MIT 8 591J - Syllabus (5 pages)

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Syllabus



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Syllabus

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Syllabus


Pages:
5
School:
Massachusetts Institute of Technology
Course:
8 591j - Systems Biology

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IV Synthetic genetic switches Reference 1 T S Gardner C R Cantor and J J Collins Construction of a genetic toggle switch in Escherichia coli Nature 403 339 342 2000 In this paper Gardner et al engineered a plasmid containing two repressor genes mutually controlling each others expression In Box 1 postulate the two equations describing the toggle switch du 1 u dt 1 v dv 2 v dt 1 u IV 1 Let s derive this equation and explore which assumptions were made during the derivation The fast equilibium reactions for this problem are K1 P1 R2 P1R2 K2 P2 R1 P2R1 IV 2 K3 R1 R1 K4 R 2 R2 The first two reactions model the binding of the repressors to the two promoters inhibiting transcription We will assume that there is only one binding site for the repressor in contrast to the lambda phage promoters However the repressor monomers can form multimers Repressor 1 multimerizes with subunits and repressor 2 with subunits Note that K3 and K4 are the effective association constants for multimerization The units of K3 and K4 are M 1 and M 1 respectively The last two equations assume that intermediate states are not allowed This is the Hill approximation as we discussed before see for example II 22 Remember that the total number of promoter site is conserved and the total concentration of both promoters is identical since they are on the same plasmid PT P1T P1 P1R2 P2T P2 P2R1 21 IV 3 7 81 8 591 9 531 Systems Biology A van Oudenaarden MIT September 2004 Now the rate of synthesis of repressor 1 and 2 can be written as Rgen1 k1 PT Rgen2 1 k1 PT P1 T k P 1 1 K1 R 2 1 K1K 4 R2 P1 P1R2 1 k 2 PT P2 T k 2 P T k P 2 1 K 2 R1 1 K 2K 3 R1 P2 P2R1 IV 4 The rates k1 and k2 are the effective synthesis rates including RNA polymerase binding transcription translation and folding of repressor protein 1 and 2 respectively Assuming a first order decay process with rate the kinetic equations are d R1 k1 PT R1 dt 1 K1K 4 R2 d R 2 k 2 PT R 2 dt 1 K 2K 3 R1 IV 5 When we introduce a dimensionless time t t



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