Ultrasensitivity and noise propagation in a synthetic transcriptional cascade

Abstract

The precise nature of information flow through a biological network, which is governed by factors such as response sensitivities and noise propagation, greatly affects the operation of biological systems. Quantitative analysis of these properties is often difficult in naturally occurring systems but can be greatly facilitated by studying simple synthetic networks. Here, we report the construction of synthetic transcriptional cascades comprising one, two, and three repression stages. These model systems enable us to analyze sensitivity and noise propagation as a function of network complexity. We demonstrate experimentally steady-state switching behavior that becomes sharper with longer cascades. The regulatory mechanisms that confer this ultrasensitive response both attenuate and amplify phenotypical variations depending on the system's input conditions. Although noise attenuation allows the cascade to act as a low-pass filter by rejecting short-lived perturbations in input conditions, noise amplification results in loss of synchrony among a cell population. The experimental results demonstrating the above network properties correlate well with simulations of a simple mathematical model of the system.

Fig. 1.

The network design of three synthetic transcriptional cascades. In all circuits, TetR is expressed constitutively from P_lacIq promoter. aTc, which freely diffuses into the cell, binds TetR and prevents the repression of P_Ltet-O1. (A) In the one-stage cascade (circuit 1), eyfp expression is under the control of TetR repressor. (B) Circuit 2 has an additional repression stage where the expression of eyfp is controlled by LacI protein, which can be repressed by the TeR repressor. (C) In circuit 3, eyfp expression is controlled by the CI repressor. cI expression is controlled by LacI protein, which is under the control of TetR.

Fig. 2.

Steady-state transfer curve and noise. (A) Mean fluorescence of cells transformed with circuits 1–3 as a function of different aTc concentrations. Circuit 3 has an improved sensitivity compared with circuit 1, and the transition from low to high output occurs on a smaller range of aTc concentrations (see Results). (B) Coefficient of variation as a function of mean fluorescence is used to measure cell–cell variability in the transition region. Circuit 3 has a higher variation in the intermediate region. The insets show three representative FACS histograms for circuits 1 and 3 for low, intermediate, and high aTc concentrations. (C) Coefficient of variation as a function of reporter proteins per cell for a seven-stage simulated cascade. Similar pattern of increase in CVs is observed in the simulations as well.

Fig. 3.

Delayed response in longer cascades. (A) Temporal fluorescence responses of all three circuits when aTc is added to cultures grown initially without inducer. (B) Cell–cell variability is shown for low to high fluorescence transition of circuits 1 and 3 (circuit 2 is shown in Fig. 6C). (C) Time to reach 50 percent maximum protein level (logarithmic scale; see Materials and Methods) for the simulated system upon aTc induction. (D) The dynamic fluorescence response of the system after aTc is removed from a culture initially grown with aTc (E) Cell–cell variability of the high to low output transition for circuits 1 and 3. (F) Time to reach 50 percent of maximum output for the simulated system upon removal of aTc.

Fig. 4.

The transcriptional cascade acts as a low-pass filter. (A) A short pulse duration of 5 min is not enough for circuit 3 to show any response, but there is an increase in fluorescence level of circuit 1 and a decrease in circuit 2 fluorescence. (B) For a pulse duration of 45 min, circuit 1 reaches its maximum value, whereas circuit 3 shows only a mild response. (C) Maximum responses of circuits 1, 2, and 3 are plotted versus pulse durations. Circuit 1 reaches its maximum output after ≈40 min and circuit 2 response decreases to its minimum after ≈60 min, whereas the response of circuit 3 is initially flat and increases gradually for longer pulses.