A Regulated Double-Negative Feedback Decodes the Temporal Gradient of Input Stimulation in a Cell Signaling Network

Abstract

Revealing the hidden mechanism of how cells sense and react to environmental signals has been a central question in cell biology. We focused on the rate of increase of stimulation, or temporal gradient, known to cause different responses of cells. We have investigated all possible three-node enzymatic networks and identified a network motif that robustly generates a transient or sustained response by acute or gradual stimulation, respectively. We also found that a regulated double-negative feedback within the motif is essential for the temporal gradient-sensitive switching. Our analysis highlights the essential structure and mechanism enabling cells to properly respond to dynamic environmental changes.

Fig 1. Overview of searching network topologies.

(A) Targeted input-output relationship. Acute or gradual input stimulation causes transient or sustained output response, respectively. Discriminability and sensitivity are introduced as two criteria characterizing the dynamic behavior of a signaling network circuit. (B) Three-node network topology with all possible link combinations. (C) A simple example circuit modeled using Michaelis-Menten equation. (D) Illustration of the simulation of a candidate network circuit with sampled parameters and the evaluation of the resulting dynamic behavior with the two criteria.

Fig 2. The input-output relationship and feedback structure of the EPNF circuit.

(A) The number of parameter sets for all the network models. The parameter set was selected if the product of the sensitivity and the discriminability is more than 0.1. The most robust three motifs, (M1, M2, and M3) are shown in the inset. Note that M1 is EPNF, which is commonly contained in M2 and M3. (B) The representative response profiles of the EPNF network to acute and gradual increase of input stimulus, which recapitulate the predefined targeted behavior. (C) Typical input signal patterns with different temporal gradients (upper panel). The representative state trajectories of EPNF that were projected to the two dimensional space of N₂ and N₃ (lower panel (D) Three feedback loops comprising the EPNF circuit. The first two positive and negative feedback loops are interlinked at the output node N₁ and these feedbacks are further controlled by the third double-negative feedback loop that might selectively turn on N₂ or N₃.

Fig 3. Bifurcation properties of the RDNF circuit.

(A) The RDNF circuit and a representative response profile to two different temporal gradient of input. (B) Response patterns of N₂ and N₃ to different amplitude and temporal gradient. (C) Steady-state responses of N₂ and N₃ to various input amplitudes and temporal gradients. Bifurcation occurs depending on not only the input amplitude but also the temporal gradient.

Fig 4. Analysis of the temporal gradient decoding mechanism.

(A) A simplified single node network. (B) Input-output relationship (top) and phase plane analysis (bottom) of the simplified model with two different temporal gradients. The temporal gradient influences the state trajectories and determines the critical state transition towards different steady-states. (C) Schematic illustration of the cellular signal decoding process by the proposed temporal gradient-sensitive switch network.