lec15_04062007_w - 10.37 Chemical and Biological Reaction...

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10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 15: Gene Expression and Trafficking Dynamics This lecture covers: Approach to steady state and receptor trafficking Central dogma of molecular biology: DNA Æ mRNA Æ protein transcription translation Material balance on one specific mRNA Accumulation = synthesis – degradation moles mRNA C mRNA cell volume () ( ) mol mRNA K r , transcription (function of gene dosage, inducers, etc.) time cell volume cell volume V i vessel volume dC mRNA V i =− KC ri VV γ dt rm R N Ai r first order rate constant for mRNA degredation V a function of time (cells grow, divide) i Æ can’t pull out of the derivative Do the chain rule: dd V im C CK R N A mRNA += dt i dt r i r C mRNA V i dC mRNA 1 d V i r r mRNA C dt mRNA V i dt simplify: 1 d V i = μ (specific growth rate in exponential growth) V i dt dC mRNA r γμ r mRNA C dt ±²³ mRNA dilution by growth term (b/c concentration is on a per-cell volume basis) Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
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lec15_04062007_w - 10.37 Chemical and Biological Reaction...

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