K yz Z st SxSx Y* Z Time Fig 4.11a: Dynamics of the I1-FFL with AND input function following an ON-step of S x. The step occurs at t=0, and X rapidly transits to its active form X*. As a Result, the repressor protein Y is produced, and represses Z production when it crosses the repression threshold K yz. In this figure, all production and decay rates are equal to 1.

Fig 4.11b: Expression dynamics of Z in an incoherent type-1 FFL with repression coefficients F=2,5,20. The repression coefficient is the ratio of the maximal expression without active repressor to the steady-state expression with active repressor. T rep is the time when repression begins, and is the moment of maximal Z concentration. T rep

T 1/2 I1-FFL T 1/2 (simple reg.) Figure 4.12a: Response time of the I1-FFL is shorter than simple regulation that reaches same steady-state level. The normalized response time of simple regulation is log(2)~0.7. Simple regulation- dashed lines, I1-FFL- full lines) I1-FFL Simple regulation Z / Z st o

Ratio of unrepressed to repressed expression, F Response time α z T 1/2 log(2) Figure 4.12b: Response time of the I1-FFL as a function of the repression coefficient F. F is the ratio of unrepressed to repressed Z expression. Green horizontal line: normalized response time of simple regulation, α z T 1/2 =log(2).

Why Some FFL are rarely selected? E.g. I1 and I4

SxSx Y Z S y present S y absent Fig 4.13: The effect of input signal S y on the dynamics of the I1-FFL. When Sy is absent, Y is not active as a repressor, and the concentration of protein Z shows an increase to a high unrepressed steady-state (dashed line)

X Y Z AND Fig 4.14: The incoherent type-1 FFL and type-4 FFL X Y Z AND I1-FFLI4-FFL

Kyz Fig 4.15: Dynamics of the I4-FFL following a step of Sx. In the presence of Sx, protein X is active and activates Z production but represses production of Y. When Y levels decay below the activation coefficient Kyz, the concentration of Z begins to drop. Production and decay rates are β Z =1, α z = α y =1, F=10. The signal Sy is present throughout. Time

X Y Z X Y X’ Y’ X Y homologous non- homologous non- homologous Z Z Z ’ Fi g 4.16: On the evolution of the FFLs. (a) The V-shaped pattern in which X and Y regulate Z is strongly selected because it allows regulation based on two inputs. The edge from X to Y (white arrow) must be selected based on the basis of an additional dynamical functions (e.g. sign sensitive delay, acceleration, pulse generation). (b) In many cases homologous genes Z and Z' in different organisms are regulated in a FFL in response to the same stimuli, but the two regulators X and Y in the FFL are not homologous to the regulators X' and Y'. Homology means sufficient similarity in the genes sequence to indicate that The genes have a common ancestor. (a) (b)

Fig 5.1 The single input module (SIM) network motif. Transcription factor X regulates a group of genes Z 1,.. Z n, with no additional transcription factor inputs. X usually regulates it self. An example of a SIM, the argninine biosynthesis pathway (in this system, all regulations are repression).

E1E2E3 S0S1S2S3 R Fig 5.2 A single-input module (SIM) regulating a three-step metabolic pathway. The master repressor R represses a group of genes that encode for enzymes, E1,E2 E3 (each on a different operon). These enzymes catalyze the conversion of substrate S0 to S1 to S2 culminating in the product S3. The product S3 binds to R, and increases the probability that R is in its active state R*, in which it binds the promoters to repress the production of enzymes. This closes a negative feedback loop, where high levels of S3 lead to a reduction in its rate of production. Gene E1 product Gene E2 Gene E3

Fig 5.3 The SIM can generate temporal programs of expression. As the activity of X gradually rises, it crosses the different thresholds for each target promoter in a defined order. When X activity declines, it crosses the thresholds in reverse order (last-in-first out or LIFO order). Source: shen-orr nature genetics 2002

Fig 5.4 Temporal order in arginine biosynthesis system with minutes between genes. Colored bars show expression from the promoters of the different operons in the system, measured by means of a luminescent reporter gene. The position of each gene product in the pathways that produce arginine is shown. Zaslaver et al Nature genetics 2004

Fig 5.5, the node directed connected subgraphs

Fig 5.6: Simple topological generalizations of the FFL. Each topological generalization corresponds to duplicating one of the nodes of the FFL and all of its edges. (a) The FFL, (b) generalizations based on duplicating one node ( c) multi-node generalizations. Source: Kashtan et al, PRE 2004.

Fig 5.7: The flagella motor of E. coli and its assembly steps info.bio.cmu.edu/.../ FlagellaMotor.html Annual Review of Microbiology    

X Y OR Z1Z1 Z2Z2 ZnZn K1K1 K2K2 KnKn K1’K1’ K2’K2’ Kn’Kn’ Fig 5.8: Schematic plan of the multi-output FFL that regulates the flagella motor genes. Shown are the logic gates at each promoter, and the activation thresholds. X=flhDC, Y=fliA, Z 1 =fliL, Z 2 =fliE etc. K xy

5.9: Temporal order in the flagella system of E. coli. Colored bars are the normalized expression of each promoter, where blue is low and red is high expression. Expression was measured by means of green fluorescent reporter gene. The temporal order matches the assembly order of the flagella, in which proteins are added going from the intra-cellular to the extra-cellular sides. Source: Kalir etal Science 2001

X Y Z1Z1 Z2Z2 K2K2 K1K1 K1’K1’K2’K2’ K 1 <K 2 K 1 ’>K 2 ’ Fig 5.10: First-in First out order (FIFO) in the multi-Z FFL with OR-logic input functions. The output genes Z 1 and Z 2 are turned on when X crosses Activation thresholds K 1 and K 2 (dashed lines). The genes Are turned off when Y decays below activation thresholds K 1 ’ and K 2 ’. When the order of K 1 and K 2 is opposite to that of K 1 ’ and K 2 ’, FIFO order is obtained. K2 K1K1 K1’K1’ K2’K2’ time

Fig 5.11: The 4-node network motifs in sensory transcription networks. X1X1 Z1Z1 X Y Z1Z1 X 2 Z2Z2 Z2Z2 Bifan Two-output Feed-forward loop

Fig 5.12 bifan Two-output FFL The main five-node network motifs in the transcription network of E. coli. The bi-fan generalizes to larger patterns with a row of inputs and a row of outputs.

