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

2. Why mathematics in biology?
input
output
Given some initial concentrations, what is output give some prescribed input?
Hana El-Samad
UCSB

3. Chemical reactions are collisions of moleculesB
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UCSB

4. Molecule A
Reactant A
time
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UCSB

5. Reactant A time Change in Concentration: DA= A2-A1 A1 A2 t1 t2
Change in time: Dt=t2-t1
Average rate of change in concentration during time Dt=
Hana El-Samad
UCSB

6. Reactant A Change in Concentration: DA= A2-A1 A1 A2 t1 t2
Derivative of A with
Respect to time t1 t2
instantaneous rate of change in concentration during time dt=
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UCSB

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

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

9. Hana El-Samad
UCSB

10. Hana El-Samad
UCSB

11. Hana El-Samad
UCSB

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

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

14. Transcription start end promoter terminator gene DNA
Transcription factor
start
promoter
end
terminator
gene
DNA
RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing
By incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.
There maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.
RNAP acts as a reading head.
Hana El-Samad
UCSB

15. mRNA Translation Proteins ribosomes mRNA Hana El-Samad UCSB
RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing
By incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.
There maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.
RNAP acts as a reading head.
ribosomes
Hana El-Samad
UCSB

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

17. Fast
but
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UCSB

18. Dissociation constant
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19. Hill Function
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20. Hana El-Samad
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21. Cooperativity
start
promoter
end
terminator
gene
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UCSB

22. Cooperativity start end promoter terminator gene n molecules
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UCSB

23. Repressor
start
promoter
end
terminator
gene
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UCSB

24. Hana El-Samad
UCSB