Network Motifs and Modules. What is a motif? A motif is a statistically over-represented subgraph in...

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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

Positive Autoregulation

Double Positive Feedback

Double Negative Feedback

CoherentFeedforward

InCoherentFeedforward

Delay orultrasensitivity unit

Network Motifs

Multi-Output FFL

Regulated Double Negative Feedback

Regulated Double Positive Feedback

Bi-Fan

Dense Overlapping

Regulons

SIM – Single Input Module

Network MotifsNegative Autoregulation Positive Autoregulation

1. Noise Suppression2. Accelerated Response3. High Fidelity Amplifier4. Feedback Oscillation

1. Bistability2. Memory Unit

Relaxation Oscillator

Network Motifs

Memory unit where bothunits are either on or off

Memory unit: when one unitis off the other unit is on

Double Positive Feedback Double Negative Feedback

Network Motifs

1. Noise rejection2. Pulse shifter

1. Pulse generator2. Concentration detector3. Response time accelerator

Coherent Feedforward InCoherent Feedforward

Network Motifs

Memory unit that recordsan 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

Network Motifs

1. Pulse Train Generator2. Temporal Sequencer – Last in last out,ie the last gene activated is the last genedeactivated.

Multi-Output FFL SIM – Single Input Module

1. Master/Salve Regulator2. Temporal Sequencer – Last in first out, ie. The last gene activated is the first gene deactivated

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.

Feed-forward Circuits

Activate

Repress

The sign of an interactioncan be determined either from basicbiochemistry studies or by looking at microarray expression profiles.

Relative abundance of different FFL types in Yeast and E. coli. Data taken fromMangan et al. 2003.

Feed-forward CircuitsDynamic Properties

First Translate Non-stoichiometric Network into a Stoichiometric Network

Feed-forward CircuitsDynamic Properties

What does this actually mean?

AND GATE? OR GATE?Or something else?

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

Feed-forward CircuitsCoherent Type I Genetic Network: AND Gate

AND GATE

Feed-forward CircuitsCoherent Type I Genetic Network

NOTE THE DELAYS.

No Delay

TimeTime

Noise Rejection Circuit

Narrow Pulse Wide Pulse

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 effecth = 1;

p.P1 = 0.3;m1 = p.sim.eval (0, 10, 100, [<p.Time>, <p.P1>, <p.P3>]);p.P1 = 0.7; // Input stimulusm2 = p.sim.eval (10, 10 + h, 100, [<p.Time>, <p.P1>, <p.P3>]);p.P1 = 0.3;m3 = p.sim.eval (10 + h, 40, 100, [<p.Time>, <p.P1>, <p.P3>]);

m = augr (m1, m2);m = augr (m, m3);graph (m);

OR GATE

Question: What behavior would you expect if the feed-forward network is governed by an OR gate?

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

OR GATETime

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 effecth = 90;

p.P1 = 0.3;m1 = p.sim.eval (0, 50, 1000, [<p.Time>, <p.P1>, <p.P3>]);p.P1 = 0.8; // Input stimulusm2 = p.sim.eval (50, 50 + h, 1000, [<p.Time>, <p.P1>, <p.P3>]);p.P1 = 0.3;m3 = p.sim.eval (50 + h, 200, 1000, [<p.Time>, <p.P1>, <p.P3>]);

m = augr (m1, m2);m = augr (m, m3);graph (m);

Feed-forward CircuitsIncoherent Type I Genetic Network

Incoherent Type I Genetic NetworkPulse Generator

P3 comes down even though P1 is still high !

Incoherent Type I Genetic NetworkPulse Generator

P3 comes down even though P1 is still high !

P1, P3

Pulses are not symmetric because the rise and fall times are not the same.

Incoherent Type I Genetic Network Digital Pulse Generator

Pulses are symmetric because the rise and fall times are the same.

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.

Inverted Pulse

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 = 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.Time>, <p.P1>, <p.P3/1>]);p.P1 = 0.4; // Input stimulusm2 = p.sim.eval (10, 50, 200, [<p.Time>, <p.P1>, <p.P3/1>]);

m = augr (m1, m2);graph (m);

Incoherent Type I genetic NetworkSteady State Concentration Detector

Circuit is off at low concentration, off at high concentrationsbut comes on intermediate concentrations. Width of the peakcan be controlled by the cooperativity transcription binding.

Incoherent Type I genetic NetworkConcentration Detector

Take the pulse generator model and use this code to control it:

// Steady state responsen = 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);

Incoherent Type I genetic NetworkResponse Accelerator

Making this strongermakes the initial risego 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.

Summary

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.

Sequence Control – Temporal ProgramsMore Complex Arrangement

Parallel Concentration Detecting Feed-Forward Networks –Generating Pulse Trains

The kinetics can be arranged so thateach successive feed-forward loop peaks at a later time.

P3 rises first, followed by P5.

This allows pulse trains to be generated.

……

Nested FFLs

Output 1

Output 2

Output 3

Nested FFLs - Counters

Output 1

Output 2

Output 3

Friedland, A. E. et al. Synthetic gene networks that count. Science 324, 1199–1202 (2009).

Lte0-1: Constitutive promoterT7 RNAP: T7 RNA PolymeraseP_T7: T7 RNAP PromoterGFP: 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).

GFP: Green Fluorescent ProteinA 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

Output 1

Output 2

Output 3

Riboregulators

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

Using RNA to Control

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])

Riboregulators

Other Motifs

1. Single-input Module (SIM)

2. Auto-regulation

Sequence Control – Temporal Programs

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

Temporal Order Control of Bacterial Flagellar Assembly

Driven by a proton gradient.Runs at approximately6,000 to 17,000 rpm. With the filament attaching rotation is slower at 200 to 1000 rpm

Can rotate in both directions.

Approximately 50 genesinvolved in assembly of themotor and control circuits.

http://www.youtube.com/watch?v=0N09BIEzDlI

Temporal Order Control of Flagellar Assembly An Introduction to Systems

Biology: Design Principles of Biological Circuits.

Temporal Order Control of Flagellar Assembly

Temporal Order Control of Metabolic Pathways - Arginine

Temporal Order Control of Metabolic Pathways Arginine

Early Late

Red means more expression of that particular gene.

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.

Auto Regulation

Auto-regulation – Negative Feedback

Auto-regulation – Positive Feedback

Negative Feedback - Homeostasis

V1, V2

Steady State!

V1, V2

P is very sensitive to changes in V2 (k2)

V1, V2

P is less sensitive to changes in V2 (k2)

V1, V2

V2 = 0.3

V2 = 0.2

V2 = 0.1

P is much less sensitive to changes in V2 (k2)

Auto-regulation – Negative Feedback Response Accelerator

Weak Feedback

Strong Feedback+ strong inputpromoter

Input, I

Amplifiers

Input, I

Output, P

Amplifiers

No Feedback

The Effect of Negative Feedback

Input, I

Output, P

Amplifiers

No Feedback

The Effect of Negative Feedback

With Feedback

Input, I

Output, P

Negative Feedbackstretches the responseand reduces the gain, but what else?

Simple Analysis of Feedback

Solve for yo:

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.

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 Suppression2. Accelerated Response3. High Fidelity Amplifier4. Feedback Oscillation

Network Motifs and Modules. What is a motif? A motif is a statistically over-represented subgraph in...

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