Team:Northwestern/Model
Model objectives
By modeling Cas9 translocation across the different bacterial compartments, this kinetic model aims to estimate the quantity of Cas9 exported to the periplasm, and ultimately Outer Membrane Vesicles, as a function of time. This mathematical model could provide answers to the following questions:
• What should the rate of Cas9 production be to package a certain protein “dose” in each OMV?
• How do the levels of inducer present affect the amount of Cas9 packaged as a function of time?
• What is the optimal time to isolate vesicles to attain a certain protein concentration?
• How many OMVs should be administered in total to achieve the effective dose if OMVs were to be given as a therapeutic?
• What fraction of the vesicles is occupied by protein?
Assumptions
• All processes are reversible with two exceptions: protein movement from the cytoplasm to the periplasm and protein export in OMVs
• The protein is homogenously distributed in the cell’s periplasm once released from Tat machinery
• The inducer remains abundant; this model does not consider inducer depletion
• TatA assemblies are pre-formed from TatA proteins and TatBC is present in the cell from t = 0
• OMVs are spherical in shape and their size is independent on a bacterium’s life-cycle
• The volume of the periplasm does not change as OMVs pinch off
• Vesicle production rate remains constant
• Protein is bound to a Tat signal peptide (TorA, YcbK etc)
Model breakdown
Step 1: DNA Transcription (and mRNA degradation)
Step 2: mRNA translation (and Cas9 degradation)
Step 3: TatBC complex binds the signal peptide of the protein in an energy-independent step. The RR consensus motif in the signal peptide is specifically recognized by a site in TatC.
Step 4: TatA protomers are recruited to the TatBC complex and polymerized. Passenger domain of the substrate protein crosses the membrane via the polymerized Tat component. Then, the signal peptide is proteolytically removed by a signal peptidase at the periplasmic face of the membrane and Tat dissociates from TatBC and depolymerizes back to free protomers.
Step 5: Cas9 is exported in outer membrane vesicles.
Mathematical representation
The processes outlined above were expressed as a set of 9 differential equations.
Model parameters
Parameters were selected from reported literature values. In combination, they provided outcomes for Cas9 export that match the expected time scale.
Simulation results
First, protein production under a constitutive promoter was considered for a range of protein and mRNA degradation rates. Initially, export was ignored.
Sensitivity analysis
Sensitivity analysis was carried out to investigate the influence of the chosen parameters on the state variables. Since the main objective of this model is to approximate the number of molecules of Cas9 incorporated in each OMV as a function of time, we focused our analysis on predicted trajectories for the incorporation of Cas9 in each vesicle.
By performing sensitivity analysis on the modeled system, we have identified key parameters that could have the biggest effect on this delivery system.
Combination analysis
Conclusions
what do these results mean and how do they affect/could they impact our project.
