A tunable dual-input system for ‘on-demand’ dynamic gene expression regulation

Cellular systems have evolved numerous mechanisms to finely control signalling pathway activation and properly respond to changing environmental stimuli. This is underpinned by dynamic spatiotemporal patterns of gene expression. Indeed, in addition to gene transcription and translation regulation, modulation of protein levels, dynamics and localization are also essential checkpoints that govern cell functions. The introduction of tetracycline-inducible promoters has allowed gene expression control using orthogonal small molecules, facilitating rapid and reversible manipulation to study gene function in biological systems. However, differing protein stabilities means this solely transcriptional regulation is insufficient to allow precise ON-OFF dynamics, thus hindering generation of temporal profiles of protein levels seen in vivo. We developed an improved Tet-On based system augmented with conditional destabilising elements at the post-translational level that permits simultaneous control of gene expression and protein stability. Integrating these properties to control expression of a fluorescent protein in mouse Embryonic Stem Cells (mESCs), we found that adding protein stability control allows faster response times to changes in small molecules, fully tunable and enhanced dynamic range, and vastly improved microfluidic-based in-silico feedback control of gene expression. Finally, we highlight the effectiveness of our dual-input system to finely modulate levels of signalling pathway components in stem cells.


Introduction
A number of perturbation approaches has been developed to study gene function in biological systems, and for gene therapy applications. It has become increasingly clear that gene expression patterns in vivo are fast and highly dynamic processes, encoding important time-dependent information that underlies many aspects of cellular behaviour 1 . Thus, precise temporal control, as well as reversible manipulation of exogenous gene expression is fundamental for interrogating cellular functions 2 . The ability to turn the expression of transgenes ON and OFF, or to finely modulate their expression levels, could greatly improve safety in gene therapy strategies by reducing unwanted off-targets and side effects 3 .
Temporal control of gene expression can be achieved by transcriptional regulation via inducible promoters 4-7 .The most widely used system for transcriptional regulation is the Tet system, which consists of two elements: the tetracycline transcriptional activator (tTA) and the DNA operator sequence (tetO) [8][9][10][11][12] . The tTA is a fusion protein of the herpes simplex virus VP16 activation domain and of the Escherichia coli Tet repressor protein (TetR) 9 . The presence of tetracycline or its derivative doxycycline prevents the interaction of the tTA to the tetO, blocking gene expression (Tet-Off system). The reverse-tTA (rtTA) is a tTA variant allowing gene expression activation in presence of an inducer; the resulting Tet-On system is generally preferred when rapid and dynamic gene induction is required 4,13 . A major limitation of inducible promoters is the significant time delay in switching proteins OFF and ON when using Tet-On and Tet-off systems, respectively 14 , diminishing the possibility of using these approaches to generate dynamic patterns of gene expression that faithfully recapitulate those observed natively 1 . Slow kinetic responses are also common to other techniques targeting precursor DNA or mRNA molecules (e.g. RNA interference 15 ), likely due to significantly different rates of innate protein degradation 15 .
Recently, an alternative approach, relying on conditional protein destabilization to modulate turnover by the cellular degradation machinery, has been harnessed to probe complex biological functions. Engineered mutants of FKBP12 that are rapidly and constitutively degraded in mammalian cells can directly confer protein destabilization to the protein they are fused with. Addition of synthetic ligands, that bind the Destabilising Domain (DD) of FKBP12, prevent degradation and so can be used to alter levels of the fused-protein of interest 16 . The plant derived AID (auxininducible degradation) system is also used to get fast and efficient proteasomal degradation of AID-tagged proteins in response to auxin hormones 17 . However, rates of AID-mediated protein degradation/recovery strongly depend on auxin uptake and metabolism, as well as on the abundance of SCF complex components, which might vary among different biological systems 18,19 . Therefore, AID is more suitable for protein knockout experiments, whereas the DD-based tool is preferred when fine temporal control of fused-protein levels is needed.
Whilst significantly enhancing the switch-off kinetics as compared to Tet-On regulation, conditional protein regulation systems do not allow independent control of both transcription and translation, which would be highly desirable when studying the correlation between protein and cognate mRNA levels under different spatial and temporal scales 20 .
To overcome these limitations, we engineered a novel, fully tuneable dual-input system, which allows orthogonal and conditional control at both transcriptional and post-translational levels of a gene of interest. Specifically, we combined a third generation Tetracycline-Inducible System (Tet-ON 3G) 12,21 for inducible and reversible transcriptional regulation with a module incorporating an improved DD from ecDHFR 22 for targeted protein degradation. We demonstrated that our system permits far greater control of both protein dynamics and expression dynamic range across different culture platforms, including microfluidics used for in silico feedback control. Moreover, we developed an ordinary differential equation model, which captures the enhanced dynamic response to inducers. The efficacy of conditional, dual regulation inherent in our system is exemplified by the ability to incorporate different genes of interest, such as fluorescent proteins, as well as the Wnt signalling effector, b-catenin, in a complex cellular chassis (mouse embryonic stem cells), paving the way for dynamically controlling mammalian cell behaviour and fate.

