Reconfigurable Analog Signal Processing by Living Cells - ACS

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Reconfigurable Analog Signal Processing by Living Cells Daniel D. Lewis, Michael Chavez, Kwan Lun Chiu, and Cheemeng Tan ACS Synth. Biol., Just Accepted Manuscript • DOI: 10.1021/acssynbio.7b00255 • Publication Date (Web): 08 Nov 2017 Downloaded from http://pubs.acs.org on November 12, 2017

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ACS Synthetic Biology

Reconfigurable Analog Signal Processing by Living Cells Authors: Daniel D. Lewis1,2, Michael Chavez1, Kwan Lun Chiu1, Cheemeng Tan1* Affiliations: 1

Department of Biomedical Engineering, University of California Davis, 1 Shields Ave, Davis,

CA 95616 2

Integrative Genetics and Genomics, University of California Davis, 1 Shields Ave, Davis, CA

95616 *Correspondence to: Cheemeng Tan at [email protected].

Abstract Living cells are known for their capacity for versatile signal processing, particularly the ability to respond differently to the same stimuli using biochemical networks that integrate environmental signals and reconfigure their dynamic responses. However, the complexity of natural biological networks confounds the discovery of fundamental mechanisms behind versatile signaling. Here, we study one specific aspect of reconfigurable signal processing in which a minimal biological network integrates two signals, using one to reconfigure the network’s transfer function with respect to the other, producing an emergent switch between induction and repression. In contrast to known mechanisms, the new mechanism reconfigures transfer functions through genetic networks without extensive protein-protein interactions. These results provide a novel explanation for the versatility of genetic programs, and suggest a new mechanism of signal integration that may govern flexibility and plasticity of gene expression. Keywords: reconfiguration, network, synthetic biology, plasticity, analog signal processing

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Cellular networks are generally studied following the classical paradigm of signal processing frameworks by assuming that individual components interact with one another through fixed transfer functions 1 that convert input signals to output signals. These static transfer functions can be tuned slightly by biological signals 2, 3 or altered by mutation 4, 5. In contrast to this paradigm, transfer functions are known to be reconfigurably inverted between induction and repression 6, 7 in bacterial biofilm formation 8, Klf4’s modulation of cell proliferation 9, and Wnt signaling during Caenorhabditis elegans development 10. The common explanation for the reconfigurable inversion of a network’s transfer function is that an environmental signal modulates receptor signaling and induces allosteric changes in a regulatory factor, turning an activator complex into a repressor or vice versa 10, 11. A recent top-down study further suggests that the underlying topology of protein networks can serve to integrate environmental signals and invert transcriptional responses in vivo 12. Continued investigation of the signaling mechanism has been inhibited by the complexity of natural biological networks 12. In contrast, our work exploits the fundamental concept that small transcriptional networks process input signals and control dynamic cellular processes 3, 13-18. We challenge the established paradigm for reconfigurable transfer-function inversion by showing how a small genetic network can integrate environmental signals to achieve the same reconfigurability as previously observed in complex protein-protein networks. Here, we show that a minimal genetic network containing an antagonistic regulatory interaction can modulate a downstream transcriptional cascade between induction and repression (Fig. 1A). In particular, we study a feedforward circuit that is usually thought to generate one transfer function as long as the regulatory relationships between circuit components remain constant 16, 17, 19. Instead, we find that the small network can integrate two signals by using one


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signal to invert the network’s transfer function with respect to the other signal. Next, we reveal a trade-off of this network by examining variability in expression levels of the product, and generalize this network through computational approaches. Our work has two primary innovations. First, we reveal a novel network topology that gives rise to inversion of a network’s transfer function. Second, we demonstrate that synthetic biology approaches can be used to study reconfigurability of biological systems from the bottom up. By creating a quantitative framework to explain transfer-function inversion, we establish a mechanism for how simple biological networks achieve versatile analog computation and show how an antagonistic regulatory interaction can cause reconfigurability in a network with fixed regulatory links. In addition, the drastic reconfiguration of transfer functions in these large networks has undermined a priori prediction of global gene network dynamics under different environmental conditions 20. Our results suggest a critical need to understand the effect of dynamic reconfiguration on the transfer functions of cellular networks.

Results Reconfigurable inversion of gene expression in a minimal synthetic network To start, we tested the activity of the PBAD promoter, which is antagonistically regulated by arabinose and IPTG (Isopropyl β-D-1-thiogalactopyranoside) 3, 21 (Fig. 1B, left panel). IPTGbased repression of PBAD is thought to be caused by competitive inhibition 3, 21, which will be further addressed using mathematical models later in this study. We observe that the PBAD promoter generates a monotonic repression transfer function with respect to IPTG, which can be tuned by the presence of arabinose (Fig. 1B, right panel). These results suggest that an



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antagonistic regulatory interaction alone is not sufficient to generate reconfigurable inversion of gene expression. Next, we tested a gene network consisting of an antagonistic interaction embedded in a feedforward loop. The circuit consists of arabinose and IPTG controlling the activity of AraC, AraC activating the production T7 RNA polymerase (T7 RNAP) from the PBAD promoter, LacI inhibiting the transcription of GFP by T7 RNAP, and IPTG inhibiting the activity of LacI (Fig. 1B-E). We used the BL21AI Escherichia coli strain with an AraC-PBAD-T7RNAP construct integrated into its genome as the antagonistically regulated module, and the pET15b plasmid with a PT7/LacO1 promoter to control production of the GFP reporter (Methods). All circuit characterization was done by inducing exponential-phase cultures in the plate reader (Methods). We determined the significance of variation between points in each transfer function using a Bonferroni method, and used the presence of significant increases and decreases in expression to classify each transfer function (Methods, Fig. S1). The Bonferroni method allows for the comparison between points in each transfer function, while correcting the significance threshold for the number of comparisons made. Transfer functions were classified as induction when they experienced only a significant increase, repression when they experienced only a significant decrease, and hybrid when they experienced both increased and decreased expression. We found that this synthetic network in E. coli demonstrated transfer-function reconfigurability, switching between induction and hybrid transfer functions (Fig. 1D & E). These results contradict the common intuition concerning transfer functions of network motifs: parameters of the transfer functions are quantitatively tunable, but the shape of the transfer functions remain qualitatively static 16. In addition, the generation of reconfigurable transfer functions is often


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thought to be a dynamic of large networks involving receptors, protein modulators, and complex eukaryotic promoters 22, 23.

Mathematical description of the gene network To gain insight into the emergent dynamics of the synthetic gene network used in this study, we formulated a system of ordinary differential equations detailing the production of X (T7 RNAP) controlled by the levels of I1 (arabinose) and I2 (IPTG) along with the production of Y (GFP) controlled by levels of X and I2 (Fig. 2, SI Section 1a-c, Eq. 1 & 2). Although the mechanism of IPTG-mediated repression of PBAD is not known, we modeled production of X based on competitive regulation by I1 and I2 with equivalent dissociation constants. We also assumed that production of X followed a Hill coefficient of n = 2 based on previous reports of cooperative induction of the PBAD promoter 24. Production of Y by X and I2 was modeled by assuming that X acts independently of I2, and I2 can only increase the activity of X, but not trigger expression on its own. Since the PT7/LacO1 promoter exhibits substantial leaky expression in the presence of T7 RNAP, and IPTG reduces LacI affinity for LacO1 to de-repress T7 RNAP, we believe that our assumptions are mechanistically sound.

