Fixed Points in Discrete Models for Regulatory Genetic Networks
Author Information
Author(s): Dorothy Bollman, Omar Colón-Reyes, Edusmildo Orozco
Primary Institution: University of Puerto Rico
Hypothesis
It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations.
Conclusion
The study develops tools for detecting steady states in genetic networks modeled by fixed points in discrete finite dynamical systems.
Supporting Evidence
- The study provides a new definition of linear finite dynamical systems.
- It establishes necessary and sufficient conditions for fixed point systems.
- It demonstrates polynomial time determination for ordinary linear systems as fixed point systems.
Takeaway
This study helps scientists understand how genes interact by finding steady states in mathematical models of gene behavior.
Methodology
The study discusses two algebraic models, a univariate model and a multivariate model, and shows their equivalence through a discrete Fourier transform.
Digital Object Identifier (DOI)
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