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Inferring Gene Regulatory Networks

Introduction

Network Inference / Systems Biology

file:./img/SysBio-2d.png

Inspired by Arkin and Schaffer (2011)

Gene Regulatory Network (GRN) models

file:./img/NordlingA10Network.png

Experimental Setup

Equations Modeling the System

at Steady State

Optimal Sparsity Selection

Sparsity

file:./img/Tjarnberg-D20131025-random-N10-L25-ID75466-Aest-L32.png

file:./img/Tjarnberg-D20131025-random-N10-L25-ID75466.png

file:./img/Tjarnberg-D20131025-random-N10-L25-ID75466-Aest-L22.png

file:./img/Glmnet-wo-all-inf.png

Work-flow

file:./img/workflow2.png

file:./img/Glmnet-co-all-inf.png

Two Independent Data sets

Single Data set comprised of Independent Samples

Linear Independence

file:./img/lin-IndependeceDark.png

file:./img/Glmnet-inf.png

Constrained Least Squares, (CLS)

file:./img/Glmnet-cls-inf.png

Results

file:./img/Tjarnberg.Fig_1.png

file:./img/Tjarnberg.Fig_2.png

file:./img/Tjarnberg.Fig_3.png

Benchmark of GRN Inference Algorithms

Aim

Preferred algorithm

Expected outcome

How: Relate to

• Network properties
• Data set properties

Network properties

# of network:	20
# states, N:	10
interampatteness degree:	low VS high
sparseness degree:	0.25
Stable	Yes

Data set properties

# of Data sets:	40
optimal designed P:	20
random double P:	20
Samples / set	2N
condition number:	low VS high
SNR levels:	5
Information level:	is 1 when SNR \leq 1000

Performance Measure

Sign Matthew Correlation Coefficient (SMCC)

A\E	1	0	-1
1	TP	FN	FN
0	FP	TN	FP
-1	FN	FN	TP

Performance

file:./img/OptimalPerformance.png

Data property dependence

file:./img/OptimalPerformanceLowk.png

file:./img/OptimalPerformanceHighk.png

Sparsity Selection

file:./img/clsRSSPerformanceLowk.png

file:./img/pureRSSPerformanceLowk.png

Sparsity Selection

file:./img/clsRSSPerformanceHighk.png

file:./img/pureRSSPerformanceHighk.png

Prior Knowledge from Functional Association Networks

Databases of Functional Association

• FunCoup (Schmitt et al., 2013)
• STRING (Szklarczyk et al., 2011)⁠

FunCoup

file:./img/FunCoup.png

Prior Incorporation

file:./img/lnacc-GNW-caus-sn-60pct-alla-diff.png

file:./img/lnacc-GNW-caus-sn-70pct-alla-diff.png

Conclusions

Optimal Sparsity

• Selection of Samples For LOOCO
• Un-biased Re-estimation of Network links

Benchmark

• Data Properties Highly Influential for Inference Performance
• Optimal Sparsity Selection is Beneficial when adding CLS estimation

Prior Incorporation

• Accurate symmetric prior helps.

Acknowledgements

Erik Sonnhammer

Matthew Studham

Dimitri Guala

Thomas Schmitt

Gabriel Östlund

Christoph Ogris

Torbjörn Nordling

Oliver Fringes

Kristoffer Forslund