Team:WHU-China/Model

Modeling




Abstract



For the light system used in the irregular reinforcement, we have built up an overall mathematical model to validate our design. And in this page, we will show you how our light system works effectively and safely with the model series.





Safety




How did the model help us?



  • In the beginning, we planned to use blue light promoter to realize irregular reinforcement.Then it came to us that the light itself would be an important source of damage, so we decided to model the process of light aging to help demonstrate the issue.

  • From the model, we got the graph below. It shows the relationship between the critical duration of exposure (longest time that the silk can be exposed to the light without valid damage) and the wavelength of the light. Thus, we developed our design from blue light system to red one, since the whole process of irregular reinforcement costs more than 20 hours. And in the future, for an even safer reinforcement, we would apply a far-red light system.


Modeling result





How did we get the result?



  • Light aging model: (quoted from J. Krochman)




Edm: Effective radiant exposure (W m-2)


Eeλ: Spectral irradiance (W m-2)- Irradiance produced by optical radiation at a unit wavelength of a specific light wavelengthp>


S(λ)dm,rel: Relative spectral responsivity


Hdm: Effective radiant exposure (Wdmh m-2)


t: Time(h)


ts: Critical duration of exposure(h)


Hs,dm: Threshold effective radiant exposure(Wdmh m-2)


λ(nm): wavelength



The equations are designed for complicated lights such as natural light for they usually contain components with various wavelength. Yet, according to our hardware, we actually use a given homogeneous light, which can be viewed as the light with a single wavelength.



  • So, our model can be simplified to:




  • Parameters:








We can do more ！



  • In order to make our model accessible for more teams, a list of parameters for different materials is showed below. Any team that uses the light system may derive useful information from the model. It is expected that more parameters would be added to this list.




We also built programs with MATLAB to help our users better understand light aging in their situations. There are four variables when determining the critical duration of exposure: distance between the light and the sample, the power of the light, the wavelength of the light and the material of the sample. Users can keep one of those variables while settle down others, and our program would plot the function and thus offer a vivid demonstration of users’ own light aging issue.


Click the link here to download the MATLAB files. When using, one needs to open and run the IO.m file while not directly open the fig file. The work interface would be like these below.











Effectiveness



Since the concentration of activator OmpR is easily affected by osmotic pressure, it is noticed that there will be osmotic noise on the promoter OmpC, which can be activated by OmpR. In order to decrease the leakage, a no-gate has been applied. However, to what degree can the no-gate solve the problem is still unclear.


This year, we managed to interpret how the red-light system would be like under different osmotic working environment when not exposed to red light, which is not only essential for us to validate our design but also important for any team to understand the light system better.



Result



Through the analysis of a great number of situations, it can be believed that though the protein expression may be high at the beginning, the expression level would decrease as the culturing time grows longer. Proteins per cell would delay constantly and reach a quite low level after 24 hours, which can be accepted in our system and thus proves the effectiveness.


  • Protein expression-time& osmotic pressure






  • Protein expression-temperature & concentration of saline ions




How did we get the result?



Part 1 PompC Analysis



In this part, we properly combine the experiment result of the parts PompC, which is believed to be the main source of osmotic noise, with the population kinetics model of E.coli. The goal is to find out the relationship between the number of proteins produced by the two promoters per cell per unit time and the different osmotic pressures.


  • A short overview of the experiment:

  1. The gene circuit is designed as below




  2. Culture two kinds of transformed E.coli in the environment with high osmotic pressure, where the promoter would be repressed according to the previous information described in the Part:BBa_R0082, until OD600=1 (the concentration of the bacteria is about 1*10^9/ml)

  3. Transfer the bacteria to different work environment with various osmotic pressures. And dilute to decrease the concentration to 2*10^7, so the total number of the bacteria in the 5-milliliter-system is 1*10^8.

  4. Culture for 24h

  5. 5.Measure the fluorescence with microplate reader (100μL liquid in each sample tank) and derive a function named m(op) to manifest the relationship between the fluorescence and osmotic pressure.






  • Modelling-Population Dynamics

In this part, we did some reasonable but maybe rough assumptions:


  1. The population of E. coli conforms to the logistic equation.

  2. Every bacterium produces same amount of proteins at a constant rate within the culturing time.

  3. Saline ions in the culture media contribute to most of the osmotic pressure.




x: numbers of the E. coli in the culture system


y: protein produced in total (mol)


t(min): culturing time


α: protein produced per bacteria



Parameters:





From the experiment, we can get these solutions of equations


  1. (x0,y0,t0）=(1×108,0,0) mentioned in the experiment part before

  2. (y1,t1)=(1.25×10-10m(op),1440) (According to the standard curve made by us.)




Thus, the number of the GFP, or any other protein (the tetR which will be described below) if ignoring the difference of size, is:






Part 2 the Not-gate







[mRNA]: numbers per cell of the transcribed mRNA of the interest protein


[protein]: numbers per cell of the interest protein


t(min): culturing time


Parameters






Model-Oscillator




The Idea of Oscillator




Actually, in order to ensure that the concentration of the AMPs inside the bacteria would not too high, we had designed an oscillator to produce AMPs sustainably. In the previous version of project, considering adding bacteria to produce AMPs in-situ instead of adding AMPs directly as the current project design, we wanted to produce AMPs and secrete them periodically. Oscillator seems to be a proper way to solve the issue, and since there are only two components needed in our design, we proposed a new binary oscillator.







Validate the new oscillator



A mathematic model is applied to evaluate different gene circuits


Assumptions


1.The regulation is mostly done by transcription, thus the ODEs of transcription and translation can be simplified to one.


2.The result of the comparison is done based on the oscillator effects and the parameters required as they reach their best effect.


Parameters:


The parameters in the traditional oscillator and the new oscillator except n (Hill coefficient) was derived from Elowitz2000 – Repressilator https://wwwdev.ebi.ac.uk/biomodels/BIOMD0000000012





Result


It turns out that the oscillator we designed has poorer oscillating effects and require bigger n (about 100 which impossible to find in reality). Besides, through the collaboration with ZJU-China we agreed that the fate of the designed binary oscillator is steady-state. Furthermore, we also found out that directly adding is an easier controlled way to functionalize. Therefore, we finally decided to give up the oscillating design.