# Model

## Overview

We modeled the viability of our system. The system receives input, processes the input and returns the output.

(1) Input is the heat from the body. So we checked if heat transfers well into the patch.

(2) Processing occurs by the system only responding to a temperature above 37.5 degrees Celcius. If it is above the threshold, it emits fluorescence. If not, it doesn't. We modeled two things. The system must exhibit proper behavior according to both temperature and time.

(3) Output is fluorescence. It must be activated and be visible.

## Input

Our system receives heat as an input. So we needed to check if the heat transfers well into our patch. Using the heat transfer equation below, we can depict a heat distribution diagram.

$${{\delta T} \over {\delta t}} = k \nabla ^2 T$$

Above is a heat distribution modeling result of a film of buffer (simplified version of our patch) that is on top of a substrate with a temperature 37.5 degrees Celsius (our threshold temperature) after 5 minutes. The other 3 boundaries are air which are 25 Celsius degrees - room temperature. Thermal diffusivities (mm^2/s) of solution in buffer, skin, air are different - 0.143, 0.15, 19 respectively. Initial temperature of the buffer was set as 25 degrees Celsius. After 5 minutes, results show that the bottom-most layer is very close to 37.5 degrees Celsius. Moreover, the system in our patch has an amplification effect. The heat sensitive RNAs at the bottom-most layer will respond to the substrate temperature and activate others that are located in the layers above, thereby amplifying the heat signal. Therefore, we concluded that the system can receive heat signals accurately.

If you’re not familiar with differential equation and programming or want to roughly model a heat transfer without proper parameters, you can easily adopt an application – transientConductionGUI – to Matlab [Link]. We didn’t use the application because we wanted to manipulate thermal diffusivities precisely. But the application must be worthy to some of the future iGEM teams because it is very easy to use.

## Processing

### [Abstract]

The patch we made detects fever of the person wearing the patch. 37.5 Celsius degree usually is the criteria used to determine fever. The RNA system in the patch ideally would emit fluorescence above 37.5 degrees Celsius and would not below 37.5 degrees Celsius. Furthermore, the fluorescence must be visible in time for the patch to be effective.

So, we did two characterizations – prediction of activation according to temperature and according to time. We made candidate sequences that may exhibit the desired behavior around 37.5 Celsius degrees and modeled their behaviors.

### [Introduction]

#### -Importance

What we made is a fluorescence activation system that is activated at 37.5 degrees Celsius. Inside the system, modified RNA parts are included and they are the main point of the system. We couldn’t reach our laboratory this year so we predicted the behaviors of the modified parts by modeling.

When we can approach our laboratory, then we can get our own data. The modeling – behaviors on temperature and time – will be used to verify whether we predicted the mechanism of our system well by comparing the modeling data to the future experimental data.

The results of ours not only predict the behaviors of our parts, but also are helpful to the future iGEM teams who will do modeling nucleic acids – RNA, DNA – hybridization on temperature.

#### -CHA system and its amplification

[Figure 1. CHA system mechanism]

CHA system operates as Figure 1 and can be described as Equations (1) ~ (3).

C+H1→C:H1 : Equation (1) Stage 1 of CHA system

C:H1+H2→H1:H2+C : Equation (2) Stage 2 of CHA system

H1:H2+Fluorophore→H1:H2:Fluorophore : Equation (3) Stage 3 of CHA system

In this system, there is an amplification effect. C binds to H1. Then, C:H1 complex binds to H2. During this process, C detaches and is available for binding to another H1. As a result, even if there is only a little amount of active C, a lot of H1 can bind to H2 due to its amplification effect. That the system has an amplification effect is explicitly stated in the reference paper. [1]

#### -Designed Parts

[Figure 2. Raw fluorescence rates of 3 systems - H1+H2, H1+H2+C, Broccoli - on temperature] [2]

CHA shows different fluorescence levels depending on temperature. In Figure 2, CHA system which is H1+H2+C in the graph emits fluorescence in temperatures over 22 degrees Celsius and does not when below 15 degrees. CHA system activity depends on temperature.

