Abstract
Whole-cell biosensors detecting the heavy metal arsenic have been widely studied for their potential in environmental monitoring. And while inducible biosensors have been shown to be an effective tool to tune the operational range, a thoroughly characterized inducible biosensor is currently lacking. Here, we present an Escherichia coli biosensor for arsenic in which the transcription factor (TF) gene arsR is inducible by naringenin, a plant-derived secondary metabolite. Increasing the naringenin concentration reduced the basal output while increasing both the dynamic range and sensing threshold of the biosensor dose-response curve, but the operational range appeared constrained by a fixed upper limit. Comparison with a previously published phenomenological model revealed good overall agreement between experimental data and model predictions, except for the behaviour of the maximum output and threshold. This work expands the biosensor toolbox with a profoundly characterized arsenic biosensor and raises a potential practical limit to dose-response curve engineering by tuning TF expression alone.
Keywords: arsenic, whole-cell biosensor, transcription factor, response curve engineering, mathematical modelling
Graphical Abstract
Graphical Abstract.

1 Introduction
Whole-cell biosensors have been extensively studied for environmental monitoring as they are cost-effective, sensitive, specific, and self-renewing [1, 2]. Among these, arsenic biosensors have received particular attention due to the widespread contamination of groundwater with arsenic [3] and the availability of the well-characterized transcription factor (TF) ArsR from Escherichia coli [4].
ArsR functions as a repressed repressor. In the absence of its effector, the ArsR dimer binds to its TF binding site (TFBS) upstream of the Pars promoter, blocking transcription of the output gene. Binding to its effector arsenic causes its dissociation from the TFBS, allowing transcription to proceed [5, 6]. The whole of these interactions governs the shape of the dose-response curve. Often, the native dose-response curve of a biosensor does not match the intended application, necessitating response curve engineering [7].
Because of the complexity of biosensors, synthetic biologists have used mathematical modelling to guide response curve engineering. The phenomenological model for TF-based biosensors of Mannan et al. [8] has gained a lot of attention from the biosensor community. It predicts the biosensor output based on eight parameters (Supplementary Table S1). The model makes minimal mechanistic assumptions, and should therefore be applicable across diverse mechanisms and TF families. The original publication focused on the effect of tuning the affinity of the TF to its TFBS and to its effector as well as the strength of the promoter controlling the output gene, and compared it to experimental data of LacI-based biosensors. Despite the attention their work has received, to our knowledge, their work has not yet been extended to other biosensors or to the other parameters.
Previous studies have shown that the expression level of arsR strongly affects the response characteristics of the biosensor. Mathematical modelling of genetic circuits showed that optimal sensitivity can be attained by placing arsR under control of a weak promoter while uncoupling its native feedback loop [9]. Wang et al. (2015) tested four biosensors with arsR expressed from constitutive promoters of different strengths. They found that the sensitivity and output fluorescence decreased for higher arsR expression levels [7]. In both studies, biosensors with inducible expression of arsR were developed as well, but thorough characterization including fitting to the Hill function and delineation of the operational range were omitted, making it impractical for the synthetic biology community to reuse them.
In this study, we developed a novel biosensor module for arsenic named pNarsenic. pNarsenic harbours arsR under control of the tight fdeR-PfdeAR naringenin-inducible system [10]. We measured detailed dose-response curves in E. coli in the presence of four different naringenin concentrations and report fits to a Hill function and operational ranges. Besides, we compared our results with simulations of the phenomenological model of Mannan et al. [8] for perturbations in
, the maximum increase in TF expression. Our work extends the analysis of the phenomenological model of Mannan et al. to include the TF expression level, a crucial parameter for biosensor development. Further, we expanded the biosensor toolbox with the plug-and-play development of a new arsenic biosensor.
2 Materials and methods
Additional experimental details are provided in the Supplementary Information (Section 1 and Supplementary Figs S1 and S2).
