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Network Motifs and Modules

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What is a motif? A motif is a statistically over-represented subgraph in a network. A pattern of connections that generates a characteristic dynamical response. A motif is a connection pattern template which could in principle be implemented.

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Network Motifs and Modules What is a module? A module is an exchangeable functional unit. Its chief characteristic is that when placed in a different context, its intrinsic functional properties do not change. All modules are motifs but not all motifs are modules.

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Network Motifs Negative Autoregulation Positive Autoregulation Double Positive Feedback Double Negative Feedback Coherent Feedforward InCoherent Feedforward Delay or ultrasensitivity unit

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Network Motifs Multi-Output FFL Regulated Double Negative Feedback Regulated Double Positive Feedback Bi-Fan Dense Overlapping Regulons SIM – Single Input Module

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Network Motifs Negative AutoregulationPositive Autoregulation 1. Noise Suppression 2. Accelerated Response 3. High Fidelity Amplifier 4. Feedback Oscillation 1.Bistability 2.Memory Unit Relaxation Oscillator

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Network Motifs Memory unit where both units are either on or off Memory unit: when one unit is off the other unit is on Double Positive FeedbackDouble Negative Feedback

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Network Motifs 1.Noise rejection 2.Pulse shifter 1. Pulse generator 2. Concentration detector 3. Response time accelerator Coherent FeedforwardInCoherent Feedforward

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Network Motifs Memory unit that records an event in Z Memory unit that where nodes switch in opposite directions due to an event in Z Regulated Double Negative Feedback Regulated Double Positive Feedback Z Z

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Network Motifs 1.Pulse Train Generator 2.Temporal Sequencer – Last in last out, ie the last gene activated is the last gene deactivated. Multi-Output FFL SIM – Single Input Module 1. Master/Salve Regulator 2. Temporal Sequencer – Last in first out, ie. The last gene activated is the first gene deactivated

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Feed-forward Networks Copyright © 2013: Sauro

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Feed-forward Networks Copyright © 2013: Sauro 1.Estimating the frequency of each isomorphic subgraph in the target network. 2.Generating a suitable random graph to test the significance of the frequency data. 3.Compare the target network with the random graph. Occurrences of the feed-forward loop motifs as generated by the software MAVisto [1]. The displayed network is part of yeast data supplied with the MAVisto software. The software is very straight forward to use and will identify a wide variety of motifs. Other similar tools include FANMOD and the original tool mFinder. F. Schreiber and H. Schwobbermeyer. MAVisto: a tool for the exploration of network motifs. Bioinformatics, 21(17):3572–3574, 2005.

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Feed-forward Circuits Copyright (c) 2013 Activate Repress 13 The sign of an interaction can be determined either from basic biochemistry studies or by looking at microarray expression profiles.

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Feed-forward Circuits Copyright (c) 201314

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Feed-forward Circuits Copyright (c) 2013 Relative abundance of different FFL types in Yeast and E. coli. Data taken from Mangan et al. 2003. I1 C1 15

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Feed-forward Circuits Dynamic Properties Copyright (c) 200816

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First Translate Non-stoichiometric Network into a Stoichiometric Network Copyright (c) 201317 C1

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First Translate Non-stoichiometric Network into a Stoichiometric Network Copyright (c) 201318 C1 ?

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Feed-forward Circuits Dynamic Properties Copyright (c) 201319 What does this actually mean? AND GATE?OR GATE? Or something else? Input AInput BANDORXOR 11110 10011 01011 00000

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Feed-forward Circuits Coherent Type I Genetic Network: AND Gate Copyright (c) 201320 C1 AND GATE

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 21 NOTE THE DELAYS. Delay No Delay Time P1 P3 Noise Rejection Circuit Narrow PulseWide Pulse

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 22 p = defn cell $G2 -> P2; Vmax2*P1^4/(Km1 + P1^4); P2 -> $w; k1*P2; $G3 -> P3; Vmax3*P1^4*P2^4/(Km1 + P1^4*P2^4); P3 -> $w; k1*P3; end; p.Vmax2 = 1; p.Vmax3 = 1; p.Km1 = 0.5; p.k1 = 0.1; p.P1 = 0; p.P2 = 0; p.P3 = 0; p.ss.eval; println p.sv; // Pulse width // Set to 1 for no effect // Set to 4 for full effect h = 1; p.P1 = 0.3; m1 = p.sim.eval (0, 10, 100, [,, ]); p.P1 = 0.7; // Input stimulus m2 = p.sim.eval (10, 10 + h, 100, [,, ]); p.P1 = 0.3; m3 = p.sim.eval (10 + h, 40, 100, [,, ]); m = augr (m1, m2); m = augr (m, m3); graph (m);

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 23 OR GATE Question: What behavior would you expect if the feed-forward network is governed by an OR gate?

