Heat Diffusion Workflow

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

  1. 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.
  2. 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.
  3. 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.


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.


  • 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.


BEL Commons is developed and maintained in an academic capacity by Charles Tapley Hoyt and Daniel Domingo-Fernández at the Fraunhofer SCAI Department of Bioinformatics with support from the IMI project, AETIONOMY. It is built on top of the open source project, PyBEL. Please feel free to contact us here to give us feedback or report any issues.