2.1 Reporter gene assays and data analysis
Precultures were started by inoculating separate, freshly transformed colonies in 200
L of MOPS EZ Rich Defined Medium in a 96-well plate and incubating them overnight at 30
C and 400 rpm. Next, naringenin dissolved in ethanol was added to the desired concentration in a black 96-well plate (Greiner Bio-One, polystyrene, F-bottom), after which the ethanol was evaporated at 50
C for 1 h in sterile conditions. Next, 170
L of MOPS EZ Rich Defined Medium was added to each well and 20
L of the appropriate stock solution of NaAsO2 was added to create an arsenic concentration gradient. Finally, 10
L of 15X diluted preculture was added, after which the plate was sealed using a Breathe-Easy Sealing Membrane (Sigma-Aldrich).
Plates were incubated at 30
C and 425 rpm in a Biotek Synergy H1 microplate reader, measuring OD600 and mKate2 fluorescence (excitation: 588 nm, emission: 633 nm, gain: 110, bottom read) every 20 min. Four biological replicates were analysed per biosensor strain and arsenic concentration.
Reporter gene expression was analysed as previously described [11] with slight modifications. Briefly, medium without cell culture was used to correct for background optical density (
) and fluorescence (
). Considering three consecutive time points around 12 h of incubation (indicated as
), the normalized corrected fluorescence for each replicate could be calculated as follows:
![]() |
(1) |
The resulting response curve was fitted to a Hill function
![]() |
(2) |
with
representing the normalized corrected fluorescence as calculated from (1),
the concentration of NaAsO2 in the growth medium (in
M),
the basal output,
the dynamic range,
the sensing threshold and
the Hill coefficient.
The maximum output was defined as the limit of the Hill function for 
![]() |
(3) |
The operational range
was computed as
![]() |
(4) |
with
a fraction fixed at 0.1 for this article, and
and
the best-fit threshold value and Hill coefficient for that response curve. Refer to the Supplementary Information for the derivation of this formula.
The
parameter was defined as the average relative standard deviation
![]() |
(5) |
where
is the number of arsenic concentration levels and
and
represent the standard deviation and mean normalized corrected fluorescence, respectively, at arsenic concentration
.
2.2 Mathematical modelling
We considered the repressed-repressor architecture of the phenomenological model of Mannan et al. for biosensor response [8]. The model computes the response
as a composite function
![]() |
(6) |
where
calculates the concentration of ‘active’ repressor that can bind to its TFBS as a function of the effector concentration
and
calculates the expression level of the output gene
as a function of the active repressor concentration
:
![]() |
(7) |
For brevity, the parameter definitions and formulae for the basal output, threshold and dynamic range can be consulted in the Supplementary Information (Supplementary Table S1 and equations (9)–(11)). All computations were performed in Python; SymPy was used for symbolic computations.
3 Results and discussion
3.1 Construction of pNarsenic
To precisely control the expression level of arsR, we cloned the chromosomal arsR gene from E. coli K-12 downstream of the fdeR-PfdeAR naringenin-inducible system [10] (Fig. 1a). FdeR is a TF from Herbaspirillum seropedicae that functions as a dual-function regulator in E. coli: it represses the PfdeA promoter in the absence of the plant secondary metabolite naringenin and induces it in the presence of naringenin [12, 13]. We chose this system because it displays an analogue response to naringenin with very tight regulation and naringenin shows low toxicity to E. coli (Supplementary Figs S3–S7) [10, 13]. Further, we chose mKate2 as a fluorescent reporter because of its fast maturation, high pH resistance, and far-red emission spectrum, which limits interference with autofluorescence emitted by E. coli [10, 14]. We cloned the mkate2 gene under transcriptional control of ParsOC2, a refactored version of Pars with lower leakiness and improved dynamic range [15]. These circuits were combined with a high-copy pUC origin of replication, yielding the 5.2 kB plasmid pNarsenic (Fig. 1a).
Figure 1.

