A modular degron library for synthetic circuits in mammalian cells

Tight control over protein degradation is a fundamental requirement for cells to respond rapidly to various stimuli and adapt to a fluctuating environment. Here we develop a versatile, easy-to-handle library of destabilizing tags (degrons) for the precise regulation of protein expression profiles in mammalian cells by modulating target protein half-lives in a predictable manner. Using the well-established tetracycline gene-regulation system as a model, we show that the dynamics of protein expression can be tuned by fusing appropriate degron tags to gene regulators. Next, we apply this degron library to tune a synthetic pulse-generating circuit in mammalian cells. With this toolbox we establish a set of pulse generators with tailored pulse lengths and magnitudes of protein expression. This methodology will prove useful in the functional roles of essential proteins, fine-tuning of gene-expression systems, and enabling a higher complexity in the design of synthetic biological systems in mammalian cells.

: Plasmids and oligonucleotides used in this study.

Supplementary Notes | Description of the mathematical model.
To quantitatively understand the molecular dynamics of our Tet gene expression system and the relationships between the two experimentally determined quantities (protein half-lives and SEAP levels) for the different degrons, we constructed a mathematical model describing in detail all involved biomolecular interactions. In this model, the different constructs (P hCMV -Tag-tTA-Dendra2-pA) consisting of the tetracycline-dependent transactivator tTA fused to Dendra2 and a degradation tag are expressed constitutively with rate !"# . We assume that, directly after expression, Dendra2 in this construct is in an unmaturated form, and we denote by tTA !"# the concentration of this unmaturated form at time . We assume that the chromophore of tTA !"# maturates with rate constant !"# , either to the neutral (nonfluorescent) or anionic (green fluorescent) form and denote by tTA !"#$ the construct with the neutral chromophore, and by tTA !"##$ the construct with the anionic chromophore. We describe the decision between the two forms with the parameter ; the value of corresponds to the probability of tTA !"##$ to maturate to tTA !"#$ , while 1 − corresponds to the probability to maturate to tTA !"##$ . Light with a wavelength of 405 nm photoconverts the neutral form tTA !"#$ to the red fluorescent form, which we denote by tTA !"# . At any given time, the rate of this photoconversion is governed by the light intensity in a small band around 405 nm and the parameter describing the efficiency of photoconversion. We assume that all four forms of the construct (tTA !"# , tTA !"##$ , tTA !"#$ , and tTA !"# ) are degraded and diluted (due to cell growth and division) with approximately the same rate constant !,!"# (tag), which is a function of the degradation tag fused to the respective construct. We assume that the differences in the activation of downstream gene transcription of SEAP by the four forms is negligible, such that the rate of SEAP transcription only depends on the total concentration tTA !"! = tTA !"# + tTA !"##$ (t) + tTA !"#$ (t) + tTA !"# ( ) of the construct. We assume that SEAP can freely diffuse through the cell membrane such that the SEAP concentration is approximately the same in each cell and in the extracellular medium. In agreement with previous work 1 we furthermore assume that the activation of SEAP by tTA !"! is described by a Hill function with Hill coefficient two, dissociation constant !"# and maximal expression rate !"#$ . Finally, !,!"#$ is the degradation rate constant of SEAP. Given these assumptions, our model is described by the following set of ordinary differential equations.
For strong degradation tags leading to a short half-life of the construct, we can assume that, at the beginning of the experiment, tTA !"! has reached its steady-state concentration. In contrast, this might not necessarily be the case for constructs leading to a long half-life time which depends on the half-life time ! ! (via the dependency of the half-life time ! ! (tag) on the tag), as well as on the time . The relative error can take values between zero and one, 0 ≤ ! ! , ≤ 1, where zero corresponds to tTA !"! having reached its steady-state, and one to tTA !"! having zero concentration. Our assumption that constructs with a small half-life time have already approximately reached their steady-state value at the beginning of the experiment implies that the relative error is small, ! ! , ≪ 1, whenever ! ! is small. The relative error however monotonically increases with the half life time of the construct, ! !! ! ! ! ! , > 1 , but decreases with the experimental time, ! !" ! ! , < 1 , since constructs with a long half-life time also eventually approach their steady-state concentration.
Since we placed the cells in fresh medium at the start of the experiment, we can assume that the initial SEAP concentration was approximately zero. Since SEAP concentrations were measured at = 24 h and SEAP is rather stable with an half-life estimated to be as long as 21 days 2 , degradation of SEAP can be neglected, corresponding to setting !,!"#$ = 0 in our model. SEAP concentrations at the time of measurement are thus expected to closely depend on the half-life time of the respective construct as described by the following integral equation For constructs with short half-life times, ! ! , ≈ 0 , such that the integral is approximately given by . For constructs with a long half-life time, in contrast, ! ! , might not be close to zero. However, since we used a comparatively strong constitutive promoter for tTA (corresponding to !"# being high), we might hypothesize that exactly those constructs with a long half-life time should correspond to experimental conditions for which the promoter of SEAP is saturated or close to saturation for most of the experimental duration, corresponding to SEAP ! ! ! ≫ 1 ≈ ! . If this hypothesis is correct, this would imply that we could use the same formula predicting the functional form of the relationship between the measured SEAP concentrations and the half-life times of the respective constructs for all constructs and not only for constructs with short half-life times, for which we originally derived it.
While it is impossible to prove that this last hypothesis is correct given our experimental data, it is however possible to test it a posteriori. Specifically, we can first assume that the hypothesis is correct and the SEAP promoter is already saturated for constructs with a long half-life time. This would then imply that the dependency of the experimentally measured SEAP concentrations on the half-life times should follow a Hill curve with Hill coefficient two, which can be checked by fitting a corresponding Hill curve to the experimental data. Given such a fit, our initial assumption that the hypothesis was true then requires that the fitted Hill curve must already be close to its maximum for the constructs with the longest half-life times. If this is not the case, the contradiction would imply that our initial assumption, that the SEAP promoter is already saturated for constructs with a long half-life time, is false. On the other hand, if the curve is close to its maximum for constructs with long half-life times, this would strongly support our initial assumption that the hypothesis was true, even though it would not represent proof. However, since nearly all mathematical models describing the dynamics of biomolecular networks have to be based on several assumptions due to limited availability of experimental data, we believe that this approach to justify this model assumption a posteriori is justified. Given that the relationship of the experimentally measured SEAP concentrations on the protein half-lives indeed follows approximately a Hill curve with Hill coefficient two, as predicted by the model, and since this curve is approximately saturated for the constructs showing the longest half-live times, we (a) Ubiquitin (N-end rule). Work done in yeast showed that Ub contains a C-terminal isopeptidase site that is recognized by deubiquitinating enzymes, such that Ub is cleaved from the fusion partner after translation to uncover a destabilizing or stabilizing amino acid at the N terminus of the target protein ( Fig. 1b) 3,4 . (b) Ubiquitin (UFD pathway). The cleavage rate of the Ub moiety is considerably reduced, leaving polyubiquitinated proteins targeted for proteasomal degradation. (c) N-or C-terminal tag. The lacS sequence contains abundant lysine residues 5 , and is known to increase the degradation rate of proteins to which it is fused.

