Functions of network motifs

12/12/07

All possible three-node connected subgraphs

Question: which graphs are used more often than randomly expected?

(Milo et al. 2002)

(Milo et al. 2002)

Auto-regulation network motif

Auto-regulation network motif

A

X

X

Modeling negative auto-regulatory network motifs

• Suppose a TF X negatively regulates its own expression. The dynamics of X can be given by

nKXXf

XXfdt

dX

)/(1)(

)(

t

X

T1/2

Xmax

Xmax/2

0)( maxmax XXf

• Saturation level

• Response time

2/)( max2/1 XTX

)1(

12/2log 11

2/1

nT

nn

)1/(1max )/( nKKX

Comparison with simple regulation

• In comparison, we consider the simple regulation

Xdt

dXsimplesimple

t

X

T1/2

Xmax

Xmax/2

simplesimpleX /max

• Saturation level

simpleT /2log2/1

• Response time

Comparison with simple regulation

• For meaningful comparison, assume that the parameters are as similar as possible.

...maxmax

ransimple

simple

XX

Comparison with simple regulation

• For meaningful comparison, assume that the parameters are as similar as possible.

...maxmax

ransimple

simple

XX

t

X

T1/2

Xmax

Xmax/2

n.a.r.simple.

p.a.r.• Negative auto-regulatory

motif speeds up response time.

Robustness to fluctuation in production rate

• The production rate, , can fluctuate in time due to noisy environment.

• Question: Is Xmax sensitive to ?

Robustness to fluctuation in production rate

• The production rate, , can fluctuate in time due to noisy environment.

• Question: Is Xmax sensitive to ?

• Sensitivity analysis– Define parameter sensitivity coefficient as

S(A, B) = A/A / B/B = (B/A) dA/dB property parameter

Robustness to fluctuation in production rate

• The production rate, , can fluctuate in time due to noisy environment.

• Question: Is Xmax sensitive to ?

• Sensitivity analysis– Define parameter sensitivity coefficient as

S(A, B) = A/A / B/B = (B/A) dA/dB

)1/(1/)/(),( maxmaxmax nddXXXS

Robustness to fluctuation in production rate

• The production rate, , can fluctuate in time due to noisy environment.

• Question: Is Xmax sensitive to ?

• Sensitivity analysis– Define parameter sensitivity coefficient as

S(A, B) = A/A / B/B = (B/A) dA/dB

1 if ,1)1/(1/)/(),( maxmaxmax nnddXXXS

Feed-forward loop (FFL)

X

Y Z

Feed-forward loop (FFL)

X

Y Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

Coherent FFL

Incoherent FFL

Coherent FFL with AND logic

• Z is activated only if both X and Y are present.

X*=X if Sx=1; X*=0 if Sx=0

Y*=Y if SY=1; Y*=0 if SY=0

X

Y

Z

AND

SX

SY

Dynamic response for coherent FFL with AND logic

simple

FFL FFL

simple

Type 1 and 4 coherent FFL with AND logic functions as a sign-sensitive delay element.

Dynamic response for coherent FFL with AND logic

Type 1 coherent FFL with AND logic can filter out small pulse fluctuations.

Dynamic response for coherent FFL with OR logic

X

Y

Z

AND

SX

SY

•Z is activated only if either X or Y is present.

Dynamic response for coherent FFL with OR logic

Dynamic response for coherent FFL with OR logic

No difference from simple regulation during the ON step.

Dynamic response for coherent FFL with OR logic

Delay element during the OFF step.

Incoherent FFL

X

Y

Z

AND

SX

SY

•Z is activated only if X but not Y is present.

Incoherent FFL

X

Y

Z

AND

SX

SY

X

X Y

Y

Strong transcription

Weak transcription

Dynamic response for incoherent FFL with AND logic

X

Y

Z

AND

SX

SYSx

t

Z

A pulse generator

Dynamic response for incoherent FFL with AND logic

Network motifs in development

• Positive feedback loop

X Y

X Y

X Y

X Y

• Create bistability

Network motif in development

• Long transcriptional cascade.

X Y Z

t (generations)1 2 3 4 5

X

Y

Z

Network motif in development

X X

P

Y Y

P

Z Z

P

Phosphorylation cascade is a common signal transduction mechanism in bacteria.

Signals are amplified by cascades.