Difference between revisions of "Team:TUDelft/DennisModel"

Overview

With our modeling we aimed to apply a control systems approach to achieve stability across bacterial species. To make expression host-independent, we proposed to include an incoherent feedforward loop in our design. Our analytical steady-state solution of this loop showed that expression was completely independent of plasmid copy number and transcriptional and translational rates. We verified this analytical solution by the implementation of a full kinetic model.

The key variables 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 transferring genetic circuits between organisms, these variables change in unpredictable ways.

The core of our design - Incoherent feed forward loop

We implemented an incoherent feedforward loop (iFFL) in a genetic circuit. In an iFFL, the input signal regulates both the activator and the repressor of the output of the system in the same way. The iFFL results in perfect adaptation to the input when the negative regulation is fully uncooperative (Segall, 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. In our system, we use a transcription activator-like effector (TALE) protein as a repressor. TALE proteins recognize DNA by a simple DNA-binding mechanism (Doyle 2013) and have been shown to bind fully uncooperative (Segall, 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 strengths of the TALE protein and the gene of interest need to maintain the same ratio.
• The ribosome binding site strengths of the TALE protein and the gene of interest need to maintain the same ratio.

Further details on our modeling approach; how we determined model output is independent of copy number, transcriptional variation and translational variation; and how we came to the design choices listed above, 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. We will step-wise derive a steady-state solution from the system of equations and describe the properties of the system. In the other sections, we 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 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
  $c$	variable	Unitless	Copy number of plasmid

  
  

  Variable	Explanation
  $m_T$	concentration of TALE mRNA
  T	concentration of TALE
  $P_G$	Promoter GFP
  $P_G.T$	Promoter GFP with TALE bound
  $m_G$	concentration of mRNA GFP
  G	concentration of 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:
  
  $$G = \left(\frac{c}{c^n}\right) \left(\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m}\right)$$
  
  
  • Full derivation

  
  

  According to our analytical solution, the level of the protein of interest only dependents on copy number, and the ratios of transcription and translation rates of the genes in the circuit. In the next sections, we 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. The amount of gene copy number can change when transferred between organisms. There is thus a need for consistent expression at a wide range of copy numbers if the same genetic circuit is used in different organisms. The steady-state solution of our model tells us that when our repressor binding is fully uncooperative, n = 1, we have complete independence of copy number:

  
  $$G = \left(\frac{\color{red}c}{\color{red}c^\color{red}n}\right)_{\color{red}n\color{red}=\color{red}1} \left(\frac{a_Gb_Gy_T^ny_m^n}{a_Tb_Ty_Gy_m}\right)$$
  

  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, with GFP as the output. We cloned the system in backbones containing different origins of replication. As a control, we also cloned GFP without TALE 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). Thus, when using the same promoter in different organisms, you can get unpredictable behavior. The steady-state solution of our model tells us that the steady-state expression level of the gene of interest (GOI) is only dependent on the rate of transcription rates of the GOI and TALE.

  
  $$G = \left(\frac{c}{c^n}\right) \left(\frac{\color{red}a_\color{red}G \color{black} b_Gy_T^ny_m^n}{\color{red}a_\color{red}T \color{black} b_Ty_Gy_m}\right)$$
  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 the transcription rate of TALE and GFP.
  • Wetlab

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

• Translational variation

  Similarly, as in transcription, our model steady-state solution tells us that the steady-state expression level of the gene of interest (GOI) is only dependent on the rate of translation the GOI and TALE,

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

  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 the translation rate of TALE and GOI.

  

  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.

• Importance of insulation

  Previous model solutions so far we assumed the promoter of the GOI to be completely insulated from expression from the TALE protein. However, in reality when two transcription units are placed in series there is a leaky expression of the second gene. This is due to the efficiency of the terminator of the first gene (Cheng, Ying-Ja et al. 2018). The iFFL system originally developed by Segall-Shapiro et al, uses the ECK120029600 terminator for the TALE protein. This terminator has a reported efficiency of 1/612, meaning that for every 612 TALE proteins produced, 1 protein of the GOI is made (Cheng, Ying-Ja et al. 2018). We add this efficiency into our model and solve again for steady-state GOI expression levels and plot against the gene copy number.

  
  The model shows that the leaky expression negatively impacts the system's ability to adapt to gene copy number. We therefore designed our system to have the transcriptional unit of TALE in a different orientation than the transcriptional unit of the GOI.
  
  

  
  

References

1. Salis, H. M., et al. (2009). "Automated design of synthetic ribosome binding sites to control protein expression." Nature Biotechnology 27(10): 946-950.
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. Doyle, E. L. (2013). Computational and experimental analysis of TALeffector-DNA binding. Plant Pathology and Microbiology, Iowa State University. Dissertation.
4. Yang, S., et al. (2018). "Construction and Characterization of Broad-Spectrum Promoters for Synthetic Biology." ACS Synthetic Biology 7(1): 287-291.
5. Jain, A. and P. Srivastava (2013). "Broad host range plasmids." FEMS Microbiology Letters 348(2): 87-96.