<figcaption>MATLAB SimBiology Model of the Promoter-Transcription Factor System, Based on Hill Kinetics</figcaption>
</figure>
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<p>All three of our genetic constructs are built using the same <spanid="highlight">heat-inducible TaHsp70d promoter which binds to the TaHsfA2b transcription factor</span>. During our literature review, we discovered the work of Reiger and colleagues<spanid="highlight"><sup>[2]</sup></span> who modeled the Hsp70 promoter and transcription factor activation pathway, providing us with most of the assumptions used in our own mathematical models. A visual from their paper summarizes the pathway efficiently and is presented below:</p>
<p>All three of our genetic constructs are built using the same <spanid="highlight">heat-inducible TaHsp70d promoter which binds to the TaHsfA2b transcription factor</span>. During our literature review, we discovered the work of Rieger and colleagues<spanid="highlight"><sup>[2]</sup></span> who modeled the Hsp70 promoter and transcription factor activation pathway, providing us with most of the assumptions used in our own mathematical models. A visual from their paper summarizes the pathway efficiently and is presented below:</p>
<figure>
<imgsrc="https://static.igem.wiki/teams/4296/wiki/drylab/image20.png"alt="Hsp70 Promoter and Transcription Factor Pathway"width="80%"style="border: none;">
<figcaption>Annotated steps of heat shock protein (HSP) expression and regulation. X:Y denotes X bound to Y. Solid lines indicate mass flow or chemical reactions, and dashed lines indicate regulatory interactions. Heat shock, or temperature (T), enters the model through switching the stress-dependent kinase (S) from its inactive to active form (S*) <spanid="highlight">(1)</span>. The stress kinase is inactivated by dephosphorylation back to its inactive form <spanid="highlight">(2)</span>. The transcription factor (HSF) binds to the promoter site (HSE) <spanid="highlight">(3)</span>, where it is bound by the active stress kinase <spanid="highlight">(4)</span> and is phosphorylated to its active form (P:HSF:HSE) <spanid="highlight">(5)</span>, that induces transcription <spanid="highlight">(6)</span> and translation <spanid="highlight">(7)</span>. HSP binds to the active form, repressing transcription <spanid="highlight">(8)</span>. The inactive form is subject to binding <spanid="highlight">(9)</span> dephosphorylation <spanid="highlight">(10)</span> by the inactivating phosphatase (I). HSP also binds HSF on the HSE, before it is phosphorylated <spanid="highlight">(11)</span>, or off the DNA HSP binds and sequesters HSF in solution (HSF:HSP) <spanid="highlight">(12, 13)</span>. The mRNA is assumed to be stabilized by S* <spanid="highlight">(14)</span>, but mRNA and HSP still turn over via first-order decay <spanid="highlight">(15, 16)</span>.</figcaption>
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<p>Using assumptions stated in the paper, we generated a system of <spanid="highlight">ODEs modelling the production of the promoter-transcription factor complex</span> as a function of transcription factor concentrations, in a typical Hill-Kinetics format. The assembly is a first-order process<spanid="highlight"><sup>[2]</sup></span>, yielding the following equation:</p>
<figcaption>[PTF] is the promoter-transcription factor complex concentration, C<sub>n</sub> is the plasmid copy number, K<sub>d</sub> is the dissociation constant, and [THA2] is the transcription factor concentration.</figcaption>
<p>In this equation, [SBP] technically only represents the free sedoheptulose 1,7 substrate in the system, but by using the Briggs-Haldane free ligand approximation, the [SBP] can be approximated as the total [SBP] present in the system, as long as the total enzyme concentration is well below the Michaelis-Menten constant. Simulating this model on SimBiology yielded the expression profile below:</p>
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<p><b><u>Modeling the ACCD-Ethylene Pathway:</u></b></p>
