Difference between revisions of "Team:TUDelft/DennisModel"

Overview

Many variables play a role in the behavior of synthetic circuits. Most (if not all) of these variables dramatically change when transferring a circuit between organisms. However, standardization and predictability is the foundation of any engineering practice. The iGEM parts registry has provided the scientific community with a plethora of characterized BioBricks, yet, a significant portion of the registry is characterized in E. coli and only a few in B. subtilis and Yeast. In order to overcome the dependence on the biological context we modeled and applied a commonly used control system motif, an incoherent feed-forward loop. Through the modeling of this system, we show it achieves perfect adaptation to copy number and is robust to transcriptional and translational variations. Based on modeling we designed experiments to demonstrate these properties, both within E. coli and across different organisms. We believe our model facilitates standardization of BioBricks across bacterial species.

To achieve a system that works predictably across bacterial species we took into account the following variables: Promoters have different strengths in different organisms. Some promoters only work in a very narrow range of bacterial species. We, therefore, explored methods to overcome this variable by utilizing orthogonal transcription through the use of T7 RNA polymerase.

A ribosome binding site contains the Shine-Dalgarno sequence where the 16s rRNA of the Ribosome binds to. However, this sequence varies across species and often ribosome binding sites are extremely inefficient when applied in phylogenetically distant species. Our solution would thus require an approach independent of the efficiency of ribosomal binding sites.

Translation rates are dependent on both translation initiation and translation elongation. Translation elongation is largely dependent on codon usage (Frumkin, Lajoie et al. 2018). To achieve predictability across species this should thus be adressed. We developed a novel cross species codon harmonization tool that gives you a coding sequence with similar codon adaptation per organisms used.

Genetic engineering wouldn't be possible or significantly more difficult if we couldn't use plasmids. However, plasmids need an origin of replication. Although origins of replication have been heavily studied we still lack the ability to easily transfer plasmids between prokaryotes and often they behave unpredictably. We, therefore, wanted to utilize an orthogonal replication system which would function in any bacterial host. To complement this approach we developed a genetic circuit independent of copy number to minimize the unpredicitable nature when transfering between organisms.

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 respressor 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.

• The kinetics

  The kinetics

  In order to model our system we have to identify all interactions and subsequently define the rate equations. Figure 2 depicts a scheme of all interactions.

  

  
  

  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

  In the case of $n = 1$, this system is independent of copy number. However, maybe more notably the system also appears to be dependent only on the ratios of the remaining variables. The dependence on the ratio of these variables has not been previously explored. This dependency on the ratio of only a few variables will be further elaborated in the section "Sensitivity to different environments" (maybe put a link so someone automatically scrolls to this section?).

• Copy number independence

• Transcriptional variation

• Translational variation