Network Motifs and Modules Network Motifs and Modules 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. 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. Network Motifs Negative Autoregulation Coherent Feedforward Positive Autoregulation InCoherent Feedforward Double Positive Feedback Double Negative Feedback Delay or ultrasensitivity unit Network Motifs Multi-Output FFL Bi-Fan Regulated Double Negative Feedback Dense Overlapping Regulons Regulated Double Positive Feedback SIM – Single Input Module Network Motifs Negative Autoregulation 1. Noise Suppression 2. Accelerated Response 3. High Fidelity Amplifier 4. Feedback Oscillation Positive Autoregulation 1. Bistability 2. Memory Unit Relaxation Oscillator Network Motifs Double Positive Feedback Memory unit where both units are either on or off Double Negative Feedback Memory unit: when one unit is off the other unit is on Network Motifs Coherent Feedforward 1. Noise rejection 2. Pulse shifter InCoherent Feedforward 1. Pulse generator 2. Concentration detector 3. Response time accelerator Network Motifs Regulated Double Positive Feedback Regulated Double Negative Feedback Z Z Memory unit that records an event in Z Memory unit that where nodes switch in opposite directions due to an event in Z Network Motifs Multi-Output FFL 1. Pulse Train Generator 2. Temporal Sequencer – Last in last out, ie the last gene activated is the last gene deactivated. 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 Feed-forward Networks Copyright © 2013: Sauro Feed-forward Networks 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. Copyright © 2013: Sauro Feed-forward Circuits The sign of an interaction can be determined either from basic biochemistry studies or by looking at microarray expression profiles. Activate Repress Copyright (c) 2013 13 Feed-forward Circuits Copyright (c) 2013 14 Feed-forward Circuits C1 I1 Relative abundance of different FFL types in Yeast and E. coli. Data taken from Mangan et al. 2003. Copyright (c) 2013 15 Feed-forward Circuits Dynamic Properties Copyright (c) 2008 16 First Translate Non-stoichiometric Network into a Stoichiometric Network C1 Copyright (c) 2013 17 First Translate Non-stoichiometric Network into a Stoichiometric Network C1 ? Copyright (c) 2013 18 Feed-forward Circuits Dynamic Properties What does this actually mean? AND GATE? Input A Input B AND OR XOR 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 OR GATE? Or something else? Copyright (c) 2013 19 Feed-forward Circuits Coherent Type I Genetic Network: AND Gate C1 AND GATE Copyright (c) 2013 20 Feed-forward Circuits Coherent Type I Genetic Network Noise Rejection Circuit No Delay P1 Narrow Pulse P1 Wide Pulse P3 Time P3 Delay Time NOTE THE DELAYS. Copyright (c) 2013 21 Feed-forward Circuits Coherent Type I Genetic Network 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 m1 = p.P1 m2 = p.P1 m3 = = 0.3; p.sim.eval (0, 10, 100, [<p.Time>, <p.P1>, <p.P3>]); = 0.7; // Input stimulus p.sim.eval (10, 10 + h, 100, [<p.Time>, <p.P1>, <p.P3>]); = 0.3; p.sim.eval (10 + h, 40, 100, [<p.Time>, <p.P1>, <p.P3>]); m = augr (m1, m2); m = augr (m, m3); graph (m); Copyright (c) 2013 22 Feed-forward Circuits Coherent Type I Genetic Network Question: What behavior would you expect if the feed-forward network is governed by an OR gate? OR GATE Copyright (c) 2013 23 Feed-forward Circuits Coherent Type I Genetic Network 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 OR GATE Copyright (c) 2013 24 Feed-forward Circuits Coherent Type I Genetic Network Time OR GATE Copyright (c) 2013 25 Feed-forward Circuits Coherent Type I Genetic Network 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 m1 = p.P1 m2 = p.P1 m3 = = 0.3; p.sim.eval (0, 50, 1000, [<p.Time>, <p.P1>, <p.P3>]); = 0.8; // Input stimulus p.sim.eval (50, 50 + h, 1000, [<p.Time>, <p.P1>, <p.P3>]); = 0.3; p.sim.eval (50 + h, 200, 1000, [<p.Time>, <p.P1>, <p.P3>]); m = augr (m1, m2); m = augr (m, m3); graph (m); Copyright (c) 2013 26 Feed-forward Circuits Incoherent Type I Genetic Network I1 Copyright (c) 2013 27 Incoherent Type I Genetic Network Pulse Generator P3 I P3 comes down even though P1 is still high ! Copyright (c) 2013 28 Incoherent Type I Genetic Network Pulse Generator P1, P3 P3 P1 Pulses are not symmetric because the rise and fall times are not the same. Time P3 comes down even though P1 is still high ! Copyright (c) 2013 29 Incoherent Type I Genetic Network Digital Pulse Generator AND Pulses are symmetric because the rise and fall times are the same. Copyright (c) 2013 30 Incoherent Type I Genetic Network Pulse Generator 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 Copyright (c) 2013 31 Incoherent Type I Genetic Network Pulse Generator 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 p.P3 p.P1 p.G3 p.G1 I1 = = = = = 0; 0; 0.01; 0; 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 m1 = p.P1 m2 = = 