Dual-input system for orthogonal regulation of transcriptional and posttranslational gene expression
We engineered a mouse Embryonic Stem Cell (mESC) line to stably express the reverse tetracycline transcriptional activator construct (rtTA) and a stable mCherry (henceforth EF1a-rtTA_TRE3G-mCherry; Fig. 1a), or conditionally destabilized DDmCherry (henceforth EF1a-rtTA_TRE3G-DDmCherry; Fig. 1c) under the control of a TRE3G promoter, which transcribes the gene of interest only in presence of the tetracycline analogue doxycycline 12 (Doxy; Fig. 1a, c). Post-translational control is achieved by applying the small molecule trimethoprim (TMP), which stabilizes the destabilizing domain (DD)-fused protein in a dose-dependent manner 22 . The two constructs allow for comparison of the standard Tet-on with the dual-input Tet-On/DD system we developed.
To quantitatively estimate the effect of inducers on protein stability, we measured protein half-life in both EF1a-rtTA_TRE3G-mCherry and EF1a-rtTA_TRE3G-DDmCherry mESCs. Cells were cultured in presence of Doxy and Doxy/TMP for 14hrs, and then plated in presence of the protein synthesis inhibitor cycloheximide with varying combinations of Doxy and TMP for 8hrs; mCherry was measured by Western Blot over the time-course (Fig. 1e). In EF1a-rtTA_TRE3G-mCherry mESCs, untagged mCherry showed no response to TMP, and the half-life (around 4hrs) was similar across conditions ( Fig. 1f; Supplementary Fig.1a). Of note, mCherry mRNA decreased following Doxy withdrawal ( Supplementary Fig. 1c), confirming no effect of Doxy or TMP on protein stability in this system. In contrast, the half-life of the conditionally destabilised mCherry increased approximately three fold in presence of TMP ( Fig. 1g; Supplementary Fig.1b; +Doxy/+TMP and -Doxy/+TMP samples). In addition, mRNA levels decreased only when Doxy was removed ( Supplementary Fig. 1d), further demonstrating the specific and independent effect of the two inducers.
Consistently, we found that MG132 blockade of the proteasome 23 enhanced DDmCherry stability, suggesting that TMP acts by preventing proteasomal degradation of DD-fused proteins only 22 (Supplementary Fig. 1e). Indeed, both MG132 and TMP treatment increased DDmCherry abundance, whereas levels of the native b-catenin, whose degradation is proteasome mediated 24 , increased only when proteasomal activity was inhibited ( Supplementary Fig. 1e). Analysing the polyubiquitination status of DDmCherry, following inducer removal and chasing with or without TMP for 12hrs, indicated that TMP likely limits addition of ubiquitin chains or promotes de-ubiquitination of DD-tagged proteins, ultimately preventing proteasomal degradation ( Supplementary Fig. 1f).
Altogether, these data show that our system allows robust control of both gene transcription and protein stability, with undetectable leakiness and specific response to inducers.

