1. 1 Analyzing the Michaelis-Menten Kinetics Model G. Goins, Dept. of Biology N.C. A&T State University Advisors: Dr. M. Chen, Dept. of Mathematics Dr. G. Goins, Dept. of Biology Sponsored by Grant No. 634598 http://blend.ncat.edu

2. 2 Biological Background Spontaneous chemical reactions that take place in living things often occur very slowly without a catalyst called an enzymeSpontaneous chemical reactions that take place in living things often occur very slowly without a catalyst called an enzyme The enzyme binds to molecules known as the substrate, and converts substrate to product,The enzyme binds to molecules known as the substrate, and converts substrate to product, Unbound enzyme repeats cycleUnbound enzyme repeats cycle

3. 3 Michaelis-Menten Mechanism The model represents how an enzyme acts on a substrate. E is the enzyme, S is the substrate, ES is the enzyme-substrate complex and P is the product. Substrate Enzyme Enzyme-substrate complex Enzyme Products Recycle Active site k -1

4. 4 What is the Michaelis-Menten Equation Commonly used in biology, the Michaelis-Menten equation describes the reaction time to convert (binding and conversion) substrate to product

5. 5 Michaelis-Menten kinetics V max approached asymptotically V 0 = V max x[S]/([S] + K m ) V 0 is moles of product formed per sec. when [P] is low (close to zero time) Michaelis-Menten Equation E + S  ES  E + P Michaelis-Menten Model V 0 varies with [S]

6. 6 Michaelis-Menten system of ODEs The four differential equations that are used in the model are

7. 7 What is Michaelis-Menton good for? Application: Any process involving an Enzyme (E) that converts a resource material (substrate, S) into another form product (P) Biochemist use the shape of the curve to determine the binding specificity of an enzyme for a substrate K m is called the Michaelis Constant, if small, then steeper curve and more specific binding

8. 8 Determining initial velocity (when [P] is low) Ignore the back reaction

9. 9 Steady-state & pre-steady-state conditions At equilibrium, no net change of [S] & [P] or of [ES] & [E] At pre-steady-state, [P] is low (close to zero time), hence, V 0 for initial reaction velocity At pre-steady state, we can ignore the back reactions

10. Albeck et al. Nature Reviews Molecular Cell Biology 7, 803–812 (November 2006) Molecular biology, proteomics and systems biology approaches Molecular biology studies traditionally focused on 1 or a few proteins with a highly mechanistic levels of detail Proteomics seeks to catalogue many proteins Systems biology seeks a mechanistic understanding of phenomena that involve many proteins molecular biology proteomics systems biology