<p>Once again, we reuse the transcription factor (Hill Kinetics) portion of the derivation to generate the same equation for the promoter-transcription factor complex. Furthermore, since we continue to use the Briggs-Haldane derivation of Michaelis-Menten kinetics, we obtain the same expression for the V<sub>max</sub> of our new enzyme system, with different species:</p>
<p>Things change as we attempt to model the relationship with <spanid="highlight">ethylene (also named ethene)and its precursor, ACC</span>, in an attempt to link ethylene regulation to promoter activity. ACC participates in a Ping-Pong-Bi-Bi reaction with the ACC oxidase enzyme<spanid="highlight"><sup>[6]</sup></span> to produce ethylene according to the following reaction scheme:</p>
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<p>Modeling the reaction scheme above, we realize that this is a three substrate reaction, and hence will be a variation of the Michaelis-Menten kinetics used so far<spanid="highlight"><sup>[7]</sup></span>. Presented below is a variation of the Briggs-Haldane derivation with multi-substrate enzyme kinetics. It has been assumed that the ACC oxidase enzyme is plentiful, the substrates are non-inhibitory, initial reaction kinetics are being observed (no product buildup), and reactant concentrations are initially very high:</p>
<p>K<sub>L-asc</sub>, K<sub>ACC</sub>, K<sub>O<sub>2</sub></sub> are the second-order rate constants, or <spanid="highlight">specificity constants</span>. The apparent second-order rate constants of each of the competing substrates dictates the partitioning between competing reactions, and is the rationale behind the name specificity constant. ACCO is the initial ACC oxidase enzyme concentration. Lastly, K<sub>0</sub> is the first-order rate constant of the ACC oxidase enzyme, displaying zero-order kinetics at high substrate concentration. The first-order rate constant is a measure of the catalytic potential of the ACC oxidase enzyme, and is called the <spanid="highlight">catalytic constant</span>. K<sub>net</sub> refers to the combined rate constant in the event of all substrates binding together (traditionally written as K<sub>L-asc-ACC-O<sub>2</sub></sub>).</p>
<p>It must be noted that the reaction velocity V<sub>3</sub> in this reaction is not the maximum velocity from traditional Michaelis-Menten models, but rather called the <spanid="highlight">limiting rate of the reaction</span>.</p>
<p>The rationale behind the 0 subscript is similar to that in previous Michaelis-Menten models: the total enzyme concentration is typically considered the enzyme concentration when time t = 0 (ie. at the instant of mixing). In this time frame (initial phase of the reaction), it can be assumed that the product concentrations are not substantial, causing the product concentration terms from the above equation to disappear. This leads to the following simplified expression:</p>
<p>K<sub>net</sub> is a term accounting for the possibility of all three substrates successfully docking with the ACC oxidase enzyme at the same time. As the likelihood of this happening is negligible, this term too can be removed to simplify the equation. It is also convention to replace the other enzyme constants with their reciprocals with the same subscripts and superscripts - which are called <spanid="highlight">Dalziel Coefficients</span>. This leads to the following further simplified expression:</p>
<p>As MATLAB SimBiology did not have a pre-built multi-substrate kinetics function, it was manually encoded as an "Undefined reaction". Modeling this system in SimBiology yields the following expression profile:</p>
<figcaption>MultiSim Interactive Voltage Plot of Device Circuit Simulation</figcaption>
</figure>
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<p>The plot shows the voltage values of the circuit at the colour coded positions on the circuit schematic. The first 0.200s, the photodiode, we had not changed the current source value. This indicated no change in light emission. From 0.400s to 1s, we had increased the current to indicate/simulate a high degree of light energy being detected. From 100s to ~1.5s, we decreased the current to indicate the opposite, lowering light energy being detected. The <spanid="highlight">results of this testing demonstrate that our circuit works as intended</span>.</p>