[Figure 3. Hairpin structures of conventional C sequence at 22 Celsius degrees modeled by mfold.]

Secondary structure of C changes according to temperature so as the fluorescence activation of the CHA system. H1 can bind to H2 only if C binds to it, H1-C complex then binds to H2. But if C forms a hairpin structure, C can’t bind to H1. Thus, the presence of a hairpin structure in C determines the activation of the system. Predicted hairpin structures (created by Mfold) of C at 22 Celsius degrees are shown in Figure 3. You can easily see that one forms a tightly bound hairpin while the other is loosely bound with a long tail which may easy to bind to the other RNAs.

Hairpin structure may denature in higher temperatures. Above a certain temperature, the hairpin structure of C denatures and is capable to bind to H1 and activate the system. Below that degree, CHA system isn’t activated. Thus, the hairpin structure of C determines whether H1 hybridizes with H2 and whether CHA system emits fluorescence.

We added new bases to C so that it would readily form hairpin structures. With the added bases, even at the same temperature, the amount of H1 which C binds to is changed. The newly added base pairs determine the threshold temperature of the system. If the elongated base pairs are manipulated well enough, the CHA system with modified C can be used as a thermal sensor.

#### -Original Parts and Newly Designed (Modified) Parts

 Original Sequences in the Reference Paper H1 GAGCGATACTGTTGGTAGATGTCGCCATGTCTTGCGACATCTACCAACAGCGAGACAACAGAGAGACGGTCGGGTCCACAGTTTCC H2 GGAAACTGTGTCGAGTAGAGTGTGGGCTCTCTGTTGTCTCGAGATGTCGCAAGACATGGCGACATCTACCAACAGCCATGTCTTG C GACATCTACCAACAGTATCGCTC Modified Sequences with 3 elongated base pairs C1 CTGGACATCTACCAACAGTATCGCTC C2 TGTGACATCTACCAACAGTATCGCTC C3 GTTGACATCTACCAACAGTATCGCTC Modified Sequences with 4 elongated base pairs C4 CTGTGACATCTACCAACAGTATCGCTC C5 TGTTGACATCTACCAACAGTATCGCTC C6 GTTGGACATCTACCAACAGTATCGCTC

Table 1. Conventional Sequences of CHA system and Newly Modified Sequences of C.

We added the new base pairs hoping them to the form a desired secondary structure. Accurately predicting the hairpin structures just with sequences is impossible. So, we decided to come up with a few options and test them. We just added nucleotides to the conventional C sequence which are complementary to a region within itself hoping that it would loop around and bind to itself. The predicted secondary structures according to Mfold shows that the new sequence does not form a structure that we expected, but further modeling shows that it is not a problem for the RNA to function properly.

#### -Time-scale prediction

Some people may not exhibit fever at the entrance, where body temperature monitoring usually occurs, but exhibit fever indoors. This has to be detected with our patch. If the patch takes too long to be activated, the patch will be useless. So, we modeled how long it takes for the patch to be activated and emit fluorescence.

#### -Temperature-scale prediction

Our system is a temperature detecting system so the fluorescence activation behavior on temperature must be predicted.

CHA system is composed of 3 stages. Stage 1, where C binds to H1, acts as a trigger in activating the CHA system. By predicting the modified C’s binding to H1 at each temperature, we can predict the activation of the modified CHA system at each temperature.

First, the behaviors of the original sequences H1, H2, C are well known and described in the reference paper. [3] Then, we suggest a prediction model of hybridization between H1 and C. We will compare the result of our model and the result of the experimental data from the paper. This comparison is used to predict the behavior of the modified sequences according to temperature.

### [Method]

#### -Rate determining step

A reaction rate is determined by the slowest sub-reaction rate. The sub-reaction is called ‘the rate determining step (RDS)’. But not every reaction has RDS. A single step of the reaction must be significantly slower than other steps to be a RDS.

