Goal

In order to see if group would oscillate just like a single cell does.

Methods

1.Establish the grow to death program according to our hypothesis;
2.Investigate reasonable parameters set from previous researches;
3.Simulation

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

For convenience, we assume that all bacteria are in rapid growth. All bacteria would synthesize protein regardless of cell fission. 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. We were also interested in lifespan of bacteria. While in rapid grow, the average lifespan of a bacterium is 20 minutes. Without further information, we assumed that the lifespan of bacterium obey a gaussian distribution with μ= 20 min, σ= 1 min.
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.
Lastly, we assumed that when started simulation, all the cell are in the oscillation phase and remain exactly the same oscillation rhythm with each other.
Based on these information, we set several rules for our computer model:
(1)Each round of simulation represent 0.1min.
(2)The lifespan of cells $x\sim (20, 1^2).$
(3)When reached their lifespan, cells division. Division is completed immediately.
(4)The expression of AraC would not be affected by division, which means the phase of AraC does not change.
(5)Certain amount of cells, which is proportion to square of population, is 'sentenced' to dead in every round. They are picked randomly.
(6)AraC's concentration is proportion to plasmid copies.
(7)When cells are dividing, the plasmid copies would increase by y, and y~Pois(50), then split evenly into two filial cells.

Colon-Specific Drug Delivery System

To simulate real-life situation, we researched for how our genetic oscillator will enter our bodies. As propionate is absorbed in human colon, so the best way to delivery those genetic engineered bacteria into colon. However, considered the possible safety issued brought by bacteria, we sought to solve it by adopting Oral Colon-Specific Drug Delivery System (OCDDS). Such system encapsulate bacteria with semipermeable polymer membrane. Patient take such microencapsulation orally and it will stay in colon for certain days. Due to the semipermeable property, small molecules such as propionate will penetrate the membrane through pores while bacteria are too large to pass through. Bacteria simply stays in microencapsulation and eventually excreted from human body. Such system can prevent bacteria from directly contacting human body and enhance the security.
Modified microencapsulation can stay in colon for 70 days. Bacteria concentration in microencapsulation can reach 70 days and diameter of microencapsulation can reach 433 67μm. For convenience, we assumed that each monocolony originated from a single bacteria. Based on that, the numbers of bacteria are approximately 81713~208333. Since numbers of bacteria remain relatively constant within microencapsulation, the feasibility and stability of supposed therapy are guaranteed.