Functional analysis of omics data

Omics measures different molecular layers

Layer	What is measured
Genomics	DNA sequence and variation
Transcriptomics	RNA abundance and transcript structure
Proteomics	Protein abundance, forms, and modifications
Metabolomics	Small molecules under defined conditions

No layer alone gives a complete description of biological function. Measurement coverage and interpretation depend on technology and study design.

Omic sciences

Overview

Omics overview (Joyce and Palsson 2006).

Some slides about Metabolomics

Definition

Metabolomics is the science that studies the lightweight chemical compounds (metabolites) and reactions that take place in organisms.

Purpose

Metabolomics measures a context-dependent part of the molecular phenotype. Its utilities include (Nicholson et al. 2002):

Finding of biomarkers for disease
Understanding of diseases
Prediction of treatment outcome

Metabolomic Analysis Workflow contributions at B2SLab (1/2)

Fernández-Albert F., Llorach R., Garcia-Aloy M, Ziyatdinov A, Andrés-Lacueva C., Perera-Lluna A. Intensity drift removal in LC/MS metabolomics by Common Variance Compensation. Bioinformatics 30 (20): 2899-2905. (2014).
Fernández-Albert F., Llorach R., Andrés-Lacueva C., Perera-Lluna A. An R package to analyse LC/MS metabolomic data: MAIT (Metabolite Automatic Identification Toolkit). Bioinformatics 30(13):1937-9 (2014).
Fernández-Albert F., Llorach R., Andrés-Lacueva C., Perera-Lluna A.Peak Aggregation as an Innovative Strategy for Improving the Predictive Power of LC-MS Metabolomic Profiles. Analytical Chemistry 86 (5), 2320-2325 (2014).

Published R packages on metabolomics (available on our website http://b2slab.upc.edu) and on Bioconductor:

MAIT: MAIT: Metabolite Automatic Identification Toolkit. An R package to perform end-to-end LC/MS metabolomic data analyses.

Metabolomic Analysis Workflow contributions at B2SLab (2/2)

intCor: This package performs an intensity drift correction for large datasets through several methods. This library is contains the non-linear methodology to perform retention time correction in LC/MS.

Metabolomic Analysis Workflow (LC/MS)

LC/MS signals

^2Wei Guan et al. BMC Bioinformatics 10:259, 2009

Signal to noise?

Metabolomics data (1/2)

Primary and secondary analyses

Primary analysis
- Detect peaks
- Annotate peaks
- Quantify metabolites
Secondary analysis
- Statistics
- Machine learning
- Enrichment techniques

Metabolomics data (2/2)

Metabolomics workflow (Sugimoto et al. 2012).

Functional Enrichment

Enrichment techniques

Experimental data can be understood in the framework of the known biological context. Enrichment techniques relate this data to biological pathways.

Enrichment in gene expression

The challenge no longer lies in obtaining gene expression profiles, but rather in interpreting the results to gain insights into biological mechanisms.

(Subramanian et al. 2005)

Three generations appear on later slides: over-representation (binary hits list, known background), gene-set enrichment (ranked full list, no cutoff), network analysis (signal propagated over a knowledge network).

Input bar of gene-level statistics feeding three labelled boxes: over-representation, gene-set enrichment and network analysis, each summarising its input type and statistic.

Annotation provenance

Computational annotation: sequence comparison, predictive models, text mining, and other algorithms.
Manual curation: expert evaluation of experimental and computational evidence.
Combined workflows: computational proposals with human review.

Read the evidence and provenance attached to a claim. Annotation categories do not guarantee certainty.

Databases (II)

Genes and gene products

Gene Ontology: contains three ontologies and a hierarchical structure reflecting the specificity of the entry (Ashburner et al. 2000).

Proteomics

UniProt: comprehensive database for protein sequence and annotation data (Consortium 2015).
STRING: protein association database, including functional and physical associations; automatic and curated evidence (Szklarczyk et al. 2015).

Metabolomics

KEGG: comprehensive and curated pathway database (Ogata et al. 1999).
Reactome, BioCyc, WikiPathways, SMPDB

Gene Ontology

An example of GO overrepresentation analysis (ORA)(Tian et al. 2014).

Databases (III) (1/2)

Examples

Glycolysis pathway in KEGG (Ogata et al. 1999).

Databases (III) (2/2)

PPI network in STRING (Szklarczyk et al. 2015).

Over-representation analysis

Define a background of N genes that could have been selected. A pathway contains K of these genes; the selected list has n genes, with overlap k.

P(X=k)=\frac{\binom Kk\binom{N-K}{n-k}}{\binom Nn}.

For enrichment, use the upper-tail probability:

p=P(X\ge k)=\sum_{j=k}^{\min(K,n)}P(X=j).

Adjust across the tested gene sets. The background and selection process determine the null model.

