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. ✓