Phenotype Control techniques for Boolean gene regulatory networks

Abstract

Modeling cell signal transduction pathways via Boolean networks (BNs) has become an established method for analyzing intracellular communications over the last few decades. What's more, BNs provide a course-grained approach, not only to understanding molecular communications, but also for targeting pathway components that alter the long-term outcomes of the system. This has come to be known as phenotype control theory. In this review we study the interplay of various approaches for controlling gene regulatory networks such as: algebraic methods, control kernel, feedback vertex set, and stable motifs. The study will also include comparative discussion between the methods, using an established cancer model of T-Cell Large Granular Lymphocyte Leukemia. Further, we explore possible options for making the control search more efficient using reduction and modularity. Finally, we will include challenges presented such as the complexity and the availability of software for implementing each of these control techniques.

Keywords: Boolean networks; Discrete dynamical systems; Network dynamics; Phenotype control theory; Regulatory networks.

Fig. 8

FDS for gene regulation (Plaugher 2022)

Fig. 9

Simple Boolean network (Plaugher 2022)

Fig. 10

Phase space of diagram 9 (Plaugher 2022)

Fig. 11

Nonlinear Boolean network (Plaugher 2022)

Fig. 12

State-space dynamical variants according to update schedules (Plaugher 2022)

Fig. 13

CA example (Plaugher 2022)

Fig. 14

CK example (Plaugher 2022)

Fig. 15

FVS example (Plaugher 2022)

Fig. 16

Stable motif example (Plaugher 2022)

Fig. 17

Simple 3-cycle (Plaugher 2022)

Fig. 18

Phase-space of simple 3-cycle. Here we show the state-space of the example from Fig. 17, using SDDS with transition probabilities, with nodes written in lexicographical ordering

Fig. 19

Simulation examples for a simple 3-cycle with 1% noise (Plaugher 2022)

Fig. 1

Reduced T-LGL network. The figure shown here indicates the smaller (reduced) T-LGL model, where black barbed arrows indicate signal expression and while red bar arrows indicate suppression (Plaugher 2022) (Color figure online)

Fig. 2

Reduced T-LGL network target overlaps. We highlight the overlapping control targets from Table 3 by overlaying them with the reduced T-LGL wiring diagram from Fig. 1, shown in two diagrams for clarity. a We show instances of CA edge (blue), CA node (green), and SM (grey). b We show instances of CK (black) and FVS (purple). Note that FVS has combinatorial controls with connecting arches, where others are strictly singleton (Color figure online)

Fig. 3

CA diagram. Here, we show a toy model that emphasizes the difference between node and edge control. The key difference with edge control (b), is that all other communications are maintained. Whereas, node control removes every signal associated with the given target

Fig. 4

Single-in-single-out removal. Here, we show how to remove FGFR from the network shown in (a) and still maintain downstream signaling shown in (b). See Eqs. (5)–(8) for functional maintenance

Fig. 5

Single-in-multi-out removal. Here, we show how to remove MEK from the network shown in (a) and still maintain downstream signaling shown in (b). See Eqs. (9)–(14) for functional maintenance

Fig. 6

Low connectivity removal. Here, we show how to remove cJUN from the network shown in (a) and still maintain downstream signaling shown in (b). See Eqs. (15)–(22) for functional maintenance

Fig. 7

Modularity example (Plaugher 2022)