We wanted to know when the system would make a visible fluorescence so we model fluorescence according to time. The CHA system is a complex system composed of 3 reactions. We added new base pairs to C, making the system more complex. It is impossible to accurately predict reaction rates of a complex system like this without experimental data. However, if we determine RDS of the system, then we can simplify the reaction that is manageable.

#### #Prediction of the behaviors on temperature

-Mfold : RNA hybridization

Mfold program is a tool for predicting behaviors of RNA including hybridization and secondary structure, mainly by using thermodynamic methods (the Gibbs free energy). That sophisticated RNA modeling program takes into account many parameters, (e.g. pH, temperature, and the local composition bias of RNA), that affect the RNA folding. We are going to use the hybridization prediction of mfold. (Mfold©: RNA modeling program, Ahmed Mansour Alzohairy, January 2010GERF Bulletin of Biosciences 1(1):1-6)

The limitation of this software is that it doesn’t provide a function of setting salt concentration when it comes to RNA hybridization.

### [Result]

#### #Prediction of the behaviors on time

[Figure 4. Fluorescence on time of CHA system with different concentrations of Target sequence and Broccoli] [4]

Figure 4 a) shows the results of CHA systems with different concentrations – 0, 2.5, 50nM – of C sequence and Broccoli plotted against time. This graph originally proves that small concentration of C is enough to amplify the CHA system since significant fluorescence is observed at 2.5nM, 50nM of C.

We will find out RDS of CHA system by analyzing Figure 4. The RDS will be used to predict the fluorescence according to time of our altered CHA system where modified Cs are contained.

To analyze how fast the reactions occur, we used the time constant concept. Time constant is used in electrical engineering as an indicator how fast the system reacts to external input. Time constant is the time it takes for the system to reach to 63% of final status. This is shown in Figure 4 b).

 System Name Time constant (min) Difference (%) [Target] = 0 35.2 47.8 [Target] = 2.5nM 26.9 13.0 [Target] = 50nM 25.9 8.70 Broccoli 23.8 Reference value

[Table 2. Time constants in Figure 4.]

Each system in Table 2 includes reaction steps as Table 3. Modified C is the system where our newly designed modified C is included in. H1, H2 in Broccoli system is Broc and Coli respectively. H1 and H2 have Broc and Coli at the end of their sequence so we include them in the same section.

 Number Reaction Folded C denatures C binds to H1 C:H1 binds to H2 H1:H2 binds to DFHBI-1T Time constant (min) 1 [Target] = 0 But this is a leakage 35.2 2 [Target] = 2.5nM 26.9 3 [Target] = 50nM 25.9 4 Broccoli 23.8 5 [Modified C] = 2.5nM unknown

: included in the reaction : not included in the reaction : noise

[Table 3. Reaction steps of Figure 4.]

In Table 3, Reaction number 2, 3, 4 has similar time constant from 23.8 min to 36.9 min. They have ‘H1:H2 binds to DFHBI-1T’ step in common. So we can conclude that the step is the RDS. If the steps before the RDS is slow enough, the time constant must be dramatically different.

Reaction number 1 also has ‘H1:H2 binds to DFHBI-1T’ step but it is a noise so it takes 35.2 which is far different from other reactions.

Our system where modified Cs are in also have the RDS. So we can conclude that the patch we made will have time constant about 25 min.

25 minutes is a proper time interval to distinguish people who have fever when they are using public places. So our patch might work well.

#### # Prediction of the behaviors on temperature

-H1 and H2 behavior prediction

[Figure 5. Molar concentration on temperature of each state where H1, H2 are in, modeled by Mfold]

(The Mfold modeling of a system containing 250nM of H1 and H2. Labels are as follows H1: unfolded H1, H2: unfolded H2, H1f: folded H1, H2f: folded H2, H1H1: H1-H1 complex, H2H2: H2-H2 complex, H1H2: H1-H2 complex.)

Figure 5 is a graph modeled by Mfold. At each temperature, the molar concentrations of folded, unfolded and duplex forms of H1, H2 are shown.