Dual-input system tunability and dynamic response
To gauge the tunability and sensitivity of our inducible system, as well as its suitability for dynamic modulation of a gene of interest, we performed steady-state titration experiments with both drugs, and measured the switch-off dynamics of EF1a-rtTA_TRE3G-mCherry and EF1a-rtTA_TRE3G-DDmCherry mESCs in flow-cytometry time-courses.
EF1a-rtTA_TRE3G-mCherry mESCs incubated with 6 different concentrations of Doxy for 24hrs showed a robust response to increasing amount of inducer, with saturation reached at Doxy 100ng/ml ( To complement these experiments, we developed a mathematical model to capture the behaviour of the dual-input system: we relied on ordinary differential equations (ODEs), commonly used to model interactions among genes and other relevant processes, such as mRNA/protein degradation, basal promoter activity and mRNA translation 25,26 . The mathematical models for the EF1a-rtTA_TRE3G-mCherry and EF1a-rtTA_TRE3G-DDmCherry systems are based on sets of 4 ODEs, describing transactivator and fluorescent gene mRNA and corresponding protein concentrations, as the result of production and degradation terms (Supplementary Information). The TET system was modelled, as previously proposed, using Hill kinetics to represent the effect of the inducer on trascription 27 . Given the observed saturating response to TMP (Fig. 2c, dots and  Next, we used the model fitted on titration data to predict the switch-off dynamic response of both the Tet-On and the Tet-On/DD systems upon inducer withdrawal; model simulations indicated much faster switch-off of the dual-input system (Fig. 2d, e, dashed lines). These predictions were validated experimentally: both EF1a-rtTA_TRE3G-mCherry and EF1a-rtTA_TRE3G-DDmCherry mESCs were able to reach full steady-state induction upon 14hrs of incubation with Doxy and Doxy/TMP, respectively, with the conditionally destabilised protein showing 80% protein reduction 8hrs after inducer removal, as compared to 40% reduction only in the Tet on system (Fig. 2d,e,dots;Supplementary Fig. 2c,d).
These results indicate that the dual-input system we developed allows fully tunable protein induction with both drugs, and faster switch-off dynamics as compared to a standard Tet system. Furthermore, the ODE model, fitted on steady-state data, satisfactory replicated experimental time-course dynamics, indicating that Hill kinetics suit modelling Destabilising Domain responses, for which a mathematical formalism has been missing.

Modular control and dynamic range of transcriptional activation and protein stability
Given the improved dynamic response of the conditionally destabilised mCherry we measured in EF1a-rtTA_TRE3G-DDmCherry mESCs, we reasoned about further exploiting the performance of the inducible system by fusing the rtTA with a Destabilising Domain. Therefore, we generated two additional mESC lines Performing time-course experiments as for EF1a-rtTA_TRE3G-DDmCherry mESCs, we did not observe any further improvement in protein switch-off kinetics upon inducer removal (compare Fig. 2e and Supplementary Fig. 2k, l, dots; corresponding data of the latter figures in Supplementary Fig. 2o, p). Validation of the models on time-course data ( Supplementary Fig. 2k, l, dashed lines) also confirmed these results.
We argue that the observed switch-off dynamics are caused by a partial persistence of protein stability despite TMP removal, as also previously shown by

Dual-input engineering of gene expression dynamics using in silico feedback control
Recently, successful attempts have been made to dynamically control and regulate gene expression patterns in living cells, applying control engineering paradigms and using microfluidics or optogenetics platforms for dynamic cell stimulation, and microscopy or flow cytometry for obtaining real-time cell read-outs. [28][29][30][31][32][33][34][35][36][37] . Applications in mammalian cells have been recently attempted 29 , controlling a Tet-Off promoter-driven fluorescent protein using tetracycline as control input; this pioneering work showed feasibility of the in silico feedback control action, but highlighted challenges in controlling a system with slow kinetic response.
We wondered if our dual-input system would allow finer in silico gene expression -feedback control using a microfluidic/microscopy platform ( Supplementary Fig. 3); thus, we tested the effectiveness of individual gene transcription or protein stability control regulation as compared to the combined modulation. EF1a-rtTA_TRE3G-DDmCherry mESCs, Doxy/TMP treated, showed the same activation profile of EF1a-rtTA_TRE3G-Cherry mESCs (Supplementary Fig. 2a Fig. 3), we applied a Relay control strategy to reduce protein expression to 50% of the maximal induction (set-point, control reference) 29 . Control inputs were: time-varying Doxy (Fig. 3a), TMP (Fig. 3b), and Doxy/TMP (Fig. 3c).
We found that the control action fails in controlling DDmCherry levels to reach and maintained the set-point when only gene transcription (Fig. 3a) or protein stability ( Fig. 3b) are modulated, whereas a vastly improved control is achieved when both TMP and Doxy are applied (Fig. 3c). Of note, cells are able to reach the set-point with much faster dynamics than the ones previously observed using a Tet-Off system 29 .
These results demonstrate that our dual-input system is preferable for in silico feedback control of gene expression in mammalian cells, and is likely to be suitable for generating more complex time varying gene-expression dynamics.

