Model

Fire Retardancy Model

Purpose

Before we start our project, we decided to test our idea to add adhesion protein to fire retardant proteins with modelling. Thus, we here built a model to predict efficiency of protein-based fire retardants across time to serve the following two purpose:

Compare and contrast the fire-retardant efficiency of various proteins.
By comparing proteins with and without adhesion domain, we can predict whether adhesion domains (cellulose-binding domain, CBD; mussel foot protein 5, mfp5) can improve fire retardancy across time.

Assumptions

The experiment conditions are the same in all data used to build the model.
The fire retardancy decay across time is the same as the decay by washing the protein out.
The fire retardancy of the protein is linearly correlated with the nitrogen level of the protein.

Symbols

MEANING	SYMBOLS
relative fire retardancy	F
percentage of nitrogen	N
protein adhered	A
Fire retardant coefficients 1	α (alpha)
Fire retardant coefficients 2	β (beta)
Euler's number	e
Molar mass	M
time	t

Modeling Process

Our modeling involved a 3-steps prediction, which (1) find the best equation (model) to predict fire-retardancy decay across time (2) find the best Fire retardant coefficients for proteins with/without adhesion proteins (3) calculate fire-retardancy decay across time using corresponding modes.

To obtain the data for our model, we emailed two PIs from previous iGEM teams, namely the 2015 Imperial College team and 2019 Linkoping Sweden.

We first used the dataset from the 2019 Linkoping Sweden iGEM team (CBD-sfGFP Column Purification data) to test what equation should be used as the decay function of fire-retardancy across time. We fit various functions using their data, and we found that the exponential decay function has the highest correlation coefficient (R) (R=0.9864) among all equations (All equations fitted as shown in the table below).

Equation	Correlation coefficient (R)
Exponential	0.9864
Fourier	0.9805
2nd polynomial	0.9613
Power	0.9594
Linear	0.7701

Therefore, we here used the following exponential function for our modeling:

A = α × e^βt (1)

In order to compare proteins with and without adhesion proteins, we used the data from the 2015 Imperial College London iGEM team. We fit the data with an exponential decay equation to find out all the corresponding coefficients of protein with (CBDcipA-sfGFP) and without adhesion (sfGFP) domains across time. Here are the coefficients we found:

A_{with CBD} = 0.8292 × e^-0.03092t (2)
A_{without CBD} = 0.9891 × e^-0.7413t (3)

To calculate the relative fire retardancy (F), we multiply the protein adhered (A) with the percentage of nitrogen (N), which is defined as:

N = M_{nitrogen in the protein}/ M_protein (4)

Therefore, the relative fire retardancy (F) would be:

F = N × A (5)

F=(M_{nitrogen in the protein}/ M_protein) x alpha × e^(beta×t) (6)

We then used the exponential function (equation 2 and 3) to predict the decay of 3 different proteins with and without adhesion domain across time, as shown by the figures below:

Figure 1. Figure illustrating fire retardancy of protein Uncharacterized histidine-rich protein (UniProt: Q8MP30) with and without adhesion domain.
(This protein was not used in the end because the DNA cannot be synthesized.)

Figure 2. Figure illustrating fire retardancy of alpha-casein with and without adhesion domain.

Figure 3. Figure illustrating fire retardancy of SR protein with and without adhesion domain.

As shown by the modeling results above, when assuming a linear relationship between fire retardancy and protein nitrogen level, the choices of fire retardant protein would not be a huge concern for the fire retardancy. On the other hand, a protein with the adhesion domain provides a stable fire retardancy across time. We, therefore, believe that the genetic fusion of fire retardant protein and adhesion domain would generate more stable fire retardant proteins.

Conclusion