= −

= 1 + −

(Eq. 1)

(Eq. 2)

I1 is a signal that activates expression of X, I2 is a signal that represses expression of X, X is an activator of Y expression, kd (s-1)is the coupled dilution and degradation rate constant, L (M2 s-1) is the leaky expression rate constant, V1 (M s-1) is the synthesis rate constant for production of X (Fig. 2A, link I1X), K1 (M)is the dissociation constants of I1 and I2 for production of X (Fig. 2A, links I1X and I2X), V2 (M s-1)is the synthesis rate constant for production of Y, (Fig. 2A,



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link XY), K2 (M) is the dissociation constant of X for production of Y (Fig. 2A, link XY), V3 (dimensionless) is the fractional synthesis rate constant of I2 for production of Y (Fig. 2A, link I2Y), K3 (M)is the dissociation constant of I2 for production of Y (Fig. 2A, link I2Y), and Y is the output of the system. Equation 1 and 2 are simplified to the expression represented in Eq. 3 (Derived in SI Section 1a, represents Eq. S6). =

( ) " !

1 +

(Eq. 3)

We classified the transfer functions of our computational model by searching for the maximum of the transfer function with respect to I2. Transfer functions that had their maximum level at the lowest value of I2 were classified as repression, functions that reached their maximum level at the highest value of I2 were classified as induction, and functions with a maximum level somewhere along the I2 spectrum were classified as hybrid (Methods). Through further analysis of the equations (SI Section 1b & c), we found that when I1 is sufficiently greater than I2, the model produced a monotonic induction transfer function with respect to I2 (Fig. 2B, SI Section 1b & c). On the other hand, when I2 is much larger than I1, the system responded with monotonic repression under some parameter regimes (Fig. 2B). Thus, the mathematical model shows that transfer-function inversion can emerge from the synthetic gene network used in this study.

Modeling-guided perturbation of the gene network In order to achieve full inversion between induction and repression from the synthetic network used in this study, we performed a magnitude analysis using the mathematical solution of our model (Fig. 3). The magnitude analysis gave insights into the dynamics of the synthetic network by generating predictions on how the relative likelihood of a certain transfer function


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changes with the value of specific parameters given a background of randomly-generated parameters (Methods). A group of 1000 randomized parameter sets was generated, the transfer function of each parameter set was classified based on the position of its maximum output, and the number of parameter sets leading to a given behavior was divided by the maximum value of that set (essentially assigning it a likelihood that a given parameter value would lead to a specific transfer function given randomized values for all other parameters). The value of these relative likelihoods for adopting a given transfer function (induction, hybrid, or repression) were plotted on the z-axis of a color plot where the x-axis was the concentration of arabinose and the y-axis was the value of the parameter of interest (Fig. 3). The magnitude analysis revealed a tradeoff between the propensity for induction and repression. We found that when the contribution of X to levels of Y was more independent of the induction effect of I2 at Y, our synthetic system was more likely to produce a repression transfer function. More specifically, the magnitude analysis predicted transfer-function inversion would be unaffected by decreasing the catalytic activity of T7 RNAP (V2- Fig. 3A), tipped towards repression by decreasing the rate of production from the PT7/LacO1 promoter (V3- Fig. 3B), predisposed for induction by increasing the dissociation constant for gene expression from the PBAD promoter (K1- Fig. 3C), and skewed in favor of induction behavior by increasing the transcription activity of PBAD (V1- Fig. 3D). These predictions served as hypotheses for validating the predictive power of the model in subsequent experiments.

Experimental validation of the model predictions Before testing the predictions generated by our magnitude analysis, we constructed a series of biochemical perturbations (Fig. 4A) and characterized their kinetic parameters (SI



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Section 2a-Table S1, Fig. S2A-C) through additional Circuits VI-IX (Methods- Table 1). These additional circuits decoupled the regulatory elements of the original gene network (Fig. 1D) to facilitate independent measurement of their kinetic parameters. Circuits VI and VII were used to measure mCherry expression from the PBAD promoter on a plasmid backbone (Fig. S2C, top panel). Circuits VIII and IX were used to measure GFP production from the PT7/LacO1 promoter (Fig. S2B, top panel), while T7 production is controlled via tetracycline induction. We found that when we mutated an A to C in the PT7 promoter, we decreased the catalytic efficiency of expression by T7 RNAP (V2) (Fig. 4B, Fig S2A). Similarly, we found that by mutating a T to a G in the LacO1 promoter, we decreased the catalytic efficiency of production by IPTG (V3) (Fig. 4C, Fig S2B). Finally, we measured expression from the PBAD promoter with and without glucose to show that supplementation of glucose increased the dissociation constant for arabinose (K1) (Fig. 4D, Fig S2C). We validated the predictions generated by the magnitude analysis by comparing the range of arabinose concentrations that led to each type of transfer function for each biochemically perturbed circuit to the predicted changes in the relative likelihood of each transfer function. This comparison is necessary because each biochemical perturbation inherently has a single set of parameters, while the magnitude analysis used a series of randomized parameters. Therefore, we expected transfer functions that showed increased probability in the magnitude analysis (Fig. 3) to demonstrate an increase in the range of arabinose concentrations that led to the synthetic network adopting that associated transfer function. When we characterized each of our biochemical circuits (Fig. 4, SI Section 2a- Table S1, Fig. S2D-H), we observed that the balance between induction and hybrid transfer functions was maintained when V2 was decreased (Circuit II, Fig. 4E), the repression function emerged when V3 was decreased (Circuit III, Fig. 4E & F),


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and the induction function was favored when K1 was increased (Circuit IV, Fig. 4E). These results confirm the predictions of our magnitude analysis. The only perturbation that did not match our predictions was the network with an increased activity of PBAD (V1) (Circuit V, Fig. 4E). The induction transfer function was likely limited by saturation of the PT7/LacO1 promoter controlling GFP production (Fig. S2H, SI Section 2b). To ensure that the characterization of each transfer function was not affected by pulsatile expression, we investigated the expression data from each biochemical perturbation of the network over time. We found that the induction, hybrid, and repression transfer functions all remained constant over the course of 6 hours (Fig. S3, SI Section 2c). The resulting transfer functions of our biochemically perturbed networks suggest that the model predictions are qualitatively consistent with the experimental perturbations, and show that there is a trade-off between the dynamic range of induction and repression. The perturbation of V3 (Circuit III, Fig. 4E & F) shows how transfer-function inversion is determined by the balance between the induction and repression activity that IPTG exerts on GFP through its opposing regulation of the activity and levels of T7 RNAP (I2, Fig. 3). Further work could use the tools we have created here to optimize the fold change for both the induction and repression transfer functions (SI Section 2d, e). These results corroborate the validity of the model and suggest that a simple genetic network can generate reconfigurable transfer-function inversion.

Dynamical and noise characteristics of synthetic transfer-function inversion Since we were able to demonstrate induction and repression in vivo with cells induced from a naïve state, we wanted to test if sequential inversion between induction and repression was possible, which is the hallmark of reconfigurable transfer-function inversion. To achieve



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this, we activated the induction behavior with a high concentration of arabinose and a gradient of IPTG, then moved the cells to an environment with a low concentration of arabinose to see if those cells would adopt a repression transfer function (Methods). We also tried the reverse experiment, moving from repression to induction. To this end, we were able to dynamically invert the network’s transfer function from induction to repression and vice-versa (Fig. 5A&B). These results suggest that the transfer functions of the gene network can be dynamically inverted, corroborate the stability of the genetic circuits, and preclude any emergent behavior due to mutation of the circuits. In addition, we investigated whether the reconfigurability of the synthetic network used in this study comes with a trade-off in the variability in the concentration of output signals. To do this, we took cells induced for four hours and fixed them before reading their fluorescence intensity on a flow cytometer, using the variability of fluorescence intensity across the population as a proxy for the gene expression noise experienced by individual cells 25-27. We examined the fluorescent intensity distributions of our cells and found that at low mean intensities, the distribution was mono-modal with a variable tail on the end of the distribution (Fig. S4A). We used the standard deviation divided by the mean of each distribution to quantify the differences in expression noise between the gene circuits. Based on this analysis, the networks that have the widest range of hybrid behavior (Circuit I & II) demonstrate the greatest noise when compared to the network without any hybrid behavior (Circuit IV) (Fig. 5C, Fig. S4B-F). These results demonstrate one drawback of achieving reconfigurability by integrating information through the synthetic network used in this study.


