Summary Lecture 3 UV Induction sugery Image by MIT OCW
Summary Lecture 3 Image by MIT OCW
L4: Cooperativity introduction 2 phage model n phage model (Hasty et al.) as example for applying mass action law K 2Ⅹ K D+Ⅹ.<2>Dx most important K fast step in OR2 OR3 modeling D+X DX K Dx,+2 DxDⅩ OR3 DX+P DX+P+nⅩ most im portant A Slow step in modeling ! biology math
L4: Cooperativity & introduction λ phage model λ phage model (Hasty et al.) as example for applying mass action law. A dk X P nX 2 DX tk P 2 DX 2 DX 2 DX 4K 2X 2 DX * 2 DX 3K 2 D X 2 DX 2K 2 D X 2X 1K 2X ⎯⎯ →⎯ + ⎯⎯ →⎯ + + + ←⎯ →⎯ + ←⎯ →⎯ + ←⎯ →⎯ ←⎯ →⎯ OR2 OR3 λ λ λ λ λ λ OR2 OR3 λ λ OR2 OR3 λ λ λ λ K1 K2 fast slow most important step in modeling !! most important step in modeling !! biology math
dx 2 K 2Ⅹ at 1+(1+,) 0×4Yx+1 K K D+X4>DX relative binding mass action K constants D+Ⅹ 2 K K DX +X DDⅩ nk.pnd toT w synthesis/basal ate k DⅩ+P-t>Dx+P+nx k degradation/basal k rate choose elegant (dimensionless, relative) variables
2K1 r K dk γ r Td0pt nk α 2K 4K 2σ 2K 3K 1σ γx 1 4 x2σ 2 )x 1 1 (1 σ 2 αx dt dx = = = = − + + + + = A dk X P nX 2 DX tk P 2 DX 2 DX 2 DX 4K 2X 2 DX * 2 DX 3K 2 D X 2 DX 2K 2 D X 2X 1K 2X ⎯⎯ →⎯ + ⎯⎯ →⎯ + + + ←⎯ →⎯ + ←⎯ →⎯ + ←⎯ →⎯ ←⎯ →⎯ relative binding constants ~ synthesis/basal rate ~ degradation/basal rate mass action choose elegant (dimensionless, relative) variables !
graphical stability analysis one stable low state creaton medium destruction rate one metastable state low destruction rate one stable high state X
graphical stability analysis
How to experimentally verify these ideas? Synthetic Biology Build your own designed network from scratch and test your model Examples for synthetic genetic switches Isaacs et al. Prediction and measurement of an autoregulatory genetic module. PNAS 100, 7714 (2003) Gardner et al. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 399(2000)
How to experimentally verify these ideas ? Synthetic Biology Build your own designed network ‘from scratch’ and test your model Examples for synthetic genetic switches: Isaacs et al. Prediction and measurement of an autoregulatory genetic module. PNAS 100, 7714 (2003) Gardner et al. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 399 (2000)