What is heat diffusion?
In the context of networks, heat diffusion refers to adding a scalar value to each node (i.e., heat)
and simulating how heat can flow across edges to neighboring nodes, and so on. In networks biology,
this allows for the assessment of connectivity and topology of a network. With directed, causal
networks, such as those encoded in BEL, heat diffusion can allow data-driven identification of
relevant/dysregulated pathways and subgraphs.
Workflow Description
- Networks are assembled and preprocessed using the query builder. Often this will include
filtering nodes and edges from undesirable contexts. For example, knowledge based on
experiments done in certain cancer cell lines or in mice are sometimes inappropriate for
research in neurodegenerative disease. Other transformations and enrichments can also be
applied, such as collapsing orthologs of similar genes. Ultimately, only causal BEL edges are
used because their directionality makes the results more biologically meaningful.
-
Data is loaded from a differential gene expression experiment. The log fold changes, which have
both a magnitude and a sign, are given as "heat" to the nodes representing their corresponding
gene/protein. This workflow uses the common simplification of collapsing the RNA and protein
nodes into their corresponding gene node.
-
Heat diffusion is often ascribed to a continuous mathematical system. In practice, the heat
diffusion algorithm is implemented in a discrete way using concepts from dynamic programming.
Because causal BEL edges have a polarity (increases or decreases), the heat diffusion algorithm
can be modified to encode greater biological meaning. When heat crosses a "decreases" edge, its
sign is also flipped.
BEL has the advantage of representing not only molecular entities, but also higher order
abstract entities such as biological processes. These nodes are well suited to help interpret a
data set, so their final heats, after diffusion has completed, are reported for visualization
and interpretation.
Implementation Details
Randomized Approaches
Since networks may contain contradictions like A increases B and also B
increases A that cannot be easily explained by their associated biological context
annotations, a network is derived that deletes one of them. For a network with only one
contradiction, this only requires deriving two networks to enumerate all possibilities. As more
contradictions arise, there are exponentially many possible derived networks. A randomized
approach is used to sample from these networks and generate scores for each. This can be used to
calculate an average score and also assess the sensitivity of that score.
Visualization
Data sets can be directly uploaded and analyzed. The results of these experiments can then be
directly overlaid to the interactive network viewer to provide a data-driven analysis of
given networks or sub-networks.
Generalization of this workflow
Heat diffusion is a general enough methodology that it can be applied to a variety of networks
and different types of data sets. For example, Leiserson et al. used undirected
protein-protein interaction networks with copy number variations as heat to identify functional
modules in the context of cancer.
Other data types, like single-nucleotide polymorphisms (SNPs), clinical measurements, or
neuroimaging features, which have been annotated to our Alzheimer Disease Knowledge assembly with
NeuroMMSig.
References
-
Leiserson, M. D. M., Vandin, F., et al. (2015). Pan-cancer network analysis identifies
combinations of rare somatic mutations across pathways and protein complexes. Nature Genetics,
47(2), 106–14.
