Towards Reliable Gene Regulatory Network Inference

Stockholm University

April 2019

Daniel Morgan

Why Networks?

Biology

• Cells replicate, grow and die
• Express genes to confer trait via proteins
• Responses to environment are robust but not infinite

Directed Perturbation

• siRNA
• shRNA
• targeted drug
• eQTL
• CRISPRi

Hecker 2009

More

Smet 2010

Protein-Protein Interaction

Metabolic pathways

Signaling pathways

Transcript factors/ Gene regulatory networks

Pathway diagrams

Protein-compound interactions

Protein sequence focused

Genetic interaction networks

Guthke 2015

Tie-In to Biochemistry

 

• Directed links but not necessarily direct binding
• Offers regulatory information
  • (more than coexpression)

Knowledge & Hypothesis

inspired by Bellot 2015

Feature Selection

• Hierarchical clustering groups elements based on how close they are to one another. The result is a tree structure, referred to as dendrogram.
  • Genie3 determines those genes directly influencing expression patterns of other genes, ranking such features via the tree building ensemble process.
• K-means clustering groups elements into a specified number of clusters, which can be useful when you know or suspect the number of clusters in the data.

Mutual Info

 

• The area contained by both circles is the joint entropy H(X,Y)
• An individual circle is the individual entropy H(X) or H(Y)
  •  the unique area is the conditional entropy H(X|Y) or H(Y|X)
• The violet is the mutual information I(X;Y)

Boolean

YES or NO

• State space of a Boolean Network
  • N=4 nodes
  •  K=1 links per node.
  • 6 (orange) attractors
  • 4 are fixed points
• Thin (black) arrows symbolise the inputs of the Boolean function.
• The thick (grey) arrows show what a synchronous update does.

Bayesian

conditional probabilities per link > DAGs

System of Equations

coupled ODE related [mRNA] of gene to all other genes

Penfold 2011

Neural Nets

(x) hidden layers connecting input and output

 

supervised

• infer the mapping implied by the (training) data

unsupervised

• inferring a function to describe hidden structure from "unlabeled" data

Mechanistic

identify direct interactions

Influence

capture information flow to understand control system 

 

 

 

 

*(not necessarily measured or direct)

Two General, Distinct Aims

Gardner 2005

Network Inference

Gardner 2005

I. GeneSPIDER

II. NestBoot        

III. Perturbation based GRNI

IV. Large-Scale Comparison

Scoring Inferred(s) vs GS

GRN

LASSO (Glmnet),(T)LSCO,

RNI,ARACNe,Genie3,CLR

Perturbation (si/shRNA)

SNR, IAA, Rank

MCC, AUROC, wRSS

inferred  network

 

 

inference methods

 

 

experimental/ data collection

 

data properties

 

scoring measures

GeneSpider

Generation and Simulation Package for Informative Data ExploRation

 https://bitbucket.org/sonnhammergrni/genespider

GS case study

GS case study

RNICO

Robust Network Inference  decouples the model selection problem from parameter estimation; is very harsh but among the best methods when noise is low

ARACNe

focuses on mutual information between links in a link by link fashion rather than upon entire system as a whole. Also disregards self-regulating elements

LASSO/Glmnet

Least Absolute Shrinkage & Selection Operator: minimizes RSS by penalizing |coefficient| rather than their square, thus harshest (zeros possible)

(T)LSCO

Fit cases to regression line minimizing difference on X and Y axis

GS case study

with self loops ∴ null ARACNe

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

NestBoot

 

LSCO / TLSCO

Glmnet / LASSO

RNI

 

Genie3,

ARACNe, CLR

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

NestBoot

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

45 gene in-silico  network performance

https://gitlab.com/Xparx/scikit-grni.git

MATLAB -> Python

Real Data Performance

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

N10 Performance

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

CLR

utilize defined perturbation design to map expression to network topologies

LASSO

LSCO

RNICO

Genie3

uses a tree ensemble approach drawing on relationships between input gene expression patterns to predict those of target genes, building trees based on bootstrapped samples to return one inferred network with ranked link strengths

applies normal distribution statistics to mutual information scores in order to identify network links

NestBoot

A Generalized Framework for Controlling FDR in Gene Regulatory Network Inference

...

...

...

...

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

qPCR of 40 genes, singly & doubly knocked down via siRNA

• 3 biological replicates
• 2 technical replicates

 

​= gene fold change

&

variance of expression measures

Y: expression data
A: network
P: perturbation matrix
E: input noise estimate
F: output noise estimate

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

1. Shuffle Topology
2. Fit parameter to data
3. Estimate Goodness of Fit

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Novel Biochemical Regulatory Mechanism

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

https://dcolin.shinyapps.io/NestBoot-Viz/

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Myc

Perturbation-based gene regulatory network inference to reliably predict oncogenic mechanisms

Subramanian et al. 2017

HEATMAP=OK

Normalizing Melanoma Data ------ Data ---------- Network

SNR=.005

Subset Selection for Noisy Data

Inference Accuracy on Less-Noisy Subsets

Inference Accuracy on Less-Noisy Subsets

Subset Selection for Noisy Data

Melanoma Network Degree

Conclusion:

Improved the confidence of inferred GRN links by the evaluation of their significance through comparison to nulls

Thanks!

Erik Sonnhammer

1. Match drug target to genes
   • infer multi-P nets
2. Time-series, delta networks
3. match DE genes to GRN hubs
4. Pathway Enrichment

Subramanian et al. 2017

Overlap

Comparison

Gehlenborg Lab

subset selection method

4 RUV methods' performance quantified by 7 endpoint measures compared to 4 standard normalization methods

aim: high AdistKS, low lambda, unifKS, slopeHoriz, slopeVerti & MAD

calculating fold change, increasing SNR

• analysis of fold change profiles estimated by a RUV method
• remove unwanted variation
• separates signal from unwanted effects
• This greatly improves signal-to-noise over standard methods