Mapping connections in signaling networks with ambiguous modularity

Abstract

Modular Response Analysis (MRA) is a suite of methods that under certain assumptions permits the precise reconstruction of both the directions and strengths of connections between network modules from network responses to perturbations. Standard MRA assumes that modules are insulated, thereby neglecting the existence of inter-modular protein complexes. Such complexes sequester proteins from different modules and propagate perturbations to the protein abundance of a downstream module retroactively to an upstream module. MRA-based network reconstruction detects retroactive, sequestration-induced connections when an enzyme from one module is substantially sequestered by its substrate that belongs to a different module. Moreover, inferred networks may surprisingly depend on the choice of protein abundances that are experimentally perturbed, and also some inferred connections might be false. Here, we extend MRA by introducing a combined computational and experimental approach, which allows for a computational restoration of modular insulation, unmistakable network reconstruction and discrimination between solely regulatory and sequestration-induced connections for a range of signaling pathways. Although not universal, our approach extends MRA methods to signaling networks with retroactive interactions between modules arising from enzyme sequestration effects.

Keywords: Applied mathematics; Biochemical networks; Computer modelling.

Fig. 1

Reaction scheme of the MEK/ERK cascade model studied by Parabakaran et al. Reaction rates are described by mass action kinetics, the appropriate rate constants are indicated at the arrows. Species of the MEK module are indicated in blue, species of the ERK module are indicated in red. Communicating species are selected as the sums of species in shaded parallelograms (Eq. 9)

Fig. 2

Dependence of elements of the connection matrix r_ij on the weight parameter a. The regulatory connection r₂₁ is depicted in red. The sequestration-induced (aka retroactivity) connection r₁₂ that changes its sign with the increase in the weight parameter a is depicted in blue. MEK and ERK module outputs were defined by a Eq. (12) or b Eq. (15). In both cases, the total concentrations of MEK and ERK (MEK^tot and ERK^tot, respectively) were perturbed. The connection matrices are shown for different weight parameter values, a = 0 (point 1), a = a^opt (2), and a = 5 (point 3). Diagonal elements are always equal to −1

Fig. 3

Reconstruction of connection matrices for three-tier cascades. Cascade modules are indicated by different colors and separated by bold horizontal lines for illustrative purposes. Dashed parallelograms indicate substances that are included into module outputs (Eq. 18). For network reconstruction, the total protein abundances, $X_1^{tot}$, $X_2^{tot}$, and $X_3^{tot}$, were perturbed. a Left panel: Scheme of a 3-tier cascade without regulatory feedback loops. Right: Reconstructed matrices of connections coefficients (r_ij) for different weight parameters a_i (including $a_i^{opt}$). b Left: Scheme of a 3-tier cascade with a regulatory feedback from module 3 to module 1. Right: reconstructed connection matrices r_ij for different weights a_i. c Left: scheme of a 3-tier cascade with a regulatory feedback from module 3 to module 2, which are also connected through feedforward activation of module 3 by module 2, creating a sequestration feedback. Right: reconstructed connection matrices r_ij for different strengths (u₂) of the positive regulatory feedback and optimal weights $a_i^{opt}$. For all right panels, the matrix elements that correspond to retroactive (i.e. sequestration) connections are depicted in red