Characterizing chemical signaling between engineered “microbial sentinels” in porous microplates
2022; Springer Nature; Volume: 18; Issue: 3 Linguagem: Inglês
10.15252/msb.202110785
ISSN1744-4292
AutoresChristopher A. Vaiana, Hyungseok Kim, J Cottet, Keiko Oai, Zhifei Ge, Kameron M. Conforti, Andrew King, Adam J. Meyer, Haorong Chen, Christopher A. Voigt, Cullen Buie,
Tópico(s)Innovative Microfluidic and Catalytic Techniques Innovation
ResumoArticle22 March 2022Open Access Transparent process Characterizing chemical signaling between engineered “microbial sentinels” in porous microplates Christopher A Vaiana Christopher A Vaiana orcid.org/0000-0002-2582-4829 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Hyungseok Kim Hyungseok Kim orcid.org/0000-0003-4364-946X Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Data curation, Investigation Search for more papers by this author Jonathan Cottet Jonathan Cottet orcid.org/0000-0001-9377-9823 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Data curation, Software, Formal analysis, Writing - original draft, Writing - review & editing Search for more papers by this author Keiko Oai Keiko Oai Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Zhifei Ge Zhifei Ge Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Methodology Search for more papers by this author Kameron Conforti Kameron Conforti orcid.org/0000-0002-0782-3048 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Software Search for more papers by this author Andrew M King Andrew M King Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Adam J Meyer Adam J Meyer Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Haorong Chen Haorong Chen Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Christopher A Voigt Corresponding Author Christopher A Voigt [email protected] orcid.org/0000-0003-0844-4776 Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Resources, Supervision, Funding acquisition, Validation, Writing - original draft, Writing - review & editing Search for more papers by this author Cullen R Buie Corresponding Author Cullen R Buie [email protected] orcid.org/0000-0002-2275-4570 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Resources, Formal analysis, Funding acquisition, Validation, Writing - original draft, Writing - review & editing Search for more papers by this author Christopher A Vaiana Christopher A Vaiana orcid.org/0000-0002-2582-4829 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review & editing Search for more papers by this author Hyungseok Kim Hyungseok Kim orcid.org/0000-0003-4364-946X Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Data curation, Investigation Search for more papers by this author Jonathan Cottet Jonathan Cottet orcid.org/0000-0001-9377-9823 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Data curation, Software, Formal analysis, Writing - original draft, Writing - review & editing Search for more papers by this author Keiko Oai Keiko Oai Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Zhifei Ge Zhifei Ge Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Methodology Search for more papers by this author Kameron Conforti Kameron Conforti orcid.org/0000-0002-0782-3048 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Software Search for more papers by this author Andrew M King Andrew M King Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Adam J Meyer Adam J Meyer Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Haorong Chen Haorong Chen Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Investigation Search for more papers by this author Christopher A Voigt Corresponding Author Christopher A Voigt [email protected] orcid.org/0000-0003-0844-4776 Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Resources, Supervision, Funding acquisition, Validation, Writing - original draft, Writing - review & editing Search for more papers by this author Cullen R Buie Corresponding Author Cullen R Buie [email protected] orcid.org/0000-0002-2275-4570 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Contribution: Conceptualization, Resources, Formal analysis, Funding acquisition, Validation, Writing - original draft, Writing - review & editing Search for more papers by this author Author Information Christopher A Vaiana1,2, Hyungseok Kim1, Jonathan Cottet1, Keiko Oai1, Zhifei Ge1, Kameron Conforti1, Andrew M King2, Adam J Meyer2, Haorong Chen2, Christopher A Voigt *,2 and Cullen R Buie *,1 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA 2Synthetic Biology Center, Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA *Corresponding author. Tel: +1 617 253 8735; E-mail: [email protected] *Corresponding author. Tel: +1 617 253 9379; E-mail: [email protected] Molecular Systems Biology (2022)18:e10785https://doi.org/10.15252/msb.202110785 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Abstract Living materials combine a material scaffold, that is often porous, with engineered cells that perform sensing, computing, and biosynthetic tasks. Designing such systems is difficult because little is known regarding signaling transport parameters in the material. Here, the development of a porous microplate is presented. Hydrogel barriers between wells have a porosity of 60% and a tortuosity factor of 1.6, allowing molecular diffusion between wells. The permeability of dyes, antibiotics, inducers, and quorum signals between wells were characterized. A “sentinel” strain was constructed by introducing orthogonal sensors into the genome of Escherichia coli MG1655 for IPTG, anhydrotetracycline, L-arabinose, and four quorum signals. The strain’s response to inducer diffusion through the wells was quantified up to 14 mm, and quorum and antibacterial signaling were measured over 16 h. Signaling distance is dictated by hydrogel adsorption, quantified using a linear finite element model that yields adsorption coefficients from 0 to 0.1 mol m−3. Parameters derived herein will aid the design of living materials for pathogen remediation, computation, and self-organizing biofilms. Synopsis Microbes interact by chemical diffusion through materials, a concept that inspires “engineered living materials”. To parameterize signaling through materials, a porous culture microplate is fabricated to measure chemical signaling between isolated wells of engineered E. coli. A porous microplate is fabricated by soft lithography of the co-polymer hydroxyethyl methacrylate-co-ethylene glycol dimethacrylate. Four homoserine lactone quorum sensors are evolved to minimize cross-talk via directed evolution. Seven total orthogonal sensors are encoded into the genome of E. coli MG1655, which serves as a “sentinel strain.” The biological response of the sentinel strain to inducer, quorum, and antibiotic signaling between isolated wells of the microplate are experimentally measured. A quantitative model is developed that explains the difference in transport kinetics of the various biological signals by differential absorption of the molecules to the hydrogel matrix. Introduction Living materials are a promising tool to be applied in such diverse applications as therapeutics (Duraj-Thatte et al, 2019), construction (Heveran et al, 2020), fashion (Bader et al, 2016), and extraterrestrial exploration (Menezes et al, 2015). They consist of cells embedded in a scaffold, such as textiles (Yao et al, 2015; Moser et al, 2019; Nguyen et al, 2021), 3D-printed substrates (Connell et al, 2013; Axpe & Oyen, 2016; Schaffner et al, 2017; Liu et al, 2018; Correia Carreira et al, 2020; Smith et al, 2020), or cement (Wiktor & Jonkers, 2011; Reddy et al, 2015; Başaran Bundur et al, 2017). It is challenging to design cells that function reliably in these environmental contexts. For example, bacteria serving as chemical sensors are typically characterized in liquid culture, but the diffusion of the chemical and the state of the cell will be different than in a more complex matrix (Masiello et al, 2013; Bereza-Malcolm et al, 2015; Del Valle et al, 2020). In particular, bacteria consume and produce molecules, including metabolites and cell-cell communication (quorum) signals. The interaction of these molecules with the materials and their transport properties impact how a cell will perform, but it is difficult to parameterize these properties to inform the design process. Materials differ in their molecular transport properties. Porous hydrogel scaffolds that have been investigated for living materials include agarose (Gerber et al, 2012; Gonzalez et al, 2020), alginate (Kim et al, 2011), acrylamide (Lin et al, 2016; Liu et al, 2017, 2018; Sankaran et al, 2019), dextran (Guo et al, 2020), methacrylates (Liu et al, 2018), and bacterial cellulose (Gilbert & Ellis, 2019; Birnbaum et al, 2020). Cross-linked agarose has pores that range from 0.5 to 500 µm depending on the fabrication processes, with porosity (the ratio of void volume to total volume of a material) of about 30% (Annabi et al, 2010; Rodriguez Corral et al, 2020). Dextran hydrogel pores are 10–100 µm and have been covalently functionalized with antibiotic-producing Escherichia Coli (E. coli); the large pore size provides free diffusion of Isopropyl β-d-1-thiogalactopyranoside (IPTG) and arabinose (ara) inducers and allows the delivery of the antibiotic lysostaphin (Guo et al, 2020). Pores of this size allow cell migration as well, unless the microbes are actively tethered to the matrix. Methacrylate hydrogels derived from Pluronic® F127 were used to print a spatially compartmentalized biosynthetic consortia; the smaller pore size of methacrylates can be less than 10 µm and can physically trap cells (Liu et al, 2018; Saha et al, 2018). Using a methacrylate “bio-ink”, a spatially segregated co-culture of E. coli and Saccharomyces cerevisiae was 3D-printed; the strains worked together to produce betaxanthins (a commercially valuable food colorant) (Johnston et al, 2020). Entrapment of cells in the ink enables their lyophilization, storage, and long-term use, while segregation of species improves their coexistence. The diffusion of chemicals through a material can be effectively modeled as its “tortuosity”—a measure of the twists and turns a solute makes during its “zig-zag” movement through the material. The tortuosity has been experimentally measured for a number of solutes, with variations in the tortuosity factor ranging from 0.5 to 4.0 (Zhang & Bishop, 1994; Melo, 2005). The diffusion coefficients in water Daq of common signaling molecules range from 5 to 50 x 10-6 cm2 s-1 (Stewart, 1998, 2003). The environment through which these molecules travel dictates how far the effective diffusion De deviates from diffusion through water. It has been suggested to use a mean De/Daq of 0.25 for organic solutes in biofilms (Stewart, 2003), although the exact value is predicted to fluctuate by approximately 50% as the biofilm porosity changes (Zhang & Bishop, 1994). Cells can perform sensing and computing functions within a living material that are otherwise difficult operations to encode in the inorganic scaffold. Genetic sensors respond to an environmental signal and control the activity of a promoter, and circuits integrate the information from sensors or enact a dynamic response. Sensors have been designed to operate in a living material by mathematically considering the impact of signaling molecule transport on the dynamics of activating the sensor. For example, the effective diffusion of small molecules through acrylamide is estimated to be 1.5 × 10−10 m2 s−1 (Lin et al, 2016; Liu et al, 2018). This was mathematically combined with the response of the promoter to predict the activation by the small molecules IPTG and N-hexanoyl-L-homoserine lactone (OC6-HSL, or OC6) as they diffused through the hydrogel (Liu et al, 2017). Bacteria communicate by exchanging small molecules, referred to as quorum signals (Waters & Bassler, 2005). These systems are commonly used to program cell-cell communication, where a sender cell produces the molecule and the receiver cell has sensor that responds to it (Balagadde et al, 2008; Bischofs et al, 2009; Wu et al, 2014; Perry et al, 2016; Scott & Hasty, 2016; preprint: Doong et al, 2017; He et al, 2017; Scott et al, 2017; Halleran & Murray, 2018; Kylilis et al, 2018; Leaman et al, 2018; preprint: Parkin & Murray, 2018; Alnahhas et al, 2020; preprint: Fedorec et al, 2020; preprint: Karkaria et al, 2020; Miano et al, 2020; Stephens & Bentley, 2020). These have been used to create many multicellular patterns in the field and could be used to differentiate cells within a living material; however, their use within complex matrixes poses a challenge (Dilanji et al, 2012; Borek et al, 2016; Gao et al, 2016a; Grant et al, 2016). LuxR-family regulators respond to acyl-homoserine lactones (HSLs), which are very small and can adsorb to materials (Kaeberlein et al, 2002; Bollmann et al, 2007; Gao et al, 2016b; Dade-Robertson et al, 2018; Mukherjee & Bassler, 2019). Between colonies, the effective distance of quorum signaling through agar or in situ is over 4 cm after 10 h (Dilanji et al, 2012; preprint: Doong et al, 2017). Material adsorption at a boundary can produce a 100-fold lower effector concentration at the receiving cell (Trovato et al, 2014). Interactive co-culture platforms have been instrumental in understanding how molecular diffusion plays a role in collective microbial function. Bulk liquid co-cultures suffer from limited throughput and one strain can overtake the other in growth, while on agar colonies do not interact until reaching late stationary growth (Zhang & Wang, 2016; Fortuin, 2020). Membrane-based co-cultures allow chemicals to