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)

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 t X T 1/2 X max X max /2 Saturation level Response time

Comparison with simple regulation In comparison, we consider the simple regulation t X T 1/2 X max X max /2 Saturation level Response time

Comparison with simple regulation For meaningful comparison, assume that the parameters are as similar as possible.

Comparison with simple regulation For meaningful comparison, assume that the parameters are as similar as possible. t X T 1/2 X max X max /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 X max sensitive to  ?

Robustness to fluctuation in production rate The production rate, , can fluctuate in time due to noisy environment. Question: Is X max sensitive to  ? Sensitivity analysis –Define parameter sensitivity coefficient as S(A, B) =  A/A /  B/B = (B/A) dA/dB propertyparameter

Robustness to fluctuation in production rate The production rate, , can fluctuate in time due to noisy environment. Question: Is X max sensitive to  ? Sensitivity analysis –Define parameter sensitivity coefficient as S(A, B) =  A/A /  B/B = (B/A) dA/dB

Robustness to fluctuation in production rate The production rate, , can fluctuate in time due to noisy environment. Question: Is X max sensitive to  ? Sensitivity analysis –Define parameter sensitivity coefficient as S(A, B) =  A/A /  B/B = (B/A) dA/dB

Feed-forward loop (FFL) X YZ

X YZ 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 S x =1; X*=0 if S x =0 Y*=Y if S Y =1; Y*=0 if S Y =0 X Y Z AND SXSX SYSY

Dynamic response for coherent FFL with AND logic simple 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 SXSX SYSY Z is activated only if either X or Y is present.

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 SXSX SYSY Z is activated only if X but not Y is present.

Incoherent FFL X Y Z AND SXSX SYSY X XY Y Strong transcription Weak transcription

Dynamic response for incoherent FFL with AND logic X Y Z AND SXSX SYSY SxSx t Z A pulse generator

Dynamic response for incoherent FFL with AND logic

Network motifs in development Positive feedback loop XY XY XY XY Create bistability

Network motif in development Long transcriptional cascade. XYZ t (generations) X Y Z

Network motif in development XX P YY P ZZ P Phosphorylation cascade is a common signal transduction mechanism in bacteria. Signals are amplified by cascades.