Metabolic perceptrons for neural computing in biological systems

Synthetic biological circuits are promising tools for developing sophisticated systems for medical, industrial, and environmental applications. So far, circuit implementations commonly rely on gene expression regulation for information processing using digital logic. Here, we present a different approach for biological computation through metabolic circuits designed by computer-aided tools, implemented in both whole-cell and cell-free systems. We first combine metabolic transducers to build an analog adder, a device that sums up the concentrations of multiple input metabolites. Next, we build a weighted adder where the contributions of the different metabolites to the sum can be adjusted. Using a computational model fitted on experimental data, we finally implement two four-input perceptrons for desired binary classification of metabolite combinations by applying model-predicted weights to the metabolic perceptron. The perceptron-mediated neural computing introduced here lays the groundwork for more advanced metabolic circuits for rapid and scalable multiplex sensing.

circuit design, we first employ computational design tools, Retropath 40 and Sensipath 41 , 1 that use biochemical retrosynthesis to predict metabolic pathways and biosensors. We 2 then build and model three whole-cell metabolic transducers and an analog adder to 3 combine their outputs. Next, we transfer our metabolic circuits to a cell-free system 42,43 in 4 order to take advantage of the higher tunability and the rapid characterization it offers 44-5 46 , expanding our system to include multiple weighted transducers and adders. Finally, 6 using our integrated model trained on the cell-free metabolic circuits we build a more 7 sophisticated device called the "metabolic perceptron", which allows desired binary 8 classification of multi-input metabolite combinations by applying model-predicted weights 9 on the input metabolites before analog addition, and demonstrate its utility through two 10 examples of four-input binary classifiers. Altogether, in this work we demonstrate the 11 potential of synthetic metabolic circuits, along with model-assisted design, to perform 12 complex computations in biological systems. 13

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Results 16 17 Whole-cell processing of hippurate, cocaine and benzaldehyde inputs 18 To identify the metabolic circuits to build, we use our metabolic pathway design tools, 19 Retropath 40 and Sensipath 41 . These tools function using a set of sink compounds at the 20 end of a metabolic pathway, here metabolites from a dataset of detectable compounds 47 , 21 and a set of source compounds that can be used as desired inputs for the circuit. The 22 tools then propose pathways and the enzymes that can catalyze the necessary reactions, 23 allowing for promiscuity. Our metabolic circuit layers are organized according to the main 24 processing functions: transduction and actuation (Figure 1a). Transducers are the 25 simplest metabolic circuits that function as sensing enabling metabolic pathways 26 (SEMP) 48 , consisting of one or more enzymes that transform an input metabolite into a 27 transduced metabolite. The transduced molecule, in turn, is detected through an actuation 28 function that is implemented using a transcriptional regulator. 29 30 We used benzoate as our transduced metabolite, its associated transcriptional activator 31 BenR, and the responsive promoter pBen to construct the actuator layer of our whole-cell 32 metabolic circuits 49 . To compare the shape of the response curve, we constructed the 33 actuator layer in two formats: (i) an open-loop circuit (Figure 1b) and (ii) a feedback-loop 34 circuit ( Figure S1). When compared to the open-loop format, the feedback-loop circuit 35 has previously been shown to exhibit linear dose-response to input 21,50 . We found that 36 while the feedback-loop format does linearize the actuator response curve, apparent 37 toxicity at high benzoate concentrations reduces the usable activator dynamic range 38 ( Figure S1). Therefore, we selected the open-loop format due to its higher dynamic range 39 of activation (Figure 1c), setting the maximum concentration of benzoate used in this 1 work to the saturation point of this open-loop circuit. 2 3 Building on our previous work 48 , we next implemented three upstream transducers that 4 convert different input metabolites into benzoate for detection by the actuator layer 5 already tested. The transducer layers were composed of enzymes HipO for hippurate 6 (Figure 1d), CocE for cocaine (Figure 1e), and vdh for benzaldehyde (Figure 1f). 7 Compared to the benzoate output signal, we found that the transduction capacities of the 8 three transducers were 99.6%, 49.2%, and 77.8%, respectively (Supplementary Figure   9 S2), indicating a partial dissipation in signal. A Whole-cell metabolic concentration adder 10 A metabolic concentration adder is a device composed of more than one transducer that 11 converts their respective input metabolites into a common transduced output metabolite. 