Dual-input control of signalling pathway in embryonic stem cells
We then tested the general applicability our dual-input system for fine-tune To test the ability of our system to modulate levels of b-catenin, the main effector of the canonical Wnt pathway 39,46 , we generated mESCs stably expressing a fusion protein comprising the destabilising domain (DD), the mCherry fluorescent protein and a constitutively active b-catenin (b-catenin S33Y ) 47 , driven by a doxycyclineinducible promoter (henceforth EF1a-rtTA_TRE3G-DDmCherryb-catenin S33Y mESCs,

Discussion
Complex time-varying and dynamic patterns of gene expression underlie numerous biological processes such as immune regulation and cell fate choice 48, 49 ; mimicking and perturbing these dynamical profiles of expression is technically challenging and requires tools that faithfully recapitulate often fluctuating kinetics.
In this study, we presented an enhanced tool for conditional gene expression encompassing a Tet-on 3G system combined with DD technology that allows fast, specific, reversible and tunable perturbation of biological macromolecules. We demonstrated experimentally and with a computational model that by incorporating control at the transcriptional level, as well as regulating protein-of-interest stability, allows a much finer and tighter control of gene expression kinetics compared to transcriptional (Tet-on) control alone. Indeed, the key advantage of our system is that genes of interest can be robustly induced but also much more rapidly switched off, likely by enhanced proteasomal degradation of the translated protein, compared to either stand-alone transcriptional or post-translational control.
Inducible promoters enable transcriptional regulation and, combined with additional systems for protein levels modulation, provide valuable tools for controlling the expression rate and amount of proteins of interest. The destabilisation domain we applied in this study, although being slower in switch-off dynamics than Auxininducible degradation, overcomes the use of hormones, which can vary across different biological systems, and requires minimal genetic manipulations 18,19 .
Furthermore, as the inducer stabilises the protein, the dynamic range of the inducible system can be fully controlled to obtain 'on demand' activation levels.
We demonstrated the applicability of our dual-input regulation system for microfluidics/microscopy-based in silico feedback control, showing that it outperforms transcriptional-and post-translational-only manipulation to reach and maintain a setpoint control reference, even using a simple and model-free control strategy.
Our system suits generation of both spatial-and temporal-patterns of gene platform, which has the potential to allow a quantitative assessment of the molecular mechanisms and dynamics underpinning cell fate choices, paves the way for controlling cellular behaviour in clinically-relevant model systems, such as stem cells.
The inducibility and switch-like behaviour of our system makes it a powerful perturbation method, and the ability to tune protein levels with a high degree of predictability (as evidenced by our faithful capture of system dynamics using a computational model) makes it a valuable resource with a broad scope of applications.
For instance, it could be harnessed to study how signalling networks or synthetic gene circuits are wired together, by fine manipulation of one 'node' in the network and observing how this affects other cognate members within the circuit. Ultimately, this approach could be used to deconvolute and quantitatively assess the interactions within these networks, which could both explain and predict the consequences of a given perturbation. The mathematical model we fitted and validated could be used to test the design of novel synthetic networks based on inducible promoters and destabilising domains 27,50,51 .
Finally, the ability of both Doxy and TMP to cross the placental barrier 52 opens up the possibility that our dual-input system could allow fine-tuning of genes and signalling pathways essential in embryonic development, and could be applicable as a novel approach for targeted and modulable gene therapy.

Flow activated cell sorting (FACS)
Cells were washed with sterile Phosphate-Buffered Saline (PBS, Gibco), trypsinised for 2-3' at room temperature and centrifuged at 1000rmp for 5'. Pelleted cells were resuspended in 500uL of complete mESCs media supplemented with DAPI. The mCherry positive fraction was sorted from DAPI negative using the BD Influx highspeed 16-parameter fluorescence activated cell sorter; the gating strategy was defined to get comparable mCherry intensity across cell lines.

Flow cytometry analysis
Cells from a 24well plate were washed with sterile Phosphate-Buffered Saline (PBS, Gibco), incubated with 50µL of trypsin for 2-3' at room temperature and collected with 150µL of PBS 2% FBS containing DAPI as cell viability marker. Cell suspension was analysed using the BD LSR Fortessa and 10000 living cells were recorded for each sample. Both % of mCherry positive cells and Median Fluorescence Intensity (MFI) were calculated over living cells, gated as DAPI negative.

qPCR
For quantitative PCR, the total RNA was extracted from cells using the RNeasy kit (Qiagen), and the cDNA was generated from 1μg of RNA. Twenty-five ng of cDNA were used as template for each qPCR reaction, in a 15μl reaction volume. iTaq Universal SYBR Green Supermix (1725120, Bio-Rad) was used with Qiagen Rotor-Gene System. Primers:
Samples were then immunoprecipitated with 2μg of anti-ubiquitn antibody (P4D1, Cell Signaling) for 4hrs before addition of Protein G for a further 1hr, followed by extensive washing and processing via SDS-PAGE and western-blotting with anti-mCherry antibody.