<p>The plot shows the voltage values of the circuit at the colour coded positions on the circuit schematic. The first 0.200s, the photodiode, we had not changed the current source value. This indicated no change in light emission. From 0.400s to 1s, we had increased the current to indicate/simulate a high degree of light energy being detected. From 1s to ~1.5s, we decreased the current to indicate the opposite, lowering light energy being detected. The <spanid="highlight">results of this testing demonstrate that our circuit works as intended</span>.</p>
<p><b><u>Proof of Concept and Printed Circuit Boards:</u></b></p>
<br>
<p>Finally, after a <spanid="highlight">rigorous and in-depth design cycle</span>, we proceeded to build the proof of concept product using a <spanid="highlight">breadboard</span>. This would allow us to hot swap different parts as needed and adjust the circuit according to real-time feedback. In lieu of constructing the whole circuit, we found it <spanid="highlight">sufficient to prototype the amplification block of the circuit</span> since this would describe how the device would perform during the actual use case.</p>
<figcaption>Voltage response of the device to light perturbation over time. The first initial down trend was the measured voltage response to increasing the light intensity of an LED; after which, we completely turned off the LED to which the voltage flattened. Subsequently, we completely turned on the LED to full power and saw the voltage response go to a constant drop. Lastly, we slowly decreased the power and saw a final upward trend.</figcaption>
</figure>
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<p>After <spanid="highlight">validating and demonstrating a proof of concept for our device</span>, the last step in our design process was to <spanid="highlight">produce a production copy of our device on a printed circuit board (PCB)</span>. This would allow for high-throughput manufacturing as well as a more compact fit within the hardware chassis that we’ve also designed. Using KiCAD, we <spanid="highlight">generated the manufacturing gerber files</span>, the files necessary to print this circuit board, and have ordered it. Unfortunately, due to the current supply chain issue, we have not yet had the opportunity to test the PCB.</p>
<p><b><u>Physical Device:</u></b></p>
<p><u>A) Cardboard Prototype</u></p>
<p>To create a device with sufficient dimensions to house all the hardware, we set out to 3D print a hardware piece that would fulfill this goal. We began by fitting our circuit components in a simple cardboard model. This fitting is to <spanid="highlight">test how we wanted the device to assemble so cardboard was used as a very cheap, accessible, and simple prototyping build</span>. Any material can be used for this intermediary step. Two cardboard prototypes were made of 10 cm and 13 cm cubes. Smaller details such as ports were drawn in for positioning. As the circuit components fit snugly within the 10cm cube, the CAD design proceeded with those dimensions. This is to ensure that the final design is simple and portable for field use in the future. Our cardboard model allowed us to define the design specifications for our 3D printed model, therefore our next step of prototyping was to make the CAD design.</p>
<p>The device is designed in <spanid="highlight">two core parts: the bottom box that houses a majority of the circuitry and the lid that must have the LEDs positioned opposite of the photodiode</span>. The bottom box will consist of three pieces. The bottom piece houses the circuitry with brackets that support Arduino and breadboard placements. Arduino connections to a computer will go through the port at the base. The top piece will close off the bottom circuitry and hold the photodiode breadboard. A hole in the corner will allow for wiring to connect to the lid unlike the original concept that had wiring traverse the outside of the hinge. These two pieces will snugly fit together sandwiching the bottom part of the