The response characteristics of the pNarsenic biosensor can be tuned by supplementing the flavonoid naringenin. (a) Plasmid map of pNarsenic with close-up of the most important features. Expression of arsR is induced by naringenin and repression of ParsOC2 by ArsR is relieved by arsenic, leading to mKate2 expression. (b) Dose-response curves of the pNarsenic biosensor in the presence of 0, 3, 6.5, 10, or 25 mg/l naringenin. The x-axis is linear from 0
M to 0.1
M and logarithmic from 0.1
M to 500
M. Error bars signify mean
standard error across three replicates, except for 0 mg/l naringenin where
. Refer to Supplementary Fig. S8 to view the response curves separately, along with their best-fit Hill functions. (c–e) Bar plots showing the basal output
, dynamic range
and threshold
for the response curves in panel B. Error bars signify the 95% confidence intervals after nonlinear regression. (f) The operational ranges of the response curves shown in panel B as computed through equation (4).
3.2 In vivo characterization of pNarsenic
In order to characterize our new biosensor module, we measured growth and fluorescence of E. coli harbouring pNarsenic in the presence of multiple naringenin concentrations and a wide gradient of NaAsO2. The dose-response curve measured in the absence of externally applied naringenin appeared entirely flat (Fig. 1b). When 3–25 mg/l naringenin was added, the same biosensor produced a sigmoidal dose-response curve in response to arsenic. These results show that ArsR endogenously expressed by E. coli or originating from leaky expression from the PfdeAR promoter was not present at a sufficient level to give rise to differential mkate2 expression.
The response curves measured in the presence of 3–25 mg/l naringenin were fitted to a Hill function to extract quantitative parameters that enable comparison of biosensor performance (Supplementary Table S2 and Supplementary Fig. S8). Figure 1c shows that the basal output
decreased with increasing naringenin concentration. As a result, the dynamic range
increased (Fig. 1d). Concurrently, the sensing threshold
shifted to higher arsenic concentrations (Fig. 1e). These trends can be explained by the mechanism of ArsR regulation. At higher naringenin concentrations, more ArsR dimers accumulate in the cell. This reduces mkate2 expression in the absence of arsenic, thereby lowering the basal output. At the same time, higher arsenic concentrations are required to displace ArsR from the TFBS, as a result of which the threshold increases. These results highlight the tunability of the biosensor, making it adaptable for applications requiring different sensitivities.
The response curves measured in the presence of 6.5 and 10 mg/l naringenin overlapped to a large extent (Fig. 1b). In addition, their values for
,
, and
did not differ significantly (Fig. 1c–e). These results suggest that the biosensor is not sensitive to this small increase in naringenin concentration.
The operational range of a biosensor, the span of effector concentrations that yield distinguishable output signals, is a key determinant of its practical applicability. At 3 mg/l naringenin, the operational range was 0.09
M to 4.73
M (Fig. 1f), thus achieving sensitivity below the World Health Organization limit for drinking water (0.133
M) [16]. Upon increasing the naringenin concentration to 6.5 mg/l, the operational range shifted towards higher arsenic concentrations while maintaining approximately the same width on a logarithmic scale. At higher naringenin concentrations, however, the operational range constricted, with an approximately constant upper bound around 30
M. This result suggests a practical limit for dose-response curve engineering by tuning TF concentration alone. Future research should investigate whether such limits apply to other biosensors as well.
Finally, the noise level of a biosensor is an important factor to consider for monitoring applications [10]. pNarsenic exhibits relatively low noise levels between 15% and 32% (for 3 and 10 mg/l naringenin, respectively; Supplementary Table S2), demonstrating its reliability.
3.3 Comparison with a phenomenological model for biosensor response
Because of the high quality of our data and fits, we were able to use them to extend the phenomenological model of Mannan et al. to the TF expression level, which is captured by the parameter
[8]. For low
values, corresponding to low TF expression levels, the model produced a high, effector-independent response, in agreement with our results in the absence of naringenin (Figs 1b and 2). For increasing
values, the basal output decreased and the threshold and dynamic range increased, which is also supported by our data for pNarsenic. However, the maximum output was independent of
(see Supplementary Information), which is in contrast with our data and data from a previous study [7], where the maximum output decreased markedly for higher-level TF expression. This observation probably results from incomplete derepression at high TF densities, a feature not accounted for by the model.