12 For our whole-cell concentration adder, we combined two transducers to build a 13 hippurate-benzaldehyde adder actuated by the benzoate circuit (Figure 2a). Unlike digital 14 bit-adders that exhibit an ON-OFF digital behavior, our metabolic adders exhibit a 15 continuous analog behavior that is natural for metabolic signal conversion 51 (Figure 2b 16 and Supplementary Figure S3) . Increasing the concentration of one of the inputs at any 17 fixed concentration of the other shows an increase in the output benzoate, and thus in the 18 resulting fluorescence (Figure 2b and Supplementary Figure S3). 19 20 The maximum output signal for our adder, when hippurate and benzaldehyde were both 21 at the maximum concentration of 1000 µM, was lower than the maximum signal produced 22 by hippurate and benzaldehyde transducers alone (Supplementary Figure S2). 23 However, as seen above, the difference between the maximum signal of their transducers 24 and the actuator was smaller. This dissipation in signal from the transducers to the adders 25 and from the actuators to the transducers (Supplementary Figure S2) could either be 26 because of resource competition (as a result of adding more genes) or because of 27 enzyme efficiency (as a result of poorly balanced enzyme stoichiometries). To test these 28 two hypotheses, we investigated the effect of the enzymes on cellular resource allocation. 29 For this purpose, the cocaine transducer and the hippurate-benzaldehyde adder were 30 characterized by adding benzoate to these circuits (Supplementary Figures S4 and S5). 31 Comparing the results of these characterizations with the benzoate actuator reveals that 32 dissipation in signal from the transducers to the adders is due to resource competition, 33 whereas that from the actuators to the transducers is due to enzyme efficiency. 34 35 In order to gain quantitative understanding of the circuits' behavior, we empirically 36 modeled their individual components to see if we were able successfully capture their 37 behavior. We first modeled the actuator (gray curve in Figure 1c) using Hill formalism 52 38 as it is the component that is common to all of our outputs and therefore constrains the 39 rest of our system. We then modeled our transducers, considering enzymes to be 40 modules that convert their respective input metabolites into benzoate, which is then 41 converted to the fluorescence output already modeled above. This simple empirical 1 modeling strategy reproduces our transducer data (results not shown). To incorporate 2 observations made in Supplementary Figure S4 and S5, we included resource 3 competition in our models to explain circuits with one or more transducers. To this end, 4 we extended the Hill model to account for resource competition following previous 5 works 53,54 , with a fixed pool of available resources for enzyme and reporter protein 6 production that is depleted by the transducers. This extension is further presented in the 7 Methods section. We trained our model on all transducers, with and without resource 8 competition (i.e. individual transducers, or transducers where another enzyme competes 9 for the resources). This model (presented in gray lines in Figure 1d,e,f and Figure 2c), 10 which was not trained on adder data but only on actuator, transducer, and transducers 11 with resource competition data, recapitulates it well. This indicates that the model 12 accounts for all important effects underlying the data. The full training process is 13 presented in the Methods section, and a table summarising scores of estimated goodness 14 of fit of our model is presented in Supplementary Table S1. Cell-free processing of multiple metabolic inputs 1 Cell-free systems have recently emerged as a promising platform 42 that provide rapid 2 prototyping of large libraries by serving as an abiotic chassis with low susceptibility to 3 toxicity. We took advantage of an E. coli cell-free system with the aim of increasing the 4 computational potential of metabolic circuits in several ways (Figure 3a). Firstly, a higher 5 number of genes can be simultaneously and combinatorially used to increase the 6 complexity and the number of inputs for our circuits. Secondly, the lower noise provided 7 by the absence of cell growth and maintenance of cellular pathways 55 improves the 8 predictability and accuracy of the computation. Thirdly, having genes cloned in separate 9 plasmids enables independent tunability of circuit behavior by varying the concentration 10 of each part individually. Finally, cell-free systems are highly adjustable for different 11 performance parameters and components. In all, these advantages of cell-free systems 12 enable us to develop more complex computations than the whole-cell adder. 