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Analysis of Boolean functions based on interaction graphs and their influence in system biology

Neural Computing and Applications volume 32, pages 7803–7821 (2020)Cite this article

Abstract

Biological regulatory network can be modeled through a set of Boolean functions. These set of functions enable graph representation of the network structure, and hence, the dynamics of the network can be seen easily. In this article, the regulations of such network have been explored in terms of interaction graph. With the help of Boolean function decomposition, this work presents an approach for construction of interaction graphs. This decomposition technique is also used to reduce the network state space of the cell cycle network of fission yeast for finding the singleton attractors. Some special classes of Boolean functions with respect to the interaction graphs have been discussed. A unique recursive procedure is devised which uses the Cartesian product of sets starting from the set of one-variable Boolean function. Interaction graphs generated with these Boolean functions have only positive/negative edges, and the corresponding state spaces have periodic attractors with length one/two.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, National Institute of Technology, Srinagar, Hazratbal, Jammu & Kashmir, 190006, India

    Ranjeet Kumar Rout

  2. Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, Botanic Garden, Howrah, West Bengal, 711103, India

    Santi P. Maity

  3. Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, West Bengal, 700108, India

    Pabitra Pal Choudhury & Jayanta Kumar Das

  4. Department of Mathematics, Pingla Thana Mahavidyalaya Vidyasagar University Maligram, West Midnapore, West Bengal, 721140, India

    Sk. Sarif Hassan

  5. Department of Computer Science, Edge Hill University, Ormskirk, Lancashire, UK

    Hari Mohan Pandey

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  1. Ranjeet Kumar Rout
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  2. Santi P. Maity
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Appendix: Boolean functions (BFs) are responsible to generate IGs having positive/negative edges only from 2 to 4-variable

Appendix: Boolean functions (BFs) are responsible to generate IGs having positive/negative edges only from 2 to 4-variable

See Tables 9, 10.

Table 9 Shows Boolean functions (BFs) responsible to generate IGs having positive edges only from 2 to 4-variable
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Table 10 Shows Boolean functions (BFs) responsible to generate IGs having negative edges only from 2 to 4-variable
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Rout, R.K., Maity, S.P., Choudhury, P.P. et al. Analysis of Boolean functions based on interaction graphs and their influence in system biology. Neural Comput & Applic 32, 7803–7821 (2020). https://doi.org/10.1007/s00521-019-04102-2

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Keywords

  • Boolean functions
  • Boolean networks
  • Interaction graphs
  • Singleton attractors
  • Classification