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Generalizing reconfigurability as a function of network topology During our model formulation, we made several assumptions to improve tractability of our proposed mechanism for transfer-function inversion. We tested alternative models to demonstrate that networks containing an antagonistic interaction modulating an incoherent feedforward loop were capable of transfer-function inversion regardless of their exact mechanistic interactions. First, we examined the possibility that IPTG and arabinose do not exhibit equal affinities with the following mathematical formulation: #

#

=

= '1 +

& # $ # & %

− & # ( #

#

(

(Eq. 4)

) −

(Eq. 5)

I1 is a signal that activates expression of X, I2 is a signal that represses expression of X, X is an activator of Y expression, kd is the dilution and degradation rate constant (s-1), L is the leaky expression rate constant (M2 s-1), V1 is the synthesis rate constant for production of X (M s-1), K1 is the dissociation constant of I1 for production of X (M), n1 is the cooperativity of arabinose induction, K2 is the dissociation constant of I2 for inhibition of X production (M), n2 is the cooperativity of IPTG inhibition of the PBAD promoter, V3 is the synthesis rate constant for production of Y (M s-1), K3 is the dissociation constant of X for production of Y (M), V4 is the fractional synthesis rate constant of I2 for production of Y, K4 is the dissociation constant of I2 for production of Y (M), n3 is the cooperativity of IPTG activating the PT7/LacO1 promoter, and Y is the output of the system. Using this modified model, we explored how varying the dissociation constants of arabinose and IPTG (K1 and K2) affected transfer-function inversion (Fig. S5). We found that the repression behavior was abolished when the affinity of arabinose for induction was one log-fold



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higher than the affinity of IPTG for repression, and that both the repression and hybrid behavior were not present when the dissociation constant of arabinose for induction was three log-fold higher than IPTG inhibition. Similarly, induction behavior disappeared when the dissociation constant of IPTG for repression was four log-fold higher than the dissociation constant of arabinose for induction, and the induction and hybrid behaviors were absent when IPTG inhibition was six log-fold greater than arabinose induction. The results suggest that the dissociation constant of IPTG repression must be within 4 log-fold of the dissociation constant of arabinose induction in order to observe reconfiguration of transfer functions between induction, repression, and hybrid behaviors. In addition, we were able to quantitatively match the dynamic behavior of Circuit III to this model (Fig. S6). Second, we implemented a model that changed the mechanism of IPTG repression.

=

= 1 + ( −

(*

$

) −

(

(Eq. 6) (Eq. 7)

I1 is a signal that activates expression of X, I2 is a signal that represses expression of X, X is an activator of Y expression, kd is the dilution and degradation rate constant (s-1), L is the leaky expression rate constant (M2 s-1), V1 is the synthesis rate constant for production of X (M s-1), K1 is the dissociation constant of I1 for production of X (M), K2 is the dissociation constant of I2 for inhibition of X production (M), V3 is the synthesis rate constant for production of Y (M s-1), K3 is the dissociation constant of X for production of Y (M), V4 is the fractional synthesis rate constant of I2 for production of Y, K4 is the dissociation constant of I2 for production of Y (M), and Y is the output of the system. This representation of IPTG-based repression of the PBAD promoter is similar to previous work that models oscillation of a genetic circuit composed of inducer-modulated LacI and AraC


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3

. We found that this alternative formulation was capable of producing induction, repression, and

hybrid dynamics similarly to our original model with some parametric alteration (Fig. S7). This observation is likely due to the fact that the alternative model formulation introduces very small terms into the denominator of the equation controlling the production of X (i.e. +$, +, ). The magnitude of these terms appears to be negligible when considering the dynamic reconfigurability of the whole genetic circuit. After analyzing the effect of small changes to the mechanism of IPTG repression on transfer-function inversion, we employed computational models to investigate whether changes to the mechanistic interactions of all network links altered or prevented the emergence of transfer-function inversion. To achieve this, we surveyed a computational library of 3 node networks with physiologically relevant parameters to look for systems capable of transferfunction inversion. The 3-node networks have different model structures than the model of our minimal gene network (Eq. 1-3). Since our original model (Eg. 1-3) already demonstrated that a competitive antagonistic interaction can give rise to reconfigurable transfer functions, we tested whether multiplicative interactions (representative of regulatory interactions such as noncompetitive inhibition) between the regulatory links can also generate reconfigurable transfer functions. Specifically, each network configuration was represented by three nodes, A, B, and C, which represent transcription factors that regulate each other according to an assigned network topology following Michaelis-Menten kinetics 19. The ODEs of the model are shown in Equation 8-10. -. -/

= k 1 + k 23 . I, ∏3,@,AB (*

8

9:

);9: ( 8

$

$

C

%9:

)D9: − k . A


(Eq. 8)


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-F

= k 1 + k 2@ . I$ ∏3,@,AB(

-I

= k 1 + k 2A . I$ ∏3,@,AB(*

-/

-/

8

*9G 8 8

9J 8

);9G (

);9J (

$

$ $

$

C

%9G

C %9J

)D9G − k . B

)D9J − k . C

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(Eq. 9)

(Eq. 10)

A, B and C represent concentrations of transcription factors, I1 and I2 represent the input signals, S represents the concentration of an activating or inhibiting factor (A, B, or C), k0 represents leaky gene expression rate constants (10-3 nM/s), kd represents degradation rate constants (10-2 1/s), kpS represents synthesis rate constants (nM/s), Kij represents binding constants corresponding to regulator i to effector j (nM). mij and nij are set to either zero or one depending on the circuit topology. Based on the model assumptions, the impact of each regulatory link on the rate of change is multiplicative. Network topology was assigned from a non-repeating library of 1670 three-node-network configurations. A node could not simultaneously activate and inhibit another node (mij and nij cannot be both equal to one). A network could only have a maximum of three regulatory links because that is the simplest unit of transcriptional networks capable of generating all possible nonlinear dynamics. For all network topologies, I2 always acted on node A, and I1 acted on either node B or C (Fig. 6A, left panel). The transfer function of the network was measured by changes in the concentration of C (Fig. 6A, right panel). Next, we generated 500 randomized parameter sets kpS and Kij for each network topology, obtained the steady-state concentrations of C for each network given a range of concentrations for I1 and I2. We note that the parameter values lie in the physiological range commonly associated with bacteria. The catalytic constants range from 0.1100 nM/min, which is consistent with the typical RNA (85 nucleotide/s 28) and protein (22 amino acids/s

29

) synthesis rate constants. The equilibrium dissociation constants range from 0.1-100

nM, which are consistent with literature data. For instance, the equilibrium dissociation constant


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is 550 nM between RNAP and lac operator lambda OR1

31

30

, and 0.79 nM between wild-type repressor and

. Since we were specifically interested in whether a network can achieve

induction and repression over the same concentration range of biological input, we looked for networks that were capable of modulating their transfer function with respect to I2 between positive and negative regulation by varying the concentration of I1. We recorded the number of parameter sets per network that gave rise to reconfigurable transfer functions. This metric was used to determine which network topologies were the most capable of modulating their transfer function between induction and repression (Fig. 6B, left panel). We found the incoherent feedforward loops are the most likely to generate emergent transfer-function inversion even though the antagonistic elements of the networks interacted through non-competitive inhibition (in contrast to competitive inhibition in the original model of the synthetic gene network). Specifically, one incoherent feedforward loop shows 98 instances (out of 500) of reconfigurability; another incoherent feedforward loop shows 22 instances; and a negative feedback loop shows 6 instances (Fig. 6B). Taken together, these experiments suggest that the underlying network topology is a sufficient condition for emergent transfer-function inversion.