Gene data enrichment: over representation

Advantages

Relates genes with biological processes.
Assesses statistical significance.
Eases exploratory analysis.

Limitations

Relies on a prior (arbitrary) cutoff method.
Sensitive on the input size.
Ignores magnitude of the gene affectation.
Simplistic context representation in a binary fashion.

Gene data enrichment: set enrichment analysis (I)

Motivation

The second generation of methods intend to take advantage of quantitative data about gene expression.

Gene Set Enrichment Analysis (Subramanian et al. 2005)

GSEA procedure from original publication (Subramanian et al. 2005).

Gene data enrichment: set enrichment analysis (II)

Advantages

Takes into account quantitative measures.
Has reported to capture subtle but consistent changes in expression data.

Limitations

Genes have complex interactions that could be accounted.
Biological pathways exhibit substantial overlapping.

Gene data enrichment: network analysis (I)

Motivation

Network-based methods take into account the topological features of biological networks in order to test pathways.

Pathway-Express (Draghici et al. 2007)

IF(P) = \underbrace{\log \frac{1}{p}}_{\text{from ORA}} + \underbrace{\frac{\sum\limits_{g \in P} |PF(g)|}{\bar{|\Delta E|} \cdot N_{de} (P)}}_{Pathway perturbation}

\log \frac{1}{p} incorporates a p-value from over-representation analysis in the original Pathway-Express formulation
PF(g) = \Delta E (g) + \sum\limits_{u \in US_g} \beta_{ug} \cdot \frac{PF(u)}{N_{ds}(u)} considers the topology of the genes within the pathway, and is similar to PageRank scores. N_{de} (P): N DE genes on P_i,

Gene data enrichment: network analysis (I)

Gene data enrichment: network analysis (II)

Advantages

Takes into account topological features.
Benefits from current knowledge and its structure.

Limitations

Pathway overlapping still remains an issue.
Rising need to incorporate cell line specificity data in order to become biologically sound.

Metabolomics data enrichment

Origin

Metabolomics is a young science that followed Genomics and Transcriptomics trends. Concepts for data enrichment have been therefore ported from them.

Differences from genomic data enrichment

Human reference genomes are available, but metabolite coverage depends strongly on the sample and measurement technology. The background for statistical tests is not obvious (Chagoyen and Pazos 2012).
Experimental devices can exhibit low sensitivity or noisy signals (Hollywood et al. 2006).
There is no technology to measure the full spectrum of compounds. Large part of the background is not observable.

Databases in Metabolomics

Main databases in Metabolomics (Booth et al. 2013). (correct link for MetaCyc is http://metacyc.org/), and I would add Reactome to the list http://reactome.org

Metabolomics data enrichment: overview (I)

Over Representation Analysis

IMPaLA (Kamburov et al. 2011)
MetaboAnalyst (Xia et al. 2012)
MPEA (Kankainen et al. 2011)

Metabolite Set Enrichment Analysis

MSEA in MetaboAnalyst (Xia and Wishart 2010b)
PAPi (Aggio et al. 2010)

Network Analysis

MetPA in MetaboAnalyst (Xia and Wishart 2010a)

Metabolomics data enrichment: overview (II)

MetaboAnalyst (Xia et al. 2012)

MetaboAnalyst gathers topological analysis (x axis) and ORA or MSEA (y axis). It also depicts metabolite significance inside each pathway.

Metabolomics tools: historical review (2013) (1/8)

MetExplore [28]

Acc.: WB

Inp.: CompID, Mass IDs

DBsd: Generally BioCyc related

Funs.: Compound mapping, graph analysis of metabolism maps.

Comm: Choice of organism database, filtering options, multiple graph analysis tools, Cytoscape integration.

Metabolomics tools: historical review (2013) (2/8)

PAPi [24]

Acc.: R

Inp.: KEGG CompID

DBsd: KEGG

Funs.: Compares activity of metabolic pathways between sample types.

Comm: Non organism specific, more difficult/powerful command line R interface. Usable with spent media results.

Metabolomics tools: historical review (2013) (3/8)

MBRole [27]

Acc.: WB

Inp.: CompID

DBsd: KEGG, HMDB, PubChem, ChEBI, SMILES

Funs.: Enrichment analysis of metabolites’ annotations.

Comm: Background set from known organisms or custom set. Metabolite ID converter.

Metabolomics tools: historical review (2013) (4/8)

MetaboAnalyst [57]

Acc.: WB

Inp.: Raw Spectra (GC and LC MS), peak lists and spectral bins (MS and NMR)

DBsd: Custom, KEGG, HMDB

Funs.: Full processing, Statistical Analysis

Comm: Comprehensive metabolomics analysis platform with easy interface, tutorials, help. Human focused though some model organisms or custom metabolite set option.