13 14 Following from our recent work 56 , we first characterized a cell-free benzoate actuator to 15 be used downstream of other metabolic transducers. Figure 3a shows a schematic of the 16 cell-free benzoate actuator composed of a plasmid encoding the BenR transcriptional 17 activator and a second plasmid expressing sfGFP reporter under the control of a pBen 18 promoter. This actuator showed a higher operational range than the whole-cell 19 counterpart (Figure 1c). The optimal concentration of the TF plasmid (30 nM) and the 20 reporter plasmid (100 nM) were taken from our recent study 56 . Following successful 21 implementation of the actuator, we proceeded to build five upstream cell-free transducers 22 for hippurate, cocaine, benzaldehyde, benzamide, and biphenyl-2,3-diol ( Figure   23 3c,d,e,f,g) that convert these compounds to benzoate. Each of the five transducers used 24 10 nM of enzyme DNA per reaction, except the biphenyl-2,3-diol transducer that used two 25 metabolic enzymes with 10 nM DNA each. 26 27 Compared to its whole-cell counterpart (Figure 1f), in the cell-free transducer reaction 28 (Figure 3e) benzaldehyde appears to spontaneously oxidise to benzoate without the 29 need of the transducer enzyme vdh. This behavioral difference between the whole-cell 30 and cell-free setups could be due to the difference in redox states inside an intact cell and 31 the cell-free reaction mix 57,58 . Furthermore, benzamide and biphenyl-2,3-diol transducers 32 exhibit inhibition in fluorescence outputs at very high (1000 μM) input concentrations. 14 15 16 17 Cell-free weighted transducers and adders 1 After characterizing different transducers in the cell-free system that enable building a 2 multiple-input metabolic circuit, we sought to rationally tune the transducers. Cell-free 3 systems allow independent tuning of each plasmid by pipetting different amounts of DNA. 4 We applied this advantage to weight the flux of enzymatic reactions in cell-free 5 transducers (Figure 4a). The concentration range we used was taken from our recent 6 study 56 , in order to have an optimal expression with minimum resource competition. We  (Figure 4d) and biphenyl-2,3-diol (Figure 4e). Increasing the concentration 9 of the enzymes produces a higher amount of benzoate from the input metabolites, and 10 hence higher GFP fluorescence. Compared to the others, the hippurate transducer 11 reached higher GFP expression at a given concentration of the enzyme and the input, 12 and biphenyl-2,3-diol reached the weakest signal. For the biphenyl-2,3-diol transducer 13 built with two enzymes (Figure 4e), both enzymes are added at the same concentration 14 (e.g., 1 nM of "enzyme DNA" indicates 1 nM each of plasmids encoding enzymes bphC 15 and bphD).   Data in Figure 4 show that similar output levels can be achieved for different input 1 concentrations, provided the appropriate transducer concentrations are used. In the next 2 step, we applied this finding to build hippurate-cocaine weighted adders by altering either 3 the concentration of the enzymes or the concentration of the inputs (Figure 5a). The 4 fixed-input adder is an adder in which the concentration of inputs, hippurate and cocaine, 5 are fixed to 100 µM and the concentration of the enzymes is altered (top panel in Figure   6 5b). In this device, the weight of the reaction fluxes is continuously tunable. We then 7 characterized a fixed-enzyme adder by fixing the concentration of the enzymes (1 nM for 8 HipO, 3 nM for CocE; the cocaine signal is weaker, which is why a higher concentration 9 of its enzyme is used) and varying the inputs, hippurate and cocaine (top panel in Figure   10 5c). 11 12 In order to have the ability to build any weighted adder with predictable results, we 13 developed a model that accounts for the previous data. We first empirically modeled the 14 actuator (gray curve in Figure 3b) since all other functions are constrained by how the 15 actuator converts metabolite data (benzoate) into a detectable signal (GFP). We then 16 trained our model with individual weighted transducers (Supplementary Figure S6) and 17 predicted the behaviors of the weighted adders (bottom panel in Figure 5b,c). The results 18 shown in Figure 5b, 22 and does not capture the inhibitory effect observed at the high concentration of 23 benzamide or biphenyl-2,3-diol, as this was not accounted for in the model. 24 25 Using the above strategy, we can build any weighted adder for which we have pre- 26 calculated the weights using the model on weighted transducers. We use this ability in 27 the following section to perform more sophisticated computation for a number of 28 classification problems.   Since our weighted transducer models have already been trained on the cell-free 14 experimental data, we checked if we could use them to calculate the weights needed to 15 classify different combinations of two inputs: hippurate and cocaine. We tested our model 16 on five different binary classification problems, A to E (Supplementary Figure 7). For 17 each problem, the two types of data were represented as a cluster of dots on the scatter 18 plot. The trained model was then used to identify weights needed to be applied to the 19 weighted transducers such that a decision threshold 'd' exists to classify the two clusters For the classifiers, the input metabolites are fixed to 100 µM, as it allows the best ON- 1 OFF behavior for all inputs and weight-tuning according to model simulations (results