Team:Manchester/Model
Overview
Computationally modelling a design can largely improve the efficiency of the design iteration cycles. As the disruption of the pandemic continues, we were unable to gain lab access to physically prototype our design. To overcome this limitation, we have modelled the key components of our design, such as the Dispersin B (DspB) production and the functional property of our hydrogel design . The results allowed us to not only predict the functions of our product, but also re-iterate over our design for better performance and highlight the directions of future developments.
Dispersin B
Firstly, our engineered bacteria is designed to detect the presence of pathogenic bacteria, through quorum sensing signals and respond by secreting DspB protein to degrade biofilms ( visit our design page for more info ). This process was modelled using a system of ordinary differential equations (ODEs) that encapsulated the autoinducer-2 (AI-2)/Lsp - Operon quorum sensing mechanism. (Bentley and Hooshangi, 2011.) We assumed that the concentration of our engineered bacteria remained the same throughout the model, the diffusion of dispersin B throughout the hydrogel was not rate limiting (an assumption gained from our hydrogel modelling) and finally that the Lsr operon (LsrABCD) production rate was equal to the production rate of our engineered Lsr-DspB mechanism. By applying the ensemble modelling approach to this system of ODEs, we were able to identify the working conditions of our product, and mitigating the problems derived from the limited access to the wet lab
For detailed documentation regarding DspB model please visit here.
Hydrogel
We have chosen to deliver our bacteria in a hydrogel matrix that is coated onto the catheter. The material is selected to be a mix of sodium carboxymethyl cellulose (NaCMC) and hydroxypropyl methyl cellulose (HPMC), as it provides high biocompatibility and potential scalability. The details of hydrogel design can be found here.
To ensure our hydrogel design is suitable for the product delivery, we need to model the diffusivity of the DspB protein in the hydrogel matrix. The diffusivity needs to be sufficiently large to allow rapid diffusion of Dispersin B once secreted. We have adopted a "multiscale diffusion model" (Axpe, et Al., 2019) that relates the mesh size of the hydrogel network to the relative diffusivity of the molecule. By adopting this model, we have assumed the diffusing molecules to behave as rigid spheres. Since there were no reported values on the mesh size of hydrogel formulation similar to our design, we have used additional models to predict this parameter. In these models, we have assumed our polymer chains to be unperturbed and charge neutral in the urethra.
We have used an innovative ensemble modelling approach to calculate the distribution of the relative diffusivity for our hydrogel. Our initial design resulted in a mesh size of about 3.3nm and the average relative diffusivity of 0.011. The ensemble modelling approach shone light on this overlooked flaw in the initial hydrogel design, as the inadequate diffusivity of Dispersin B was caused by the restricting mesh size in the hydrogel. We have improved our hydrogel design using this insight , as the changed the crosslinker concentration to increase the mesh size. The updated hydrogel design was then modelled and the results demonstrated sufficient diffusivity in the hydrogel. The predicted average mesh size and relative diffusivity of our final design was 18.7nm and 0.66 respectively. The ensemble model approach thus not only facilitated the design iteration cycle, but also emphasised the significance of parameter uncertainty analysis. This systemic, “bottom-up” approach to quantitatively analyse the functional property of hydrogel material can be easily adopted to other hydrogel systems by changing the key parameter values.
The details of our models and assumptions can be found on our hydrogel page.
Urease inhibitor
We have performed molecular docking between different ligands and the urease of Helicobacter pylori and Klebsiella aerogenes in order to find a potential urease inhibitor that could be both secreted by our chassis and safe for therapeutic use. We used the AutoDock Vina tool to search for a ligand with a good affinity and finally settled on quercetin and structural derivatives Quercetin 3,4'-diglucoside and Quercetin 7-O-glucoside.
Kill Switch
In addition to the DspB and hydrogel models, we have proposed a system of differential equations that describe the function of our kill switch design. Due to lack of lab access, we were not able to determine the rate constants such as the expression levels of MazE and MazF. We hope these equations can lay the groundwork for future teams.
$$ \frac{d\left[MazF\right]}{dt}\ =\ k_{toxin}\ -\ k_{neut}\left[MazE\right]\ -\ k_{deg}\left[MazF\right] $$ $$ \frac{d\left[N-Term\right]}{dt\ }\ =\ \frac{k_{1}}{1+\exp\left(-\left(\left[Urea\right]-C_{1}\right)\right)}-\ k_{deg}\left[N-Term\right] $$ $$\frac{d\left[C-Term\right]}{dt\ }\ =\ \frac{k_{2}}{1+\exp\left(-\left(\left[Sar\right]-C_{2}\right)\right)}-\ k_{deg}\left[C-Term\right] $$ $$\left[MazE\right]\ \ =\ \min\left(\left[N-Term\right],\left[C-Term\right]\right) $$
Parameters:
- Ktoxin: production rate of toxin MazF
- Kneut: neutralisation rate between MazE and MazF
- K1: expression level of pUreD
- K2: expression level of pGlyA
- C1: threshold concentration for urea
- C2: threshold concentration for sarcosine
- Kdeg: protein degradation rate
Assumptions:
- The production rate of toxin (MazF) is not affected by the concentration of antitoxin
- MazE is only expressed when both N and C terminals are produced
- All proteins have same degradation rate in this system
To find out more about kill switch please visit our safety page.
References
Axpe, E., Chan, D., Offeddu, G. S., Chang, Y., Merida, D., Hernandez, H. L., & Appel, E. A. (2019). A Multiscale Model for Solute Diffusion in Hydrogels. Macromolecules, 52(18), 6889–6897. https://doi.org/10.1021/acs.macromol.9b00753
Hooshangi, S., & Bentley, W. E. (2011). LsrR quorum sensing "switch" is revealed by a bottom-up approach. PLoS computational biology, 7(9), e1002172. https://doi.org/10.1371/journal.pcbi.1002172