Nucleus/Cytosol fractionation
For Nuclear and Cytosolic protein fractionation, cells were processed as in 56 .

Mathematical modelling
The mathematical models for the EF1a-rtTA_TRE3G-mCherry, EF1a-rtTA_TRE3G-DDmCherry, EF1a-DDrtTA_TRE3G-mCherry and EF1a-DDrtTA_TRE3G-DDmCherry systems are based on sets of 4 ODEs, describing transactivator and fluorescent gene mRNA and correspondent protein concentrations, as the result of a production term and a degradation term. We formulated the parameters estimation problem as a constrained optimization problem:

Microfluidics/microscopy-based time lapses
Microfluidics/microscopy-based experiments were performed using the device designed and optimised for mammalian cells in the laboratory of Prof Jeff Hasty at the University California in San Diego 2 . The topology of the device ensures controlled flow perfusion, minimised cell stress and controlled CO2 diffusion. As described in 1 , cells from a sub-confluent 60cm petri dished were washed with sterile Phosphate-Buffered Saline (PBS, Gibco), trypsinised for 2-3' at room temperature and centrifuged at 1000rmp for 5'. Pelleted cells were resuspended in 200uL of complete mESC media supplemented with Doxy and TMP and chip-loaded. Before loading, the chip was fulfilled with media containing both inducers from port 5 first and port 1 after. Cell suspension was loaded from port 1 while the vacuum applied to ports 3 and 4. The vacuum allows air to be released from chambers, facilitating cell trapping. Cells were cultured for 24hrs in a tissue culture incubator (5% CO2, 37 •C) under constant perfusion with inducer's containing media. Media was perfused with a syringe directly connected to port 2 via 24-gauge PTFE tubing (Cole-Parmer Inc.). Port 5 was used for waste media whereas ports 1, 6 and 7 were plugged to avoid media spillage. The day after, the device was transferred on the widefield microscope for in silico feedback control experiments. The actuation system consists of two motor-controlled syringes (http://biodynamics.ucsd.edu/dialawave/) connected to port 6 and 7. One syringe always contains Doxy/TMP media, whereas the other contains plain media (Figs. 3c, 4e and Supplementary Fig. 4f), or Doxy- (Fig. 3a) or TMP- (Fig. 3b) supplemented media, depending on experimental set-up. Ports 1, 2 and 5 are also connected to static syringes working as waste tanks. If the height of the waste tanks is fixed, the one of the perfusing media ports is automatically adjusted during the experiment to change the input provided to cells. Input administration was measured using a green dye (1uM Atto488 dye from ThermoFisher), added to Doxy/TMP containing syringe.

Image segmentation
The segmentation algorithm follows the methodology illustrated in 1 . Briefly, a threshold is defined to generate a binary image selecting only pixels belonging to cell edges.
Then, by using dilation and filling operators, it derives a binary image (mask) that selects the portion of the original image covered by cells. The mask obtained is applied to the red field image. In order to calculate the average intensity fluorescence of pixels belonging to cells, the background signal measured in a cell-free portion of the chamber is subtracted from the value of mask pixels.

Fluorescence microscopy
The control platform consists of a Leica DMi8 inverted microscope equipped with the digital camera Andor iXON 897 ultra back-illuminated EMCCD (512x512 16μm pixels, 16 bit, 56 fps at full frame), and an environmental control chamber (PeCon) for longterm temperature control and CO2 enrichment. The Adaptive Focus Control (AFC) ensures focus is maintained during the entire time-course experiment. The experimental set-up includes consecutive acquisition in three channels (phase contrast, green and red fluorescence) with a 20X objective every 60mins.

Relay control
The Relay control strategy can be expressed as follows: *(0) = _ *`a b = 1 d5 e(0) > 0 *`g h = 0 d5 e(0) < 0 where the control error e(0) = j(0) − :(0) is the difference between the control reference signal j and the system output :. * is the control input. The Relay controller requires only the computation of the control error at each sampling time e(kZ ), where Z = 60mins, whose sign dictates which input must be provided to the cells.
Specifically, cells are treated with inducers-containing medium for the next 60mins if e(kZ ) > 0 or medium without inducer otherwise. A 5% hysteresis interval to the controller, corresponding to a tolerance interval around the set-point in which the Relay algorithm ignores the control error, was added to avoid chattering 1 .