not 2 shown). The model accurately predicted weights to obtain the simple "full OR" classifier 3 behavior (Figure 6d), as well as cocaine, benzamide, and biphenyl-2,3-diol weights for 4 the second complex classifier. The initial weights computed by the model are presented 5 in Supplementary Figure S8. The optimal weight of HipO (hippurate transducing 6 enzyme) was calculated to be 0.1 nM, which leads to higher signals than predicted, 7 particularly for the "ON" behavior with only hippurate. To further characterize the HipO 8 weights at still lower concentrations of the enzyme, we performed an additional 9 complementary characterization (Supplementary Figure S9). Our aim here was to find 10 a weight for HipO through which a classifier outputs a low signal ("OFF") with only 11 hippurate and high signal ("ON") when coupled with other inputs. We arrived at 0.03 nM 12 HipO which exhibited this shifting behavior between "OFF" and "ON" (Figure 6d and 13 Supplementary Figure S9). Using our model-guided design and rapid cell-free 14 prototyping on the HipO weight, we were able to design two 4-input binary classifiers. In   Computing in synthetic biological circuits has largely relied on digital logic-gate circuitry 10 for almost two decades 5,62 , treating inputs as either absent (0) or present (1). While such 11 digital abstraction of input signals provides conceptual modularity for circuit design, it is 12 less compatible with the physical-world input signals that vary between low and high 13 values on a continuum 37 . As a result, digital biological circuits must carefully match input- 14 output dynamic ranges at each layer of signal transmission to ensure successful signal 15 processing 2,30 . More recently, the higher efficiency of analog computation on continuous 16 input has been recognized 63 , and some analog biological circuits have started 17 emerging 21 . In this regard, using metabolic pathways for cellular computing seems like a 18 natural progression for analog computation in biological systems 21,30 . 19 20 In this study, we investigated the potential of metabolism to perform analog computations 21 using synthetic metabolic circuits. To that end, we first established a benzoate actuator 22 to report the output from our metabolic circuits in both whole-cell and cell-free systems 23 (Figures 1c and 3b). Upstream of the actuator, we constructed hippurate, cocaine, and 24 benzaldehyde transducers in the whole-cell system (Figures 1d,e,f) and a metabolic 25 adder by combining the benzaldehyde and hippurate transducers (Figure 2). Similarly, 26 we constructed hippurate, cocaine, benzaldehyde, benzamide, and biphenyl-2,3-diol 27 transducers in the cell-free system (Figures 3c,d,e,f,g) and weighted adders by 28 combining them (Figure 5). Compared to the numerous digital biological devices, which 29 compute through multi-layered genetic logic circuits, the metabolic adder is a simple one-30 layered device with fast execution times.

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Our computational models trained only on the actuator and transducer data predicted 33 adder behaviors with high accuracy (Supplementary Tables S1 and S2). This further 34 enabled us to calculate the required weights for more complex "metabolic perceptrons" 35 that compute weighted sums from multiple inputs and use them to classify the multi-input 36 combinations in a binary manner (Figures 6 and S7). To the best of our knowledge, the metabolic adders 2 and perceptrons presented in this work are the first engineered biological circuits that use 3 metabolism for analog computation. 4 5 Unlike genetic circuits that experience expression delays 2 , metabolic circuits have the 6 advantage of faster response times since the enzymes have already been expressed in 7 the system. Yet, metabolic circuits can be connected with the other layers of cellular 8 information processing (like genetic or signal transduction layers) when needed, to build 9 more complex sense-and-respond behaviors. The actuator layer of our perceptrons is a 10 good example of this, where the calculated weighted sum is converted to fluorescence 11 output via the genetic layer. In addition, we took advantage of the properties of cell-free 12 systems, such as higher tunability and lack of toxicity 56,64 , to rapidly build and characterize 13 multiple combinations of transducer-actuator circuits. Cell-free systems can be lyophilized 14 on paper and stored at ambient temperature for <1 year for diagnostic applications 16 . This 15 expands the potential scope of cell-free metabolic perceptrons for use in multiplex 16 detection of metabolic profiles in medical or environmental samples 16,56 . 17 18 Here, we have built a single-layer perceptron, with positive weights, that can classify 19 different profiles of input metabolites by applying different weights to each transducer. In 20 the future, by adding competing or attenuating reactions that reduce the concentration of 21 the transduced metabolite in response to an input, it may be possible to expand the 22 training space by applying negative weights to certain inputs 65 . Furthermore, a single-23 layer perceptron can only classify data that is linearly separable 66 , which means that it 24 should be possible to draw a line between the two classes of data points in order for the 25 perceptron to classify them (Supplementary Figure S7). In contrast, multi-layer 26 perceptrons, can approximate any function 67 and can be used for more complex pattern   16 approved the final manuscript. 