Dynamic allocation of orthogonal ribosomes facilitates uncoupling of co-expressed genes

Introduction of synthetic circuits into microbes creates competition between circuit and host genes for shared cellular resources, such as ribosomes. This can lead to the emergence of unwanted coupling between the expression of different circuit genes, complicating the design process and potentially leading to circuit failure. By expressing a synthetic 16S rRNA with altered specificity, we can partition the ribosome pool into host-specific and circuit-specific activities. We show mathematically and experimentally that the effects of resource competition can be alleviated by targeting genes to different ribosomal pools. This division of labour can be used to increase flux through a metabolic pathway. We develop a model of cell physiology which is able to capture these observations and use it to design a dynamic resource allocation controller. When implemented, this controller acts to decouple genes by increasing orthogonal ribosome production as the demand for translational resources by a synthetic circuit increases.

Supplementary Table 1: Model parameters Most model rate constants were derived in [2] by fitting to the data in [1]. We assume that the ribosomal protein complex (denoted R) has the same parameters as the ribosome as a whole in [2]. We assume that the transcriptional threshold o r is the same as for the protein component. We assume that the rRNA has the same stability as host mRNAs (i.e. δ r = δ m X ) and that the binding/unbinding rates are diffusion limited (i.e. b r = u r = 1). We fit ω r to the data in [1]. * , Fit in this study. Units: aa, amino acids, mc, number of molecules.  Table 2: Parameter values for circuit gene, o-ribosome and controller production * , determined in the optimisation routine. Units: aa, amino acids, mc, number of molecules.
Supplementary Figure 3: Simulations of the impact of orthogonal ribosomes on host physiology. The impact of orthogonal ribosome production was assessed by simulating the response to increasing o-rRNA transcription rate (ω ρ ). Single markers show the results when using the host ribosome pool in the absence of orthogonal ribosome production. Host effects are assessed by observing changes in the proteome, ribosome biosynthesis and macroscopic effects such as ribosome distribution and growth rate. See Supplementary Note 2 for further discussion. Legend explanation: p T + p E , metabolic enzymes; p H , host proteins; p G , reporter protein; p R , 'empty' ribosome; ΣR, free and translating host ribosomes; ΣP , free and translating o-ribosomes; m R , mRNA of the ribosomal protein; r, host 16S rRNA; ρ, o-16S rRNA; Total, sum of all ribosomes; λ, growth rate. (A) Impact of orthogonal ribosomes production on host genes in the absence of circuit genes (i.e. ω G = 0). (B) Impact of orthogonal ribosome production on a circuit gene which utilises the host ribosome pool (i.e. ω G = 100). Inset in host proteome: Simulations across a o-rRNA induction of 100x ω ρ .
(C) Impact of using the orthogonal ribosome pool for circuit gene expression (i.e. ω G = 100).
Supplementary Figure 4: The effect of the accumulation of orthogonal ribosomes on cellular growth. Growth of the MG1655 strain harbouring orthogonal or host rRNA expression system was monitored over time. Overnight grown cells were diluted into fresh LB medium and grown to the exponential phase. 2 µL of culture was transferred into 1 mL fresh medium containing IPTG at the stated concentration. OD 600 was recorded using a microplate reader. Orthogonal ribosome assembly may be inefficient. Simulations of the steady state protein outputs for different RBS strengths (b G -to-u G ratio) and assembly of the orthogonal ribosome (b ρ -to-u ρ ratio) for the given orthogonal ribosome induction (ω ρ , molecules per min). Circuit gene is induction is constant at ω G = 100 molecules per min throughout. Results are reported as a ratio of the production utilising the host ribosome pool for the same circuit, with values greater than 2 truncated to 2. See Supplementary Note 4 for further discussion.
Supplementary Figure 8: Isocost lines of the gene circuits used in this study. Isocost lines for each circuit were determined by fitting a straight line through the mean steady state fluorescence. Error bars represent ±1 S.D.. The induced gene output is plotted on the x-axis and the constitutive gene output is plotted on the y-axis. IPTG was varied as shown to change the size of the o-ribosome pool. Note the different scales on each subplot. Plots are titled as follows X | Y, where X represents the strain and Y represents the circuit. The strains are named as follows: oribo, o-ribosome producing strain; controller, oribosome producing strain where o-rRNA production is under control of the o-lacI; ox-h-ribo, host 16S rRNA over-expressing strain.