The modeling may differ from the real-world behavior since this modeling assumes an ideal condition where H1, H2 exist in a linear form at t=0. Because both exist in linear forms, they can hybridize and form H1-H2 complexes. This behavior is observed in our modeled results. In reality, H1, H2 would form secondary structures by its own so there would be no H1-H2 complexes at the beginning of the reaction. From this modeling, we understood that the affinity between H1 and H2 is very strong and that C:H1 complex would immediately binds to H2.

- Comparison of modeled data and experimental data

[Figure 6. H1 250nM, C 2.5nM, where H1C is the concentration of H1-C complex modeled by Mfold]

Although we couldn’t conduct experiments in our lab, we could still compare our results with already published results. Figure 6 is a graph predicting behaviors of C and H1 by Mfold. As temperature increases, the concentration of H1:C complex changes. We found two notable points in the results.

First, in Figure 2, which are the published results, fluorescence levels are high at 22 degrees Celsius but not at 15 degrees. This is consistent with our modeling result (Figure 6) since H1:C complex concentrations increases around 22 degrees.

Our explanation for the fluorescence increase at 22 degrees in the published results is that as temperature goes up, the hairpin structure of C denatures. The denatured, linearized C can activate a series of reactions of the CHA system to fluorescence. Since the affinity between H1 and H2 is very strong, as shown in Figure 5, so the transition from H1-C to H1-H2 is expected to be very rapid. So, we should focus on the H1-C forming step. Furthermore, formation of H1-C is important due to the amplification effect in CHA system where even a small fraction of H1-C complex activates the whole system.

From this, we can predict the required concentration of H1:C complex to activate the CHA system.

At 1.96226e-15M, the concentration at 15 degrees, the CHA system is not activated. At 3.87569e-13M, the concentration at 22 degrees, the CHA system is activated.

Therefore, in our following models, if H1:C complex concentration is larger than 3.87569e-13M, we assumed that the CHA system is activated.

-Modeling the modified sequences and prediction of the threshold temperature of the CHA fluorescence activation

 Modified Sequences with 3 elongated base pairs ad their behaviors Temperature (°C) Concentration (M) C1 50 3.6243e-13 51 4.03587e-13 Threshold Temperature (°C) 51 C2 33 3.45655e-13 34 4.61157e-13 Threshold Temperature (°C) 34 C3 39 3.07702e-13 40 3.94798e-13 Threshold Temperature (°C) 40 Modified Sequences with 4 elongated base pairs and their behaviors Temperature (°C) Concentration (M) C4 33 3.15525e-13 34 4.17362e-13 Threshold Temperature (°C) 34 C5 41 3.47076e-13 42 4.39994e-13 Threshold Temperature (°C) 42 C6 No concentration at any temperature is larger than 3.87569e-13 M

Table 4. Thermal behaviors of each modified C and its threshold temperature modeled by Mfold]

As In table 4, modeling results of each system containing different modified C are depicted as graphs by Mfold. For each graph, we identified the minimum temperature where the H1:C complex concentration is larger than our criteria - 3.87569e-13M. The minimum temperatures are assumed to be threshold temperatures that activate the CHA system.

The results are summarized in Table 5.

 Modified Sequences with elongated base pairs Threshold Temperature (°C) C1 CTGGACATCTACCAACAGTATCGCTC 51 C2 TGTGACATCTACCAACAGTATCGCTC 34 C3 GTTGACATCTACCAACAGTATCGCTC 40 C4 CTGTGACATCTACCAACAGTATCGCTC 34 C5 TGTTGACATCTACCAACAGTATCGCTC 42 C6 GTTGGACATCTACCAACAGTATCGCTC Not found

[Table 5. The threshold temperatures of modified Cs]

### [Conclusion]

We draw two meaningful results from our modeling. First, we predict our system to reach 63% of the maximum fluorescence in about 25minutes. Second, we plotted the behaviors of each newly designed C according to temperature.