Transfer-function inversion topologies in natural networks To demonstrate that the topology of the synthetic network (Fig. 2A) occurs in natural genetic networks, we formulated an algorithm to look for specific arrangements of positive and negative interactions in the RegulonDB V8.0 E. coli transcriptional interaction database. We compared the incidence of the topology of the synthetic genetic network in the natural network to the incidence of that same topology inside 1000 randomly perturbed biochemical networks. If



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the topology of our network has functional significance to its host, we assumed that the topology of the synthetic network will be present more often in the natural network than in randomized networks. We found that the topology of the synthetic system capable of reconfigurable transferfunction inversion was overrepresented in the natural transcriptional network, with a p-value of .003 (Fig. 6C). This result suggests that E. coli may be capable of reconfigurable transferfunction inversion through the transcriptional networks identified by our algorithm.

Discussion We present a mechanism for the reconfigurable inversion of a network’s transfer function in a synthetic biological system. Existing work studies transfer-function inversion in the context of complex protein-protein interactions typical of eukaryotic signal transduction and gene regulatory systems 10, 11. In contrast, we develop a simple mathematical model to explain transfer-function inversion in a genetic network (Fig. 2), validate the model with biochemical perturbations (Fig. 3 & 4), and characterize the expression variability of the network (Fig. 5). We find that our system requires an antagonistic regulatory interaction to modulate a regulator between induction and repression. This work suggests that transfer-function inversion can happen in a considerably simpler network than previously thought. Computational analysis of the synthetic network used in this study shows that emergent transfer-function inversion can be consistently achieved even when the exact mechanistic relationships between the network components are varied. The mathematical model of the synthetic circuit uses competitive inhibition to represent the antagonistic regulatory event and assigns X as the dominant regulator over I2 during feedforward induction of Y expression. However, subsequent testing of transfer-function inversion in a library of three node networks


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shows that circuits with non-competitive antagonistic interactions can also achieve the same reconfigurable network dynamics. Based on these computation analyses, the specific nature of the interactions between elements of the synthetic network appear to be less important for transfer-function inversion than the topological arrangement of the network. We note that the emergence of transfer-function inversion still depends on network kinetics, similar to any emergent nonlinear dynamics of cells. Our analysis of the biological incidence of the synthetic network also suggests the potential inversion of transfer-function in prokaryotic transcriptional networks (Fig. 6C), which has been generally neglected in the literature. The topology of the synthetic network used in this study may also provide a mechanism for how other prokaryotes with unexplained instances of transfer-function inversion perform this regulation in vivo 8. To examine the biological feasibility of our results, we further study known mechanistic information for one of the 44 networks (Fig. 6C) using EcoCyc 32. We find that the effectors CRA and CRP are controlled by fructose 1,6-bisphosphate and cyclic AMP respectively 32. They also act through adjacent regulatory sites to control MarA production 33, 34, which suggests that these factors competitively displace each other. Both MarA and CRA are thought to feed forward to induce production of PoxB 32, 35, which is a pyruvate oxidase that reduces oxidative burden during the transition between exponential and stationary phase in aerobic E. coli cultures 36, 37. Since analog transcriptional regulation is thought to be important for processes that require highly energy-efficient control 38, it is intriguing to see a metabolic enzyme in a network that may exhibit transfer-function inversion. While our results suggest that transfer-function inversion could be quite common in E. coli transcriptional networks, further work has to be conducted to characterize this phenomenon in a natural context. Besides identifying a network with topology that mediates transfer-function



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inversion, future experiments may further investigate transfer-function inversion based on the insights garnered from the synthetic gene network. For instance, the mathematical equation (Eq. 1-3) may be used as the initial model to study plausible emergence of transfer-function inversion in a natural network. Our results also indicate several critical parameters (Fig. 3 & 4) and conditions (SI, Section 1) that modulate the emergence of transfer-function inversion. These insights on mechanisms and kinetics of biological reconfigurability are obtained through a synthetic and bottom-up approach, in contrast to the difficulty of studying reconfigurability in complex natural networks. Since we show that transfer-function inversion can emerge from a small set of regulatory links, we also challenge the conception of network motifs as static information processing units. Previous work on network motifs has associated a single transfer function with certain topological arrangements of regulatory factors, but we discover how a ubiquitous antagonistic interaction can drastically alter the transfer function of a network. Previous work has shown that antagonistic interactions can mediate erythroid differentiation 39, and cause different dynamic behaviors through evolutionary changes in a prokaryotic gene circuit 4. By demonstrating how small networks can generate emergent reconfigurability, we also provide insight into how large biochemical networks might engage in high-level regulation of phenotypic reconfigurability by integrating the static information processing properties of small subnetworks.

Methods Contact for reagent and resource sharing Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Cheemeng Tan ([email protected]).


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Experimental model and subject details Characterization of biochemical circuits in vivo All transfer functions (dose-response curves) were generated using a plate reader (Tecan M1000pro). Cells were grown overnight at 37ºC with 200 rpm shaking in LB with antibiotics from a single colony, diluted to a constant OD600 value, then further diluted 1:100 into LB media with antibiotics. These cells were incubated for 1.5 hours at 37ºC with 200 rpm shaking until they reached the beginning of exponential growth, at which point they were distributed into a 96-well plate with indicated concentrations of inducers, covered with a lid, and put into the plate reader at 37ºC. OD600 and fluorescence of each well was monitored in the plate reader, with 10 seconds of orbital shaking (amplitude 3) every minute, and measurements taken every 10 minutes. All transfer functions in this paper were derived from cells grown in plate culture for 240 min. Circuits with supplemental glucose had glucose added to the media before growth to exponential phase. All transfer functions were replicated 4 times: two sets of two samples were collected on distinct days. No blinding or randomization was performed. A sample size of 4 was selected according to standard synthetic biology practices of sample replication inside a plate reader for significance testing, but these tests have no established effect size 40, 41.

Dynamic transfer-function inversion BL21AI cells with Circuit III were cultured overnight at 37ºC with 200 rpm shaking in LB with antibiotics from a single colony, diluted to a constant OD600, then further diluted 1:100 into LB media with antibiotics. These cells were incubated for 1.5 hours at 37ºC with 200 rpm shaking



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until they reached the beginning of exponential growth, at which point they were induced with a constant concentration of arabinose and a series of IPTG concentrations. Cells were incubated in tube cultures at 37ºC with 200 rpm shaking for 2 hours. A 200 µL sample was taken from each tube after 2 hours and analyzed for OD600 and fluorescence intensity using the Tecan M1000pro plate reader. After 2 hours of induction, each tube was diluted 1:10,000 into fresh LB with antibiotics and grown for 16 hours at 37ºC with 200 rpm shaking. After growth, each tube was diluted to a constant OD600, then further diluted 1:100 into LB media with antibiotics. Each tube was grown for 1.5 hours until they reached the beginning of exponential growth, at which point they were induced with a different concentration of arabinose and the same concentration of IPTG. Cells were incubated in tube cultures at 37ºC with 200 rpm shaking for 2 hours. A 200 µL sample was taken from each tube after 2 hours and analyzed for OD600 and fluorescence intensity using the Tecan M1000pro plate reader.

Characterizing fold-change of induction and repression BL21AI cells with Circuit III were cultured overnight at 37ºC with 200 rpm shaking in LB with antibiotics from a single colony, diluted to a constant OD600, then further diluted 1:100 into LB media with antibiotics. These cells were incubated for 1.5 hours at 37ºC with 200 rpm shaking until they reached the beginning of exponential growth, at which point they were induced with a constant concentration of arabinose and a series of IPTG concentrations. Cells were incubated in tube cultures at 37ºC with 200 rpm shaking for 240 minutes. After 240 min, cells were spun down at 17,000xg for 1 min, resuspended in 1 mL of sonication buffer (10 mM Tris-acetate pH 7.6, 14 mM Magnesium acetate, 60 mM Potassium gluconate, 1 mM DTT). Resuspended cells were put on ice, then lysed using the sonicator (QSONICA Q125) at 67% amplitude for 8


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rounds with 15 seconds of sonication followed by 45 seconds of rest. Lysed cells were spun down for 50 minutes @ 20,000xg at 4ºC. The lysate was analyzed for GFP content using the Tecan M1000pro nanoquantification plate.