Metabolomics tools: historical review (2013) (5/8)

MetaboAnalyst (MSEA) [58]

Acc.: WB.

Inp.: CompID and abundances

DBsd: Custom, KEGG, HMDB

Funs.: Enrichment Analysis

Comm: Comprehensive metabolomics analysis platform with easy interface, tutorials, help. Human focused though some model organisms or custom metabolite set option.

Metabolomics tools: historical review (2013) (6/8)

MetaboAnalyst (MetPa [59])

Acc.: WB

Inp.: CompID and abundances

DBsd: KEGG

Funs.: Pathway Analysis

Comm: Select model organisms. Network topology analysis. Intuitive network visualization.

Metabolomics tools: historical review (2013) (7/8)

MPEA [29]

Acc.: WB

Inp.: CompID, GC-MS Spectrum as ranked list

DBsd: KEGG, GMD, SMPDB

Funs.: Pathway enrichment analysis.

Comm: Optional background set. Limited to top-down/bottom-up analysis.

Metabolomics tools: historical review (2013) (8/8)

MeltDB (MSEA) [30 and 60]

Acc.: WB, (L)

Inp.: Raw GC/LC-MS spectra, processed spectra, CompID and abundances

DBsd: GMD, KEGG, ChEBI, CAS

Funs.: Comprehensive preprocessing, statistical analysis and metabolite mapping, enrichment analysis.

Comm: Integrated comprehensive online system, accessible by multiple users. Many statistical tools, custom metrics and sets for enrichment analysis.

Adapted from a very nice review from (Booth et al. 2013)

Metabolomics tools: historical review (2013) (1/9)

Meta P-server [61]

Acc.: WB

Inp.: CompID, sample meta-data

DBsd: KEGG, HMDB, LipidMaps, PubChem

Funs.: Data quality control, statistical analysis, hypothesis testing.

Comm: No use of organismal databases. Focus mainly on global statistical analysis.

Metabolomics tools: historical review (2013) (2/9)

MassTrix [62 and 63]

Acc.: WB

Inp.: MS spectra

DBsd: KEGG, HMDB, LipidMaps

Funs.: Compound mapping

Comm: Choice of KEGG organism. Optional background set. Color-coding.

Metabolomics tools: historical review (2013) (3/9)

BioCyc (Pathway Tools) [52]

Acc.: Ins

Inp.: Annotated genome, ’omics data

DBsd: MetaCyc

Funs.: Network exploration, genome annotation, ’omics data painting.

Comm: Comprehensive systems biology network analysis.

Metabolomics tools: historical review (2013) (4/9)

Pathos [64]

Acc.: WB

Inp.: Simple m/z values, CompID

DBsd: KEGG

Funs.: Compound mapping

Comm: Choice of limited organism databases.

Metabolomics tools: historical review (2013) (5/9)

PaintOmics [65]

Acc.: WB

Inp.: KEGG formatted metabolites and/or genes

DBsd: KEGG

Funs.: Compound mapping

Comm: Choice of 100 hundred top species. Colours pathway metabolites and genes according to increase/decrease.

Metabolomics tools: historical review (2013) (6/9)

IMPaLA [66]

Acc.: WB

Inp.: Gene IDs and/or CompID

DBsd: KEGG, HMDB, CAS, ChEBI, PubChem, Reactome, Wikipathways

Funs.: Enrichment Analysis

Comm: Combined analysis with proteins or transcripts. Organism independent. Optional background set.

Metabolomics tools: historical review (2013) (7/9)

MetaMapp [25]

Acc.: WB

Inp.: CompID

DBsd: KEGG

Funs.: Metabolite networking

Comm: Organism independent. Network construction based on chemical similarity.

Metabolomics tools: historical review (2013) (8/9)

VANTED [67]

Acc.: Ins

Inp.: Compound abundances

DBsd: KEGG

Funs.: Metabolite networking, compound mapping, statistical analysis

Comm: Combined analysis with proteins and transcripts. Organism independent. Direct visualization of results on networks. Time course analysis. Statistical analysis.

Metabolomics tools: historical review (2013) (9/9)

TICL[68]

Acc.: WB

Inp.: Compound IDs

DBsd: KEGG

Funs.: Enrichment analysis.

Comm: No choice of organism. Reported as non-functional in the source review

Adapted from a very nice review from (Booth et al. 2013)

Subnetwork analysis

Subnetwork methods combine molecular measurements with a network to identify connected groups of relevant entities.

Scored modules

Methods such as jActiveModules search for subnetworks with strong aggregate evidence. Search procedures need not find a guaranteed global optimum. (Ideker et al. 2002)

Diffusion methods

Methods such as HotNet propagate influence through a network and identify affected modules. Heat diffusion is not the same as maximum-flow optimisation. (Vandin et al. 2011)

Mining knowledge through B2SLab Fella

Problem addressed: enrichment techniques

LC/MS provides data in terms of compounds of statistical relevance, but…
The researcher needs to understand what is going on the underlying biology.
A key concept are the metabolic pathways.
Pathway enrichment techniques bridge between both worlds.

