Difference between revisions of "Team:TUDelft/DennisModel"

Overview

The aim of our modeling was to apply a control systems approach to achieve stability across bacterial species. We modeled the kinetics of a genetic implementation of an incoherent feedforward loop. An analytical steady-state solution of this system showed complete independence of plasmid copy number and transcriptional and translational variations. We verified this analytical solution by the implementation of a full Ordinary Differential Equation (ODE) model..

Variables most often considered in the design of genetic circuits are plasmid copy number and transcriptional and translational rates. These variables play a major role in the steady-state levels of gene expression. However, when transfering genetic circuits between organisms these variables change in unpredictable ways:

The core of our model - Incoherent feed forward loop

Our genetic circuit is a genetic implementation of an incoherent feedforward loop (iFFL). In an iFFL an input signal regulates both the activator and the repressor of the output of the system in the same way. An iFFL results in perfect adaptation to the input when the negative regulation is fully uncooperative (Segall-Shapiro, 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. The repression in our 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 (Segall-Shapiro, Sontag et al. 2018). The promoter driving the gene of interest has been engineered to contain a binding site of a TALE protein. When the TALE protein is bound to the promoter the expression of the gene of interest is repressed.

We have extensively modeled the functioning of the genetic implementation of this system. An analytical steady-state solution of the system showed that the steady-state expression level of a gene of interest is completely independent of plasmid copy number and can be independent transcriptional and translational rates when the right design choices are made. After further verification through the implementation of a full ODE model we designed experiments to test the independence on these variables. Key design choices were identified by modeling. These consist of:

The need for good insulation of the genes The promoter strength of the TALE protein and of the gene of interest need to maintain the same ratio. The ribosome binding site strength of the TALE protein and of the gene of interest need to maintain the same ratio.

More detail on how we modeled the output of our system and determined it is independent of copy number, transcriptional and translational variations, and how we came to these design choices can be found in the sections below.

• 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 stepwise 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