If hybridization dynamics of RNA could be predicted by software, the kinetics of fluorescence of our system may have been more precise and accurate. There is a recently published paper about predicting hybridization kinetics of DNA from its sequence. [5] The abstract of the paper states there had been no research predicting DNA hybridization kinetics from sequence up till now. If there were other research articles that deals with predicting the hybridization kinetics of RNA, those articles must have been referenced. But since there were no articles referenced, we concluded that there is no precise tool that predicts the hybridization kinetics of RNA. So, we believe our simplified modeling done with the RDS concept is meaningful.

The data of the reference paper only contains results at few temperature points. Significant increase in activity is shown at 22 degrees. But concentration at 22 degrees must not be the minimum concentration which is sufficient to activate the system. If we had experimental data at other temperature points in between 15-22 degrees, we would have selected a better threshold concentration. So, the threshold temperature we used for modeling must be higher than reality. With at a lower threshold temperature, the minimum concentration required should be also be lower than 3.87569e-13 M. The modeling of ours had to compromise the lack of data availability and we are aware that our criterions may not be the best choice. However, the criteria chosen by modeling allowed us to design our wet lab protocols, and the predicted values will be useful in understanding the experimental data in the future.

Our modeling results may be helpful for future iGEM teams who are interested in thermal behaviors of RNA aptamers. Some simplification ideas included here may also be useful for them as well.

### #Reference

[1] Genetically Encoded Catalytic Hairpin Assembly for Sensitive RNA Imaging in Live Cells, Aruni P. K. K. Karunanayake Mudiyanselage et al., J. Am. Chem. Soc. 2018.

[2] Genetically Encoded Catalytic Hairpin Assembly for Sensitive RNA Imaging in Live Cells, Aruni P. K. K. Karunanayake Mudiyanselage et al., J. Am. Chem. Soc. 2018.

[3] Genetically Encoded Catalytic Hairpin Assembly for Sensitive RNA Imaging in Live Cells, Aruni P. K. K. Karunanayake Mudiyanselage et al., J. Am. Chem. Soc. 2018.

[4] Genetically Encoded Catalytic Hairpin Assembly for Sensitive RNA Imaging in Live Cells, Aruni P. K. K. Karunanayake Mudiyanselage et al., J. Am. Chem. Soc. 2018.

[5] Predicting DNA hybridization kinetics from sequence, Jinny X. Zhang et al., Nature Chemistry, 2017.

## Output

### #Introduction

First, we discuss how much Broc:Coli:DFHBI-1T complexes are needed for the fluorescence to be visible. Then, we infer how much H1:H2:DFHBI-1T complexes are needed using the ratio between Broc-coli system and CHA system.

### #How much molar concentration of Broc:Coli:DFHBI-1T complexes are needed to be visible.

A single quantum from Broc:Coli:DFHBI-1T complex can be described as below.

 Name Physical quantity Value Reference The wavelength of the quantum λ 507nm Plug-and-Play Fluorophores The energy of the quantum E $$3.91 \times 10^-19 J$$ $$E = {{hc} \over λ}$$ The power of the quantum W $$3.91 \times 10 ^-14 Watt$$ $$W= {E \over t}$$ Where t is assumed to be s referring to 2011 iGEM KAIST (http://2011.igem.org/Team:KAIST-Korea/Projects/report_4) The lumen of the quantum lumen $$1.19 \times 10^{-11} lm$$ $$lm = Watt \times conversion \textrm rate$$ The conversion rate at 507nm is 303.464. Watt to lumen conversion table (http://hyperphysics.phy-astr.gsu.edu/hbase/vision/efficacy.html) The lux of the quantum lux $$2.97 \times 10^{-12}$$ $$lux = {lm \over {r^2}}$$ where r is assumed to be 2m. 2m is the distance between the sticker and observer.

Table 6. Derivation a brightness of a single quantum from Broccoli.

“Brightness” is a quantity which is difficult to define. It is different from person to person, on the environment – background effect, and Conformity and Dark adaptation. We chose lux to quantify the brightness which is used to measure a luminous intensity. If the value of a light source is as much as 0.1lux, then the source is as bright as a full moon in the night. [1]

Table 7. the amounts of lux of various conditions.

