Team:HUST-China/Modelling/MCOS

We notice that a single oscillator cell would not excrete enough propionate to lower blood pressure - we need a group of them. Standing on the basis that a single cell would generate periodical signal, we wanted to know if a group of these cells would oscillate as well. So we built a computer model to simulate this situation.

Methods

1.Establish behaviors of cells according to life circle of E.coli;
2.Investigate reasonable parameters set from previous researches;
3.Examine simulation result and fitting it with our wet-lab result.

Results

Fig 1.Population of bacteria against time. Average = 105180, largest difference Δ = 5667

The population of bacteria is fluctuating within a small range (5667/105180 = 0.0539) and generally steady, showing that the logistic model is feasible and this model is successfully simulating the population within microencapsulation.

Fig 2.AraC concentration of simulated multi oscillating cells within microencapsulation from 100000 minutes to 100800 minutes since the simulation started.

The multi cells oscillation simulation suggests that even with that amount of cells, the oscillation will still exist just like a single one does. Such result is because of the synchronous of all cells' oscillations throughout the whole process.

Background

Life cycle of E.coli is approximately 60 minutes. They would take 40 minutes preparing for cell fission and during that time they will express proteins, which in our case is mRFP. Then they would start to divide themselves and cease to express protein in a 20 minutes interval. In terms of death of cells, according to logistic model of cell population, death rate is linear to population itself. Based on this, we set that a certain amount of cells, which is proportion to squares of population, would be killed due to limited food. Those cells are picked randomly.
In terms of population of cells, we take real-life situation in to consideration. For safety(hyperlink), we planned to wrap our engineered cells into microencapsulation. Such drug deliver system is called OCDDS. Modified microencapsulation can stay in colon for 70 days. Bacteria concentration in microencapsulation can reach $10^{10}cfu/mL$ and diameter of microencapsulation can reach 433 67μm. For convenience, we assumed that each monocolony originated from a single bacteria. Based on that, the number of bacteria are approximately 81713~208333. We set the population to 10000.
Moreover, we assumed that the quantity of AraC are linear with plasmid copies. Given a specific environment, the number of initial plasmid copies are a constant. The replication of plasmids can be thought to be completed instantly (within 0.05min). When cells started to divide, the plasmids are allocated into two filial cells evenly. During the lifespan of a single cell, the number of replicated plasmids obey Poisson distribution.

Assumption

(1)The expression interval of cells $x\sim (40, 2^2).$
(2) When cells exit expression interval, they start to divide and cease to express mRFP.
(3)The division interval of cells $x\sim (20, 1^2).$
(4)Certain amount of cells, which is proportion to square of population, is 'sentenced' to dead in every round. They are picked randomly.
(5)AraC's concentration is proportion to plasmid copies.
(6)When cells are dividing, the plasmid copies would increase by y, and y~Pois(50), then split evenly into two filial cells.
(7)All the cell generate the same AraC's curve, whose period is 44.8 minutes and is a numeric solve of DDEs mentioned in the last section. (8)AraC output of each cell are not synchronized in the beginning.