Introduction to Chemical Kinetics and Computational Modeling

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Presentation transcript:

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

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

Chemical reactions are collisions of molecules B Hana El-Samad UCSB

Molecule A Reactant A time Hana El-Samad UCSB

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

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= Hana El-Samad UCSB

Concentration of A Rate of change of A Degradation constant Hana El-Samad UCSB

Production constant Concentration of D Concentration of A Rate of change of A Production constant Concentration of D Degradation constant Concentration of A Hana El-Samad UCSB

Hana El-Samad UCSB

Hana El-Samad UCSB

Hana El-Samad UCSB

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

Chemical Reactions inside the cell Central Dogma of Molecular Biology Hana El-Samad UCSB

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

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

Modeling activator binding and production of mRNA start promoter end terminator gene Fast slow Hana El-Samad UCSB

Fast but Hana El-Samad UCSB

Dissociation constant Hana El-Samad UCSB

Hill Function Hana El-Samad UCSB

Hana El-Samad UCSB

Cooperativity start promoter end terminator gene Hana El-Samad UCSB

Cooperativity start end promoter terminator gene n molecules Hana El-Samad UCSB

Repressor start promoter end terminator gene Hana El-Samad UCSB

Hana El-Samad UCSB