17 18 19 Competing financial interests 20 The authors declare no competing financial interest. allowing promiscuity, between compounds from the sink and compounds from the source. 34 To design the adder, the Retropath software was used with a set of detectable 35 compounds as the sink and the molecules we wish to use as circuit inputs as the source. 36 The results were potential pathways and the associated enzymes, which were then 37 analyzed for feasibility. The sequences of the enzymes were codon-optimized, 38 synthesized and implemented in E. coli or taken from a previous study.  Supplementary Table S5. Synthetic sequences were provided by 11 Twist Bioscience. Enzymes for cloning including Q5 DNA polymerase, BsaI, and T4 DNA 12 ligase were purchased from New England Biolabs. DNA plasmids for cell-free reactions 13 were prepared using the Macherey-Nagel maxiprep kit. 14

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Characterization of whole-cell circuits 17 For each circuit separate colonies of E. coli top10 strains harboring the circuit plasmids 18 were cultured overnight at 37℃ in LB with appropriate antibiotic. The next day each culture nitrogen before storing at -80°C. 6 7 Cell pellets were thawed on ice and resuspended in 1 mL S30A buffer per gram of cell 8 pellet. Cell suspensions were lysed via a single pass through a French press 9 homogenizer (Avestin; Emulsiflex-C3) at 15000-20000 psi and then centrifuged at 12000 10 x g at 4°C for 30 minutes to separate out cellular cytoplasm. After centrifugation, the 11 supernatant was collected and incubated at 37°C with 220 rpm shaking for 60 minutes. 12 The extract was recentrifuged at 12000 x g at 4°C for 30 minutes, and the supernatant 13 was transferred to 12-14 kDa MWCO dialysis tubing (Spectrum Labs; Spectra/Por4) and 14 dialyzed against 2 L of S30B buffer (14 mM Mg-glutamate, 60 mM K-glutamate, ~5 mM 15 Tris, pH 8.2) overnight at 4°C. The following day, the extract was re-centrifuged one final 16 time at 12000 x g at 4°C for 30 minutes, aliquoted, and flash frozen in liquid nitrogen 17 before storage at -80°C. 18 19 The buffer for cell-free reactions is composed such that final reaction concentrations were 20 as follows: 1.5 mM each amino acid except leucine, 1.25 mM leucine, 50 mM HEPES, For whole-cell data, we use the following normalization: Reference: cells harboring empty plasmids 6 7 For cell-free data, we consider Relative Fluorescence Unit (RFU): Reference: 20 ng/µL of a plasmid expressing the constitutive sfGFP under OR2-OR1-Pr 11 promoter 56 . 12 13 Simulation tools and parameter fitting: 14 All data analysis and simulations were run on R (version 3.2.3) 74 . Dose-response curves 15 were fitted using ordinary least squares errors and the R optim function (from Package 16 stats version 3.2.3, using the L-BFGS-B method implementing the Limited-memory 17 Broyden Fletcher Goldfarb Shanno algorithm, which is a quasi-Newton method). For the 18 random parameter sampling around the mean fit, values were sampled from within +-1.96 19 standard error of the mean of the parameter estimation. The seed was set so as to ensure 20 reproducibility. All simulations were run in the Rstudio development environment 75 . 21 All parameters are presented in Supplementary Tables S3 and S4.   22  23  24 Whole-cell model 25 The whole-cell model is composed of three parts: the actuator, the transducers (which all 26 obey the same law) and the resource competition. Where input is the input concentration in µM and range_enzyme is a dimensionless 2 number characterizing the capacity of the enzyme to transduce the signal. When 3 combining transducers with the actuator, transducer results are added before being fed 4 into the actuator equation, just as benzoate concentrations are added before being 5 converted to a fluorescent signal in the cell. 6 7 To account for resource competition, given our experimental results where there is little 8 competition with one enzyme and significant competition with two, we used an equation 9 including cooperativity of resource competition. This reduces the fold change of the 10 actuator as there are less resources available for producing transcription factors and 11 GFP. where value is the result of the actuator transfer function before accounting for resource 17 competition, range_resources, total_enzyme, cooperativity resources characterize the 18 Hill function that accounts for competition, coce, benz and hipo are the enzyme plasmid 19 concentrations. ratio_hip_benz accounts for the differences in burden from different 20 enzymes, its value around 0.8 is close to the ratio between enzyme lengths (1500 for 21 benzaldehyde transducing enzyme and 1200 for HipO).