Supplementary Figure 9: Comparison of experimentally determined isocost lines. Absolute gradient of the isocost lines for each circuit tested in this study as calculated from data presented in Fig. 8. The bars represent the strains and circuits at each IPTG level shown as follows: Supplementary Figure 10: Kinetics of fluorescent reporters production and cell growth of the oribosome producing strain carrying the h-RFP, h-GFP circuit Kinetics for the circuit at IPTG concentration shown. In each case the time-series analysis of GFP and RFP expression in response to different concentrations of AHL is depicted (upper subpanels). The mean of the fluorescent intensities and the standard deviation from three biological replicates were measured by flow cytometry. Histograms of fluorescent reporter production in the population at the steady state are also shown (lower subpanels). 20,000 cells from each sample were analysed. Bar plots represent growth rates.
Supplementary Figure 11: Kinetics of fluorescent reporters production and cell growth of the oribosome producing strain carrying the o-RFP, o-GFP circuit Kinetics for the circuit at IPTG concentration shown. In each case the time-series analysis of GFP and RFP expression in response to different concentrations of AHL is depicted (upper subpanels). The mean of the fluorescent intensities and the standard deviation from three biological replicates were measured by flow cytometry. Histograms of fluorescent reporter production in the population at the steady state are also shown (lower subpanels). 20,000 cells from each sample were analysed. Bar plots represent growth rates.
Supplementary Figure 12: Over expression of host 16S rRNA does not improve coupling. The wild type host 16S rRNA was overexpressed by induction with IPTG at the levels shown from the host expression system. Coupling is assessed by inducing RFP with AHL from 0 to 20 nM. Points are mean steady state fluorescence ±1 S.D. normalised by maximum GFP expression obtained across different levels of IPTG treatment. N = 3. Raw data is shown in Supplementary Fig. 8. Fluorescence was determined by FACS from cultures at 3 hours post induction during mid-exponential growth. The isocost line is fit to the mean fluorescence values and gradients calculated shown in Supplementary Fig. 9. FACS profiles are shown in Supplementary Fig. 13.
Supplementary Figure 13: Kinetics of fluorescent-reporters production and cell growth of the host 16S rRNA over-expressing strain carrying the h-RFP, h-GFP circuit Kinetics for the circuit at IPTG concentration shown. In each case the time-series analysis of GFP and RFP expression in response to different concentrations of AHL is depicted (upper subpanels). The mean of the fluorescent intensities and the standard deviation from three biological replicates were measured by flow cytometry. Histograms of fluorescent reporter production in the population at the steady state are also shown (lower subpanels). 20,000 cells from each sample were analysed. Bar plots represent growth rates.  The expression of rRNAs, which include the orthogonal 16S rRNA, is controlled by the repressor LacI present in the plasmid [3]. The feedback controller is constructed replacing the original RBS of LacI with the orthogonal RBS. (C) Plasmid carrying genes which enable violacein production.

E. coli strains Description
Ref.

Model description and numerical methods
Given that our work focuses on influencing the host ribosome pool, we initially developed a simple model of microbial physiology which allows us to assess the effect of orthogonal ribosome production and usage on host physiology. We based our model on the ordinary differential equation We refine this base model by extending the ribosome biosynthesis reactions to include the production of both protein and ribosomal RNA components. We introduce the necessary species to describe the production of orthogonal rRNAs and partition the ribosome pool. This model allows us to characterise the impact of dividing the cell's translational capacity between host and circuit genes.

Model description
The model represents a simplified microbe with:  Table 1 for a description of the model's rate constants.