Fig 5.13 The Dense-overlapping regulons (DOR) network motif, and an example in the E. coli stress response and stationary phase system. Source: Shen-Orr, R Milo, S Mangan & U Alon, Nature Genetics, 31:64-68 (2002).

Fig 5.14 The global structure of part of the E. coli transcription network. Ellipses represent transcription factors that read the signals from the environment. Circles are output genes and operons. Rectangles are DORs. Triangles are outputs of single- or multi-output FFLs. Squares are outputs of SIMs. Blue and red lines correspond to activation and repression interactions.

X Y Z Fig 5.15 Network Motifs in sensory transcription networks X Y Z Sign-sensitive delay Filters out brief ON (OFF) input pulses when the Z-input function Is AND (OR) logic. Pulse generation Signs-sensitive Response acceleration Negative Auto-regulation Positive Auto-regulation Coherent Feed-forward loop C1- FFL Incoherent Feed-forward loop I1-FFL X Slows response time Possible bi-stability Chapter X speeds response time, steady-state robust to fluctuations in production Chapter 3 Chapter Chapter 4.7

Single- Input Module (SIM) X Y 1 Y 2... Y n Coordinated control Temporal (LIFO) order of Promoter activity X Y Z2Z2 ZnZn Multi-output Feed-forward loop (multi-output FFL) Acts as FFL for each input (sign-sensitive delay, etc) FIFO temporal order of promoter activity X1X1 X2X2 XnXn Y1Y1 Y2Y2 YmYm Dense overlapping Regulons) DOR( Combinatorial logic based on multiple inputs, depends on Input-function of each gene Chapter Chapter 5.5 Chapter 5.6 Bifan X1X1 X2X2 Y1Y1 Y2Y2 Fig 5.15 cont: Network Motifs in Sensory transcription networks Z1Z1

XY XY XY Z XY Z X Y Z ON OFF Steady-State 1 Steady-State 2 X Y Z ON OFF ON Steady-State 1 Steady-State 2 Double-positive feedback loop Double-negative feedback loop Fig 6.1 Positive transcriptional feedback loops with two nodes. The double positive loop has two activation interactions, and the double negative is made of two repression interactions. An output gene Z is regulated as shown. Each of the feedback loops has two steady states: both X and Y genes ON or OFF in the double-positive loop, and either ON in the double-negative loop.

X Y X Y Fig 6.2: a) Two-node feedback loops with auto-regulation are a common network motif In developmental transcription networks. b) The ten distinct types of regulating feedback motifs, each corresponding to a different combination of regulation signs. XY Z XY Z XY Z XY Z XY Z XY Z XY Z XY Z XY Z XY Z a) b)

X Y Z XY Z Z* X Y time memory 6.3 The regulated-feedback network motif in developmental transcription networks. (a) Double positive feedback loop. When Z is activated, X and Y begin to be produced They can remain locked ON even when Z is deactivated (at times after the dashed line). (b) Double negative feedback loop. Here Z acts to switch the steady states. Initially Y is high and represses X. After Z is activated, X is produced and Y is repressed. This state can persist even after Z is deactivated. Thus, in both a and b, the feedback Implements a memory. a) b) memory Z* X Y

X Y Z Kxy Kyz X YZ Cell generations X YZ X Y Z Fig 6.4 Transcription cascades can generate delays on the order of the cell-generation time (in the case of stable proteins). Each step in the cascade activates or represses the next step when it crosses its threshold (dashed lines). Shown are a cascade of activators and a cascade of repressors. a) b)

X1X1 Y1Y1 Z1Z1 AND X2X2 Y2Y2 Z2Z2 Z3Z3 Z1Z1 Z2Z2 Z3Z3 time Z Fig 6.5: The transcription network guiding development of the B. subtilis spore. Z 1, Z 2 and Z 3 represent groups of tens to hundreds of genes. This network is made of two type-1 incoherent FFLs, that generate pulses of Z 1 and Z 2, and two type-1 coherent FFLs, one of which generates a delayed step of Z 3. Based on R. Losick, PLOS 2004

X-p X v v Y-p Y v v Z-p Z v v T* T v v Transcription of genes Ligand binds receptor activating the phosphorylation of kinase X Phosphatase 6.6 Protein kinase cascade: Ligand binds the receptor which leads, usually through adaptor proteins, to Phosphorylation of kinase X. Kinase X is active When phosphorylated, X-p. X-p phosphorylates kinase Y. Y-p, in turn, phosphorylates Z. The last kinase, Z-p, Phosphorylates transcription factor T, making it active, T*. T* enters the nucleus and activates (or represses) transcription of genes. Phoaphatases remove the phosphoryl groups (light arrows).

6.7 Network motifs in signal-transduction networks. The main four-node motifs are the diamond and the bifan. The diamond has four nodes, and three different roles, labeled 1,2 and 3. Each generalization is obtained by duplicating one of the nodes and all of its edges. These generalizations are all also network motifs in signal transduction networks. bifan diamond