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Cell-free model 25 The model is composed of two parts: the actuator and the transducers. Where range_enzyme is a dimensionless number characterizing the capacity of the 1 enzyme to transduce the signal. The activity of the enzyme is characterized by a Hill 2 function as increasing concentrations do not lead to a linear increase but enzymes 3 saturate (E is the enzyme quantity in nM, KE and hillE are its Hill constants), and similarly, 4 input is the input metabolite concentration in µM with KI and hill_input as its Hill constants. 5 6 When combining transducers, transducer results are added before being fed into the 7 actuator equation, just as benzoate concentrations are added before being converted to 8 the fluorescent signal in the cell. 9 10 Full model training process 11 Our training process is detailed in the Readme files supporting our modeling scripts 12 provided in GitHub and is summarized here. 13 14 As the first step, the actuator transfer function model (benzoate transformed into 15 fluorescence) is fitted 100 times on the actuator data, with all actuator parameters allowed 16 to vary. The mean, standard deviation, standard error of the mean and confidence interval 17 were saved at 95% of the estimation of those parameters. For transducer fitting (all 18 transducers in cell-free and all except cocaine in whole-cell), we constrained the actuator 19 characteristics in the following way: upper and lower allowed values are within the 95% 20 confidence interval (or plus or minus one standard deviation from the mean for fold 21 change and baseline in cell-free as it allowed a wider range, accounting for the decrease 22 in actuator signal in transducer experiments without affecting the shape of the sigmoid). 23 The initial values for the fitting process were sampled from a Gaussian distribution 24 centered on the mean parameter estimation and spread with a standard deviation equal 25 to the standard error of this parameter estimation. We then allowed fitting of all transducer 26 parameters freely and of the actuator parameters within their 95% confidence interval.

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Once this is done, all common parameters (actuator transfer function and resource 29 competition) were sampled using the same procedure and fitting on the cocaine 30 transducer was performed. To show that parameters are well constrained (proving they 31 minimally explain the data), Supplementary Figures S11 and S12 show results of 32 sampling parameters from the final parameters distribution (without fitting at that stage) 33 and how they compare to the data.

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Objective functions and model scoring: 36 In order to evaluate and compare our models, we used the following functions.  Supplementary Tables S1 and S2. 16 17 18 19 Perceptron weights calculation 20 In order to calculate the weights for the classifiers presented in Figure 6, we followed the 21 following procedure. First, we defined the expected results (expressed in "OFF"s and 22 "ON"s). We also defined a list of weights to test for each enzyme (here, between 0.1 nM 23 and 10 nM, as tested in our weighted transducers). Then, for each combination of enzyme 24 weights, we simulated the outcome of the classifiers for all possible input combinations. 25 We then tested various possible thresholds and kept the enzyme combinations for which 26 a threshold exists that allows for the expected behavior. As the last step, we manually 27 analyzed the classifier to keep the ones both a high difference between ON and OFF, 28 and a minimal enzyme weight to prevent resource competitions issues that could arise as 29 we are adding more genes than previous experiments. In order to perform clusterings of that curve will be classified to "ON" and all combinations below will be classified to 13 "OFF". 14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 Code and data availability: 1 All scripts and data for generating results presented in this paper are available at 2 https://github.com/brsynth. 3 4 5 Biological and chemical identifiers 6 In order to allow easier parsing of our article by bioinformatics tools, we provide here the 7 identifiers of our biological sequences and chemical compounds.     To study these effects on the single-enzyme metabolic circuit, the following experiment was performed: cocaine transducer (with the highest signal dissipation among the three tested in Figure 1) was supplied with benzoate input, to test the effect of enzymes on only cellular resource allocation but not conversion of inputs to benzoate. The cocaine transducer with benzoate input shows a behavior similar or close to the benzoate actuator. All data points and the error bars are the mean and standard deviation of normalized values from three measurements.