So the single quantum from the Broc:Coli:DFHBI-1T complex has a brightness of $$2.97 \times 10^{-12} lux$$. Then, N of Broc:Coli:DFHBI-1T emits $$N \times {{0.94} \over {100}}$$. Because the quantum yield of the complex is 0.94%. [2] As a result, N of the complexes are as bright as $$N \times 2.79 \times 10^{-14} lux$$

$$N \times 2.79 \times 10^{-14} lux \ge 0.1 lux$$

In order to make brighter light than 0.1lux, the inequality above must be solved. N must be larger than $$3.58 \times 10^12 \times 5.96 \times 10^{-12} mol$$.

Figure 7. The patch 3D model

The volume of the patch is 1.26ml – 2cm radius, 0.1cm height cylinder. Now we can induce that the molar concentration of the Broc:Coli:DFHBI-1T is $$4.74 \times 10^{-9} M$$. If the patch has $$4.74 \times 10^{-9} M$$ of the complex, then the light from the patch must be as bright as a full moon.

The dissociation constant of the Broc:Coli;DFHBI-1T complex is 360 [5]. So an equation follows as below.

$$K_D={{Broc:Coli:DFHBI-1T}\over{[Broc:Coli][DFHBI-1T]}}=360$$

We are following the condition in the reference paper where [DFHBI-1T]=5uM. If the values are inserted, the [Broc:Coli] is calculated as below.

$${K_D} = { {Broc:Coli:DFHBI-1T} \over {[Broc:Coli][DFHBI-1T]} } = { {4.76 \times 10^{-9}} \over {[Broc:Coli] \times 5 \times 10^{-6}}} = 360$$

Then, $$[Broc:Coli]=2.64 \times 10^{-6} M$$. As a result, the initial [Broc:Coli] is $$2.64 \times 10^{-6}+4.76 \times 10^{-9}=2.65 \times 10^{-6} M$$. So we must put [Broc] and [Coli] $$2.65 \times 10^{-6} M$$ into the patch.

### #How much molar concentrations of H1, H2, C and Fluorophore are needed

Figure 8. Fluorescence at each Target condition. [3]

This is the graph about target concentrations and their fluorescence. The green bar is where Broc and Coli were 250nM. And other bars are the results when H1 and H2 are 250nM and the target sequence Cs are varying from 0nM to 250nM.

The system we built was designed to follow the behavior of the result when the target concentration is 2.5nM. Then the light of the system must be 0.65 times smaller than the Broccoli system. 0.65 is approximately the value of fluorescence at 2.5nM of target on the graph above. As a result, we need $$1 \over {0.65 \times 250nM}$$ molar concentration of H1, H2 and $$2.5 \times 10 ^{-9} \times {250 \times 10^{-9}}$$ times the concentration of C. The ratio $${2.5 \times 10}^{-9} \over {250 \times 10^{-9}}$$ is the ratio between C and H1 where the modeling was done.

The concentrations we need are below

 Name Molar concentration (M) H1 $$4.08 \times 10^{-06}$$ H2 $$4.08 \times 10^{-06}$$ Cs $$4.08 \times 10^{-09}$$ DFHBI-1T $$8.15 \times 10^{-05}$$

Table 8. Predicted molar concentration to make the patch visible.

### #Conclusion

The concentrations needed to make the patch visible is calculated as table 8. This is not a normal approach to find out the fluorescence rate. Usually, molar extinction coefficient and quantum yield are used to find out the rate [4]. But that method only produeces relative values. In order to find absolute values, we calculated the values taking a bottom-up approach.

### #Reference

[1] https://2019.igem.org/Team:KUAS_Korea/Model

[2] Broccoli: Rapid Selection of an RNA Mimic of Green Fluorescent, Filonov GS et al., J Am Chem Soc, 2014.

[3] Genetically Encoded Catalytic Hairpin Assembly for Sensitive RNA Imaging in Live Cells, Aruni P. K. K. Karunanayake Mudiyanselage et al., J. Am. Chem. Soc. 2018.