Figure 2.

The phenomenological model of Mannan et al. [8] predicts that increasing the TF expression level leads to decreasing basal output
and increasing threshold
and dynamic range
. Plots show simulations of the dose-response curve for eight values of
and the predicted behaviour of
,
and
. In this study,
corresponds to the arsenic concentration,
to the normalized corrected fluorescence, and
to the naringenin concentration controlling TF expression. Simulations were made by setting
,
,
,
,
,
,
in equations (6) and (9)–(11) with
values spanning the range 0.1–300.
As shown in the Supplementary Information, the basal output and dynamic range are monotonic and converge to an asymptotic value for
, but this is not true for the threshold. Although we were not able to compute
symbolically due to its complexity, simulations across a wide parameter scan suggest that the threshold goes to infinity for
. This was expected as the model does not consider a limit for total intracellular protein. Besides, depending on the parameter values,
could reach a minimum value (Supplementary Fig. S9), implying that further decreasing the TF concentration increases the threshold. We were not able to attach a biological explanation to this phenomenon; it could be a mathematical artefact stemming from the nonlinear dependence of
on
in equation (6).
Supplementary Material
Acknowledgements
We thank Karl Jonckheere for technical assistance. The authors acknowledge the use of generative artificial intelligence for improving the clarity and style of this manuscript and for writing code. All conceptual, analytical, and interpretative aspects of the work were conducted by the authors.
Contributor Information
Vincent Crabbe, Research Group of Microbiology, Department of Bioengineering Sciences, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium; Interuniversity Institute of Bioinformatics in Brussels, ULB-VUB, La Plaine Campus, B-1050 Brussels, Belgium.
Ezgi Unal, Research Group of Microbiology, Department of Bioengineering Sciences, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium; Research Group of Ecology, Evolution and Genetics, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium.
Stijn De Graeve, Open BioLab Brussels, Erasmushogeschool Brussel, Laarbeeklaan 121, B-1090 Brussels, Belgium; NovelYeast bv, Gaston Geenslaan 3, B-3001 Leuven, Belgium.
Daniel G Guerra, Laboratorio de Moléculas Individuales, Laboratorios de Investigación y Desarrollo, Facultad de Ciencias e Ingeniería, Universidad Peruana Cayetano Heredia, 15102 Lima, Peru.
Tom Peeters, Open BioLab Brussels, Erasmushogeschool Brussel, Laarbeeklaan 121, B-1090 Brussels, Belgium.
Sophie de Buyl, Interuniversity Institute of Bioinformatics in Brussels, ULB-VUB, La Plaine Campus, B-1050 Brussels, Belgium; Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium; Data Analytics Laboratory, Vrije Universiteit Brussel, Pleinlaan 5, B-1050 Brussels, Belgium.
Eveline Peeters, Research Group of Microbiology, Department of Bioengineering Sciences, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium.
Indra Bervoets, Research Group of Microbiology, Department of Bioengineering Sciences, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium.
Author contributions
Vincent Crabbe (Conceptualization, Methodology, Software, Formal analysis, Investigation, Writing—original draft, Writing—review & editing, Visualization), Ezgi Unal (Investigation), Stijn De Graeve (Investigation), Daniel G. Giraldez (Funding acquisition), Tom Peeters (Funding acquisition), Sophie de Buyl (Methodology), Eveline Peeters (Supervision, Funding acquisition), and Indra Bervoets (Conceptualization, Methodology, Supervision)
Conflict of interest: No potential conflict of interest was reported by the authors.
Funding
This work was supported by VLIRUOS [grant number PE2024TEA560A105] and Vrije Universiteit Brussel [Strategic Research Program SRP91]. Vincent Crabbe holds a doctoral fellowship from Research Foundation—Flanders (FWO) [grant number 11Q3S24N].
Material availability
Plasmids generated in this study have been deposited to Addgene. Plasmid IDs 247320–247321.
Data availability
All data and software code generated during this study are publicly available: https://doi.org/10.5281/zenodo.17154084.