Supplementary Figure S5. Examining the effect of enzyme efficiency on the whole-cell metabolic adder. To study these effects on the two-enzyme metabolic circuit (adder) the following experiment was performed: hippurate-benzaldehyde adder was supplied with benzoate input, to test the effect of enzymes on only cellular resource allocation but not conversion of inputs to benzoate. The adder with benzoate input shows a behavior similar to the adder inputted with hippurate and benzaldehyde. All data points and the error bars are the mean and standard deviation of normalized values from three measurements.   ATGGCGACAATCCGTCCCGATGACAACGCAATTGACACGGCGGCCCGCCATTATGGCATCACCCTTGACCAAAGC  GCGCGTCTTGAGTGGCCCGCACTTATTGACGGAGCCTTAGGGAGCTACGACGTTGTTGACCAGCTGTACGCTGAT  GAAGCCACGCCGCCAACAACGTCGCGTGAACATACTGTCCCTACTGCTAGCGAAAATCCCCTTTCCGCCTGGTAC  GTTACGACCTCTATCCCCCCCACAAGTGACGGAGTGTTGACTGGACGCCGCGTCGCCATCAAAGATAACGTCACA  GTAGCTGGCGTGCCAATGATGAACGGCTCGCGTACCGTTGAGGGATTTACTCCGTCACGCGACGCCACTGTAGTC  ACTCGCCTGCTGGCTGCTGGTGCAACAGTAGCTGGAAAGGCTGTCTGTGAGGACTTATGCTTTTCTGGCTCTAGTT  TTACCCCAGCCTCGGGACCTGTTCGCAATCCCTGGGATCCGCAGCGCGAGGCAGGAGGAAGTTCCGGCGGAAGT  GCAGCATTAGTAGCAAATGGCGATGTCGACTTCGCAATTGGAGGTGACCAGGGTGGCTCCATCCGTATCCCGGCT  GCCTTTTGCGGCGTAGTCGGCCACAAGCCTACATTTGGACTTGTACCATATACGGGAGCCTTCCCAATCGAACGCA  CGATTGACCACCTTGGACCGATTACACGCACTGTCCATGACGCTGCACTTATGCTGTCAGTTATCGCAGGCCGCGA  TGGAAACGACCCTCGTCAAGCGGATAGTGTGGAAGCGGGCGACTACCTTAGTACTTTAGATAGCGACGTCGACGG  GTTACGTATCGGAATCGTACGTGAGGGTTTTGGCCACGCAGTCAGCCAACCGGAGGTAGACGACGCGGTTCGTGC  AGCGGCTCACAGCTTAGCAGAAATCGGATGCACAGTGGAAGAAGTGAACATTCCATGGCACCTGCATGCGTTTCAT  ATCTGGAATGTGATTGCCACCGATGGCGGTGCTTACCAAATGTTAGACGGGAACGGTTATGGAATGAATGCAGAAG  GTTTATACGACCCTGAACTTATGGCTCACTTCGCATCTCGTCGTCTTCAACATGCAGATGCCTTGTCTGAAACCGTT  AAGCTTGTAGCTCTGACCGGCCACCACGGGATTACGACATTAGGGGGCGCTTCGTACGGGAAAGCCCGCAACTTG  GTTCCGTTAGCGCGTGCAGCTTACGACACCGCGCTTCGTCAGTTCGACGTGCTTGTAATGCCAACTTTACCTTATG  TCGCCTCAGAATTACCAGCCAATGATGTCGACCGTGCAACTTTTATTACTAAGGCGCTTGGTATGATCGCTAACACA  GCACCTTTCGATGTAACAGGGCACCCGAGCTTATCAGTTCCAGCTGGCCTTGTAAATGGGTTACCTGTCGGTATGA  TGATTACTGGAAAGACTTTTGATGATGCGACAGTGCTTCGTGTAGGGCGTGCCTTTGAGAAATTACGTGGGGCCTT  TCCGACCCCTGCAGATCACATTTCGGATAGTGCCCCGCAATTAAGCCCTGCGTAA