diffuse between strains. For example, the isolation chip—a culture chamber sandwiched between membranes with 30 nm pores—has increased the cultivability of soil microbes by allowing microbes to exchange chemicals with their native environment (Kaeberlein et al, 2002; Nichols et al, 2010; Berdy et al, 2017). This has been used to induce antibiotic production from otherwise silent gene clusters (Ling et al, 2015; Shi et al, 2017; Lodhi et al, 2018). The throughput can be massively improved using microfluidics, but these can be difficult to use, requiring specialized pumps and channels (Rogers et al, 2021). In this manuscript, we describe a “porous microplate” consisting of spatially isolated culture wells separated by porous methacrylate barriers (Ge et al, 2016; Kim et al, 2021). The methacrylate we choose, hydroxyethyl methacrylate-co-ethylene glycol dimethacrylate (HEMA-EDMA), has amorphous pores of 10–100 nm in size and a porosity of 60 percent. This culturing system allows the exchange of small molecules, but not cells, between wells. Unlike membrane-based co-cultures, the geometry of our plate has each well surrounded by six wells, each of which could isolate a separate strain. It is also easy to fabricate and pipette into the wells and does not require specialized equipment, in contrast to microfluidic approaches. To evaluate this system, we constructed a strain of E. coli that contains genetically-encoded sensors for IPTG, anhydrotetracycline (aTc), and ara as well as four orthogonal HSLs. Using our system, we measured the effective diffusion through the HEMA-EDMA barrier as well as an adsorption coefficient and tortuosity. These data parameterize a quantitative model of diffusion through a porous medium. In addition, we use the system to parameterize the diffusion of antibiotics. This work provides a method to separate strains as a means to study interactions between species making up a microbiota or to parameter models to aid the design of cells that functionalize living materials. Results Microplate fabrication and characterization The dimensions of the porous microplate were designed with a hexagonal layout to maximize neighboring well interactions and to facilitate manual cell recovery (Fig 1A, Appendix Fig S1). A hexagonal layout allows each well to have six immediate neighbors. The well centers were spaced out 3.6 mm apart horizontally which matches the spacing of a conventional 364-well plate. The well width of 2.2 mm is large enough to fit a standard 20-µl pipette tip for manual loading. In addition to the hexagonal well layout, alternative microplate designs can be fabricated that conform to standard commercial microplate dimensions. These include 96-well, 384-well, and 1536-well formats (Appendix Fig S2). A range of feature sizes can be made, with a minimum of 0.56 mm observed in this work (the width of the walls between the wells in the 1536-well dimensioned microplate (Appendix Fig S2C)). Figure 1. A porous microplate for chemically interactive cell culture A. Two-dimensional graphical depiction of a hexagonal porous microplate is shown. The plate is constructed from cross-linked hydroxyethyl methacrylate-co-ethylene glycol dimethacrylate (HEMA-EDMA, large filled hexagon). Liquid culture wells hold a volume of 10.0 µl (small open hexagons). The lower left inset depicts well dimensions. Scale bar = 3.6 mm. The lower right inset describes the utility of the plate to isolate culture wells and allow chemical communication between cultures. B. Schematic depiction of the microplate fabrication process. C. Photograph of a porous microplate; scale bar = 20.0 mm. D. The experimentally determined porosity ε is plotted as a function of the ratio of 1-decanol to cyclohexanol used during fabrication. Three devices for each condition were fabricated and measured. Each data point represents a single measured device. All collect data points are plotted. A linear equation was fit to the data; y = 0.1x + 0.5887, R2 = 0.5 based on a regression analysis. E. Scanning electron micrograph of cross-linked HEMA-EMDA; scale bar = 1.0 µm. F. Schematic depiction of dye diffusion measurements is shown. G, H. Diffusion of cotton blue (G) and rhodamine B (H) through the microplate. After 24 h, the concentration of dye in a selection of wells was measured and plotted as a function of distance from the center well. The experiment was repeated on different days, and all collected data are reported (open circles, n = 3 total data points for the center well, and n = 6 data points for the remainder wells). An exponential equation was fit to the average cotton blue data; y = 0.3 e−0.29x, R2 = 0.96). Download figure Download PowerPoint The co-polymer HEMA-EDMA was chosen due to its biocompatibility and tunable porosity. The ratio of the two precursor monomers dictates the porosity of the final product. In this work, a 24 percentage by weight (wt %) of HEMA and 16 wt % of EDMA were used. The solvents 1-decanol and cyclohexanol were added to the hydrogel precursor to act as “porogens” as the methacrylates cross-linked around them. Different solvent choices and combinations can tune the porosity and pore size of the final material (Geyer et al, 2011; Ge et al, 2016). To fabricate the microplates, conventional soft lithography techniques were used. An acrylic mold was first laser cut to the proper dimensions and used to generate a PDMS master. The PDMS master then shapes the hydrogel, and the molded hydrogel precursor was cross-linked with ultraviolet light to bond to a methacrylate-functionalized glass slide (Fig 1B and C). Several methanol washes were employed to remove excess hydrogel precursors before the microplate was incubated in an appropriate buffer or culture medium for further use. To explore the effect of solvent ratio on porosity, the 1-decanol-to-cyclohexanol ratio was adjusted between 0.25 and 0.60, and an upward linear trend was observed between increasing solvent ratio and porosity (Fig 1D). As the ratio of 1-decanol to cyclohexanol increases beyond 0.60, the integrity of the device suffers. Therefore, a ratio of 0.25 was used throughout the remainder of the work. The pores of the final cross-linked material were examined using scanning electron microscopy. The amorphous porous mesh appears to have a distribution of pores of less than 1 µm in diameter, which is smaller than E. coli cells, and is consistent with previous measurements (Fig 1E, Appendix Fig S3) (Ge et al, 2016). To test the permeability of the microplate walls, we measured the effective diffusion of the visible dyes cotton blue and rhodamine B from the center well (Fig 1F). These dyes were selected because of their comparable molecular weight, but different water solubilities. To the center well of separate microplates was added an aqueous solution of dye, and to the remaining wells was added Milli-Q water. Each device was incubated at 30°C for 24 h before being assayed for the presence of the dyes. After incubation, cotton blue was present in the outer wells and its concentration as function of distance from the center exponentially decays (Fig 1G). In contrast, rhodamine B was not detected in any outer wells, and the center well was nearly depleted of the starting dye solution (Fig 1H). While rhodamine was not detected in solution in the well, the hydrogel surface was visibly stained with the dye, suggesting a strong attraction of rhodamine to the polymer. Our observations suggest that interactions between the solute and the HEMA-EDMA microplate walls are molecule-dependent and that rhodamine B was adsorbed by the polymer. Construction and evaluation of a E. coli sensor strain Bacteria can provide a sensing function to a living material. To evaluate a sensor strain in our device, we engineered E. coli to contain an array of small molecule sensors. Four LuxR-family acyl-homoserine lactone activators were included: luxR, cinR, lasR, and rpaR. Specific mutations were made to the sensors, as well as libraries of directed evolution, to reduce cross-reactivity and improve performance (Appendix Tables S1 and S2, Appendix Fig S4A). Genes for the four mutated quorum sensors were combined with those of three previously optimized sensors tetRAM, lacIAM, and araCA from E. coli Marionette, as well as an araE transporter (Meyer et al, 2019), to create a seven-sensor array integrated into landing pads previously placed in the E. coli MG1655 genome (Fig 2A, Appendix Fig S5). Receiver strains that respond to each small molecule were built by transforming the strain carrying the array with a p15a plasmid that contains a sensor output promoter driving the expression of YFP (Appendix Fig S6A). The sensors were optimized to increase the dynamic range and tested for cross reactivity (Fig 2B, Appendix Figs S6B and S7). The dose response curves for the final sensors are shown in Fig 2C and parameters from a fit to a response function are provided in Table 1. Figure 2. The sentinel strain responds orthogonally to small molecule inducers and quorum signals The genetic and molecule schematic depictions of the Marionette-Q cluster are shown. The chemical cross-reactivity heatmap of the 7 output promoters with each inducer is shown. The mean promoter activity of three replicates done on different days is plotted. Individual data points are plotted in Appendix Fig S8. The resulting dose–response curves of the seven sensors and output promoters in response to their cognate inducer: 3-oxohexanoyl-homoserine lactone (OC6) with PLux*TA, 3-hydroxytetradecanoyl-homoserine lactone (OHC14) with PCin, N-3-oxododecanoyl-homoserine lactone (OC12) with PLas, para-coumaroyl-homoserine lactone (pC-HSL) with PRpa*A, isopropyl β-D-1-thiogalactopyranoside (IPTG) with PTac, L-arabinose (ara) with PBad, and anhydrotetracycline (aTc) with PTet. The experiment was repeated on different days, and all collected data are reported (n = at least 3). Response profiles are each fit to a Hill equation using Excel (line; see Table 1 for coefficients). Data (open circles) are collected as median fluorescent signal of at least 20,000 cells and converted to RNAP/s units (see Materials and Methods). Download figure Download PowerPoint Table 1. Output promoter response parameters. Output promoter ymin (RNAP/s) ymax (RNAP/s) K n PLux*TA 0.0008 0.4 9.4 × 10−5 1.13 PCin 0.0015 0.3 2.9 × 10−5 1.46 PLas 0.0011 0.02 1.5 × 10−2 1.08 PRpa*A 0.0011 0.3 6.6 × 10−6 0.98 PTac 0.0030 1.2 1.4 × 100 1.35 PTet 0.0011 0.9 9.0 × 10−6 1.50 PBad 0.0017 0.7 1.5 × 100 1.49 Characterizing the transport of inducers through the microplate Transport in the device is influenced by diffusion and adsorption. As diffusion of molecules in porous media depends on the structure of the porous material and the phases involved, we considered the effective diffusivity De to be that of a saturated porous media: D e = D aq ε τ - 1 (1)where Daq is the diffusion coefficient in water (m2 s−1), ε is the porosity, and τ is the tortuosity factor. The tortuosity factor accounts for the reduced diffusivity due to solid grains of the hydrogel that impede Brownian motion. The adsorption of the molecule to the surface of the porous matrix can be accounted for by different adsorption isotherm models. In our case, a linear model (Henry’s adsorption isotherm) was used, Q e = K H C e (2)where Q e is the mass adsorbed (mol kg−1), C e is the adsorbate concentration at equilibrium (mol m−3), and KH (m3 kg−1) is the partition coefficient. We used published values for Daq of glycine (1.1 × 10−9 m2 s−1) and De of glycine through HEMA-EDMA (3.47 × 10−10 m2 s−1) (Stewart, 2003; Ge et al, 2016), and our experimentally determined porosity fraction ε = 0.6 to calculate the tortuosity τ = 1.9. Diffusion was modeled in the wells using Daq of glycine (1.1 × 10−9 m2 s−1). Using these data, we simulated transport through the microplate of the seven inducers that activate the receiver strains (Fig 3A). The diffusion coefficients and tortuosity were held constant while the adsorption coefficient was swept from 0 to 0.1 mol m−3. The resulting cross-sectional values for inducer concentration at 5 h were collected. The inducer concentration was then transformed with a Hill equation using the coefficients listed in Table 1. The result of the simulation was the predicted output of an inducer-sensor pair as a function of distance from the center well. Figure 3. Simulation and experimental measurement of inducer diffusion through the porous microplate Flow chart representing the simulation of inducer transport through the microplate using a linear finite element model of effective diffusion through a porous medium. Inducer concentration in the center well was set to an initial value [inducer]i at time t = 0 h filled red hexagon: (20.0 mM IPTG, 0.0004 mM aTc, 160.0 mM L-arabinose, 0.1 mM OHC6-HSL, 0.1 mM pC-HSL, or 0.4 mM OHC12-HSL), and constants were defined for both the polymer (large filled hexagon) and the liquid culture wells (small open hexagons). The resulting cross-sectional concentration profile (dashed arrow) after 5-h simulated diffusion time was collected as inducer concentration (mM) as a function of distance from the center of the center well (“x”). The resulting concentration values were converted to promoter activity (RNAP/s) using the Hill coefficients for each inducer with output strain (Table 1). The resulting output is a plot of the cross-sectional simulated promoter activity for each inducer with promoter pair as a function of distance from the center well. The gray regions between dotted vertical lines represent the location of wells (not including the center)
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