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 included an incoherent feedforward loop (iFFL) in our design. Our analytical steady-state solution of this loop showed that expression was completely independent of plasmid copy number and transcriptional-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-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-Shapiro, 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 to plasmid copy number and can be independent from transcriptional and translational rates when the right design choices are made. After further verification through the implementation of a full ordinary differential equation (ODE) model, we designed experiments to test the independence to 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, can be found in the sections below.

The kinetics

In this section, we explain the kinetics of our iFFL and derive a system of ordinary differential equations to describe the interactions within the genetic circuit. We 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 the steady-state solution and ODE model to describe how our circuit can be used to transfer genetic circuits between prokaryotes. The following scheme depicts all interactions considered in our system.

• To find out more about the kinetics

  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 (Segall-Shapiro, et al. 2018):

  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. When the promoter is repressed the expression level is negligable.
  
  Using these assumptions, we can derive analytically a steady-state solution for this system. 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 is 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 wet lab page is given.

  
  

Copy number

The expression levels in a genetic circuit is strongly correlated to the copy number of the DNA template Segall-Shapiro et al.. 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.

The model without assumptions has the same expression level independent of plasmid copy number (figure 1).

Wet lab

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 into the same backbones to demonstrate different levels of expression. More info can be found here.

Transcriptional variations

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.

$$G = \left(\frac{c}{c^n}\right) \left(\frac{\color{red}a_\color{red}G \color{black} b_Gy_T^ny_m^n}{\color{red}a_\color{red}T \color{black} b_Ty_Gy_m}\right)$$
The 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.

The full kinetic model shows that the expression level of GFP is the same when the transcription rate of TALE and of GFP remain constant (figure 5). In order to achieve constant ratio of transcription rates in our genetic circuit we use the T7 orthogonal transcription system which is transcribed by its own RNA polymerase. We implemented T7 promoters with varying strengths compared to the wild-type, developed by Ryo Komura, et al. (2018). More information can be found here (link to design page).

Wet lab

We demonstrated the prediction of transcription rate independence when the same ratio in transcription rate of both genes is maintained.

[graph]
We made variations of the system where we changed both promoters in the same way. As a control, we also cloned GFP without repression under the control of these same promoters.

We also tested the functioning of the system when different IPTG induction is used. Again, as a control, we also cloned GFP without repression under the control of these same promoters.

[graph]
More info can be found here [link to result page].

Translational variations

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,

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

We plot the resulting steady-state solutions as a function of the translation rate of TALE and GOI using the full kinetic model to validate the assumptions.

The full kinetic model maintains the same level of GFP expression when the translation rates for both genes remain in a constant ratio. To keep the same ratio in translation rates across organisms we used the same ribosome binding site (RBS) for both genes. Using the same RBS ensures that translation initiation for both genes change in a similar manner (Salis, H. M., et al. 2009), more on the design choices can be found here (link to design page).

Wet lab

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.

However, translation isn’t only dependent on initiation, translation elongation is dependent on codon usage.

[text from Osman here]

Importance of insulation

In our 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 incorporate this efficiency into our model and solve again for steady-state GOI expression levels to see the effect of terminator efficiency on copy number independence.

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.