# Cameron M. Rehmani Seraji Week 7

## Purpose

• The purpose of this weeks assignment was to create a presentation on the mathematical models of nitrogen metabolism that were generated in the week 6 assignment.

## Methods

• Created new differential equations from week 6 and modeled them in Matlab. The function and script are shown below.
• Created the function 'YeastGrowthCR.m'
```function dx = YeastGrowthCR(t,x)
global D u1 u2 u3 V1  K R
dx = zeros(size(x));
dx(1) = ((D*u1) - (D*x(1)) - (x(3))*(V1)*((x(1)/x(1)+K)*(x(2)/x(2)+K)));
dx(2) = ((D*u2) - (D*x(2)) - (x(3))*(V1)*((x(1)/x(1)+K)*(x(2)/x(2)+K)));
dx(3) = (x(3))*(R)*(V1)*((x(1)/x(1)+K)*(x(2)/x(2)+K)) - (D*x(3));
dx(4) = (D*u3) - (D*x(4)) -((x(3)*x(4)*V1)/K+x(4));
dx(5) = ((x(3)*x(4)*V1)/(K+x(4))) - (D*x(5));
end
```
• created the script 'YeastGrowthCRscript.m'
```global D u1 u2 u3 V1 K R
D=0.15;
u1=120;
u2=60;
u3=40;
V1=0.5;
K=5;
R=1.0;
t0=0;
t1=100;
tt = [t0:t1];
x0 = [1.5;9.5;5;0;2.6];
[t,x] = ode45('YeastGrowthCR',tt,x0);
plot(t,x)
xlabel('time')
ylabel('concentrations')
title('Nitrogen Metabolism Model')
legend('Ammonia','Glucose','Yeast','O2','CO2')
```

## Results

• Powerpoint presentation can be found here.
• Updated powerpoint presentation can be found here

## Conclusion

• The systems of equations were modeled and a presentation was made to present the results that were found while modeling the system of equations.