Petri net on expanded networks computes the dynamics of finite multilevel models

We discuss connections between different types of models of gene-regulatory network dynamics that include Boolean, finite multilevel and monotone Boolean models. We recast the methodology of describing attractors of Boolean and finite multilevel dynamics using motifs of the expanded network <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>e</mml:mi> <mml:mi>R</mml:mi> <mml:mi>N</mml:mi></mml:mrow> </mml:math> in terms of Petri net dynamics on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>e</mml:mi> <mml:mi>R</mml:mi> <mml:mi>N</mml:mi></mml:mrow> </mml:math> . We show that the Petri net can be used to recover dynamics of the finite multilevel dynamics on the state transition graph. We conclude with new insights that the expanded network viewpoint offers for the robustness of equilibria and complex attractors.