Metabolism
The metabolism is made up of an extracellular substrate (s e ) which is imported by the transport enzyme (p T ) to become the intracellular species s i . The intracellular species is converted to the universal energy substrate (e) by enzyme (p E ). Both of these enzyme mediated reactions are described by Michaelis-Menten kinetics. In addition to these processes, the intracellular substrate is diluted by cell growth (λ · s i term in Each molecule of intracellular substrate creates ϕ e molecules of energy. This is a measure of the nutrient efficiency, which we maintain as high throughout (see [2] for a detailed discussion of energy implementation in their original model). Translation of each protein encoding mRNA by translation complexes consumes energy ( (. . . ) term). This energy consumption is proportional to both protein length (n X ) and number of translation complexes of that gene (c X in the T L function). The energy species is also diluted due to cell Host protein production Upon birth, host mRNAs can reversibly bind/unbind free host ribosomes (R) to form translation complexes (c X ). Upon the termination of translation, mRNAs are released (T L (c X , e) term, see Supplementary Equation The dynamics of the translation complex (c X ) follow from the description of the ribosome-mRNA interactions above, with the added degradation and dilution terms: The T L function describes the rate of translation of gene X. This expression, derived in [2], relates the translation rate of individual genes to the cell's global translation rate (γ max term), the gene's length (n X ) and the number of complexes currently translating that gene's mRNA (c X ).
Host proteins are born from translation complexes and are subject to decay and dilution: Note that this expression does not include the refinement of the 'empty' ribosome, p R , into functional host ribosomes R, and so only describes the production of the protein component (see Supplementary Equation 9 for a full description of the dynamics when X = R).
Note also we have not included expressions describing the binding/unbinding of proteins to promoters to exert their action but rather use Hill functions to scale the mRNA production rate. For example, when we consider the auto-inhibitory effect of host proteins (i.e. when X = H) the derivative dp H /dt follows the same form as dp X /dt, and the interaction effect is only seen in dm H /dt, i.e. the effect of the R term in Supplementary Equation 4. There are no terms describing the interaction of the transcription factor and promoter as there would be in a detailed mechanistic model.

Ribosome biosynthesis
As briefly described in the main text, we refined the original ribosome synthesis reactions to include the separate production of protein and rRNA based components. For the protein components, we consider the production of a single large protein which represents the small and large ribosomal subunits and any accessory protein complexes.
We assume that host rRNAs are born spontaneously at a maximal rate scaled by the cell's internal energy, in a manner similar to the host mRNAs. This rRNA (r) reversibly binds empty ribosomes (p R ) to form free host ribosomes (R). The rRNA is subject to degradation and dilution. The dynamics of the host rRNA are therefore: As previously described the protein component of the ribosome (p R ) follows the same dynamics as for other host proteins, as outlined in subsection Host protein production when X = R. In addition to the production and decay dynamics described in Supplementary Equation 7, p R undergoes processing by binding with the rRNA to produce the final functional free host ribosomes, R. We account for ribosome complex disassembly by allowing this reaction to be reversible.
Free host ribosomes are produced by the reversible binding of host rRNA and empty ribosomes. They take part in translation of each protein coding gene ( (. . . ) term). Free ribosomes bind mRNAs to form translation complexes (the m X term) and are produced when these complexes dissociate before (u X · c X term) or upon the termination of protein synthesis (T L function term). Concurrently translation complexes are lost through degradation and dilution.

Determination of growth rate
The growth rate is calculated within the model, thus allowing effects on host physiology to be assessed by observing the change in this one value. In this way the model captures the effect of high exogenous protein production such as decreasing growth rate leading to the accumulation of intermediates. Growth rate (λ) is proportional to the product of the global translation rate (γ max term) and number of translating complexes ( (c X )). See [2] for a full derivation in terms of protein production and dilution.