Expression noise measurement A BD FACScan flow cytometer was used to measure fluorescence intensities of E. coli expressing GFP. Cells were grown overnight at 37ºC with shaking in LB with antibiotics from a single colony, diluted to a constant OD600, then further diluted 1:100 into LB media with antibiotics. Circuits with supplemental glucose had glucose added to the media before growth to exponential phase. These cells were incubated for 1.5 hours at 37ºC with 200 rpm shaking until they reached the beginning of exponential growth, at which point they were distributed into a 96well plate with indicated concentrations of inducers, covered with a lid, and put into the plate reader at 37ºC. OD600 and fluorescence of each well was monitored in the plate reader, with 10 seconds of orbital shaking (amplitude 3) every minute, and measurements taken every 10 minutes. After 240 minutes of growth, the cells were fixed by diluting them 1:100 in 4% paraformaldehyde in 1x PBS. The cells were then analyzed using a FACScan. The FACScan was configured with a 35mW 488nm blue laser and a 30mW 635nm red laser. Signals from blue laser excitation were collected using three filters – a 530/30, a 585/42 and a 650LP (long pass). Signals from the red laser were detected using two filters, a 666/27 and a 740LP.

Method details Plasmid construction and expression control Expression cassettes were generated by directional and Gibson cloning.



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Component 1- pET15b(PT7/LacO1 -GFP)- was cloned by digesting the pET15b vector with NcoI and XhoI, amplifying a DNA fragment containing GFP and 30 base-pair overhangs with the vector, then assembling the backbone and insert together with the Gibson Assembly Master Mix from NEB, and transforming the assembled vector into Top10 cells.

Component II- pET15b(PT7/LacO1 -V14-GFP)- was cloned by digesting the pET15b(PT7/LacO1 GFP) vector with XbaI and BglII, annealing two short single stranded DNA oligomers together to form an insert with a mutated PT7 site, then phosphorylating the insert, ligating the insert with the vector, and transforming the assembled vector into Top10 cells.

Component III- pET15b(PT7/LacO1 -V27-GFP)- was cloned by using the Q5® Site-Directed Mutagenesis Kit to introduce a single base pair mutation into the LacO1 site, then transforming the mutated vector into Top10 cells.

Component IV- pSC(PBAD-T7 RNAP (RNA polymerase))- was cloned by digesting the pSC(Tet T7 RNAP) vector with XbaI and XhoI, amplifying the PBAD-T7 polymerase sequence from the BL21AI genome with primers containing 30 base-pair overhangs with the vector, then assembling the backbone and insert together with the Gibson Assembly Master Mix from NEB, and transforming the assembled vector into Top10 cells.

Component V- pSC(mOrange-RBSII-PC/PBAD-RBSI-mCherry)- was cloned by digesting pSC(Tet-T7 RNAP) vector with XbaI and BglII, then amplifying mOrange, PBAD, and mCherry DNA fragments with 30 base pairs of overlap between each other and the digested vector, then


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assembling the backbone and insert together with the Gibson Assembly Master Mix from NEB, and transforming the assembled vector into Top10 cells.

All transformations were done using competent bacteria made by the Mix & Go E. coli Transformation kit & Buffer Set (Zymo Research, Irvine CA). Cells were thawed on ice, then mixed with DNA, heat shocked at 42ºC for 45 seconds, then allowed to recover in SOC media for 1 hour before being plated via plate spreading beads on a LB-agar plate with the appropriate antibiotics.

Component VI- pSC(Tet-T7)- Details of construction in 42.

The BL21AI strain of E. coli was used to achieve arabinose-sensitive expression of T7 RNA polymerase. The BL21pro strain of E. coli was used to characterize the PT7/LacO1 promoter variants (Component I,II, III) in conjunction with pSC(Tet-T7) (Component VI) as a constitutive source of T7 RNAP (Fig. 2a & 2b). The pSC backbone was used to increase the copy number of T7 RNAP, and control expression of mCherry via PBAD. The pET15b backbone was used to control expression of GFP and LacI. All cells grown with the pSC backbone had 30 µg/mL kanamycin included in the media, and all cells grown with the pET15b backbone had 50 µg/mL carbenicillin included in the media.



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Table 1: Constructs and cell lines used in this study. Circuit I

Circuit II

Circuit III

Circuit IV

Circuit V

Circuit VI

Circuit VII

Circuit VIII

Circuit IX


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Magnitude analysis The magnitude analysis was performed by using the analytical solution derived in the SI (Eq. S6). We evaluated circuit transfer functions using 1000 parameter sets randomly generated from previously defined ranges. Each transfer function for these 1000 parameter sets was classified using the corresponding I2 value of the maximum system output. If the maximum system output occurred at the highest value of I2, the transfer function was classified as induction. If the maximum system output occurred at the lowest value of I2, the transfer function was classified as repression. If the maximum system output occurred at an intermediate value of I2, the transfer function was classified as hybrid. Then, the number of parameters sets leading to a given behavior was divided by the maximum value of that set (essentially assigning it a relative likelihood that a given parameter value would lead to a specific transfer function given randomized values for all other parameters) (Fig. 3).

Generality analysis Each network configuration within a library of networks was represented by three nodes, A, B, and C, which represent biological molecules that regulate each other according to an assigned network topology following Michaelis-Menten kinetics 19. The computational library we used to survey different network topologies was composed of three nodes that could regulate each other or themselves negatively or positively (*

8

9:

for positive regulation and 8

$

$

C %9:

for negative

regulation). Integration of multiple signals was done by multiplying terms together. Each network could have no more than three links, as that is the simplest functional unit of information processing in transcriptional networks. We generated 500 randomized parameter sets



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for each network topology, obtained the steady-state concentrations of C for each network given a range of concentrations for Input 1 and Input 2. We evaluated the reconfigurability of the resulting transfer functions by looking for which value of Input 2 had the largest value of C. Functions that had their maximal value of C at the maximum value of Input 2 were classified as induction, functions that had their maximal value of C at the minimum value of Input 2 were classified as repression, and functions that had the maximum value of C at some intermediate value of Input 2 were classified as hybrid. We recorded the number of parameter sets per network that gave rise to transfer-function inversion and used this as a metric to determine which network topologies were the most capable of modulating their transfer function between induction and repression.

Quantification and statistical analysis Classification of transfer functions It is common practice to use t-tests to determine the significance between experimental measurements of gene expression 41. Since we are trying to determine the significance of differences between many points in a gene expression transfer function, we chose to use a multiple comparisons test instead of a normal t-test. For experimental data, each transfer function (dose-response curve) was subjected to a Bonferroni multiple comparisons test, which performs significance testing between each point within the transfer function, correcting for false positives by adjusting the p-value of the test by dividing it by the number of comparisons being made. With this technique, we established confidence intervals between the values in each transfer function using a p-value of 0.001. The transfer functions were evaluated on whether they exhibited a significant increase from their fluorescence intensity at 0.001 mM IPTG (∆x1) and a


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significant decrease from their maximum fluorescence intensity (∆x2). Concentrations of arabinose that resulted in IPTG transfer functions that exhibited a significant ∆x1 but no significant ∆x2 were classified as ‘induction’. Concentrations of arabinose that resulted in IPTG transfer functions that exhibited no significant ∆x1 but a significant ∆x2 were classified as ‘repression’. Concentrations of arabinose that resulted in IPTG transfer functions that did not exhibit a significant increase between their maximum fluorescent intensity and fluorescence intensity of wild-type bacteria were classified as ‘no behavior’. Concentrations of arabinose that resulted in IPTG transfer functions that exhibited no significant change in fluorescence intensity, while exhibiting fluorescence intensities near the maximum expression levels observed in this study were classified as ‘saturated’ with T7 RNAP. Transfer functions that exhibited no significant changes in fluorescence intensity at a sub-maximal level or experienced significant ∆x1 and ∆x2 were classified as hybrid. Examples of each behavior and associated transfer functions with experimental data are shown in Fig. S1. The consistency of the confidence intervals between each point shows that the variance between experimental points in a transfer function is fairly uniform.

