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	Value	Unit	Explanation	Source
  $a_T$	1.03	(nM/min)	Transcription rate TALE	2018 iGEM Thessaloniki
  $y_m$	log(2)/5	(1/min)	degradation rate mRNA	Kushwaha and Salis 2015
  $b_T$	0.44	(1/min)	Translation rate TALE	2018 iGEM Thessaloniki.
  $y_T$	0.0347	(1/min)	Degradation rate TALE
  n	1	-	Cooperativity of binding	Segall-Shapiro, Sontag et al.
  $k_{on}$	9.85	(1/(nM*min))	Binding of TALE to promoter	2018 iGEM Thessaloniki.
  $k_{off}$	2.19	(1/(min))	Unbinding of TALE to promoter	2018 iGEM Thessaloniki.
  $a_{Gmax}$	3.78	(1/(nM*Min))	Maximum transcription of GFP	2018 iGEM Thessaloniki
  $a_{Gmin}$	0	(1/(nM*Min))	Maximum transcription of GFP	Segall-Shapiro, Sontag et al.
  $b_G$	3.65	(1/Min)	Translation rate GFP	2018 iGEM Thessaloniki
  $y_G$	0.0347	1/min	Degradation rate GFP

  
  

  Variable	Explanation
  $m_T$	mRNA TALE
  T	TALE
  $P_G$	Promoter GFP
  $P_G.T$	Promoter GFP with TALE bound
  $m_G$	mRNA GFP
  G	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
  
  Using these assumptions, we can derive a steady-state solution for this system analytically. This derivation 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

  
  

  According to our analytical solution our genetic circuit is only dependent on copy number, and the ratio of transcription and translation rates of the genes in the circuit. In the next sections we will use this steady-state solution to demonstrate how it can be used to transfer genetic circuits between organisms. Furthermore, since this steady-state solution is based on assumptions we solve the full system of ordinary differential equations in Matlab to validate our assumptions. In each segment a link to our corresponding wetlab page is given.

  
  
• 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, n = 1, we have complete independence of copy number:

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

  This formula is however based on a few assumptions. We, therefore, implemented the full system of ordinary differential equations to validate our assumptions.

  
  • Wetlab

    We tested the prediction of copy number independence by implementing the iFFL system where the output is GFP. We cloned the system in backbones containing different origins of replication. As a control we also cloned GFP without repression into different backbones with different origins of replication. More info can be found here.

• Transcriptional variation

  Every promoter might have a different strength when used in different organisms (Yang, Liu et al. 2018). This adds unpredictability to the gene expression levels of your genetic circuit when used in a different organism. Our model steady-state solution tells us that the steady-state expression levels of the gene of interest (GOI) is only dependent on the rate of transcription rates of the GOI and TALE.

  
  $$G = (\frac{c}{c^n}) (\frac{\color{red}a_\color{red}G \color{black} b_Gy_T^ny_m^n}{\color{red}a_\color{red}T \color{black} b_Ty_Gy_m})$$
  This formula is however based on a few assumptions. We, therefore, implemented the full system of ordinary differential equations to validate our assumptions. We vary both transcription parameters. We plot the resulting steady-state solutions as a function of these two variables, a line is plotted to indicate the steady-state solutions resulting from a constant ratio in transcription rates.
  • Wetlab

    We tested the prediction of transcription rate independence by implementing the iFFL system where the output is GFP. We made variations of the system where we change both promoters in the same way. As a control we also cloned GFP without repression into under control of these promoters. More info can be found here.

• Translational variation

  Ribosome binding sites contain the Shine-Dalgarno sequence where the 16s rRNA of the ribosome binds. However, this sequence varies across species and often ribosome binding sites are extremely inefficient when applied in phylogenetically distant species (Damilola Omotajo 2015). This adds unpredictability the gene expression levels of your genetic circuit when used in a different organism. Our model steady-state solution tells us that the steady-state expression levels of the gene of interest (GOI) is only dependent on the rate of translation rates of the GOI and TALE, similarly as in transcription.

  
  $$G = (\frac{c}{c^n}) (\frac{a_G \color{red}b_\color{red}Gy_T^ny_m^n}{a_T \color{red}b_\color{red}Ty_Gy_m})$$
  

  To validate our assumptions we implemented the full system of ordinary differential equations. We vary both translation parameters. We plot the resulting steady-state solutions as a function of these two variables, a line is plotted to indicate the steady-state solutions resulting from a constant ratio in translation rates.

  However, translation isn’t only dependent on initiation, translation elongation is dependent on codon usage. [text from Osman here]
  • Wetlab

    We tested the prediction of translational rate independence by implementing the iFFL system where the output is GFP. We made variations of the system where we change both ribosome binding sites in the same way. As a control we also cloned GFP without repression into under control of these ribosome binding sites. More info can be found here.

References

1. Frumkin, I., et al. (2018). "Codon usage of highly expressed genes affects proteome-wide translation efficiency." Proceedings of the National Academy of Sciences 115(21): E4940..
2. Segall-Shapiro, T. H., et al. (2018). "Engineered promoters enable constant gene expression at any copy number in bacteria." Nature Biotechnology 36: 352.
3. Wang, W. et al. Bacteriophage T7 transcription system: an enabling tool in synthetic biology. Biotechnol . Adv. 36, 2129–2137 (2018).