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

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Presentation transcript:

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

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

Chemical reactions are collisions of molecules Molecule B Molecule A

Reactant A time Molecule A

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=

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

Rate of change of A Degradation constant Concentration of A

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

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

Chemical Reactions inside the cell Central Dogma of Molecular Biology

start promoter end terminator gene Transcription factor DNA Transcription

mRNA Translation Proteins ribosomes mRNA

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

Fast but

Dissociation constant

Hill Function

Cooperativity start promoter end terminator gene

Cooperativity start promoter end terminator gene n molecules

start promoter end terminator gene Repressor