Introduction of circuit genes
We introduce circuit genes by introducing new species and equations describing the production of mRNA, translation complexes and proteins. We assign these genes to the set Y . These take the same form as in Supplementary Equation 7 with the ribosome pool specified as either host or orthogonal as appropriate. Orthogonal ribosomes are specified by modifying R to P .

Supplementary Equation 4, Supplementary Equation 5 and
We modify Supplementary Equation 2 to take account of the additional energy demand due to the circuit protein production ( (. . . ) term).
We modify the growth rate Supplementary Equation 11 to include the effect of circuit gene translation complexes ( (c Y ) term):

Addition of orthogonal ribosomes
We assume that the orthogonal 16S rRNA (ρ) follows the same dynamics as the host rRNA being produced in an energy dependent manner and reacting with empty ribosomes. We assume that this plasmid-carried gene will respond to energy changes in a manner similar to host genes (See parametrisation in Table 1).
We modify Supplementary Equation 10 to take account of the o-rRNA -empty ribosome interactions which mirror the host rRNA interactions (red terms). We assume that these interactions have the same kinetics as the host (See Supplementary Table 1).
In the same manner as host ribosomes, free orthogonal ribosomes are produced by reversible binding of orthogonal rRNA and empty ribosomes. Functional orthogonal ribosomes bind and translate mRNAs which are specified to them (i.e. circuit genes, denoted by Y ) in the same manner as host ribosomes do host mRNAs.
Free ribosomes are subject to degradation and dilution due to growth.

Introduction of the controller
To implement the feedback controller in the model we introduce the new equations and species required to describe its mRNA, translation complex and protein. We denote these components with F . As described in th subsection Introduction of circuit genes, we modify the expressions for the energy species de/dt, orthogonal ribosomes dP/dt and growth rate λ to take account of the additional energy usage and translation complexes.
To implement (i.e. 'close') the feedback loop, we modify Supplementary Equation 15 to include the inhibitory action of the protein p F . As before we use a simple Hill function to describe the inhibition (red term).

Parametrisation
We used the parameters derived by Weiße et al. , using the original protein-only ribosome production parameters for the new empty ribosome (x R ) species. We assumed that the transcription of the host ribosomal rRNA showed the same energy dependence as the protein component (i.e. θ r = θ R ). See Supplementary   Table 1 for full details.
We optimised the host rRNA gene maximum transcription rate (ω r ) using MATLAB's genetic algorithm using 0 and 10 5 as the lower and upper bounds respectively. We choose our upper bound by assuming that maximal gene expression for a protein encoding gene is on the order of 10 3 RNAs per min and as rRNAs are present in multiple copy number and also driven from strong promoters we allow ω r to vary significantly above that ω for a protein coding gene.
The original model was parametrised using the growth rate and ribosomal mass fraction data produced by Scott et al. [1,2]. The association between growth rate (λ) and ribosomal mass fraction (Φ) was determined by growing cells on different carbon sources and in the presence of a ribosome inhibitor. We take the same approach described in [2] by incorporating the presence of inhibited ribosomes which cannot translate and by varying nutrient efficiency (ϕ e ). Our optimisation aims to minimise the sum of the squared errors between the data and our simulation (Supplementary Equation 19).
The full host model shows good quantitative agreement with the data for cellular growth rate ( Supplementary   Fig. 2). The simulations of the ribosomal mass fraction replicate the general trends observed in the data with ribosomal fraction increasing with antibiotic concentration and nutrient quality. There is good quantitative agreement with the experimental data at high levels of nutrient quality and low antibiotic concentration which were used in this study.
Numerical methods

Simulations
The system of ordinary differential equations was implemented in MATLAB 2016a (The MathWorks Inc., MA, USA) and its behaviour simulated using the in-built stiff solver ode15s. All simulations were initiated with RNAs and translation complexes as zero and protein species at 10 molecules and are then run to steady state by repeatedly increasing the simulation time span until the maximum absolute value of the derivative vector was less than 1 unit per time unit. Before simulations of the circuit, the host model, with orthogonal ribosomes as appropriate, was simulated to steady state. All simulations were initiated with 10 molecules of each protein species and 10 3 molecules of energy.

