Difference between revisions of "Team:TUDelft/DennisModel"

Overview

The aim of our modeling was to apply a control systems approach to achieve predictability across bacterial species. In order to achieve predictability, we identified a number of parameters that need to be addressed. For each of these parameters, we demonstrate through modeling how our system can account for all of these variables which have guided lab experiments.


To achieve a system that works predictably across bacterial species we took into account the following variables:

The core of our model - Incoherent feed forward loop

In our system, we exploit a commonly applied control system motif known as an Incoherent Feed-Forward Loop (iFFL), in which an input signal regulates both the activator and the repressor of the output of the system. An iFFL results in perfect adaptation when the negative regulation is uncooperative (Sontag et al. (2018)).
The input in our case is the copy number of the DNA template and the output is the steady-state expression of a gene of interest. This control system is established through the expression of a Transcription activator-like effector (TALE) protein. TALE proteins recognize DNA by a simple DNA-binding mechanism and have been shown to bind fully uncooperative (source). The TALE protein has been engineered to bind to the promoter of a gene of interest and thus repress the expression of it.

We further analyzed this system through the use of modeling, which revealed that it's insensitive to many other variables as well, which hasn't been explored yet. Transferring genetic circuits between organisms yield large variation in most (if not all) of the parameters in the system, we exploited the robustness of this model to maintain predictability even when crossing species barriers.

• The kinetics

  The kinetics

  In this section we explain the kinetics of our system and derive a system of ordinary differential equations to describe the interactions within the genetic circuit. From this, we will step-wise derive a steady-state solution and describe the properties of the system. In the other sections, we will use these properties to describe how we can utilize them to transfer genetic circuits between prokaryotes.
  The following scheme depicts all interactions considered in our system:

  

  
  

  From these interactions we can derive the following system of ordinary differential equations:
  

  ${dm_T \over dt} = {c \cdot a_T - y_m \cdot m_T}$
  
  $\frac{dT}{dt} = b_T \cdot m_T - y_T \cdot T - n \cdot k_{on}\cdot T^n \cdot P_G + n \cdot k_{off} \cdot P_{G.T}$
  
  $\frac{dP_G}{dt} = k_{off} \cdot P_{G.T} - n \cdot k_{on} \cdot T^n \cdot P_G + n \cdot y_T \cdot P_{G.T}$
  
  $\frac{dP_{G.T}}{dt} = n \cdot k_{on} \cdot T^n \cdot P_G - k_{off} \cdot P_{G.T} - n \cdot y_T \cdot P_{G.T} $
  
  $\frac{dm_G}{dt} = a_{Gmax} \cdot P_G + a_{Gmin} \cdot P_{G.T} - y_m \cdot m_G $
  
  $\frac{dm_G}{dt} = b_G \cdot m_G - y_G \cdot G $
  
  

  Parameter	Explanation
  $a_T$	Transcription rate TALE
  c	copy number plasmid
  $y_m$	degradation rate mRNA
  $b_T$	Translation rate TALE
  $y_T$	Degradation rate TALE
  n	Cooperativity of binding
  $k_{on} /k_{off}$	(un)Binding of TALE to promoter
  $a_{Gmax}/a_{Gmin}$	Maximum and minimum transcription of GFP
  $b_G$	Translation rate GFP
  $y_G$	Degradation rate GFP

  Simplification of the system

  This system can be simplified by making a few assumptions:

  1. Amount of TALE protein is much larger than binding sites for TALE
  2. TALE binding and unbinding occurs much more rapidly than protein production and degradation
  3. There is negligable expression when the promoter is repressed

  
  This results in the following steady-state solution:
  
  $$G = (\frac{c}{c^n}) (\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m})$$
  
  

  • Full derivation

  Conclusion

  Our system yields a very simple dependency on only the transcription, translation and degradation rates for each gene involved in the genetic network. This allows us to design circuits where the output of our system is independent of these variables. We can use this to analyze how the system behaves when transferring between organisms.

• Copy number independence

  Copy number

  A big factor in every genetic circuit is the copy number of the DNA template. Broad host range plasmids are often used when using different hosts however, they do not guarantee the same copy number in every organism (Jain and Srivastava 2013). In some organisms, it is not common practice to use a plasmid but rather insert into the genome. The need for consistent expression at a wide range of copy number is thus a desirable feature of any synthetic circuit.
  Our model steady-state solution tells us that when our repressor binding is fully uncooperative we have complete independence of copy number:

  
  $$G = (\frac{c}{c^n}) (\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m})$$

  We, therefore, have simulated this system from a range of 1 to 600 (genome integration to high-copy number plasmid).

• Transcriptional variation

• Translational variation