Motif incidence and significance To find the incidence of the topology of the synthetic genetic network in this study, we used a MATLAB script to match its topological configuration with all subnetworks of the Regulon DB V 8.0 transcription factor-transcription unit database. Prior to implementing the motif search, we removed all autoregulatory links from the database. We used 0 to represent no interaction, 1 to represent positive regulation and -1 to represent negative regulation. Next, we generated 1000 randomized networks from the RegulonDB database by generating a random pair of indices and



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swapping them if they would result in two new connections (ie. We did not swap two ‘0’ node connections) until each network was well randomized. We measured the incidence of our topological configuration in each of these randomized networks (Fig. 6C) and looked for how many times the incidence of our subnetwork inside a randomized network exceeded the incidence of our subnetwork inside the natural network. The number of times this subnetwork was found more often in a randomized network was divided by the total number of random networks to find the p-value of the synthetic network’s incidence.

Data and software availability The datasets and simulations generated during and/or analyzed during the current study are available from the corresponding author upon request. Acknowledgements Thanks to Dr. Fernando Villarreal for providing the plasmid that sparked this line of inquiry. Thanks to Fan Wu for providing help with coding in MATLAB. We appreciate the discussion of the manuscript with Prof Lingchong You, Prof Robert Smith, and Prof John Albeck. This research was partially supported by an industry/campus supported fellowship under the Training Program in Biomolecular Technology (T32-GM008799) at the University of California, Davis, as well as the Society-in-Science: Branco-Weiss Fellowship (C.T.) and Human Frontier Science Program (C.T.). This research was also partially supported by the University of California Davis Flow Cytometry Shared Resource Laboratory with funding from the NCI P30 CA093373, and NIH NCRR C06-RR12088, S10 RR12964 and S10 RR 026825 grants and with technical assistance from Ms. Bridget McLaughlin and Mr. Jonathan Van Dyke.


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Author contributions DL and CT designed the study and wrote the manuscript. DL performed all wet lab experiments, wrote Matlab scripts, and derived analytical solutions. MC assisted with the analysis of network motifs. KC assisted with parameter formulation for biochemical model. CT derived analytical solutions and wrote Matlab scripts for generality analysis.

Competing financial interests The authors declare no competing financial interests.

Supporting Information -

Derivation of analytical solutions of mathematical models used in main text

-

Quantification and discussion of biochemical perturbations used to validate the magnitude analysis

-

Plots of individual replicates for dose-response curves

-

Data and discussion concerning the temporal stability of reconfigured transfer functions

-

Data and discussion concerning the optimization the fold-change of each transfer function

-

Extended analysis of multiple model formulations



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Figures and Legends

Figure 1: Reconfigurable Inversion of Protein Expression in a Genetic Network (A) Graph depicting transfer-function inversion. (B) (Left Panel) Topological diagram depicting the regulation of the PBAD promoter (Right Panel) The PBAD promoter (Circuit VI, Table 1) produces mCherry under the control of arabinose and IPTG. Arabinose induces expression of mCherry, and IPTG represses mCherry expression. These results show that the PBAD promoter alone cannot generate transfer-function inversion.


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Black squares, solid line- .2% arabinose. Black circles, dashed line- .001% arabinose. Black triangles, dotted line- .0004% arabinose. (C) (Left Panel) Topological diagram depicting the regulation of the PT7/LacO1 promoter. (Right Panel) The PT7/LacO1 promoter induced by IPTG (Circuit VIII, Table 1). IPTG represses LacI binding to LacO1, allowing T7 RNAP to transcribe GFP. This circuit induces expression of GFP in response to increasing concentrations of IPTG. (D) Topology of the real (Left Panel) and abstracted (Right Panel) synthetic genetic network. We constructed a synthetic gene network to examine transfer-function inversion. The network consists of two sub-modules from (B) and (C): the PBAD promoter is regulated by arabinose and IPTG, producing T7 RNAP; and the PT7-LacO1 promoter is regulated by both IPTG and T7 RNAP. (E) Transfer functions of the circuit in (D) are modulated between two distinct types by arabinose without genetic changes. Solid line, squares- .2% arabinose (induction behavior). Dashed line, circles, .001% arabinose (hybrid behavior). Individual replicates plotted in Fig. S2. (A-E) Points represent experimental data, lines highlight trend. Black lines with arrowheads represent activating links, blue lines with flat heads represent repressing links.



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Figure 2: Model Formulation for Reconfigurable Inversion of Transfer Function (A) Topology of a network where two inducers, I1 and I2 control the production of two proteins, X and Y. Refer to SI, Section 1a for equations that detail network dynamics. (B) A chart demonstrating the relationship between inducer concentration, effective network topology, and the analytical solution of the model that shows how the synthetic network used in this study can give rise to induction, repression, and hybrid transfer functions. See Eq. S3-S19 in Supporting Information for the derivation of the analytical solutions.


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Figure 3: Magnitude Analysis - Predicted Impact of Kinetic Parameters on Transfer-Function Inversion. Each row is labeled with the name of the parameter that is being varied. The z-axis of each graph represents the qualitative changes in the likelihood of each transfer function that occur when the parameter of interest is varied on the y-axis and the concentration of arabinose (I1) is varied on the x-axis. On the z-axis, red represents high likelihood, blue represents low likelihood, and green/yellow represents moderate likelihood. Column 1 shows changes in the likelihood of repression behavior, column 2 shows changes in the likelihood of hybrid behavior, and column 3 shows changes in the likelihood of induction behavior (Methods). (A) Perturbation of the kinetic efficiency of T7 RNAP (V2)- V2 does not affect dynamic behavior of circuit. (B) Perturbation of the kinetic efficiency of IPTG induction of GFP (V3)- Low values of V3 increase the likelihood of the repression transfer function, while high values of V3 increase the likelihood of the induction transfer function.



1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(C) Perturbation of the dissociation constant for arabinose of PBAD (K1)- Low values of K1 increase the likelihood of the repression transfer function, intermediate values of K1 increase the likelihood of the range of the hybrid transfer function, and high values of K1 increase the likelihood of the induction transfer function. (D) Perturbation of the kinetic efficiency of arabinose induction of T7 RNAP (V1)- Low values of V1 increase the likelihood of the repression and hybrid transfer functions, while high values of V1 increase the likelihood of the induction transfer function.