Circuit design process
Gene circuits were designed by fixing circuit topologies and varying parameters in biologically feasible ranges.
To achieve specific behaviours, we utilised the genetic algorithm functions from MATLAB's Global Optimi- We wished our protein outputs to mirror the behaviour of the mRNA inputs. During the circuit design processes we scored coupling between two genes by simulating the increasing production of one gene (by increasing ω 1 from 1 to 10 4 ) while maintaining the production of a second (ω 2 is constant). We quantified coupling by taking logs (base 10) of the induction of the first gene (ω 1 ) and the protein levels (p 1 and p 2 ) to produce the transformed data w, x and y. Using the inbuilt polyfit function we fit lines through the points w We assessed the efficiency of a particular method to decouple two genes by calculating the sum of scores over a range of inductions of protein p 2 (vectors of induction, ω 2 ) (Supplementary Equation 21).
We utilise this method rather than minimising the isocost line gradient as this allows us to identify designs which successfully insulate the constitutive gene whilst not necessarily relieving the resource limitation which can create a saturating response in the induced gene.

Impact of orthogonal ribosome usage on host physiology
To assess the impact of orthogonal ribosome production on host physiology and to test the ability of our model to capture previously reported qualitative behaviour of o-ribosome producing cells, we simulated the production of o-rRNAs and the use of o-ribosomes for gene expression (Supplementary Fig. 3).
We initially consider the production of o-ribosomes on the host cell in the absence of circuit gene expression ( Supplementary Fig. 3A). We simulated the production of o-rRNAs over a number of orders of magnitude.
Our results recreate previous experimental results (e.g. [11,12]) that o-ribosome production has little effect on growth rate, with up to 20% of the ribosome pool being coopted resulting in less than a 10% fall in growth rate. Analysis of the ribosomal biosynthesis reactions (assessing rRNAs, free ribosomes etc.) shows that the 'empty ribosome' (p R ) fraction decreases significantly. Concurrently, host 16S rRNAs and mRNAs needed for ribosome assembly increase in response to ribosome sequestration by orthogonal rRNAs. The cell is able to compensate for o-ribosome sequestration by increasing the total number of ribosomes by 20%. This allows the number of orthogonal ribosomes to rise by 40% of the original ribosome number (i.e. number of host ribosomes when ω ρ = 0) whilst the number of host ribosomes falls by only 20%.
We initially simulated the expression of a simple one gene circuit which is induced at ω ρ = 100 mRNAs per minute and utilises host ribosomes for its gene expression. At this level of expression, protein output p G is approximately 25% of the total proteome and the growth rate is predicted to be 0.024 per hour (corresponding to a doubling time of approximately 80 minutes). This is comparable to the observations of Scott et al. [1]. We assess the impact of orthogonal ribosome production on this gene by increasing ω ρ over several orders of magnitude. Our model predicts a negligible fall (< 5% at ω ρ = 1000) in expression as orthogonal ribosome production increases. We do not see an increase in orthogonal ribosome production at low ω ρ as induction of o-rRNA increases, as expected. Given the high level of predicted protein expression, there is a concurrent decrease in transcription rate due to its energy dependence (the (e/(o ρ + e)) term in Supplementary Equation 15). This energy usage by protein synthesis moves the o-rRNA curve to the right and also raises the production of host rRNA and empty ribosome mRNA. If the transcription rate is increased beyond values which are biologically feasible then we observe similar effects on o-rRNA production ( Supplementary Fig. 3B, inset in Host proteome).
We simulated the use of the orthogonal ribosome pool for circuit gene expression. For a constitutively expressed gene (induction held at ω G = 100) we show that protein levels, p G , increase as o-rRNA transcription increases, demonstrating that the size of the orthogonal ribosome pool acts as another 'dial' for controlling transgene expression (Fig. 3C). The ribosomal species, including host ribosome (R) and empty ribosomes (p R ), are most sensitive to orthogonal ribosome expression and use. Comparison of the host proteome in response to o-ribosome production ( Supplementary Fig. 3A) and use ( Supplementary Fig. 3C) demonstrates that use of the orthogonal ribosome pool causes more perturbation that production alone. Analysis of the ribosome biosynthesis shows that orthogonal ribosome production rises until ω ρ = 40 rRNAs per min before falling. Additionally we observe that total ribosome number falls as ω ρ rises. This is due to the higher protein production (> 33% of the total proteome) brought about by high o-ribosome number. Translation acts to stabilise o-ribosomes, and therefore, prevents them from dissociating and releasing empty ribosomes (p R ). This means that empty ribosomes are not free to be converted into host ribosomes. This results in a decrease in the host's translational capacity, which in turn results in less translation of ribosomal mRNAs.
In our simulations, we find that at an o-rRNA induction ω ρ ≈ 32 and circuit expression of ω G = 100 mRNAs per min the protein production utilising the o-ribosome is the same as when utilising the host ribosome pool ( Supplementary Fig. 3C). At these equivalent levels of gene expression there is negligible change (< 1%) in host protein expression (p T + p E , p H ) and growth rate (change < 1%). We find significant reallocation of translational capacity with up to 25% of the ribosome pool rendered orthogonal and only negligible changes in the total number of ribosomes.

