1. Introduction to Chemical Kinetics and Computational Modeling Hana El-Samad Byers Hall (QB3), Rm 403D

2. Why mathematics in biology? input output Given some initial concentrations, what is output give some prescribed input?

3. Chemical reactions are collisions of molecules Molecule B Molecule A

4. Reactant A time Molecule A

5. A1A1 A2A2 t1t1 Reactant A time t2t2 Change in Concentration:  A= A 2 -A 1 Change in time:  t=t 2 -t 1 Average rate of change in concentration during time  t=

6. A1A1 A2A2 t1t1 Reactant A t2t2 Change in Concentration:  A= A 2 -A 1 instantaneous rate of change in concentration during time dt= Derivative of A with Respect to time

7. Rate of change of A Degradation constant Concentration of A

8. Rate of change of A Degradation constant Concentration of A Concentration of D Production constant

12. Reaching steady-state (equilibrium) Steady-state: No more change in A Production of A balances degradation A is constant

13. Chemical Reactions inside the cell Central Dogma of Molecular Biology

14. start promoter end terminator gene Transcription factor DNA Transcription

15. mRNA Translation Proteins ribosomes mRNA

16. Modeling activator binding and production of mRNA start promoter end terminator gene Fast slow

17. Fast but

18. Dissociation constant

19. Hill Function

21. Cooperativity start promoter end terminator gene

22. Cooperativity start promoter end terminator gene n molecules

23. start promoter end terminator gene Repressor