hinge. This separation is to ensure easier 3D printing of the device as <spanid="highlight">our 3D printing method is fused deposition modeling (FDM) with PLA filament</span>. The final part of the assembly is the lid that will house the LEDs through the small loop in the center. The top half of the hinge will be attached to the lid as one piece. These specifications, which were checked for size compatibility with our Arduino and breadboard parts, were designed with <ahref="https://www.autodesk.ca/en/products/fusion-360/overview"target="_blank">Autodesk 360 Fusion</a>. Drawings designed on CAD are commonplace for 3D printing with third-party providers.</p>
<p>Our parts were printed in PLA plastic with 0.2 mm resolution and 20% infill, and the Arduino and breadboard prototypes were fitted into the 3D printed device. The optical bandpass filter has not yet been delivered at this time of writing so the prototype seen here will have an additional 10x10 mm 525 nm FWHM 50 nm filter covering the photodiode on the breadboard.</p>
<p><spanid='highlight'>[1]</span> Ricardo Ramirez-Gonzalez, Philippa Borrill et al. <i>The transcriptional landscape of hexaploid wheat across tissues and cultivars</i> Science 2018: Vol. 361, Issue 6403, eaar6089. <ahref="doi:10.1126/science.aar6089"target="_blank">doi:10.1126/science.aar6089</a></p>
<p><spanid='highlight'>[2]</span> Rieger, T. R., Morimoto, R. I., & Hatzimanikatis, V. (2005). Mathematical modeling of the eukaryotic heat-shock response: dynamics of the hsp70 promoter. <i>Biophysical journal, 88(3), 1646–1658.</i><ahref="https://doi.org/10.1529/biophysj.104.055301"target="_blank">https://doi.org/10.1529/biophysj.104.055301</a></p>
<p><spanid='highlight'>[3]</span> Zhang, X. Y., Trame, M. N., Lesko, L. J., & Schmidt, S. (2015). Sobol Sensitivity Analysis: A Tool to Guide the Development and Evaluation of Systems Pharmacology Models. <i>CPT: pharmacometrics & systems pharmacology, 4(2), 69–79.</i><ahref="https://doi.org/10.1002/psp4.6"target="_blank">https://doi.org/10.1002/psp4.6</a></p>
<p><spanid='highlight'>[4]</span> Nath, A. Enzyme Kinetics & Simulations. <ahref="https://depts.washington.edu/wmatkins/kinetics/">https://depts.washington.edu/wmatkins/kinetics/</a></p>
<p><spanid='highlight'>[5]</span> Jablonsky, J., Bauwe, H. & Wolkenhauer, O. (2011). Modeling the Calvin-Benson cycle. <i>BMC Syst Biol 5, 185.</i><ahref="https://doi.org/10.1186/1752-0509-5-185"target="_blank">https://doi.org/10.1186/1752-0509-5-185</a></p>
<p><spanid='highlight'>[6]</span> Yang, S.F. & Hoffman, N.E. (1984). Ethylene biosynthesis and its regulation in higher plants. <i>Annual Review of Plant Physiology, 35, 155-189.</i><ahref="https://doi.org/10.1146/annurev.pp.35.060184.001103"target="_blank">https://doi.org/10.1146/annurev.pp.35.060184.001103</a></p>
<p><spanid='highlight'>[7]</span> "Symbolism and Terminology in Enzyme Kinetics - Recommendation 1981", School of Physical and Chemical Sciences, Queen Mary University of London</p>
<p><spanid='highlight'>[8]</span> Parthiban V, Gromiha MM and Schomburg D: CUPSAT: prediction of protein stability upon point mutations.</p>
<p><spanid='highlight'>[9]</span> Parthiban V, Gromiha MM, Hoppe C and Schomburg D: Structural Analysis and Prediction of Protein Mutant Stability using Distance and Torsion Potentials: Role of Secondary Structure and Solvent Accessibility.</p>
<p><spanid='highlight'>[10]</span> Parthiban V, Gromiha MM, Abhinandan M and Schomburg D: Computational modeling of protein mutant stability: analysis and optimization of statistical potentials and structural features reveal insights into prediction model development.</p>
<p><spanid='highlight'>[11]</span> S. Arnott, P.J. Campbell-Smith & R. Chandrasekaran. In Handbook of Biochemistry and Molecular Biology, 3rd ed. Nucleic Acids--Volume II, G.P. Fasman, Ed. Cleveland: CRC Press, (1976). pp. 411-422.</p>
<p><spanid='highlight'>[12]</span> Manna, R. (2019). Towards development of an integrated system for diagnosis of infectious diseases of the blood. <ahref="https://doi.org/10.13140/RG.2.2.34351.28325"target="_blank">https://doi.org/10.13140/RG.2.2.34351.28325</a></p>