Crosstalk is removed in high-competition circuits
In Fig. 1B we find that as the o-ribosome pool is increased with IPTG there is a concurrent increase in h-RFP expression. This is potenally This is likely due to incomplete orthogonality, i.e. translation of h-RFP by o-ribosomes, leading to interference. To explore this further, we introduced bi-directional crosstalk into our model, allowing o-ribosomes to translate mRNAs with host RBSs and vice versa.
To incorporate crosstalk we allow mRNAs to bind to their non-target ribosome at rate β to produce the translation complex c . The unbinding rate is µ, which we set at 1 throughout. The translation complexes c follow the same dynamics described in Supplementary Equation 5.
The dynamics of host-translated mRNAs m X and proteins p X become (with the crosstalk modifications shown in red): . To assess the impact of circuit demand on crosstalk we simulate the production of a single protein which utilises the host ribosome pool for its expression while varying β to control the propensity of o-ribosomes to translate host and circuit mRNAs. We vary the circuit demand by changing both the translation rate (ω RF P ) and RBS strength (b RF P ). Our simulations show that in the presence of a low demand circuit, crosstalk can have a significant effect. When β = b RF P = 0.1, i.e. there is no distinction between the two ribosome pools, production is increased by increasing ω ρ there is a net increase in ribosome number (Supplementary Fig. 3B).
These results suggest that the h-RFP circuit, which contains only one gene that has low demand for ribosomes and so crosstalk results in increased h-RFP expression as o-ribosomes are produced ( Supplementary Fig. 5B).
Increasing the circuit demand by increasing both ω RF P and b RF P to their maximum feasible values effectively removes the impact of crosstalk with protein levels falling negligibly ( Supplementary Fig. 5C). Comparing our high demand simulations to the experimental results of the h-RFP, h-GFP circuit shows that our gene coupling assessments are carried out in a context of high enough competition to allow crosstalk to be considered negligible throughout (Supplementary Fig. 5D) and therefore throughout our experimental system.