References
- 1. van der Meer JR, Belkin S. Where microbiology meets microengineering: Design and applications of reporter bacteria. Nat Rev Microbiol 2010; 8:511–22. 10.1038/nrmicro2392 [DOI] [PubMed] [Google Scholar]
- 2. Liu C, Yu H, Zhang B et al. Engineering whole-cell microbial biosensors: Design principles and applications in monitoring and treatment of heavy metals and organic pollutants. Biotechnol Adv 2022; 60:108019. 10.1016/j.biotechadv.2022.108019 [DOI] [PubMed] [Google Scholar]
- 3. Podgorski J, Berg M. Global threat of arsenic in groundwater. Science 2020; 368:845–50. 10.1126/science.aba1510 [DOI] [PubMed] [Google Scholar]
- 4. Fernandez-López R, Ruiz R, de la Cruz F et al. Transcription factor-based biosensors enlightened by the analyte. Front Microbiol 2015; 6:648. 10.3389/fmicb.2015.00648 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5. Wu J, Rosen BP. Metalloregulated expression of the ars operon. J Biol Chem 1993; 268:52–8. 10.1016/S0021-9258(18)54113-2 [DOI] [PubMed] [Google Scholar]
- 6. Carlin A, Shi W, Dey S et al. The ars operon of Escherichia coli confers arsenical and antimonial resistance. J Bacteriol 1995; 177:981–6. 10.1128/jb.177.4.981-986.1995 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 7. Wang B, Barahona M, Buck M. Amplification of small molecule-inducible gene expression via tuning of intracellular receptor densities. Nucleic Acids Res 2015; 43:1955–64. 10.1093/nar/gku1388 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8. Mannan AA, Liu D, Zhang F et al. Fundamental design principles for transcription-factor-based metabolite biosensors. ACS Synth Biol 2017; 6:1851–9. 10.1021/acssynbio.7b00172 [DOI] [PubMed] [Google Scholar]
- 9. Merulla D, Hatzimanikatis V, van der Meer JR et al. Tunable reporter signal production in feedback-uncoupled arsenic bioreporters. Microb Biotechnol 2013; 6:503–14. 10.1111/1751-7915.12031 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10. De Paepe B, Maertens J, Vanholme B et al. Modularization and response curve engineering of a naringenin-responsive transcriptional biosensor. ACS Synth Biol 2018; 7:1303–14. 10.1021/acssynbio.7b00419 [DOI] [PubMed] [Google Scholar]
-
11.
Bernauw AJ, Crabbe V, Ryssegem F et al. Molecular mechanisms of regulation by a
-alanine-responsive Lrp-type transcription factor from Acidianus hospitalis. MicrobiologyOpen 2023; 12:e1356. 10.1002/mbo3.1356
[DOI] [PMC free article] [PubMed] [Google Scholar] - 12. Marin AM, Souza EM, Pedrosa FO et al. Naringenin degradation by the endophytic diazotroph Herbaspirillum seropedicae SmR1. Microbiology 2013; 159:167–75. 10.1099/mic.0.061135-0 [DOI] [PubMed] [Google Scholar]
- 13. Kashiwagi FM, Miranda BW, de Souza EM et al. The naringenin-dependent regulator FdeR can be applied as a NIMPLY gate controlled by naringenin and arabinose. Synth Biol 2024; 9:ysae001. 10.1093/synbio/ysae001 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 14. Shcherbo D, Murphy CS, Ermakova GV et al. Far-red fluorescent tags for protein imaging in living tissues. Biochem J 2009; 418:567–74. 10.1042/BJ20081949 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 15. Chen S-Y, Zhang Y, Li R et al. De novo design of the ArsR regulated Pars promoter enables a highly sensitive whole-cell biosensor for arsenic contamination. Anal Chem 2022; 94:7210–8. 10.1021/acs.analchem.2c00055 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 16. Guidelines for Drinking-Water Quality: Fourth Edition Incorporating the First and Second Addenda. Geneva: World Health Organization, 2022. [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data and software code generated during this study are publicly available: https://doi.org/10.5281/zenodo.17154084.







