APh 161, Lecture 7: Biological Circuit (Design)Richard M. MurrayControl and Dynamical Systems25 January 2007Goals:•Talk about the role of switches as an example of a biological circuit•Walk through “stick in the sand” calculation of switch dynamics•Walk through “fingers on the keyboard” calculation of oscillator circuitReading•Kondev, Phillips and Theriot, Physical Biology of the Cell, Chapter 19•Gardner et al, “Construction of a genetic toggle switch...”, Nature 2000•Cherry and Adler, “How to make a biological switch”, J. Theor Bio, 2000•Elowitz and Leibler, A synthetic oscillatory network of transcriptional regulators, Nature, 2000Richard M. Murray, Caltech CDSAPh 161, 23 Jan 06Phage !2http://www.uccs.edu/~rmelamed/MicroFall2002/Chapter%2010/Lysogeny.jpgRichard M. Murray, Caltech CDSAPh 161, 23 Jan 06Phage ! CircuitControl logic•Set of operator regions controls expression of both cI and cro genes•Cooperativity (multiple copies of repressor bound to operator region) plays important role•As in lac operon, multiple feedback loops interacting with each other => complex to analyze3http://bio.classes.ucsc.edu/bio105l/EXERCISES/PHAGE/map.gifRichard M. Murray, Caltech CDSAPh 161, 23 Jan 06Gardner, Cantor and Collins (Nature, 2000)Method: interconnect lacI, ! genes•lacI: gene for repressor from lac operon-Can be repressed through IPTG•cI from !-Can be repressed using temperature•Also tried tetR (regulates resistance to tetracycline)Results•Where able to show they could induce a change from one state to the other through inducers4T. S. Gardner, C. R. Cantor and J. J. CollinsConstruction of a genetic toggle switch in Escherichia coliNature, 2000Richard M. Murray, Caltech CDSAPh 161, 23 Jan 06RepressilatorBasic idea•Three genes whose proteins are each repressors of the next gene in the sequenceModel:•6 states: m_tetR, m_cI, m_LacI, p_tetR, p_cI, p_laci•“Stick in the sand” calculations are hard, but “fingers on the keyboard” works wellMATLAB implementation•repressilator.m - file with dynamics•repressilator_plot.m - commands to run simulation and generate plots•Also: geneticswitch.m for Gardner et al switch5ampRSC101 originPLtetO1! cI-lite! PRlacI-litePLlacO1tetR-liteTetRLacI! cIdmidt= −Kmmi+γ1 + Kbpni−1+ γ0dpidt= −Kppi+ T miM. ElowitzRichard M. Murray, Caltech CDSAPh 161, 23 Jan 06RepressilatorBasic idea•Three genes whose proteins are each repressors of the next gene in the sequenceModel:•6 states: m_tetR, m_cI, m_LacI, p_tetR, p_cI, p_laci•“Stick in the sand” calculations are hard, but “fingers on the keyboard” works well6ampRSC101 originPLtetO1! cI-lite! PRlacI-litePLlacO1tetR-liteTetRLacI! cIdmidt= −Kmmi+γ1 + Kbpni−1+ γ0dpidt= −Kppi+ T miM. ElowitzA synthetic oscillatory network of transcriptional regulatorsMichael B. Elowitz and Stanislas LeiblerNature 403, 335-338 (20 January
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