Inefficient o-ribosome assembly may explain poor gene expression from the o-system
Our simulations predict that for a given gene induction, utilisation of the orthogonal ribosome pool results in higher protein production due to the lack of competition ( Supplementary Fig. 3). However, experimentally we find significantly reduced expression (Fig. 1).
This may be due to lower production of the o-rRNA in comparison to the host rRNA operons but at moderate to high levels of o-rRNA induction and (assuming b G = 1 and b ρ = 1, i.e. a strong orthogonal RBS and complete assembly) simulations suggest that use of the orthogonal ribosome pool produces higher gene expression than the host. Therefore, we propose that our experimental observations may be due to inefficient translation (i.e. the orthogonal RBS is weak) or inefficient orthogonal ribosome assembly. To assess these effects we simulate the production of a single protein (induced at ω G = 100 molecules per min) using both the host ribosome pool (with maximal RBS strength b G = 1) and o-ribosome pool. In the latter simulations, we vary the mRNA-ribosome association rate (b G < 1) and the o-rRNA-empty ribosome association rate (b ρ < 1). We leave the unbinding rates as maximal, i.e. u G = 1 and u ρ = 1 and set the maximum o-rRNA rate ω ρ = 100 molecules per min.
Varying each parameter alone is sufficient to cause decrease in gene expression to less than 40% of the production achieved using the host pool. If both b G and b ρ are significantly weaker than those of the host (b G < 0.1 and b ρ < 0.1, Fig. 7) then the ratio of the protein production using the orthogonal to the host pool falls to ranges we see experimentally.  Fig. 16, ω ρ = 500). This in turn results in a concurrent fall in expression of the host ribosome-utilising GFP by over 80% at medium levels of RFP induction (ω RF P = 100, ω ρ = 500 molecules per min.)

Multiple orthogonal ribosome pools decouple co-expressed genes
In the main text we demonstrate both numerically and experimentally that utilising both the host and orthogonal ribosomes pools alters gene coupling profiles. We extend this analysis by considering the effect of using two orthogonal ribosome pools. Biologically these can be created by expressing multiple different synthetic 16S rRNAs [11]. We implement a second orthogonal ribosome pool by replicating the changes outlined in Supplementary Note 1. At high levels of o-rRNA expression, competition for empty ribosomes (p R ) results in high levels of gene coupling.
We optimise the production of the two orthogonal 16S rRNAs to minimise gene coupling (ω ρ1 = ω ρ2 = 10 molecules per min) which yields near complete decoupling. However this assumes that there is no cross talk between the two orthogonal ribosome pools -i.e. that each pool translates its, and only its, target mRNAs.
In reality, to date, orthogonal rRNA sequences are often not sufficiently distinct to achieve this and each orthogonal pool will translate mRNAs targeted for the other pool due to cross talk -i.e. erroneous interactions between one 16S rRNA and its non-target mRNA. To test the impact of cross talk we introduce interactions between each mRNA and its non-target o-ribosome, as in Section Supplementary Note 3. Messenger RNAs bind to their non-target o-ribosome at rate β to produce the translation complex c 1 . The unbinding rate is µ. The dynamics of an mRNA m 1 which is designed to be translated by P 1 and erroneous translated by P 2 (the effect of crosstalk is highlighted in red) are: We vary the level of crosstalk between none (β = 0) and high (β = 0.1). Coupling increases seven fold as crosstalk increases from 0 to 0.1 (the second represents 10% of the interaction between o-ribosome and its target mRNA). As cross talk increases, gene coupling (as measured by the slope of the isocost line) also increases ( Supplementary Fig. 19B). Whilst our simulations suggest that some level of crosstalk can be tolerated, this must be relatively small (β ≤ 0.01), and may not be achievable with currently published o-ribosomes.

