Lkelly9 Week 7 Redo

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• Lauren M. Kelly
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Purpose

• The purpose of this assignment is to apply all of the modeling skills we have learned and reevaluate the equations we developed for the project in which we learned more about the behavior of yeast and attempted to model how the population reacts to changes in nitrogen or glucose.

Methods

• Re-evaluated the equations so that they "talk to each other" more effectively.
  • Added "Zqy" to the glucose equation to account for trend between glucose and CO2: As CO2 increases, glucose decreases.
  • The dilution rate, q, was included to account for the chemostat environment.
• Defined V1, V2, and V as separate variables
  • V1 and V2 are the maximum velocity of the reaction, while V is the volume.
• Graphed the revised equations in MATLAB using the following script and function:
  • Script:

global q u1 u2 y K1 K2 V R Z V1 V2
q= 6;
u1= 100;
u2 = 100;
y = 10;
K1 = 3;
K2 = 5;
R = 150;
V = 100;
Z = 5;
V1 = 4;
V2 = 6;
tt = 0:0.1:1;
x0 = [400;300;50;0];
[t,x] = ode45('week7function',tt,x0);
plot(t,x)
xlabel('time')
ylabel('abundance')
title('Population and Fermentation')
legend('Population','Food')

• • Function:

function dx = week7function(t,x)
global q u1 u2 y K1 K2 V R Z V1 V2
dx = zeros(size(x));
dx(1) = (q*u1) - (q*x(1)) - x(3)*V1*((x(1))/((x(1))+K1))*((x(2))/((x(2))+K2));
dx(2) = (q*u2) - (q*x(2)) - x(3)*V2*((x(1))/((x(1))+K1))*((x(2))/((x(2))+K2))-(Z*q*y);
dx(3) = y*R*((x(1))/((x(1))+K1))*((x(2))/((x(2))+K2))-(q*y);
dx(4) = Z*(1-(Z./y)).*V;
end

Results

Equations

• 

q = dilution rate
u = concentration of nutrient fed into the reactor(nitrogen is u1,  glucose is u2)
K = constant
V1, V2 = maximum velocity of the reaction
V = volume
Z = CO2 production rate
y = concentration of yeast
c = concentration of nutrient (nitrogen is c1,  glucose is c2)

Graphs

• 

q= 6;
u1= 100;
u2 = 100;
y = 10;
K1 = 3;
K2 = 5;
R = 150;
V = 100;
Z = 5;
V1 = 4;
V2 = 6;

Acknowledgements

==References