Team:KUAS Korea/Model
Model |
Mathematical model
Because we have to know about the relation of microbial growth rates in an aqueous environment with the concentration of a limiting nutrient, we used monod equation for design cheater and cooperators mathematical model. In our case, limiting nutrient will be cellobiose. Also, in our experiment we have to find out the quantificated information of the dependence of the growth rate on substance. Finally, we can compare the growth rates of two E.coli strains.
[Fig 1] Monod Equation
This is basic monod Equation. S is glucose released from cellobiose by cooperators. S can be derived from multiplication of q, p, x. q refers the glucose released from cellobiose by cooperators, p is the number of total cell density, and x is the frequency of the cooperator
[Fig 2] Cooperator Equation
[Fig 3] Cheater Equation
Then, we modified monod equation for Cooperator and Cheater. _š_0_ is specific growth rate without glucose and c is the cost of the cooperation. Cost of the cooperation will decrease the growth rate of the cooperator. And šæ is an advantage of cooperation. The cheater will not get the benefit of the cooperation. So we should minus from the cheaterās growth rate. And, we think that disadvantage comes from the glucose capture efficiency. Cheater could not catch efficiently like cooperator. So we give disadvantage to cheater by multiplying (1 ā š) .
[Fig 4] relative fitness
And we divided _š_š_ by _š_š·_ to express the relative fitness of cooperator.
Glucose Capture Efficiency
-
1. Calculation of the flux of glucose into a cooperator cell
ā¢ Measurement of displayed Ī²-glucosidase per cell using whole-cell activity
- Ā Vmax = 2.49 x 107 glucoseĀ·s-1 per cell
- Ā The specific growth rate = 0.61 h-1 in 0.004% (w/v) glucose (5.16 x 105 cellsĀ·Ī¼L-1)
- Ā Glucose creation rate = 2.40 x 107 glucoseĀ·s-1 per cell
- Ā Glucose consumption = 2.59 x 108 glucose per cell
ā¢ The resulting flux of glucose into a single cell
= the growth rate x the number of glucose molecules per cell = 4.39 x 104 glucose Ā·s-1 per cell
[Fig 5] glucose capture efficiency
And we esitmated the efficency of glucose capture with dividing glucose flux by glucose creation rate. We assumed that the glucose molecules produced by Ī²-glucosidase directly diffuse into media because it is located in the outer membrane of E.coli. And this will cause temporary increase of glucose concentration by forming a local cloud of glucose at the surface. And this will benefit to influx rate of the glucose into the cell.
[Fig 6] Cooperator Equation & Cheater Equation
Sponsors