The use of tethered o-ribosomes may increase yields and increase decoupling in some contexts
So far our analysis has focused on the assessing the feasibility using synthetic 16S rRNAs to produce a synthetic orthogonal ribosomes. These ribosomes function in the same manner as natural host ribosomes with altered specificity; for example, these o-ribosomes dissociate into their respective large and small subunits when not translating. By expressing synthetic 23S rRNAs or additional synthetic RNAs then 'tethered' ribosomes can be created [13,14]. In these semi-synthetic ribosomes the two subunits are permanently linked and so are not able to dissociate.
Here we assess the effect of using tethered ribosomes for synthetic gene expression and its impact on gene coupling by simulating simple two-gene circuits. Ribosome tethering can be modelled by assuming that the o-rRNA and protein components could not dissociate upon creation of the functional o-ribosome, i.e. we set u ρ to 0. We set b ρ = 0.45 to take into account the experimental observation that tethered ribosomes shown reduced expression in comparison to host ribosomes [13].
The expression of tethered ribosomes results significant decrease in expression of circuits using the host ribosome pool due to the lack of recycling of the ribosomal proteins p R (Supplementary Fig. 20A). Utilising the tethered o-ribosome pool for gene expression significantly increases gene expression from the circuit ( Supplementary Fig. 20B). Simulating a circuit when the two circuits genes are distributed across both host and tethered o-ribosome pools replicates results observed with orthogonal ribosomes. When the constitutively expressed gene is translated by the tethered o-ribosome pool and the induced gene by the host pool we observe complete decoupling and increased gene expression at all levels of o-ribosome pool ( Supplementary Fig. 20C).
Gene expression plateauing is mediated by saturation of the ribosome pool As RFP induction increases the output levels begin to plateau (both experimentally Fig. 2c,3c and theoretically Fig. 5). To assess the potential reasons for this saturation effect we simulate the different circuit conformations and assess the mRNA (input) -protein(output) relationship. The internal intermediate, e, does not fall to below 85% across all inductions ( Supplementary Fig. 24). This metabolite represents the outputs of metabolism; such as 'energy' (approximating the function ATP/GTP) but also the precursers needed for protein synthesis (such as amino acids). As this metabolite is well maintained across inductions we propose that this is not the cause of the saturation effect. The transcription rates in our model are not limiting with GFP mRNA outputs being maintained across RFP inductions and RFP mRNAs increasing linearly with induction. Whilst our model does not explicitly include RNA polymerase sharing across the genes the propensity for genes to be expressed under different energy conditions, and therefore different make ups of the cellular economy, is included via the transcriptional thresholds (θ terms). See [2] for original discussion. Therefore we propose that the saturation effect observed in our experimental system remains due to reduced free ribosome number rather than other factors.

Modelling of a biochemical pathway
We consider a simple five-part linear biochemical pathway which converts the intracellular 'energy' metabolite, e, to an output substrate, s 5 , via four intermediates (Supplementary Equation 25).
We model the conversion of each metabolite, s i , into the next as an enzyme catalysed reaction by protein p i+1 with the reaction dynamics described by Michaelis-Menten kinetics.
The dynamics of the first metabolite are: The dynamics of the intermediate metabolites are (where i = {2...4}): The dynamics of the final metabolite, the output, are defined by: We also modify Supplementary Equation 12 to account for the conversion of e into s 1 . This represents the drain on the host metabolic flux of the new pathway. ϕ s represents the number of molecules of e required to make one molecule of s 1 .
X∈{T,E,H,R,Y } n X · T L (c X , e) − λ · e −ϕ s · v 1 · e · p 1 k 1 + p 1 We model the production of the enzymes as we modelled the reporter genes before (described in Supplementary Note 1). Whilst, experimentally vioBCDE is expressed as an operon from one promoter, for simplicity we model these genes as four separate mRNAs (i.e. one mRNA for vioB etc) to maintain the number of equal (i.e. ω i , o i and δ mi for i = {2...5}) to model the fact these genes are co-regulated.
We assumed that pathway enzymes have the same kinetics as the host's lumped enzyme function (v i = 5800 molecules per min and k i = 1000 molecules). We set ϕ s to be 0.01 to model the impact of the additional flux through the pathway on the central metabolism. We also increase the nutrient efficiency to ϕ to 1 to model the additional media supplementation. We take the enzyme sizes, in amino acids, for the components of the violacein producing pathway from UniProt: n 1 = 418, n 2 = 998, n 3 = 429, n 4 = 373, n 5 = 196. Other parameters, where set as found in Supplementary Table 2. Note that for simplicity of language and to allow the same nomenclature with the experimental implementation of the violacein pathway the enzymes are referred to by the a letter in the main text, such that A = 1, B = 2 etc.