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

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.


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

Z Z

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

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 (c) 2013 13

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.

I1

C1


Feed-forward CircuitsDynamic Properties


First Translate Non-stoichiometric Network into a Stoichiometric Network

C1


First Translate Non-stoichiometric Network into a Stoichiometric Network

C1

?


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

C1

AND GATE

21

Feed-forward CircuitsCoherent Type I Genetic Network

Copyright (c) 2013

NOTE THE DELAYS.

Delay

No Delay

TimeTime

P1 P1

P3 P3

Noise Rejection Circuit

Narrow Pulse Wide Pulse

22


Copyright (c) 2013

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);

23


Copyright (c) 2013

OR GATE

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

24


Copyright (c) 2013

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

25


Copyright (c) 2013

OR GATETime

26


Copyright (c) 2013

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

I1


Incoherent Type I Genetic NetworkPulse Generator

P3 comes down even though P1 is still high !

I

P3


Incoherent Type I Genetic NetworkPulse Generator

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.


Incoherent Type I Genetic Network Digital Pulse Generator

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

AND


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


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);

I1


Incoherent Type I genetic NetworkSteady State Concentration Detector

I1

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);

I1


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.

C1 I1


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.

……

38

Nested FFLs

Copyright (c) 2013

Input

Output 1

Output 2

Output 3

39

Nested FFLs - Counters

Copyright (c) 2013

Input

Output 1

Output 2

Output 3

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

40


Copyright (c) 2013

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).

41

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

42


Copyright (c) 2013

Input

Output 1

Output 2

Output 3

43

Riboregulators

Copyright (c) 2013

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

44

Using RNA to Control

Copyright (c) 2013

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])

45

Riboregulators

Copyright (c) 2013


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

E1

E2E3


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

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


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

V1

P


V1, V2

V1

P

V2

Steady State!


V1, V2

V1

P

V2

V2

P is very sensitive to changes in V2 (k2)


V1, V2

V1

P

V2

V2

P is less sensitive to changes in V2 (k2)


V1, V2

V1

V2 = 0.3

V2 = 0.2

V2 = 0.1

S1

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


Auto-regulation – Negative Feedback Response Accelerator

Weak Feedback

Strong Feedback+ strong inputpromoter

Input, I

P

Amplifiers

Input, I

Output, P

Amplifiers

Amplifiers

No Feedback

The Effect of Negative Feedback

Input, I

Output, P

Amplifiers

No Feedback

The Effect of Negative Feedback

With Feedback

Input, I

Input, I

Output, P

Output, P

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

Simple Analysis of Feedback

A

k

yoyi


Solve for yo:

A

k

yoyi


Solve for yo:

A

k

yoyi


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

Date post:	31-Mar-2015
Category:	Documents
Upload:	jonas-vails
View:	216 times
Download:	0 times

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

Documents