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1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4: Perturbations of the Synthetic Network to Validate Model Predictions. (A) Each box represents a perturbed circuit state. These boxes are located next to the biochemical link they perturb. Each box contains the circuit name, a short description of the biochemical perturbation, and the effect on the network parameters. Circuit I contains all of these links, unperturbed. Circuit II- Single base pair mutation of the PT7 portion of the PT7-LacO1 promoter (Component characterized in Fig. 4B) Circuit III- Single base pair mutation of the LacO1 portion of the PT7-LacO1 promoter (Component characterized in Fig. 4C) Circuit IV- Supplementation of media with 1% glucose (Component characterized in Fig. 4D) Circuit V- Addition of PBAD-T7 RNAP in the pSC vector to the existing circuit, increasing the copy number of T7 RNAP gene available for expression. (B) Comparative characterization of the PT7-LacO1 promoter in Circuit I and Circuit II with respect to T7 RNAP induced by arabinose. Expression data are normalized to OD600. These results demonstrate the change in the catalytic activity of the PT7-LacO1 promoter caused by a sequence change (SI Section 2a, Table S1). (C) Comparison of the PT7-LacO1 promoter of Circuit VIII and Circuit IX (Methods, Fig. S2B) with respect to IPTG. Expression values of each circuit are normalized to OD600 and the lowest value within each circuit’s transfer function. These results demonstrate a change in the catalytic activity and sensitivity of the PT7-LacO1 caused by a sequence change (SI Section 2a, Table S1). (D) Comparison of the PBAD promoter of Circuit VI and Circuit VII (Methods, Fig. S2C) with respect to arabinose. Expression data are normalized to OD600. These results demonstrate the


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change in the sensitivity of the PBAD promoter with respect to the concentration of arabinose in response to media supplemented with glucose (SI Section 2a, Table S1). (B-D) Points represent mean of experimental data from plate reader, lines represent MichaelisMenten equations fitted to experimental data. Black Squares- Original Circuit, Grey TrianglesWeakened pT7, Grey Circles- Weakened LacO1, Grey Diamonds- 1% Supplemental Glucose. Error bars represents SEM of 4 replicates. Individual replicates plotted in Fig. S2. (E) Summary of transfer-function inversion in response to biochemical perturbations. Circuit III allows inversion between transfer functions, while Circuit IV generates only one transfer function. Topology of each perturbation is indicated above each column. Black lines with arrowheads represent activating links, blue lines with flat heads represent repressing links, red links and red nodes represent perturbed biochemical parameters. Circuit I- Original Circuit, Circuit II- Weakened PT7, Circuit III- Weakened LacO1, Circuit IV- 1% Supplemental Glucose, Circuit V- Increased PBAD-T7 RNAP copy number. Dynamic behavior with respect to IPTG is classified as either induction (white), hybrid (grey), repression (dark grey) using the Bonferroni comparison (Fig. S1, Methods). Grey stripes represent non-informative data, either ‘no response’ in column 4 or T7 RNAP saturation in column 5 (SI Section 2b). (F) Transfer functions of Circuit III, including emergent repression behavior predicted by analytical solution (SI Section 1a-c). Black squares, solid line- Induction (.2% arabinose). Black circles, dashed line- Hybrid (.004% arabinose). Black Triangles, dotted line- Repression (.001% arabinose). Points represent mean of experimental data, error bars represent SEM of 4 replicates. Individual replicates plotted in Fig. S2. Lines demonstrate transfer function trend.



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Figure 5: Dynamic Transfer-Function Reconfiguration and Variation of Expression in Synthetic Networks Capable of Transfer-Function Inversion Transfer functions of the synthetic network (Weakened LacO1 Site, Circuit III, Fig. 4A) were induced at one concentration of arabinose and a series of IPTG concentrations, then diluted and re-induced at a different concentration of arabinose and the same concentration of IPTG. Expression variability of biochemically perturbed versions of the synthetic network were analyzed and compared. (A) Dynamic transfer-function reconfiguration (first series of replicates). (B) Dynamic transfer-function reconfiguration (second series of replicates). Each line represents a trend line composed of two replicates per concentration of IPTG and arabinose. Grey- .2% arabinose transitioned to .001% arabinose, Black- .001% arabinose transitioned to .2% Arabinose. Points represent experimental data taken from tube culture and measured on a


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plate reader, lines highlight trend. Solid line- Initial arabinose concentration, dashed lineSecondary arabinose concentration. Effective topological configurations shown next to curves. Black lines with arrowheads represent activating links, blue lines with flat heads represent repressing links. For more information on dynamical transfer-function inversion, see Methods. (C) GFP expression noise in biochemically perturbed versions of the synthetic network. Circuits I and II with a greater range of hybrid behavior (Fig. 4E) demonstrate greater noise at low fluorescence intensities than Circuit IV, which has a smaller range of hybrid behavior. Noise is measured by the standard deviation of GFP fluorescent intensity normalized by the mean of the distribution. Points represent experimental data obtained from a flow cytometer. Black squaresCircuit I, dark grey triangles- Circuit II, black dashed diamonds- Circuit IV. Lines highlight experimental trend. See Table 1 for the corresponding circuit topology. Fig. S4B-F shows individual trends for Circuits I-V.



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Figure 6: Generality Analysis for the Reconfigurable Inversion of Transfer Function (A) We investigate the transfer-function inversion using an abstracted library of biological networks represented by three nodes A, B, and C, and two input signals Input 1 and Input 2 (Methods). (Left Panel) Dotted lines represent potential network connections between the three nodes. (Right Panel) Example of transfer-function inversion. This computational method allows us to survey a large number of networks to find topologies that allow transfer-function inversion. (B) Histogram showing network index (identifier of unique network topology) versus number of parameters sets (out of 500) capable of transfer-function inversion. Red asterisks indicate top three topologies most likely to demonstrate transfer-function inversion. (C) (Left Panel) Histogram depicting the incidence of unique subnetworks sharing the same topology as the synthetic network used in this study. The values in the histogram are calculated based on the synthetic network topology’s incidence inside 1000 randomized networks generated from the RegulonDB V8.0 E. coli transcription factor-transcriptional unit database. The topology


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of the synthetic network used in this study occurs 44 times in the natural E. coli network. (Right Panel) Two examples of subnetworks found in the natural E. coli network. This analysis suggests that the topology of a network capable of transfer-function inversion is overrepresented in the transcriptional network of E. coli (Methods). (A-C) Black lines with arrowheads represent activating links, blue lines with flat heads represent repressing links.



Abstract Graphic I1

Y (Output)

1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42

Induction

I2

High I1 X

Repression

Low I1

Y

I2


Page 46 of 54

Figure 1

(A)

(B)

Transfer Function Inversion

Output

Induction

Hybrid

High I1

Mid I1

Arabinose

IPTG

AraC

PBAD-mCherry

Repression Low I1

I2

(C) T7 RNAP IPTG

LacI

PT7/LacO1-GFP

x 103

GFP Fluorescence Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42


30

15

0 10-6

10-5 10-4 10-3 [IPTG] M ACS Paragon Plus Environment

mCherry Fluorescence Intensity

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.2% Arabinose

600

.001%

300

0

.0004%

10-6

10-5 10-4 [IPTG] M

10-3

Figure 1 - continued (D)

Arabinose

(E)

IPTG I1

AraC

T7

I2

X LacI

GFP


1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42


Page 48 of 54

x 103 40 30 20

.001% Arabinose (Hybrid)

10 0 10-6

Y

.2% Arabinose (Induction)

10-5

10-4

[IPTG] M


10-3

Figure 2 (A)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 𝑑𝑋 27 28 𝑑𝑡 29 30 31 𝑑𝑌 32 33 𝑑𝑡 34 35 36 37 38 39 40 41 42

I1


(B)

𝐾1

𝑉1 , 𝐾1

I2

Transfer Function Category

Inducer Condition

Induction

I1 >> I2

Effective Circuit Topology

Analytical Solution

X

𝑉2 , 𝐾2

𝑌𝑠𝑠 =

𝑉3 , 𝐾3

𝑉2

𝑘𝑑 2 𝐾2 + 1 𝑉12 𝑘𝑑

Repression

𝑉3 𝐼2 𝐾2 1 (𝐾3 + 𝐼2 ) 2+𝑘 𝑉1 𝑑

Y

I1 ~ 0 𝑌𝑠𝑠 =

=

+

[I2]

Y

𝐿 + 𝑉12 𝐼12 𝐾12 + 𝐼12 + 𝐼22

1

Shape of Transfer Function

− 𝑘𝑑 𝑋

𝑉2 𝑋 𝑉3 𝐼2 = 1+ − 𝑘𝑑 𝑌 𝐾2 + 𝑋 𝐾3 + 𝐼2

𝑉2

𝐾3 + 𝐼2 + 𝑉3 𝐼2

𝑘𝑑 2

𝐾12 + 𝐼22 1 (𝐾2 + )(𝐾3 + 𝐼2 ) 𝐿 𝑘𝑑

Y [I2]

