A quantitative comparison of sRNA-based and protein-based gene regulation

Abstract

Small non-coding RNAs (sRNAs) have important functions as genetic regulators in prokaryotes. sRNAs act post-transcriptionally through complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. Although the mean steady-state behavior of sRNA-regulated proteins exhibits a distinctive tunable threshold linear behavior, our analysis shows that transcriptional bursting leads to significantly higher intrinsic noise in sRNA-based regulation than in TF-based regulation in a large range of expression levels and limits the ability of sRNAs to perform quantitative signaling. Nonetheless, we find that sRNAs are better than TFs at filtering noise in input signals. Additionally, we find that sRNAs allow cells to respond rapidly to large changes in input signals. These features suggest a 'niche' for sRNAs in allowing cells to transition quickly yet reliably between distinct states. This functional niche is consistent with the widespread appearance of sRNAs in stress response and quasi-developmental networks in prokaryotes.

Figure 1

Genetic regulation through sRNAs. Left: small non-coding RNAs (sRNAs) regulate protein expression as part of a larger genetic network with a specific biological task (e.g. quorum sensing in Vibrio bacteria; Lenz et al, 2004). The sRNAs (stem loops) regulate target proteins by destabilizing target protein mRNAs (wavy lines), a stoichiometric process mediated by the RNA chaperone Hfq (hexagons). When the rate of sRNA transcription α_s greatly exceeds the rate of mRNA transcription α_m, i.e. when, α_s≫α_m, nearly all the mRNAs are bound by sRNAs and cannot be translated. By contrast, when α_m≫α_s, there are many more mRNAs than sRNAs, and protein is highly produced. Right: the stochasticity (randomness) of cellular processes results in noise—statistical fluctuations in the molecular numbers. It is helpful to classify the total noise in the output (output noise) into (i) input noise—noise in the input signal from upstream components in the gene circuit, (ii) intrinsic noise—noise from stochasticity inherent in gene regulation through sRNAs, and (iii) extrinsic noise—all other sources of noise impinging on the signal processing system.

Figure 2

Steady-state behavior for gene regulation through sRNAs. For the regulated protein, the steady-state mean number p̄ exhibits an approximately threshold linear behavior as a function of the mRNA transcription rate α_m. The threshold is set by the sRNA transcription rate α_s. Protein expression can be classified into three regimens: repressed (α_s≫α_m), crossover (α_s≈α_m), and expressing (α_s≪α_m). In the repressed regimen, the average protein number is low. By contrast, the protein number increases almost linearly with α_m in the expressing regimen. The typical behavior of the noise α_p, the standard deviation of the protein number, is shown for the three regimens.

Figure 3

Schematic drawing showing our comparison of transcriptional and post-transcriptional sRNA-mediated regulation. We take as the input signal to both systems a protein regulator (blue discs) that either directly transcriptionally regulates the relevant gene by acting as a repressor or transcriptionally regulates an sRNA acting as an activator. The protein regulator is chosen to have identical kinetic properties in both cases.

Figure 4

Protein noise with or without transcriptional bursting. Noise in protein expression σ_p²/p̄² (variance divided by mean squared) as a function of the ratio of the sRNA and mRNA transcription rates, α_s/α_m, for different levels of transcriptional bursting. We have assumed that both the sRNAs and mRNAs are produced in bursts. The noise peaks in the crossover regimen, α_s≈α_m. A slower unbinding rate k₋ for the repressor proteins controlling sRNA and mRNA expression results in larger transcriptional bursts. Parameters are (in min⁻¹): α_m=3, α_m^on=10, α_s^on=30, τ_m=10, τ_s=30, μ=0.02, α_p=4, τ_p=30, and k₊ is adjusted to set the mean protein levels (for a discussion of parameter dependence, see Supplementary information).

Figure 5

Comparison of analytic expressions for the intrinsic protein noise for TF- and sRNA-based regulation. The intrinsic noise for sRNA-based regulation as a function of normalized average protein concentration, p̄/p_max, with and without transcriptional bursting, is shown. All parameters as in Figure 4.

Figure 6

Normalized frequency-dependent gain, g(ω)/g(0), as a function of the frequency, ω, for a small input signal for TF- and sRNA-based regulation in the repressed and expressing regimens. The amplitude of the frequency-dependent gain decreases rapidly ∝ω⁻⁴ at high frequencies for sRNAs compared with ∝ω⁻³ for TFs. Consequently, sRNA-based regulation is less sensitive to high-frequency input noise than TF-based regulation. Parameters as in Figure 4.

Figure 7

Large signal switching. Normalized mRNA level m/m_max, as a function of time, in response to step changes in the input, for both the sRNA- and TF-based regulation. Switching from high mRNA level (on state) to low mRNA level (off state) and vice versa. Switching from off to on state has a lag in the case of sRNA-based regulation, whereas the switching time from the on to off state for sRNAs is faster or comparable to that for TFs, depending on the choice of kinetic parameters. For sRNA-based regulation, α_m=3.5 and α_s goes from ∼0.35 to 4.5 for switching from low to high and vice versa for high to low. For TF-based switching, α_m is such that both schemes have same steady states. Other parameters as in Figure 4.