Open Access Research article

Home and away- the evolutionary dynamics of homing endonucleases

Adi Barzel12*, Uri Obolski3, Johann Peter Gogarten4, Martin Kupiec1 and Lilach Hadany3

Author Affiliations

1 Department of Molecular Microbiology and Biotechnology, Tel Aviv University, Ramat Aviv, 69978, Israel

2 Department of Pediatrics, Stanford University, California, 94305, USA

3 Department of Molecular Biology and Ecology of Plants, Faculty of Life Sciences. Tel Aviv University, Ramat Aviv, 69978, Israel

4 Department of Molecular and Cell Biology, University of Connecticut, 91 North Eagleville Road, Storrs, CT 06269-3125 USA

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BMC Evolutionary Biology 2011, 11:324  doi:10.1186/1471-2148-11-324

Published: 4 November 2011

Additional files

Additional file 1:

Table S1 - Parameter index. A table containing an index of all parameters being used as well as a comparison to the Notation in Yahara et al[29].

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Additional file 2:

Table S2 - Derivation of recursive functions describing the dynamics of allele distribution. A table containing the derivation of the recursive functions describing the dynamics of allele distribution.

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Additional file 3:

Proof S1 - Proof of analytical bound 1. Proof of analytical bound 1.

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Additional file 4:

Proof S2 - Proof of analytical bound 2. Proof of analytical bound 2.

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Additional file 5:

Proof S3 - Proof of analytical bound 3. Proof of analytical bound 3.

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Additional file 6:

Figure S1 - Examples of Homing endonuclease persistence in Yahara's model. Examples of Homing endonuclease persistence in Yahara's model obtained using the parameters: α = 0.989, <a onClick="popup('http://www.biomedcentral.com/1471-2148/11/324/mathml/M19','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1471-2148/11/324/mathml/M19">View MathML</a>, r = 0.0123, u = 10-4, v = 10-6 and the initial frequency (in Yahara's notation): x = 0.9999, y = 10-4, z = 0. Iterating it for one million generations in Yahara's model, we get a stable equilibrium (determined using numeric computations of the eigenvalues) with frequencies X ≅ 0.51, y ≅ 0.41, z ≅ 0.081.

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Additional file 7:

Figure S2 - Examples of Homing endonuclease persistence at a high frequency. Examples of Homing endonuclease persistence at a high frequency in both ours and Yahara's models. Initial frequencies are the same as in Additional file 6. A) Stable equilibrium, using our model, with final z frequency of 0.314 obtained using the parameters: s = 0.01, t = 0.001, hm = 0.0323, u = 10-4 and v = 10-6. B) Stable equilibrium, using Yahara's model, with final z frequency of 0.655 obtained using parameters that are analogous the the parameters in A (as explained in Additional file 1, Table S1).

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Additional file 8:

Figure S3 - Example of model predictions for finite populations. Example of model predictions for finite populations. Random noise was added to our deterministic model as expected from binomial sampling in a population of size N = 105, 106, 107, 108 (A-D, respectively). The parameters used result in a stable equilibrium in the deterministic model: s = 0.01, t = 0.001, hm = 0.0165, u = 10-4 and v = 10-6.

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