Hybrid

I1 ~ I2 𝑌𝑠𝑠 = 𝑘𝑑 ACS Paragon Plus Environment

𝑉2 𝑘𝑑 2 𝐾1 + 𝐼12 + 𝐼22 1 𝐾2 ( 2 2 )+𝑘 𝐿 + 𝑉1 𝐼1 𝑑

1+

𝑉3 𝐼2 𝐾3 + 𝐼2

Y [I2]


6

6

4 2

10

1

Hybrid

0.7

4

0.7

2

0.6

2

0.6

0

0.5

-2

0.4

0

0.5

-2

0.4

-4

-4

-6

-6

0.2

-8

-8

0.1

10-9 -6 -5 -4 -3 -10 -10 -5 -1.5 -5 -4.5 1.3x10 -4 -3.5 1.3x10 -3 -2.5 -2 1.3x10 1.3x10 Ara [Arabinose] M

2

2

10 1.5

1.5

0.3

-4.5 0

-4

-3.5

-3

-2.5

-4

0.3

-6

0.2

-8

0.1

-10 -5 -1.5 -4.5 0 -2

1 0.9

-0.5

0.5 0.4 0.3

0.5

[Arabinose] M

-3.5

-3

-2.5

-2

-1.5

0

(D) 0.9 0.8

0.6

Arabinose Catalytic Activity (V1) 0.5 0.4

0.3

0.3

-1 0.2

-1.5

-4.5 0

0.7

0.4

-0.5

-4

-3.5

-3 Ara

-2.5

-2

-2 -1.5 -5

0.2

0.1

0.1

0

-4.5

-2

-2

15 -3

10-3

Transfer Function Likelihood 1 1

-4

-3.5

-3 Ara

-2.5

-2

-1.5

0

-3

0.8

0.7

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

-2

0.6 0.5

-3

0.4

-5

-5

0.2

5

0.1

-4

0.3

-6 -5 -1.5

10 -4.5 -4 -3.5 -3 -2.5 -2 -6 -5 -4 -3 Ara 1.3x10 1.3x10 1.3x10 1.3x10 0

[Arabinose] M 20 1020

-4

-3.5

-3

-6 -2 -5 -1.5 -4.5

-2.5

20 15

0.9 0.8

10

-10

5 0.6

0

0.5

-15

0.4

-5

0 -5

0.3

-5

-10

1.3x10 1.3x10


-3.5 -5

-3

-4-2.5

-2

-1.5

0.6

0

0.5 .5

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

-2

-20 -5 -1.5

Ara 1.3x10 1.3x10

-3

0.4 0.3 0.2 0.1

0.2

0.2

-4.5

-4

0.1

-4

-2.5

-10

-20 -15 -5 -4.5 -6

-3

0.7

10

0.7

5

-5

-20 10-20

-3.5

0.8

1

10

-15

-4

0.9

Ara

20

15

-10

0

Ara

-5

5

0.8

-5

-4.50

15

1000

0.9

0.9

-1

10 -4

-6-6 -5

1

1

0.8

-4

1

0.5

0.1

-2

-4

0.6

0

0.2

-2 10-2 -5 -6 -5 -4-2.5 -5 -4.5 -4 -3.5 -3 -2 -3 -1.5 Ara 1.3x10 1.3x10 1.3x10 1.3x10

0.1

0.7

-1.5

-1.5

0.2

1

0.6

-1

-1

0.3

0.8

0.5

-0.5

0.4

0.9

1.5

0.7

0

0.5

1

2

IPTG Dynamic Range

1000

0.6

Ara

1

0.5

Arabinose Dissociation Constant (K1)

Ara

0.8 1

0.7

-1 20

-1

kdAra

4

0.8

Vmax pBAD

0.8

0

1 0.9

Vmax pBAD

6

0

100

(M) X-I1-I2 Dissociation kdAra

0.8

0.9

(M s-1) Rate X SynthesisVmax pBAD

8

T7 Vmax

T7 Vmax

T7 Vmax

-2

0.9

0.9

Induction

1

0

100

2

1

kdAra

8

Repression

(C)

Induction

Vmax pBAD

10

1098

IPTG Dynamic Range

(B)

Hybrid 10

Synthesis Rate I2 Fractional IPTG Dynamic Range

1 2 3 4 5 6 7 8 9 T7 RNAP 10 Catalytic 11 Activity 12 (V2) 13 14 15 16 17 18 19 20 21 IPTG 22 23 Catalytic 24 Activity 25 (V3) 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Y Synthesis Rate (M s-1)

Figure 3 Repression (A)

Page 50 of 54

-4.5

0

-4

-3.5

-3 Ara

-3.5-15 -3 Ara -2.5

-20 -2-5

-1.5 -4.5

0.1 0 -4

-2

-3.5

-3 Ara

-2.5

-1.5 -2

-1.5

0

0

0.2

-2.5

0.1 0

Figure 4

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(A)

1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42


IPTG

Arabinose

Circuit IV Supp. Glucose (Increased K1)

Pconst T7 RNAP

AraC

PBAD AraC

LacI

Circuit V Increased PBADT7 RNAP Copy # (Increased V1) LacI

Pconst

T7 RNAP Circuit II Decreased T7 Affinity for PT7/LacO1 (Decreased V2) GFP


PT7/LacO1

Circuit III Decreased LacI Affinity for PT7/LacO1 (Decreased V3)

C

Circuit IOriginal pT7

1000

(E)

% Arabinose (W/V)

GFP

Circuit II- Weakened pT7 0 2x10-5 2x10-4 2x10-3 2x10-2 2x10-1

% Arabinose (W/V) Circuit II Circuit I

Glucose

AATTGTG

(C)

pT7

2

1

LacO1

(D)

GFP

Circuit VIIIOriginal LacO1

0 10-6

Circuit III

Circuit IXWeakened LacO1 10-5

10-4

[IPTG] M Circuit IV

10-3

Circuit V

Circuit VI- no supplemented glucose

250

Circuit VII+1% Glucose 0 2x10-5 2x10-4 2x10-3 2x10-2 2x10-1

(F) .2% Arabinose (Induction)

40

Induction

Induction

Induction

20 10 0

2 x 10-3 Hybrid

Hybrid

.006% Arabinose (Hybrid)

30

Induction Hybrid

2 x 10-4

500

T7 RNAP

% Arabinose (W/V)

2 x 10-1

2 x 10-2

PBAD

Normalized Fluorescence Intensity x 103

2000

LacO1

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Normalized Fluorescence Intensity


pT7


ACGACTC

(B) 1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42

G ACS Synthetic Biology

Repression ACS Paragon Plus Environment

Induction Hybrid

.001% Arabinose (Repression) 10-6

10-5

10-4

[IPTG] M

10-3

Figure 5 (A)


.2% Arabinose (Induction)

7.5 5

10 .2% Arabinose (Induction)

7.5 5

2.5

2.5 .001% Arabinose (Repression)

0 10-6

10-5

10-4

10-3

.001% Arabinose (Repression)

0 10-6

10-5

6

Circuit II

5 4 Circuit I 3 2 1 0 100

Circuit IV 101

10-4

[IPTG] M

[IPTG] M

(C)


(B)

10

GFP Fluorescence SD/Mean

1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42


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102


3 10 ACS Paragon Plus Environment

10-3

Figure 6 (A)

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Input 2

A

B

Input 1

Response

(B)

C

Transfer Function 1

Input 1

Transfer Function 2

Input 1

Input 2

OR

Count of Transfer Function Inversion

1 2 3 4 5 6 7 8 9 10 11 12 13 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 41 42


*

I1

* *

Response

(C)

ArcA

HNS

240

Count

200

GadE

160 FliC 120 CRP

80

40 0

CRA

MarA 0

20

40

60

80

# of motifs found in randomized networks

PoxB


I2

Motif index

Reconfigurable Analog Signal Processing by Living Cells - ACS

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