The incoherent feedforward loop can provide fold-change detection in gene regulation

Abstract

Many sensory systems (e.g., vision and hearing) show a response that is proportional to the fold-change in the stimulus relative to the background, a feature related to Weber's Law. Recent experiments suggest such a fold-change detection feature in signaling systems in cells: a response that depends on the fold-change in the input signal, and not on its absolute level. It is therefore of interest to find molecular mechanisms of gene regulation that can provide such fold-change detection. Here, we demonstrate theoretically that fold-change detection can be generated by one of the most common network motifs in transcription networks, the incoherent feedforward loop (I1-FFL), in which an activator regulates both a gene and a repressor of the gene. The fold-change detection feature of the I1-FFL applies to the entire shape of the response, including its amplitude and duration, and is valid for a wide range of biochemical parameters.

Figure 1

Fold-change detection means that the dynamics of the output (amplitude and duration of the transcription of gene Z) depends only on the fold-changes in the level of the input signal, not on the absolute levels of the input signal.

Figure 2. The incoherent feedforward loop can provide fold-change detection

(A) In a simple gene regulation, two inputs with different absolute levels but identical fold-changes give two different profiles of Z transcription. (B) In a properly designed I1-FFL (see text), two inputs with different absolute levels but identical fold-changes give two identical profiles of Z transcription (dashed and full lines overlap). (C-D) The amplitude and duration of the response Z can be increased by slowing the dynamics of Y (C) or by introducing a delay in the response of Y to X (D). In all the plots, time is in arbitrary units. Using typical biochemical rate constants, the response time is in the range of minutes to hours (see text). The plots were generated using equations 7-8 in Box with r=0.1, except in Fig C where r varies.

Figure 3. I1-FFL shows fold-change detection over a wide range of parameters

(A) Model parameters were varied. For each choice of parameters, we provided two step inputs with the same fold-change F=10, and different absolute levels X₀’=10 X₀. As a measure of the fold-change detection property, we computed the relative difference (ε) in the amplitude of the Z response (Z_max) for the two step inputs. (B-D) Three detailed designs of the Z promoter input function were considered, in which binding of X and Y is exclusive (B), independent (C), or cooperative (D). In all cases, the light region indicates the parameter range where fold-change detection occurs, in the sense that the two step inputs produce identical outputs within 10% (contour line delineates ε=0.1). Parameters: Ki’s are binding constants, X₀ is the basal input level, and Y₀= β₁X₀/α₁, with β₁ and α₁ defined in equation 3 in Box.

Figure 4. Fold-change detection may provide signaling advantages in noisy environment

(A) Fold-change detection ensures that each cell responds reliably to an external signal despite variation in the basal level of X. In fold-change detection, cells sense relative changes from the basal level, and not absolute levels or absolute changes. (B) Fold-change detection rescales the meaningful change in signal according to the background noise. In fold-change detection, ΔX = 1 when background X = 1 gives the same information as ΔX = 10 when background X = 10. (C) Fold-change detection in the I1-FFL can provide a transcriptional analog of Weber’s Law in sensory system, which states that the minimal detectable change in signal scales linearly with the background signal.

Box