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 24 OR GATE Question: What behavior would you expect if the feed-forward network is governed by an OR gate? 1. No delay on activation. 2. Delay on deactivation. 3. Pulse Stretcher and Shifter

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 25 OR GATE Time

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Feed-forward Circuits Coherent Type I Genetic Network Copyright (c) 2013 26 p = defn cell $G2 -> P2; Vmax2*P1^4/(Km1 + P1^4); P2 -> $w; k1*P2; $G3 -> P3; Vmax3*(P1^4 + P2^4)/(Km1 + P1^4 + P2^4); P3 -> $w; k1*P3; end; p.Vmax2 = 1; p.Vmax3 = 0.1; p.Km1 = 0.5; p.k1 = 0.1; p.P1 = 0; p.P2 = 0; p.P3 = 0; p.ss.eval; println p.sv; // Pulse width // Set to 1 for no effect // Set to 4 for full effect h = 90; p.P1 = 0.3; m1 = p.sim.eval (0, 50, 1000, [,, ]); p.P1 = 0.8; // Input stimulus m2 = p.sim.eval (50, 50 + h, 1000, [,, ]); p.P1 = 0.3; m3 = p.sim.eval (50 + h, 200, 1000, [,, ]); m = augr (m1, m2); m = augr (m, m3); graph (m);

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Feed-forward Circuits Incoherent Type I Genetic Network Copyright (c) 201327 I1

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Incoherent Type I Genetic Network Pulse Generator Copyright (c) 201328 P3 comes down even though P1 is still high ! I P3

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Incoherent Type I Genetic Network Pulse Generator Copyright (c) 201329 P3 comes down even though P1 is still high ! Time P1, P3 P1 P3 Pulses are not symmetric because the rise and fall times are not the same.

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Incoherent Type I Genetic Network Digital Pulse Generator Copyright (c) 201330 Pulses are symmetric because the rise and fall times are the same. AND

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Incoherent Type I Genetic Network Pulse Generator Copyright (c) 201331 One potential problem, if the base line for P3 is not at zero, the off transition will result in an inverted pulse. Avoid this by arranging the base line of P3 to be at zero. TIME Inverted Pulse

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Incoherent Type I Genetic Network Pulse Generator Copyright (c) 2013 p = defn cell $G1 -> P2; t1*a1*P1/(1 + A1*P1); P2 -> $w; gamma_1*P2; $G3 -> P3; t2*b1*P1/(1 + b1*P1 + b2*P2 + b3*P1*P2^8); P3 -> $w; gamma_2*P3; end; p.P2 = 0; p.P3 = 0; p.P1 = 0.01; p.G3 = 0; p.G1 = 0; p.t1 = 5; p.a1 = 0.1; p.t2 = 1; p.b1 = 1; p.b2 = 0.1; p.b3 = 10; p.gamma_1 = 0.1; p.gamma_2 = 0.1; // Time course response for a step pulse p.P1 = 0.0; m1 = p.sim.eval (0, 10, 100, [,, ]); p.P1 = 0.4; // Input stimulus m2 = p.sim.eval (10, 50, 200, [,, ]); m = augr (m1, m2); graph (m); 32 I1

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Incoherent Type I genetic Network Steady State Concentration Detector Copyright (c) 201333 I1 Circuit is off at low concentration, off at high concentrations but comes on intermediate concentrations. Width of the peak can be controlled by the cooperativity transcription binding.

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Incoherent Type I genetic Network Concentration Detector Copyright (c) 2013 Take the pulse generator model and use this code to control it: // Steady state response n = 200; m = matrix (n, 2); for i = 1 to n do begin m[i,1] = p.P1; m[i,2] = p.P3; p.ss.eval; p.P1 = p.P1 + 0.005; end; graph (m); 34 I1

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Incoherent Type I genetic Network Response Accelerator Copyright (c) 201335 Making this stronger makes the initial rise go faster. Then, bring the overshoot down to the desired steady state with the repression feed- forward. An Introduction to Systems Biology: Design Principles of Biological Circuits.

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Summary Copyright (c) 201336 1.Persistence detector. Does not respond to transient signals. AND: Delay on start, no delay on deactivate. 2. Pulse stretcher and shifter. OR: No delay on start, delay on deactivate. 1. Pulse generator 2. Concentration detector. 3. Response time accelerator. C1I1

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Sequence Control – Temporal Programs More Complex Arrangement Copyright (c) 201337 Parallel Concentration Detecting Feed-Forward Networks – Generating Pulse Trains The kinetics can be arranged so that each successive feed-forward loop peaks at a later time. P3 rises first, followed by P5. This allows pulse trains to be generated. ……

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Nested FFLs Copyright (c) 2013 38 Input Output 1 Output 2 Output 3

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Nested FFLs - Counters Copyright (c) 2013 39 Input Output 1 Output 2 Output 3 Friedland, A. E. et al. Synthetic gene networks that count. Science 324, 1199–1202 (2009).

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Nested FFLs - Counters Copyright (c) 2013 40 Lte0-1: Constitutive promoter T7 RNAP: T7 RNA Polymerase P_T7: T7 RNAP Promoter GFP: Green fluorescent protein P_BAD: Arabinose Operator taRNA/cr - Riboregulator Friedland, A. E. et al. Synthetic gene networks that count. Science 324, 1199–1202 (2009).

