What we talk about  when we talk about networks

Introduction

Networks and network concepts are very common in cellular and molecular biology

Ideker et al. (2013). A gene ontology inferred from molecular networks. Nature Biotechnology

Califano et. al (2014). Identification of Causal Genetic Drivers of Human Disease throughSystems-Level Analysis of Regulatory Networks. Cell

'Network' biology can describe different things

'modelling networks' ≠ 'network modelling'

This work is about building graph models to gain biological insight

Different methods for making networks from biological data

Association-based methods: network edges represent association or similarity between variables

Bayesian methods: network edges represent conditional probabilities

Regression-based methods (e.g. MIKANA): network edges represent terms in a system of equations

Key concept: the biological meaning of a network model comes from:

1. The source data2. The operations used to make it

Which is the best method?

• Dialogue on Reverse Engineering Assessment and Methods (DREAM) attempts to benchmark and evaluate methods competively
• But different methods create networks representing quite different things
• Choose approaches based on a detailed understanding of the data and possible hypotheses

• Evaluating differences between approaches is very difficult.
• Current methods are designed and applied ad hoc and each uses their own idiosyncratic language
• The meaning of a network and its elements depends on the generating data, and on the fine detail of each step in its construction
• Each problem requires different applications of different methods

The problem of disparate approaches with different language has persisted for the last 6+ years

..but we have no language to describe the 'details of implementation'!

The consequences

• Lots of methods, but few principles
• We can make complex mathematical objects
• But we cannot reason from the details of their construction, to their meaning
• We know more data will improve things..
• But we can't say what 'improvement' means in biological terms

Progress since 2006 has been slower than expected

Not a network

(Magritte picture here)

Not a network

• In this description, a 'network' is a 'graph model' built from biological data
• We are interested in the relationship between graph properties and biological meaning

Uncovering meaning

How do we uncover meaning in language?

¿Donde esta el zapateria?

But then

I began to understand the grammar

¿Donde esta el zapateria?

Where is   the shoestore?

Concept of a grammar

• A set of principles that govern the construction and interpretation of phrases
• Meaning (semantics) arises from context (situation) and syntax (rules that govern the structure of sentences)
• Two ways to get to semantics from context and syntax: formal, and empirical

So

To get to biological meaning from networks, we need a grammar of graph methods

A grammar of graph methods

Find common features in all network methods

Work out a language to describe them

• Must be general enough to be comprehensive (able to describe all analyses of this type
• But specific enough to be useful (able to provide meaningful insight)

The focus

Three common steps:

1.Data -> Graph

2.Graph -> Graph

3.Graph (element) -> Hypothesis

Influenced by previous work

• Wilkinson, L. (2010). The grammar of graphics.
• Wickham, H. (2008). ggplot2: an Implementation of the Grammar of Graphics.
• Wickham, H. dplyr: A Grammar of Data Manipulation
• Declarative SQL-type syntax - this is a specification, so it must describe what things are
• Cypher, the graph language for Neo4j:
• Gremlin, a graph traversal language

But quite different

1.Focus on process, not data visualisation

2.Not a data standard (e.g. 'minimum information')

3.Not an ontology/controlled vocabulary - represents process, not knowledge. Syntax carries meaning

4.Divisions, syntax and vocabulary are completely new

Empirical grammar, not formal grammar

(translation: constructed by observation and experiment)

A grammar of graph methods

• Elements (nouns)

• Operators (verbs)

'Parts of speech'

1.Data -> Graph

2.Graph -> Graph

3.Graph (element) -> Hypothesis

'Sentences' represent analyses

Expressing analyses using a structured grammar lets us:

1.Recognise difference and similarity between approaches

2.Link biological conclusions to the details of an analysis

-> no more black boxes

Data -> Graph

DATATRANS

Put data in 'long' format - less intuitive for non-statisticians, but allows us to be really precise about preprocessing and data manipulation before building a network. A very good example in R is dplyr.

What do we need to make a graph?

1.Index variable

2.Generative element

3.Operation

DATATRANS: Index variable

The index variable is the variable that differentiates nodes in the network

It partitions the dataset

Examples: probeID/protein ID for transcriptomic/proteomic networks, or metabolite ID for metabolic networks

Typically not unique in 'long' format data (multiple observations) Always unique in the network (because each node is different)

DATATRANS: Generative element

The generative element is the smallest part of the graph required to build the network

Get the partitioned data associated with each generative element

New result: methods with the same generative element respond in a similar way to changes in the data

DATATRANS: Generative element

What is the generative element for an association network (e.g. ARACNE/CLR/WCGNA)?

Answer: the edge

DATATRANS: Generative element

What is the generative element for a dynamical systems network?

Answer: the subgraph

Different ge = different response to changes in data

DATATRANS: Operation

• The operation is performed on the data associated with the generative element
• It returns a property (scalar or vector) which gets assigned to the generative element

Putting it all together

DATATRANS{index('probeID')
ge('edge'),
operation('mi','value'))}
GRAPHTRANS{select ('edges') %.%
filter %.%
select ('triplets') %.%
filter}
ASSERT{select ('edges') %.%
filter}

Some examples

Califano, Iavarone et al. Nature (2010) EMT in glioma

ge('edge'), operation('mi')
select ('edges') %.%, filter
select ('triplets') %.%, filter
group_by(graph set,'edge') %.%, summarise('count')
select('edges') %.%, filter

Carro, M. S., Lim, W. K., Alvarez, M. J., Bollo, R. J., Zhao, X., Snyder, E. Y., Iavarone, A. (2010). The transcriptional network for mesenchymal transformation of brain tumours. Nature, 463(7279), 318-25. doi:10.1038/nature08712

Ideker et al. Science (2010) Differential network analysis

ge('edge'), operation('interaction_score > +/-2.0')
group_by(graph set,'edge') %.%
summarise('count')
select('all edges') %.%
filter

Bandyopadhyay, S., Mehta, M., Kuo, D., Sung, M.-K., Chuang, R., Jaehnig, E. J., Ideker, T. (2010). Rewiring of genetic networks in response to DNA damage. Science (New York, N.Y.), 330, 1385-1389. doi:10.1126/science.1195618

Alon et al. Nature Genetics (2002) Persistent network motifs

select('motif') %.%
filter
group_by(graph set,'edge') %.%
summarise('count')
select('edges.count') %.%
filter

Shen-Orr, S. S., Milo, R., Mangan, S., & Alon, U. (2002). Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31(1), 64-68. doi:10.1038/ng881

Implementation

• This is a practical tool as well as a conceptual framework
• We have embedded the grammar in a domain-specific language
• Prototype implementation running in R, extend into Python, based on the igraph library
• Construct analyses directly using the grammar

Work in progress:

• Inheritance of properties
• Iterators for common tasks (shortcuts)
• Store the generative history of elements
• Caching layer
• Forward chaining (infix) operators (= pipes)