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Strong regulatory graphs

Patric Gustafsson, Ion Petre

TL;DR

The concept of strong regulation is introduced, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous.

Abstract

Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.

Strong regulatory graphs

TL;DR

The concept of strong regulation is introduced, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous.

Abstract

Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.
Paper Structure (5 sections, 5 theorems, 3 equations, 4 figures)

This paper contains 5 sections, 5 theorems, 3 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Strong regulatory graphs (SRG)
  3. Phenotype attractors
  4. Application to a regulatory cancer network
  5. Discussion

Key Result

Lemma 2.4

Let $G=(V,E)$ be a strong regulatory graph and $v\in V$. For any state $x$ with $\mathop{\mathrm{\mathsf{Reg}}}\nolimits_+(x,v)=\mathop{\mathrm{\mathsf{Reg}}}\nolimits_-(x,v)=\emptyset$, we have $f_G(x)_v=x_v$.

Figures (4)

  • Figure 1: Two simple regulatory graphs naldi_decision_2007. The vertices are shown with rectangles, the activation edges with pointed arrows and the inhibition edges with blunt arrows.
  • Figure 2: The state transition graphs of the regulatory graphs in Example \ref{['ex_two_srg']} and Figure \ref{['fig-naldi']}.
  • Figure 3: The MAPK-PI3K/AKT signaling pathways.
  • Figure 4: The basins of attractors of the state transition graph of the MAPK-PI3K/AKT model.

Theorems & Definitions (9)

  • Definition 2.1
  • Definition 2.2
  • Example 2.3
  • Lemma 2.4
  • Theorem 2.5
  • Lemma 2.6
  • Definition 3.1
  • Theorem 3.2
  • Theorem 3.3