Non-equilibrium strategies for ligand specificity in signaling networks

Reviewer #1 (Public review):

Summary:

The authors study the steady-state solutions of ODE models for molecular signaling involving ligand binding coupled to multi-site phosphorylation at saturating ligand concentrations. Although the results are in principle general, the work highlights the receptor tyrosine kinases (RTK) as model systems. After presenting previous ODE model solutions, the authors present their own "kinetic sorting" model, which is distinguished by ligand-induced phosphorylation-dependent receptor degradation and the property that every phosphorylation state is signaling competent. The authors show that this model recovers the two types of non-monotonicity experimentally reported for RTKs: maximum activity for intermediate ligand affinity and maximum activity for intermediate kinase activity.

The main contribution of the work is in demonstrating that their model can capture both types of non-monotonicity, whereas previous models could at most capture non-monotonicity of ligand binding.

Strengths:

The question of how energy-dissipating, and thus non-equilibrium, molecular systems can achieve steady-state solutions not accessible to equilibrium systems is of fundamental importance in biomolecular information processing and self-organization. Although the authors do not address the energy requirements of their non-equilibrium model, their comparative analysis of different alternative non-equilibrium models provides insight into the design choices necessary to achieve non-monotonic control, a property that is inaccessible at equilibrium.

The paper is succinctly written and easy to follow, and the authors achieve their aims by providing convincing numerical solutions demonstrating non-monotonicity over the range of parameter values encompassing the biologically relevant regime.

Weaknesses:

(1) A key motivating framework for this work is the argument that the ability to tune to recognize intermediate ligand affinities provides a control knob for signal selection that is available to non-equilibrium systems. As such, this seems like a compelling type of ligand selectivity, which is a question of broad interest. However, as the authors note in the results, the previously published "limited signaling model" already achieves such non-monotonicity in ligand binding affinity. The introduction and abstract do not clearly delineate the new contributions of the model.

The novel benefit of the model introduced by the authors is that it also achieves a non-monotonic response to kinase activity. Because such non-monotonicity is observed for RTK, this would make the authors' model a better fit for capturing RTK behavior. However, the broad significance of achieving non-monotonicity to kinase activity is not motivated or supported by empirical evidence in the paper. As such, the conceptual significance of the modified model presented by the authors is not clear.

(2) Whereas previous models used in the literature are schematized in Figure 1, the model proposed by the authors is missing (see line 97 of page 3). Without the schematic, the text description of the model is incomplete.

(3) The authors use the activity of the first phosphorylation site as the default measure of activity. This choice needs to be justified. Why not use the sum of the activities at all sites?

Reviewer #2 (Public review):

Summary:

In classical models of signaling networks, the signaling activity increases monotonically with the ligand affinity. However, certain receptors prefer ligands of intermediate affinity. In the paper, the authors present a new minimal model to derive generic conditions for ligand specificity. In brief, this requires multi-site phosphorylation and that high-affinity complexes be more prone to degrade. This particular type of kinetic discrimination allows for overcoming equilibrium constraints.

Strengths:

The model is simple, and it adds only a few parameters to classical generic models. Moreover, the authors vary these additional parameters in ranges based on experimental observations. They explain how the introduction of these new parameters is essential to ligand specificity. Their model quantitatively reproduces the ligand specificity of a certain receptor. Finally, they provide a testable prediction.

Weaknesses:

The naming of certain variables may be confusing to readers.