Goal

Integrate existing knowledge Base in form of a database with statistical results from compound analyses to perform a LC/MS pathway enrichment.

In addition…

Offer a complete interpretation of the biological elements involved in the experiment.
Allow further integration with other omics.

Adding a Knowledge Base

Pathway hsa00010 in the cell

Pathway hsa00010 in the cell
Image extracted from www.nature.com

Pathway hsa00010 in KEGG

Knowledge Base: KEGG contents

Knowledge Model

Diffusion on graphs (I) (1/2)

Motivation

How can we find relevant parts of a graph? We will generate heat on certain nodes and analyse the hottest subgraph.

Heat diffusion in a meshed object. Image extracted from www.cd-adapco.com.

Diffusion on graphs (I) (2/2)

Heat diffusion in a graph: some nodes introduce heat to the structure.

Diffusion on graphs (II) (1/2)

Basics

We apply the finite difference formulation of the heat equation:

T^{n+1} = T^{n} + DTC \cdot [ KI \cdot T^{n} + KC \cdot TC + G ]

T^{k}: are the node temperatures in the k-th instant of time.
DTC: is a diagonal matrix relating the time step and heat capacities of the nodes.
KI: is the matrix containing the conductances between nodes.

Diffusion on graphs (II) (2/2)

KC: is the matrix containing the conductances between the nodes in the graph and the boundary nodes.
TC: are the temperatures of the boundary nodes.
G: is the inner heat generation of the graph nodes.

Input set

Null model (I)

Deterministic input

In this case, we know who the affected nodes are. Thus, we get a deterministic temperature:

T_{input} = R \cdot q

… but how can we know if a node is hot or not?

Temperatures are not explicative by themselves
Temperatures are not comparable between nodes

Random input

However, what happens if the input contains no signal, i.e. is random?

T_{null} = R \cdot X

Where X is a random variable that randomly selects compounds.

Null model (II)

Meaning of the null model

Analysing the distribution of temperatures for random cases allows the comparison between nodes in terms of their distributions. Is the temperature of node A as extreme as node B?

Statistical moments

We have determined the exact first and second moments of the temperature distributions:

\mathbb{E}(T(X)_i) = \frac{n_{in}}{n_p} \left[\sum_{j}r_{ij} \right]

V(T(X)_i) = \frac{n_{in}(n_p - n_{in})}{n_p(n_p - 1)} \left[\sum\limits_{j}r_{ij}^2 - \frac{1}{n_p}\left(\sum\limits_{j}r_{ij}\right)^2 \right]

Node significance under a null model

Parametric approximation

Choose and assess a distributional approximation for the null temperature, then calculate an upper-tail probability.

Monte Carlo estimate

For B null simulations, a common estimate is

\hat p=\frac{1+\#\{b:T_i^{(b)}\ge T_i^{\mathrm{obs}}\}}{B+1}.

The null sampling scheme, ties, and number of simulations matter. Adjust for the family of nodes tested.

Node-base test

Latent background (I)

Motivation

In practice, not all the nodes of interest can be measured. Technology only allow us to measure a subset of possible compounds in the database. Thus, there is a portion of nodes that introduce uncertainty. Assuming that they are not affected may be altering the results, depending on their amount…

Proposed solution

We suggest splitting a null model consisting of two parts:

Observable pool: contains the nodes that can be measured. The affected nodes are a subset of the observable pool.
Latent pool: contains the nodes that cannot be measured through current technology.

We want to see how the presence of the latent pool modifies our statistical tests.

Assuming Latent Variance

Assuming Latent Variance
Our original input

Assuming Latent Variance

Assuming Latent Variance
Barred nodes are not observable

Latent background (II)

Modification of statistical moments

We will call ALL the full model, OBS the observable model and LAT the latent model.

\mu_{ALL} \text{ remains unaffected}

\Sigma_{ALL} = \Sigma_{OBS} + 2\cdot \Sigma_{LAT}

Interpretation

By introducing the latent pool all the variances grow. The magnitude of this enlargement will assess how sensitive a particular node is to experimental uncertainty.

Assuming Latent Variance

Assuming Latent Variance
Barred nodes are not observable

Assuming Latent Variance
Proportion of variance explained by non-observability (red)

Assuming Latent Variance

Assuming Latent Variance
All graph is observable. Including the 5 non-observable nodes from the null model as non-affected (not fair)

Assuming Latent Variance
Part of the graph is not observable. There is a compound which is affected but not observed by the experiment (fair statistics)