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GFP: Green Fluorescent Protein 41 A protein of 238 amino acids that exhibits bright green light (at about 509nm) when exposed to light in the blue range (395 nm and 475 nm). Comes from the Jellyfish Aequorea victoria. Many derivatives now available, eg Azurite (blue), Venus (yellow), ECFP (cyan), RFP (red). Advantages: 1.Small, expressed in most if not all organisms. 2.Is self-contained, doesnt require other molecules to work

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Nested FFLs - Counters Copyright (c) 2013 42 Input Output 1 Output 2 Output 3

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Riboregulators Copyright (c) 2013 43 Nature Biotechnology 22, 841 - 847 (2004) Published online: 20 June 2004; | doi:10.1038/nbt986 Engineered riboregulators enable post-transcriptional control of gene expression Farren J Isaacs, Daniel J Dwyer, Chunming Ding, Dmitri D Pervouchine, Charles R Cantor & James J Collins

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Using RNA to Control Copyright (c) 2013 44 Modular: crRNA can be inserted upstream of any gene Can change levels of cis- repression and trans-activation with different promoters (tried with PLAC also) driving expression of taRNA and crRNA transcripts Unfolds hairpin to expose RBS (non-coding RNA [ncRNA])

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Riboregulators Copyright (c) 2013 45

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Other Motifs Copyright (c) 201346 1.Single-input Module (SIM) 2.Auto-regulation

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Sequence Control – Temporal Programs Copyright (c) 201347 Single-input Module (SIM) The simplest approach is to have different thresholds can be achieved by assigning a different K and Vmax to each expression rate law, easily generated through evolutionary selection. An Introduction to Systems Biology: Design Principles of Biological Circuits. Input: X E1 E2 E3

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Temporal Order Control of Bacterial Flagellar Assembly Copyright (c) 201348 Driven by a proton gradient. Runs at approximately 6,000 to 17,000 rpm. With the filament attaching rotation is slower at 200 to 1000 rpm Can rotate in both directions. Approximately 50 genes involved in assembly of the motor and control circuits. http://www.youtube.com/watch?v=0N09BIEzDlI

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Temporal Order Control of Flagellar Assembly Copyright (c) 201349 An Introduction to Systems Biology: Design Principles of Biological Circuits.

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Temporal Order Control of Flagellar Assembly Copyright (c) 201350

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Temporal Order Control of Metabolic Pathways - Arginine Copyright (c) 201351

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Temporal Order Control of Metabolic Pathways Arginine Copyright (c) 201352 EarlyLate Red means more expression of that particular gene.

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Temporal Order Control of Metabolic Pathways Methionine Copyright (c) 201353

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Temporal Order Control of Metabolic Pathways Methionine Copyright (c) 201354 Increasing a pathways capacity by sequential ordering of expression is probably only employed when the pathway is empty. For pathways already in operation, eg pathways like glycolysis, increasing the capacity is achieved by simultaneous increases. This is done to avoid wild swings in existing metabolite pools.

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Auto Regulation Copyright © 2013: Sauro

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Auto-regulation – Negative Feedback Copyright (c) 201356

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Auto-regulation – Positive Feedback Copyright (c) 201357

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Negative Feedback - Homeostasis V1, V2 V1 P

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Negative Feedback - Homeostasis V1, V2 V1 P V2 Steady State!

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Negative Feedback - Homeostasis V1, V2 V1 P V2 P is very sensitive to changes in V2 (k2)

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Negative Feedback - Homeostasis V1, V2 V1 P V2 P is less sensitive to changes in V2 (k2)

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Negative Feedback - Homeostasis V1, V2 V1 V2 = 0.3 V2 = 0.2 V2 = 0.1 S1 P is much less sensitive to changes in V2 (k2)

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Auto-regulation – Negative Feedback Response Accelerator Copyright (c) 201363 Weak Feedback Strong Feedback + strong input promoter Input, I P

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Amplifiers Input, I Output, P

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Amplifiers

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No Feedback The Effect of Negative Feedback Input, I Output, P

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Amplifiers No Feedback The Effect of Negative Feedback With Feedback Input, I Output, P Negative Feedback stretches the response and reduces the gain, but what else?

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Simple Analysis of Feedback A k yo yi

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Simple Analysis of Feedback Solve for yo: A k yo yi

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Simple Analysis of Feedback Solve for yo: A k yo yi

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Simple Analysis of Feedback At high amplifier gain (A k > 1): In other words, the output is completely independent of the amplifier and is linearly dependent on the feedback.

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Simple Analysis of Feedback Basic properties of a feedback amplifier: 1.Robust to variation in amplifier characteristics. 2.Linearization of the amplifier response. 3.Reduced gain The addition of negative feedback to a gene circuit will reduce the level of noise (intrinsic noise) that originates from the gene circuit itself.

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Summary of Negative Feedback 1. Noise Suppression 2. Accelerated Response 3. High Fidelity Amplifier 4. Feedback Oscillation

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