Gene-CluEDO: Hox gene clustering

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Gene Cluster Evolution Determined Order

  • Expansion of Gene Clusters and the Shortest Hamiltonian Path Problem*, Prohaska et al, 2017

Calculate the most likely order of genes in a gene cluster.

Apart from being an interesting problem in computational biology, it also serves as an example problem for dynamic programming over unordered sets with interfaces.

Binaries available from github:

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Dependencies ADPfusion (>=0.5.2 && <0.5.3), ADPfusionSet (>=0.0.0 && <0.0.1), base (>=4.7 && <5.0), cmdargs (>=0.10), containers, filepath, FormalGrammars (>=0.3.1 && <0.3.2), Gene-CluEDO, log-domain (>=0.10), PrimitiveArray (>=0.8.0 && <0.8.1), PrimitiveArray-Pretty (>=0.0.0 && <0.0.1), ShortestPathProblems (>=0.0.0 && <0.0.1), text (>=1.0), vector (>=0.11) [details]
License GPL-3.0-only
Copyright Christian Hoener zu Siederdissen, 2017
Author Christian Hoener zu Siederdissen, 2017
Category Bioinformatics
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Source repo head: git clone git://
this: git clone git://
Uploaded by ChristianHoener at 2017-09-11T12:12:23Z
Executables GeneCluEDO
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Readme for Gene-CluEDO-

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generalized Algebraic Dynamic Programming Homepage

Gene-CluEDO: Gene Cluster Evolution Determined Order

The first paper describes the biological problem. The 2nd and 3rd paper provide algorithmic background.

  1. Prohaska, Sonja J. and Berkemer, Sarah and Externbrink, Fabian and Gatter, Thomas
    and Retzlaff, Nancy and The Students of the Graphs and Biological Networks Lab 2017
    and Hoener zu Siederdissen, Christian and Stadler, Peter F.
    Expansion of Gene Clusters and the Shortest Hamiltonian Path Problem

  2. Hoener zu Siederdissen, Christian and Prohaska, Sonja J. and Stadler, Peter F.
    Algebraic Dynamic Programming over General Data Structures
    2015, BMC Bioinformatics

  3. Hoener zu Siederdissen, Christian and Prohaska, Sonja J. and Stadler, Peter F.
    Dynamic Programming for Set Data Types
    2014, Lecture Notes in Bioinformatics, 8826,

This program accepts a matrix with distances between nodes (see below for an example). It then proceeds to calculate the Hamiltonian path with the shortest distance between each pair of nodes, where the path has to travel from the start, then to all other nodes, finally stopping at the last node.

We further calculate all neighbour probabilities via Inside/Outside. This means that for any two nodes we calculate the weight of the edge between these two nodes. The weight is between [0, ... ,1] where 0 denotes the the nodes are almost surely not direct neighbours on a weighted-randomly drawn path, while 1 denotes that they almost surely are.

Finally, we calculate the probability that a node is one of the terminal nodes in the Hamiltonian path, i.e. either the first or the last node.

Installation / Pre-compiled Binaries

Input data used for the Expansion of Gene Clusters paper

The data sets are available together with the sources or the binary release. Check the data folder. The script runs the four examples.

The Biological Problem We Solve

Wikipedia on Hox clusters.

Hox clusters are a set of genes that are linearly ordered. The genes are (assumed) to have a single originating gene, and repeated duplication has led to the cluster with unknown duplication tree.

The long time scales involved make it hard to produce a tree that can be trusted. This program therefore produces summary information in the form of edge path probabilities.

Example matrix:

In this artificial distance matrix, we have prime numbers as distances between nodes. Store the matrix in a file, say mat.dat.

#   A   B   C   D   E
A   0   2   3   5   7
B   2   0  11  13  17
C   3  11   0  19  23
D   5  13  19   0  27
E   7  17  23  27   0

Now, run the algorithm ./GeneCluEDO -o ./mat.dat. After the program has run, contains the a wealth of information about the input. The maximum likelihood path, the edge weights, end probabilities, and maximum expected accuracy path are calculated. Two additional files, here output.boundary.svg, and output.edge.svg are produced. The boundary plot provides graphical output of the probability that a node (or gene) is the start or end node. The edge probability plot provides probabilities for each edge (i,j) between nodes. This shows the most likely neighbors, and therefore genetic relationship, over all possible gene orders.


Christian Hoener zu Siederdissen
Leipzig University, Leipzig, Germany