This work
Abbreviations: B3, Zygosaccharomyces bisporus recombinase; C/Dbox, RNA motif specifically binding to the L7Ae protein; dCas9, Streptococcus pyogenes dead CRISPR associated protein 9; Citrine, improved version of EYFP; CRISPR, clustered regularly interspaced short palindromic repeats; EYFP, enhanced yellow fluorescent protein; FT, fluorescent timer; GCaMP6s, ultrasensitive protein calcium sensor; GFP, green fluorescent protein; H2B, histone cluster 2; lacS, lac repressor protein spacer; L7Ae, archaeal ribosomal protein L7Ae; mCherry, Discosoma-derived red fluorescent protein; MCS, multiple cloning site; miR124, microRNA precursor 124; MCP, RNA-binding coat protein from the bacteriophage MS2; P2A, porcine teschovirus-1 2A self-cleaving peptide; p65, transactivating subunit of NF-kappa B; pA, polyadenylation signal; PEST, mouse ornithine decarboxylase-derived peptide sequence rich in proline (P), glutamic acid (E), serine (S), and threonine (T) acting as a protein degradation signal; PESTmod, modified PEST; PCR, polymerase chain reaction; PCAG, chicken β-actin promoter; PhEF1α, human elongation factor-1 alpha promoter; PETR2, macrolide-responsive promoter; PH1, human histone 1 promoter; PhCMV, human cytomegalovirus immediate early promoter; PhCMVmin, minimal version of PhCMV; PhCMV*-1, tTA-specific tetracycline-responsive promoter; PhINS, human insulin promoter (-881 to +54); PhU6, human U6 promoter; PPGK, murine phosphoglycerate kinase 1 promoter; PTRE, tTA-specific tetracycline-responsive promoter; PTRT, L-tryptophan-responsive promoter; PTtgR1, phloretin-responsive promoter; rtTA, reverse tetracycline-dependent transactivator; PSPA, SCB1-responsive promoter (OpapRI-PhCMVmin); PSV40, simian virus 40 promoter; Rta, Epstein-Barr virus R transactivator; SEAP, human placental secreted alkaline phosphatase; sgRNA, single guide RNA; shRNA, short hairpin RNA; tetR, Escherichia coli Tn10-derived tetracycline repressor; tTA, tetracycline-dependent transactivator (tetR-VP16); TtgR, repressor of the Pseudomonas putida DOT-T1E ABC multidrug efflux pump; Ub, ubiquitin degradation signal; UbAR, ubiquitin fusion construct in which alanine is introduced at the G76 residue of the C-terminal isopeptidase site and fused to the transcription factor such that Ub is partly cleaved from the fusion partner after translation to reveal arginine at the N terminus of the transcription factor; UbAV, ubiquitin fusion construct in which alanine is introduced at the G76 residue of the C-terminal isopeptidase site and fused to the transcription factor such that Ub is partly cleaved from the fusion partner after translation to reveal valine at the N terminus of the trancription factor; UbVR, ubiquitin fusion construct in which valine is introduced at the G76 residue of the C-terminal isopeptidase site and fused to the transcription factor such that Ub is partly cleaved from the fusion partner after translation to reveal arginine at the N terminus of the trancription factor; UbVV, ubiquitin fusion construct in which valine is introduced at the G76 residue of the C-terminal isopeptidase site and fused to the transcription factor such that Ub is partly cleaved from the fusion partner after translation to reveal valine at the N terminus of the trancription factor; UbX, ubiquitin fusion construct with its C-terminal isopeptidase site intact fused to the transcription factor such that ubiquitin is cleaved from the fusion partner after translation to reveal an amino acid (X) at the N terminus of the trancription factor (X: