novel in vivo concentration detector

Novel In Vivo Lead Concentration Detector

Proposal By: Gerard Trimberger and Felix Ekness June 2, 2012

Abstract The field of synthetic biology has its sights set on designing and constructing new biological functions and systems not found in nature. Because of this, we are proposing a novel genetic circuit that would be in Escherichia coli (E. coli) that would detect safe and harmful lead concentrations within liquid samples. This novel genetic circuit is designed so that phenotype changes within E. coli will represent the degree of biological safety of liquid samples with respect to aqueous lead concentrations. The proposed genetic circuit utilizes already designed lead binding proteins and lead binding protein promoters as well as commonly used metabolite signals, fluorescent reports, and terminator sequences. Although actual construction of the lead concentration detector genetic circuit isn’t feasible yet, through simulating the proposed kinetics of the circuit, it can be seen that the genetic circuit could be possible given the correct biological parts.

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Table of Contents Introduction to Synthetic Biology…………………………………………………………………………….pp. 03 Project Overview…………………………………………………………………………………………………….pp. 03 Project Design Specifications………………………………………………………………………………...…pp. 04 Internal Design Specifications……………………………………………………………………………….…pp. 04 Design Overview…………………………………………………………………………………………..pp. 04 Overview…………………………………………………………………………………………...pp. 04 Concentration Detector………………………………………………………………………pp. 04 Memory Unit…………………………………………………………………………………...…pp. 05 Signal Amplifying Fluorescent Reporter……………………………………………...pp. 05 Specifications of Proposed Kinetic Responses.……………………………………………….pp. 06 Overview…………………………………………………………………………………………...pp. 06 Concentration Detector……………………………………………………………………...pp. 06 Memory Unit……………………………………………………………………………………..pp. 06 Signal Amplifying Fluorescent Reporter……………………………………………...pp. 07 Degradation……………………………………………………………………………………….pp. 07 Computer Simulation Test Implementation………………………………………………………………pp. 08 Complete Circuit Simulations………………………………………………………………………...pp. 08 Concentration Detector Module Simulations………………………………………………….pp. 09 Memory Unit Module Simulations……………………………………………………….…………pp. 09

Signal Amplifying Fluorescent Reporter Module Simulations………………………….pp. 09 Implementation Details…………………………………………………………………………………………...pp. 10 Appendix………………………………………………………………………………………………………………...pp. 11 Device Pricing in 2025…………………………………………………………………………………..pp. 11 Design Specification Sheet………………………………………………………………...…………..pp. 11 Overview…………………………………………………………………………………………...pp. 11 Concentration Detector………………………………………………………………………pp. 12 Memory Unit……………………………………………………………………………………...pp. 13 Signal Amplifying Fluorescent Reporter……………………………………………...pp. 14 Jarnac Script…………………………………………………………………………………………………pp. 15 Overview (Complete System Simulation) ……………………………………………pp. 15 Concentration Detector……………………………………………………………………...pp. 16 Memory Unit……………………………………………………………………………………..pp. 17 Signal Amplifying Fluorescent Reporter……………………………………………...pp. 18 Sources………………………………………………………………………………………………………...pp. 18

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Introduction to Synthetic Biology Before the age of digital computers, man lived a simple life. Science was primarily a pencil and paper type of exploration with observations of the natural world deriving from actual observations of nature. Digital computers changed all of this. Currently almost all complex calculations, modeling, and observations are aided by digital computers. It was predicted by Intel co-‐founder Gorgon E. Moore that the number of transitions that can be placed inexpensively on an integrated circuit would double every two years [1]. Since Moore’s law was realized in 1965, transistors per area have been increasing in line with the law’s predictions, giving way to an exponential increase in computing power over the past few decades. This increase in computing power has given scientists the ability to effortlessly create numerical models of complex natural processes, shedding new insights into traditionally difficult to explore areas. In 1990 the Human Genome Project (HGP) was announced [2]. This project aimed to sequence all of the genes of the human genome. Without the aid of digital computers, the project would have been near impossible. It was expected, at the time, to take 15 years of work but the project finished in 2003, 2 years early [2]. The early completing of the HGP can be partly attributed to the exponential increase in computing power between 1990 and 2003. Since that time, biologists have been harnessing digital computers more and more to help acquire data, model biological processes, sequence organisms, and clone DNA and RNA. This increase in digital computing power and prevalence of digital computers in the biology community has given way to a new field: synthetic biology. Synthetic biology is a relatively new field that focuses on designing and constructing new biological functions and systems not found in nature. Without digital computers, synthetic biology wouldn’t be the field it is today. Computer programs, such as Fold It (a numerical modeling program for proteins), have been integral to synthetic biologists’ understand of tertiary and quaternary structures of normally occurring, as well as engineered, proteins and enzymes. Natural and engineered enzymatic and gene pathways are actively being modeled with programs such as MatLab, Mathematica, and Jarnac. Together, the use of these modeling programs has lead to quantization of traditionally qualitative biological processes and functions. Because of this, the field of biology has become more of a quantitative science as well as leading many to question nature’s autonomy. Due to how computers have shaped the field synthetic biology thus far, many synthetic biologists believe that through the use of computers the field will be able to characterize biology to the point where the construction of novel genetic circuits/pathways within organisms is as straightforward as electrical engineers utilizing capacitors, resistors, and inductors in building complex electrical circuits. It has been electrical engineers up to this point building computers but as Moore’s law becomes increasingly more difficult to satisfy, new types of machinery will be required, some of which is bound to come from the field of synthetic biology. Project Overview Aqueous lead is a major problem around the world. When lead is ingested by humans, both neurological and severe tissue damage can occur. Although lead test kits are readily available in the market for relatively cheap prices, to create a biologic test for lead in bacteria or micro-‐organism eukaryotes would yield even cheaper tests and would act as a proof of concept for engineering complex genetic circuits within bacteria and/or micro-‐organism eukaryotes. The proposed project is to build a novel genetic circuit within Escherichia coli (E. coli) that enables lead (Pb2+) concentration detection within liquid environments. The circuit is designed to allow varying concentrations of lead to be detected in liquid samples through phenotypic changes in the E. coli. By

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visualizing the relative levels of lead within sampled liquids, accurate decisions can be made about whether or not the liquids are safe for human consumption. With the creation of this novel genetic circuit, it is hoped that humans will gain one more tool in monitoring the safety of their environment. Product Design Specifications The proposed novel genetic lead concentration detector circuit works within E. coli that is in a liquid environment. Depending on the initial concentration of lead imported into the E. coli, one of two incoherent feed forward networks will activate causing a regulated double negative feedback network to activate one of two fluorescence outputs. Once activated, the fluorescent output will auto regulate itself to stay activated until the E. coli runs out of nutrients. Only concentrations of lead that exceed harmful levels will cause the E. coli to fluoresce red while lower non-‐harmful levels of lead will cause the E. coli to fluoresce green. If no to very little amounts of lead are present in the liquid sample, the E. coli will not fluoresce. Internal Design Specifications A) Design Overview Overview The engineered lead concentration detector circuit is comprised of a concentration detector, a memory unit, and a fluorescence reporter (Figure 1). As a whole, these components are comprised of three main modules, and two submodules: two incoherent feedforward networks (concentration detector), a regulated double negative feedback network (memory unit), and two positive autoregulation modules (signal amplifying fluorescent reporters).

Figure 1 – Component overview of the proposed lead concentration detector genetic circuit

Concentration Detector

The circuit will activate from the binding of Pb2+ molecules to lead binding proteins, forming lead-‐binding protein dimers (LBPD). These formed dimers act to bind to specially designed promoters that enable transcription of two initial substrates (S and P) that are interfaced with the designed circuit in Figure 2. It can be seen from Figure 2 that the two main motifs that initial substrates S and P interact with are incoherent feedforward networks A and B. Incoherent feedforward networks only activate when an initial substrate concentration is at or above a given threshold value (threshold value dependent on network tuning). In the case of incoherent feedforward networks A and B, network A will produce S2 only for high concentrations of initial substrate S while network B will produce P2 at a lower initial substrate concentration of P. Since initial substrates S and P are equally produced from the

transcription initiated by the binding of the lead protein dimer to the lead binding promoter ([S] = [P]), network A will be active when network B is active but when B is active A will not be (side effect of

Figure 2 – Circuit diagram for the concentration detector module

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differing activation thresholds). To make these two network motifs act as a concentration detector, network A‘s product must inhibit B’s product, causing either A (high initial substrate concentration activation) or B (lower initial substrate concentration activation) to produce a product at any one point in time. With this in effect, networks A and B act as a concentration detector for lead. Memory Unit In order to produce a high fidelity visual representation of the concentration of lead within the liquid sample, a decision must be made within the gene circuit. The regulated double negative feedback module will receive the signal from the two concentration detectors, and will decide which signal to transmit to the fluorescence reporter module. Depending on the concentration of LBPD, either protein S2 or P2 will be produced by the concentration detector module. If the concentration of substrate is high, above the “high concentration” threshold, S2 will be produced, however if the concentration of the substrate is low, below the “high concentration ” threshold but above zero, P2 will be produced. These input signals will activate the transcription of a secondary species, either S3 or P3 depending on the concentration of the input molecules. This set of species will activate the transcription of a tertiary species, S4 or P4, and inhibit the transcription of its compliment species (i.e. S3 will activate S4 production and repress P4 production; P3 will activate P4 production and inhibit S4 production). The accumulation of either tertiary species, S4 or P4, will continuously repress the production of the other unless a stimulus is great enough to reverse it. In this way, the regulated double negative feedback module will act as a memory unit that remembers which tertiary signal it should display given an input signal of S2 or P2. Signal Amplifying Fluorescent Reporter

Depending on the upstream effects, one of the tertiary species S4 or P4 will be found in abundance. This species will then be amplified via its auto regulation pathway which also compliments the memory unit module through complete inhibition of the transcription of its compliment species (i.e. S4 will self-‐replicate and shut down P4 or P4 will self-‐replicate and shut down S4 production). In order to visually display the results of the concentration detector module, the tertiary species will activate the transcription of a fluorescent protein. Red fluorescent protein (RFP) will be used to visually represent high

concentrations of lead. Transcription of RFP will be activated by tertiary species S4. The presence of low concentrations of lead will be designated by the production of green fluorescent protein (GFP), which will be activated by tertiary species P4. If no lead is found within the liquid, neither fluorescent reporter will be produced. In this way, the auto regulation module displays the behavior of a single amplifying fluorescent reporter. Thus, the E. Coli will continuously present its detection level, ignoring minimal fluctuations in the concentration of lead, given an initial concentration of lead.

Figure 3 -‐ Circuit diagram for the memory unit module

Figure 4 -‐ Circuit diagram for the signal amplifying fluorescence module

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B) Specification of the Proposed Kinetic Responses Concentration Detector The kinetics of the concentration detector module is assumed to contain both mass-‐action kinetics and Michaelis-‐Menten kinetics. The activation of species S1 and P1 will be governed by the Michaelis-‐Menten equation for activation based on the concentration of the LBPD:

𝑣 = (𝑉!"# ∗ 𝐿𝐵𝑃𝐷!)/(𝐾! + 𝐿𝐵𝑃𝐷!) where LBPD represents the concentration of the lead binding protein dimer. No cooperativity of the enzyme is assumed in this particular case; therefore the hill coefficient of this reaction, n, is expected to be one. The production of species S2 is governed by mass action kinetics as well, which is activated by LBPD and repressed by S1. Therefore the appropriate reaction rate for S2 production is assumed to be:

𝑣 = (𝑘 ∗ 𝐿𝐵𝑃𝐷)/(1+ 𝑘 ∗ 𝐿𝐵𝑃𝐷 + 𝑘! ∗ 𝑆! + 𝑘 ∗ 𝑘! ∗ 𝐿𝐵𝑃𝐷 ∗ 𝑆!) where k and k1 are set to a value of one to simplify the kinetics. The production of species P2 is slightly more complicated than S2 due to the additional repression by species S2. Therefore, the reaction rate for P2 production is presumed to follow mass-‐action kinetics by the following equation:

𝑣 = (𝑘 ∗ 𝐿𝐵𝑃𝐷)/(1+ 𝑘 ∗ 𝐿𝐵𝑃𝐷 + 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑆! + 𝑘 ∗ 𝑘! ∗ 𝐿𝐵𝑃𝐷 ∗ 𝑃! +𝑘 ∗ 𝑘! ∗ 𝐿𝐵𝑃𝐷 ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! + 𝑘 ∗ 𝑘! ∗ 𝑘! ∗ 𝐿𝐵𝑃𝐷 ∗ 𝑃! ∗ 𝑆!)

Again the kinetic constant k is assumed to be one, but the kinetic constant k1 is assumed to be greater to enable adequate repression of the production P2 with increased concentrations of P1. The constant k2 is assumed to be 0.1, which will enable repression of S2 by P2 at only significant levels of S2.

Memory Unit The kinetics of the regulated double negative feedback module (memory unit) are assumed to be mass action governed. The transduction of the signal from the incoherent feed forward modules to the regulated double negative feedback module needs to be quick and simple with high signal fidelity to accomplish the functionality of the double regulated negative feedback network. Simple linear mass action kinetics enables this functionality. These kinetics are expected to be (i.e. S2 to S3 and P2 to P3):

S3 production: 𝑣 = (𝑘! ∗ 𝑆!) P3 production: 𝑣 = (𝑘! ∗ 𝑃!)

where the kinetic coefficients ks and kp were set to values of 10 for quick reaction response. These secondary species (i.e. S3 and P3) will influence the tertiary components (i.e. S4 and P4) both as activators and repressors. These interactions are assumed to have mass action kinetics similar to those in the concentration detector. Each tertiary species will be activated by its secondary species and repressed by both the secondary and tertiary species of its compliment species (i.e. S4 is activated by S3 and repressed by P3 and P4 while P4 is activated by P3 and repressed by S3 and S4). These interactions are shown in the following equations:

S4 production: 𝑣 = (𝑘! ∗ 𝑆!)/(1+ 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! +𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! ∗ 𝑃!)

P4 production: 𝑣 = (𝑘! ∗ 𝑃!)/(1+ 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! +𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! ∗ 𝑆!)

where k1 represents the kinetic coefficient for activation and is assumed to be one. k2 and k3 represent the kinetic coefficients for repression and are assumed to be greater than k1 to allow repression of S4 and P4 production to be greater than activation of S4 and P4 production. The kinetic coefficients could be changed for the different species, but for simplification they are assumed to be the same values.

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Signal Amplifying Fluorescent Reporter The kinetics of the signal amplifying fluorescent reporter are similar to those of the memory unit because the positive autoregulation of the species S4 and P4 is assumed to be repressed by the secondary and tertiary species of the species compliment (i.e. the positive autoregulation of S4 was repressed by P3 and P4 while the positive autoregulation of P4 is expected to be repressed by the presence of species S3 and S4). Similar to the memory unit these reaction rates are assumed to follow mass-‐action kinetics and are simulated by the following equations:

S4 positive autoregulation: 𝑣 = (𝑘! ∗ 𝑆!)/(1+ 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! +𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑃! + 𝑘! ∗ 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑃! ∗ 𝑃!)

P4 positive autoregulation: 𝑣 = (𝑘! ∗ 𝑃!)/(1+ 𝑘! ∗ 𝑃! + 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! +𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑆! ∗ 𝑆! + 𝑘! ∗ 𝑘! ∗ 𝑘! ∗ 𝑃! ∗ 𝑆! ∗ 𝑆!)

where the kinetic coefficients for the different species could be represented by different values but are assumed to be constant for both species. The activation coefficient, k1, is set to a value of one, while the inhibition coefficients, k2 and k3, are set to a value of two to represent repression governing activation. In this particular case this was necessary because the positive autoregulation is expected to be suppressed by the presence of the compliment species. The production of the fluorescent species, RFP or GFP, are assumed to be linearly correlated with their respective tertiary species, S4 or P4, through mass action kinetics by the following equations:

RFP production: 𝑣 = (𝑘! ∗ 𝑆!) GFP production: 𝑣 = (𝑘! ∗ 𝑃!)

The kinetic coefficients for these reactions are assumed to be at unity so that the production of RFP or GFP does not dominate over the other given equal S2 and P2 concentrations. Degradation The majority of the species produced in this genetic circuit are assumed to have similar degradation rates. The degradation for all species is assumed to follow linear mass-‐action kinetics by the following equation:

Degradation rates: 𝑣 = (𝑘! ∗ 𝐴!)

where Ai represents all species in the genetic circuit (i.e. LBPD, S1 to S4, P1 to P4, RFP, and GFP). The kinetic degradation coefficient for all species besides S4, P4, RFP, and GFP are assumed to be a value of one. The degradation kinetic coefficient for these other species must be a value of 0.1 to allow for the signal to remain within the E. Coli for long periods of time (200+ seconds).

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Computer Simulation Test Implementation Complete Circuit Simulations Using the kinetic equations for the concentration detector, memory unit, and signal amplifying fluorescence unit as well as the kinetic equations for degradation, the bellow simulations were carried out. These simulations illustrate the projected characteristics of the proposed novel lead concentration detector genetic circuit engineered into E. coli. Given no initial lead concentration, the circuit does not turn on (Figure 5). At low levels of normalized initial lead concentration (0.5 units), the circuit activates, producing GFP as the reported molecule to signify safe initial concentrations of lead (Figure 6). At medium levels of normalized initial lead concentration (2 units) the circuit activates, producing RFP to signify dangerous levels of initial lead concentration (Figure 7). It can be seen from this graph that it takes longer than at lower levels of initial lead concentration to reach a steady state signaling molecule concentration, indicating that the initial normalized lead concentration is close to safe and unsafe levels of lead concentration. At high levels of normalized initial lead concentration (10 units), the circuit activates, producing RFP to signify dangerous levels of initial lead concentration (Figure 8). Figures 5 – 8 together illustrate the complete proposed dynamics of the lead concentration detector genetic circuit. The Jarnac script used to generate Figures 5 – 8 can be found in the Jarnac Script section of the Appendix.

Figure 5 – With no initial lead concentration (p.G), the lead Figure 6 – With a small amount of initial lead concentration (p.G), the lead concentration circuit does not activate. concentration circuit activates, with GFP dominated the output signal (p.GFPa).

Figure 7 – With elevated levels of initial lead concentration (p.G) Figure 8 – At high levels of initial lead concentration (p.G) the the lead concentration circuit fluoresces red (p.RFPa). lead concentration circuit fluoresces red (p.RFPa).

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Concentration Detector Module Simulations The concentration detector module makes up the decision making portion of the lead concentration detector genetic circuit. It can be seen from the first peak in Figure 9 that at low levels of normalized initial lead concentrations (0.5 units) production of P2 is higher than S2 (p.P2a and p.S2a respectively). The greater production of P2 translates to GFP production in the finalized circuit (Figure 6). At normalized initial lead concentrations of 2 units, production of P2 and S2 are very similar, with S2 just barely out producing P2 (second peak in Figure 9). This slightly greater production of P2 leads to RFP production from the circuit as a whole (Figure 7). At normalized initial lead concentrations of 10 units, signifying dangerous levels of initial lead concentration, S2 production largely out weighs P2 production (third peak in Figure 9), which leads to the quick reach of steady state production of RFP in the completed circuit (Figure 8). The equations used to simulate these proposed characteristics of the concentration detector module are those found in Internal Design Specifications section. The Jarnac scrip for these simulations can be found in the Jarnac Scrip section of the Appendix. Memory Unit Module Simulations The memory unit module acts as a temporary state chooser. When S3 dominates P3, the production of S4 occurs while no production of P4 is seen (first peak in Figure 10). The opposite is also true, if the concentration of P3 is greater than S3, P4 is produced while no S4 is produced (second peak in Figure 10). The equations used to simulate these proposed characteristics of the memory unit are those found in Internal Design Specifications section. The Jarnac scrip for these simulations can be found in the Jarnac Script section of the Appendix. Signal Amplifying Fluorescent Reporter Module Simulations The signal amplifying fluorescent reporter module causes the “decisions” that the memory unit module makes to become permanent. When a decision is made by the memory unit the corresponding output molecule S4 or P4 becomes constitutively produced from the autoregulation inherent within this module (Figure 4). It can be seen from Figure 11 that when P4 is produced, it autoregulates itself to saturation. The same is true for S4 and can be seen in Figure 12. This autoregulation is tied to fluorescence, causing saturated P4 concentrations to enable large amounts of GFP production as well as saturated S4 concentrations enables large amounts of RFP production. In this manner, the signal amplifying fluorescent reporter module acts as a final memory unit and reporter of the initial lead concentration. The equations used to simulate these proposed characteristics of the signal amplifying fluorescent

Figure 9 -‐ Concentration detector module simulations; the peaks correspond to low (0.5 u), medium (2 u,) and high (10 u) normalized initial concentrations of lead respectively.

Figure 10 – Memory unit simulations illustrating that when one initial substrate (p.S3 or p.P3) is greater than the other (p.S4a(green) peak corresponds to p.S3 > p.P3 and p.P4a(purple)) a spike in the corresponding reporter molecule occurs.

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reporter module are those found in Internal Design Specifications section. The Jarnac script for these simulations can be found in the Jarnac Script section of the Appendix.

Figure 11 – At elevated levels of P4 (p.P4a), it self regulates itself Figure 12 -‐ At elevated levels of S4 (p.S4a), it self regulates itself to saturation. to saturation. Implementation Details Some of the parts that could be used to build this lead concentration detector genetic circuit are: Name: BioBrick ID: Description: Length: *Cost: Genes: Lead Binding

Protein BBa_I721002 This gene expresses a protein that

forms a protein dimer with Pb2+. Useful in initiating transcription of initial substrates.

399 bp $199.50

Superfolder GFP (sfGFP)

BBa_I746916 This gene expresses sfGFP that acts as a reporter protein. Useful in reporting safe concentrations of aqueous lead.

720 bp $360.00

mCherry (RFP) BBa_K180008 This gene expresses a form of RFP that acts as a reporter protein. Useful in reporting dangerous concentrations of aqueous lead.

708 bp $356.00

Promoters Lead Binding Promoter

BBa_I721001 This coding sequence allows for the lead binding protein-‐dimer to bind to DNA and instigate transcription. Useful in initiating transcription of initial substrates.

94 bp $47.00

LacI Regulated Promoter

BBa_R0010 This promoter allows for transcription inhibition caused by LacI and CAP. Will be useful in negative feedback loops

200 bp $100.00

Terminators T1 from E. coli rrnB

BBa_B0010 This DNA sequence initiates transcription termination. Useful in stopping transcription at desired areas.

64 bp $32.00

*Cost was calculated based off of 50 cents per base pair **Total cost for all parts listed above: $1,094.50 ***Total length of proposed genetic circuit would be > 3000 bp †** All parts found within the Standard parts registry [3]

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Appendix Device Pricing in 2025 Employees: 12 people at $120,000/year Fixed Costs: Building, Electricity, Water, etc. = $1,000,000/year Estimated Market Size: 1000 units/year

12 𝑝𝑒𝑜𝑝𝑙𝑒 ∗ $120,000

𝑝𝑒𝑜𝑝𝑙𝑒 𝑎 𝑦𝑒𝑎𝑟 +$1,000,000

𝑦𝑒𝑎𝑟 =1,000 𝑢𝑛𝑖𝑡𝑠

𝑦𝑒𝑎𝑟 ∗ 𝑿𝑃𝑟𝑖𝑐𝑒𝑢𝑛𝑖𝑡

Thus total price per unit = $2,440

It can be seen from the above numbers that in order for the company to break even given the expenses and total units sold in the fiscal year of 2025, each unit would need to be sold at $2,440. Along with this, the actual production of the E. coli strain that harbors the lead concentration genetic circuit does not factor into the total company expenditures, meaning that as long as the price per unit can be maintained, the actual production costs of the E. coli strain are irrelevant in the year 2025. Design Specification Sheet Overview Final schematic of the lead concentration detector genetic circuit. Module A and B comprise the concentration detector module and are both incoherent feedforward networks, module C is the memory unit and is comprised of a regulated double negative feedback network, and modules D and E comprise the signal amplifying fluorescent reporter module and are both autoregulation networks.

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Bellow are the simulated responses of the lead concentration detector genetic circuit with 0.0 units, 0.5 units, 2 units, and 10 units of normalized initial lead concentration (from left to right) where production of GFP (p.GFPa) resembles safe concentrations of lead and production of RFP (p.RFPa) resembles unsafe initial lead concentrations.

Concentration Detector Bellow is the schematic diagram for the concentration detector module of the lead concentration detector genetic circuit. Modules A and B are incoherent feedfoward networks.

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Bellow are the simulated results of the concentration detector given 0.5 units, 2 units, and 10 units of normalized initial lead concentration (from left to right).

Memory Unit Bellow is the schematic of the memory unit for the lead concentration detector genetic circuit, which is a double regulated negative feedback network.

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Bellow are the simulated results of the memory unit given greater concentration of S3 or P3 (from left to right). At greater initial S3 concentrations than P3 concentrations, only S4 is produced (p.S4a) and at greater initial P3 concentrations than S3 concentrations, only P4 is produced (p.P4a).

Signal Amplifying Fluorescent Reporter Bellow is the schematic diagram for the signal amplifying fluorescent reporter module of the lead concentration detector genetic circuit. Once either P4 or S4 is produced, it up regulates itself, causing either GFP or RFP to be constitutively produced, respectively.

Bellow are the simulated response of the signal amplifying fluorescent reporter module for initial substrate P3 being in greater quantity (left graph) than S3, and S3 being in greater initial quantity than P3 (right graph). With either P3 or S3 being initially produced in greater quantity, P4 or S4 respectively will be autoregulated to a maximum sustained value as seen in the graphs bellow.

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Jarnac Script Overview (Complete System Simulation) p = defn cell $S1 -‐> S1a; Vm1*G/(Km1 + G); // productions of activated S1 given michaelis-‐menten kinetics // activation of S2 given michaelis-‐menten kinetics with substrate inhibition $S2 -‐> S2a; k*G/(1 + k*G + ks1*S1a + k*ks1*S1a*G); S1a -‐> $W; S1a*d; // degradation of activated S1 via mass action S2a -‐> $W; S2a*d; // degradation of activated S2 via mass action $P1 -‐> P1a; Vm2*G/(Km2 + G); // production of activated P1 given michaelis-‐menten kinetics // activation of S2 given michaelis-‐menten kinetics with substrate inhibition $P2 -‐> P2a; k*G/(1 + k*G + kp1*P1a + k*kp1*P1a*G + ksp*S2a + k*kp1*ksp*P1a*G*S2a + kp1*ksp*P1a*S2a + k*ksp*G*S2a); G -‐> $W; G*d; // degradation of initial substrate (lead binding protein) P1a -‐> $W; P1a*d; // degradation of activated P1 P2a -‐> $W; P2a*d; // degradation of activated P2 $S3-‐> S3a; kp*S2a; // production of activated S3 via mass action kinetics $P3 -‐> P3a; ks*P2a; // production of activated P3 via mass action kinetics // activation of S4 via michaelis-‐menten kinetics with substrate inhibition $S4 -‐> S4a; (k1*S3a)/(1+k1*S3a+k2*P3a+k3*P4a+k1*k2*S3a*P3a+k1*k3*S3a*P4a+ k2*k3*P3a*P4a+k1*k2*k3*S3a*P3a*P4a); // activation of P4 via michaelis-‐menten kinetics with substrate inhibition $P4 -‐> P4a; (k4*P3a)/(1+k4*P3a+k5*S3a+k6*S4a+k4*k5*P3a*S3a+k4*k6*P3a*S4a+ k5*k6*S3a*S4a+k4*k5*k6*P3a*S3a*S4a); S3a -‐> $w; d1*S3a; // degradation of activated S3 via mass action kinetics S4a -‐> $w; d2*S4a; // degradation of activated S4 via mass action kinetics P3a -‐> $w; d3*P3a; // degradation of activated P3 via mass action kinetics P4a -‐> $w; d4*P4a; // degradation of activated P4 via mass action kinetics // autoregulation production of activated S4 via michaelis-‐menten kinetics with substrate inhibition $S4 -‐> S4a; (k7*S4a)/(1+k7*S4a+k8*P3a+k9*P4a+k7*k8*S4a*P3a+k7*k9*S4a*P4a+ k8*k9*P3a*P4a+k7*k8*k9*S4a*P3a*P4a); // autoregulation production of activated P4 via michaelis-‐menten kinetics with substrate inhibition $P4 -‐> P4a; (k10*P4a)/(1+k10*P4a+k11*S3a+k12*S4a+k10*k11*P4a*S3a+k10*k12*P4a*S4a+ k11*k12*S3a*S4a+k10*k11*k12*P4a*S3a*S4a); $RFP-‐> RFPa; kr*S4a; // production of activated RFP via mass action kinetics $GFP -‐> GFPa; kg*P4a; // production of activated GFP via mass action kinetics S4a -‐> $w; d5*S4a; // additional degradation of activated S4 via mass action kinetics P4a -‐> $w; d6*P4a; // additional degradation of activated P4 via mass action kinetics RFPa -‐> $w; d7*RFPa; // degradation of activated RFP via mass action kinetics GFPa -‐> $w; d8*GFPa; // degradation of activated GFP via mass action kinetics end; // rate kinetics and initial conditions for the given model p.d = 0.1; p.Vm1 = 1; p.Km1 = 0.5; p.k = 1; p.ks1 = 1; p.Vm2 = 1; p.Km2 = 5; p.kp1 = 3; p.ksp = 0.1; p.ks = 10; p.kp = 10; p.k1 = 1; p.k2 = 2; p.k3 = 2; p.k4 = 1; p.k5 = 2; p.k6 = 2; p.d1 = 0.1; p.d2 = 0.1; p.d3 = 0.1; p.d4 = 0.1; p.kr = 1; p.kg = 1; p.k7 = 1; p.k8 = 2;

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p.k9 = 2; p.k10 = 1; p.k11 = 2; p.k12 = 2; p.d5 = 0.1; p.d6 = 0.1; p.d7 = 0.1; p.d8 = 0.1; h1 = 10; // modular time step interval // simulation of given model p.G = 0.5; // 0.5 units of normalized initial lead concentration m1 = p.sim.eval(0,h1,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); p.G = 0; m2 = p.sim.eval(h1,300,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); p.G = 2; // 2 units of normalized initial lead concentration m3 = p.sim.eval(200,200+h1,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); p.G = 0; m4 = p.sim.eval(200+h1,300,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); p.G = 10; // 10 units of normalized initial lead concentration m5 = p.sim.eval(300,300+h1,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); p.G = 0; m6 = p.sim.eval(300+h1,400,50,[<p.Time>,<p.G>,<p.RFPa>,<p.GFPa>]); // list augmentations m = augr(m1, m2); m = augr(m, m4); m = augr(m, m5); m = augr(m, m6); graph(m); //graphed simulated results Concentration Detector p = defn cell // low sensitivity incoherent feedforward network $S1 -‐> S1a; Vm1*G/(Km1 + G); // activation of S1 via michaelis-‐menten kinetics // activation of S2 via michaelis-‐menten kinetics with substrate inhibition $S2 -‐> S2a; k*G/(1 + k*G + ks1*S1a + k*ks1*S1a*G); S1a -‐> $W; S1a*d; // degradation of activated S1 via mass action kinetics S2a -‐> $W; S2a*d; // degradation of activated S2 via mass action kinetics // high sensitivity incoherent feedforward network $P1 -‐> P1a; Vm2*G/(Km2 + G); // activation of P1 via michaelis-‐menten kinetics // activation of P2 via michaelis-‐menten kinetics with substrate inhibition $P2 -‐> P2a; k*G/(1 + k*G + kp1*P1a + k*kp1*P1a*G + ksp*S2a + k*kp1*ksp*P1a*G*S2a + kp1*ksp*P1a*S2a + k*ksp*G*S2a); G -‐> $W; G*d; // degradation of initial lead concentration bound protein via mass action kinetics P1a -‐> $W; P1a*d; // degradation of activated P1 via mass action kinetics P2a -‐> $W; P2a*d; // degradation of activated P2 via mass action kinetics end; // rate kinetics and initial conditions for the given model p.d = 0.1; p.Vm1 = 1; p.Km1 = 0.5; p.k = 1; p.ks1 = 1; p.Vm2 = 1; p.Km2 = 5; p.kp1 = 3; p.ksp = 0.1; // modular time intervals for simulation h1 = 10; h2 = 10; h3 = 10; p.G = 0; // simulation of given model m1 = p.sim.eval(0, 100, 100, [<p.Time>, <p.S2a>, <p.P2a>]); p.G = 0.5; // 0.5 units of normalized initial lead concentration m2 = p.sim.eval(100, 100+h1, 100, [<p.Time>, <p.S2a>, <p.P2a>]);

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p.G = 0; m3 = p.sim.eval(100+h1, 200, 100, [<p.Time>, <p.S2a>, <p.P2a>]); p.G = 2; // 2 units of normalized initial lead concentration m4 = p.sim.eval(200, 200+h1, 100, [<p.Time>, <p.S2a>, <p.P2a>]); p.G = 0; m5 = p.sim.eval(200+h1, 300, 100, [<p.Time>, <p.S2a>, <p.P2a>]); p.G = 10; // 10 units of normalized initial lead concentration m6 = p.sim.eval(300, 300+h3, 100, [<p.Time>, <p.S2a>, <p.P2a>]); p.G = 0; m7 = p.sim.eval(300+h3, 400, 100, [<p.Time>, <p.S2a>, <p.P2a>]); // list augmentations m = augr(m1,m2); m = augr(m,m3); m = augr(m,m4); m = augr(m,m5); m = augr(m,m6); m = augr(m,m7); graph(m); // graphed simulated results Memory Unit p = defn cell $S3-‐> S3; kp*S3a; // production of additional S3 from activated S3 via mass action kinetics $P3 -‐> P3; ks*P3a; // production of additional P3 from activated P3 via mass action kinetics // activation of S4 via michaelis-‐menten kinetics with substrate inhibition $S4 -‐> S4a; (k1*S3a)/(1+k1*S3a+k2*P3a+k3*P4a+k1*k2*S3a*P3a+k1*k3*S3a*P4a+ k2*k3*P3a*P4a+k1*k2*k3*S3a*P3a*P4a); // activation of P4 via michaelis-‐menten kinetics with substrate inhibition $P4 -‐> P4a; (k4*P3a)/(1+k4*P3a+k5*S3a+k6*S4a+k4*k5*P3a*S3a+k4*k6*P3a*S4a+ k5*k6*S3a*S4a+k4*k5*k6*P3a*S3a*S4a); S3a -‐> $w; d1*S3a; //degradation of activated S3 via mass action kinetics S4a -‐> $w; d2*S4a; //degradation of activated S4 via mass action kinetics P3a -‐> $w; d3*P3a; //degradation of activated P3 via mass action kinetics P4a -‐> $w; d4*P4a; //degradation of activated P4 via mass action kinetics end; // rate kinetics and initial conditions for the given model p.ks = 10; p.kp = 10; p.k1 = 1; p.k2 = 2; p.k3 = 2; p.k4 = 1; p.k5 = 2; p.k6 = 2; p.d1 = 0.1; p.d2 = 0.1; p.d3 = 0.1; p.d4 = 0.1; p.S3 = 0; p.P3 = 0; // modular time intervals for simulation h1 = 10; h2 = 10; // simulation of given model m1 = p.sim.eval(0,100,50,[<p.Time>,<p.S3>,<p.P3>,<p.S4a>,<p.P4a>]); p.S3a = 2; // initial substrate of activated S3 fed into the memory unit m2 = p.sim.eval(100,100+h1,50,[<p.Time>,<p.S3>,<p.P3>,<p.S4a>,<p.P4a>]); p.S3a = 0; m3 = p.sim.eval(100+h1,200,50,[<p.Time>,<p.S3>,<p.P3>,<p.S4a>,<p.P4a>]); p.P3a = 2; // initial substrate fed of activated P3 into the memory unit m4 = p.sim.eval(200,200+h2,50,[<p.Time>,<p.S3>,<p.P3>,<p.S4a>,<p.P4a>]); p.P3a = 0; m5 = p.sim.eval(200+h2,300,50,[<p.Time>,<p.S3>,<p.P3>,<p.S4a>,<p.P4a>]); // list augmentations m = augr(m1, m2); m = augr(m, m3); m = augr(m, m4); m = augr(m, m5); graph(m); //graphed simulated results

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Signal Amplifying Fluorescent Reporter p = defn cell // activation of S4 via michaelis-‐menten kinetics with substrate inhibition $S4 -‐> S4a; (k7*S4a)/(1+k7*S4a+k8*P3a+k9*P4a+k7*k8*S4a*P3a+k7*k9*S4a*P4a+ k8*k9*P3a*P4a+k7*k8*k9*S4a*P3a*P4a); // activation of P4 via michaelis-‐menten kinetics with substrate inhibition $P4 -‐> P4a; (k10*P4a)/(1+k10*P4a+k11*S3a+k12*S4a+k10*k11*P4a*S3a+k10*k12*P4a*S4a+ k11*k12*S3a*S4a+k10*k11*k12*P4a*S3a*S4a); $RFP-‐> RFPa; kr*S4a; // activation of RFP via mass action kinetics $GFP -‐> GFPa; kg*P4a; // activation of GFP via mass action kinetics S4a -‐> $w; d5*S4a; // degradation of activated S4 via mass action kinetics P4a -‐> $w; d6*P4a; // degradation of activated P4 via mass action kinetics RFPa -‐> $w; d7*RFPa; // degradation of activated RFP via mass action kinetics GFPa -‐> $w; d8*GFPa; // degradation of activated GFP via mass action kinetics end; // rate kinetics and initial conditions for the given model p.kr = 1; p.kg = 1; p.k7 = 1; p.k8 = 2; p.k9 = 2; p.k10 = 1; p.k11 = 2; p.k12 = 2; p.d5 = 0.1; p.d6 = 0.1; p.d7 = 0.1; p.d8 = 0.1; p.P3a = 0; p.S3a = 0; p.S4a = 0; p.P4a = 0; // modular time intervals for simulation h1 = 10; h2 = 10; // simulation of given model m1 = p.sim.eval(0,10,50,[<p.Time>,<p.S4a>,<p.P4a>]); p.P4a = 0; m2 = p.sim.eval(10,10+h1,50,[<p.Time>,<p.S4a>,<p.P4a>]); m3 = p.sim.eval(10+h1,100,50,[<p.Time>,<p.S4a>,<p.P4a>]); m4 = p.sim.eval(100,100+h2,50,[<p.Time>,<p.S4a>,<p.P4a>]); m5 = p.sim.eval(100+h2,1000,50,[<p.Time>,<p.S4a>,<p.P4a>]); // list augmentations m = augr(m1, m2); m = augr(m, m3); m = augr(m, m4); m = augr(m, m5); graph(m); // graphing of simulated results References [1] G. E. Moore, “Cramming more components onto integrated circuits,” Electronics, vol. 38, no. 8, pp. 1-‐4,

April 1965. [2] US Department of Energy Genome (2011, Sept. 19). Human Genome Project [Online]. Available:

http://www.ornl.gov/sci/techresources/Human_Genome/home.shtml [3] Registry of Standard Biological Parts. Available: http://partsregistry.org/

novel in vivo concentration detector

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