Uri Alon’s lab 10/02

Network of transcriptional interactions in E. coli Thieffry, Collado-Vides, 1998 Shen-Orr, Alon, Nature Genetics 2002

(Rosenfeld,Elowitz,Alon, JMB 323: )

The assumptions X is always expressed X requires S x to be active X* Y requires S y to be active Y* Functional FFL - a change in Sx causes a change in Y sufficient to cause a change in Z

Changes in Y’s concentration X Y Rate of basal transcription + Rate of transcription due to TF binding X effect of TF on gene’s expression - (rate of protein degradation + protein dilution) X level of protein = Change in Y concentration

Regulation function Activator f(X*,Kxy) = (X*/Kxy) H / (1 + (X*/Kxy) H ) Repressor f(X*,Kxy) = 1 / (1 + (X*/Kxy) H )

Changes in Z’s concentration X Z Rate of basal transcription + Rate of transcription due to TF binding X effect of TFs on gene’s expression - (rate of protein degradation + protein dilution) X level of protein = Change in Z concentration Y

Mangan et. al, PNAS (2003)

Logical gate AND gate –f(X*,Kxz) * f(Y*,Kyz) where X and Y are either activators or repressors OR gate –Sum of X and Y regulation functions taking competitive binding into account –question – why not allow for competitive binding in AND gate

Steady state :Coherent Type 1 – AND gate X Y Z SxSx SySy SxSy Change in Z Z production requires Sx AND Sy

Steady state :Coherent Type 2 – AND gate X Y Z SxSx SySy SxSy Change in Z Z production requires Not Sx AND Sy

Steady state :Coherent Type 3 – AND gate X Y Z SxSx SySy SxSy Change in Z Z production requires (Not Sx +Sy) OR (Not Sx + Not Sy) in other words Not Sx Sy does not matter because Y is not expressed

Steady state :Coherent Type 4 – AND gate X Y Z SxSx SySy SxSy Change in Z Z production requires Sx Sy does not matter because Y is repressed

Steady state: Summary of coherent AND gate FFL Type 1Sx AND Sy Type 2Not Sx AND Sy Type 3Not Sx Type 4Sx Type 1 & 2 appear abundantly in coli and yeast unlike type 3 & 4

Steady state: Quick Summary of incoherent AND gate FFL Type 1Sx AND Not Sy Type 2Not Sx AND Not Sy Type 30 Type 40 Again, only 1 & 2 use both Sx and Sy and in yeast they are the only ones to appear abundantly (in coli incoherent FFL are rare)

Kinetics: Coherent FFL are sign sensitive delay elements Sign sensitive – Get response (i.e. delay) in one direction (i.e. on to off) but not in the other (off to on) X Y Z SxSx SySy Sign sensitivity direction depends on Z’s steady state activation functions – when Sx is required for activation delay is in on step and when NOT Sx delay is in off step

FFL function – a filter Persistence detector A sign-sensitive delay Database -> Motifs -> Theory -> Experiments Threshold for Y being active Mangan et. al, PNAS (2003)

Maximal response to a pulse is filtered by FFL Simulation X Z X Y Z Input pulse to X of duration T T Response Pulse duration T

Glucose pulse experiment shows filtering by arabinose FFL Max response crp lacZ crp araC araB Pulse duration [min] Mangan, et. al. JMB (2003). Delay per cascade step ~ one cell cycle

Kinetics: Incoherent FFL can generate pulses controlled by Sy X Y Z SxSx SySy X Y SxSx SySy Z

Kinetics: Incoherent FFL can accelerate response X Y SxSx SySy Z make promoter stronger X Y Z SxSx SySy

Comparing basal to no basal Y X Y SySy Z SxSx No basal Y Basal Assumption: effect of Y on Z is not complete < Kxz < Kxy < Kyz Basal Y TFS in basal case are weaker There is a strong pulse here and it is achieved solely because Y is lowly expressed

OR gates – generally reversed X Y Z SxSx SySy

comparing networks of different sizes for similarity in local structure Different Subgraphs Normalized significance

Uri Alon’s lab 10/02