0.0; p.sim.eval (0, 10, 100, [<p.Time>, <p.P1>, <p.P3/1>]); = 0.4; // Input stimulus p.sim.eval (10, 50, 200, [<p.Time>, <p.P1>, <p.P3/1>]); m = augr (m1, m2); graph (m); Copyright (c) 2013 32 Incoherent Type I genetic Network Steady State Concentration Detector 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. Copyright (c) 2013 33 Incoherent Type I genetic Network Concentration Detector Take the pulse generator model and use this code to control it: I1 // 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); Copyright (c) 2013 34 Incoherent Type I genetic Network Response Accelerator Making this stronger makes the initial rise go faster. Then, bring the overshoot down to the desired steady state with the repression feedforward. Copyright (c) 2013 An Introduction to Systems Biology: Design Principles of 35 Biological Circuits. Summary C1 1. Persistence detector. Does not respond to transient signals. I1 1. Pulse generator 2. Concentration detector. AND: Delay on start, no delay on deactivate. 3. Response time accelerator. 2. Pulse stretcher and shifter. OR: No delay on start, delay on deactivate. Copyright (c) 2013 36 Sequence Control – Temporal Programs More Complex Arrangement 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. Copyright (c) 2013 37 Input Nested FFLs Output 1 Output 2 Output 3 Copyright (c) 2013 38 Input Nested FFLs - Counters Output 1 Friedland, A. E. et al. Synthetic gene networks that count. Science 324, 1199–1202 (2009). Output 2 Output 3 Copyright (c) 2013 39 Nested FFLs - Counters Lte0-1: Constitutive promoter T7 RNAP: T7 RNA Polymerase P_T7: T7 RNAP Promoter GFP: Green fluorescent protein Friedland, A. E. et al. Synthetic gene networks that count. Science 324, 1199–1202 (2009). P_BAD: Arabinose Operator taRNA/cr - Riboregulator Copyright (c) 2013 40 GFP: Green Fluorescent Protein 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, doesn’t require other molecules to work 41 Input Nested FFLs - Counters Output 1 Output 2 Output 3 Copyright (c) 2013 42 Riboregulators 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 Copyright (c) 2013 43 Using RNA to Control Modular: crRNA can be inserted upstream of any gene Can change levels of cisrepression and trans-activation with different promoters (tried with PLAC also) driving expression of taRNA and crRNA transcripts Unfolds hairpin to expose RBS Copyright (c) 2013 (non-coding RNA [ncRNA]) 44 Riboregulators Copyright (c) 2013 45 Other Motifs 1. Single-input Module (SIM) 2. Auto-regulation Copyright (c) 2013 46 Sequence Control – Temporal Programs Single-input Module (SIM) E1 E2 E3 Input: X 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 Copyright (c) 2013 Biology: Design Principles of 47 Biological Circuits. Temporal Order Control of Bacterial Flagellar Assembly 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 Copyright (c) 2013 48 Temporal Order Control of Flagellar Assembly An Introduction to Systems Biology: Design Principles of Biological Circuits. Copyright (c) 2013 49 Temporal Order Control of Flagellar Assembly Copyright (c) 2013 50 Temporal Order Control of Metabolic Pathways - Arginine Copyright (c) 2013 51 Temporal Order Control of Metabolic Pathways Arginine Early Late Red means more expression of that particular gene. Copyright (c) 2013 52 Temporal Order Control of Metabolic Pathways Methionine Copyright (c) 2013 53 Temporal Order Control of Metabolic Pathways Methionine Increasing a pathway’s 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. Copyright (c) 2013 54 Auto Regulation Copyright © 2013: Sauro Auto-regulation – Negative Feedback Copyright (c) 2013 56 Auto-regulation – Positive Feedback Copyright (c) 2013 57 Negative Feedback - Homeostasis V1 V1, V2 P Negative Feedback - Homeostasis V1 V2 V1, V2 Steady State! P Negative Feedback - Homeostasis V2 V1, V2 V2 V1 P P is very sensitive to changes in V2 (k2) Negative Feedback - Homeostasis V2 V1 V1, V2 V2 P P is less sensitive to changes in V2 (k2) Negative Feedback - Homeostasis V2 = 0.3 V1 V2 = 0.2 V1, V2 V2 = 0.1 S1 P is much less sensitive to changes in V2 (k2) Auto-regulation – Negative Feedback Response Accelerator Strong Feedback + strong input promoter P Weak Feedback Input, I Copyright (c) 2013 63 Amplifiers Output, P Input, I Amplifiers Amplifiers The Effect of Negative Feedback No Feedback Output, P Input, I Amplifiers The Effect of Negative Feedback Negative Feedback stretches the response and reduces the gain, but what else? No Feedback Output, P Input, I With Feedback Output, P Input, I Simple Analysis of Feedback yi A k yo Simple Analysis of Feedback yi A k Solve for yo: yo Simple Analysis of Feedback yi A k Solve for yo: yo 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. 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. Summary of Negative Feedback 1. Noise Suppression 2. Accelerated Response 3. High Fidelity Amplifier 4. Feedback Oscillation