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The Regulation Of Cellular Systems

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Question:

Describe about the The Regulation of Cellular Systems?
 
 

Answer:

Introduction

In this assignment, we have studied the chemical process in a mixing tank, where hydrogen peroxide is mixed with water containing metal ions, where a decomposition reaction of hydrogen peroxide takes place.

The tank is a closed tank with two inlets and one outlet, which is the overflow outlet, and keeps the level of solution to be 1 litre.

The equation of decomposition of hydrogen peroxide is a first order reaction, ad all the analysis and simulations has been done accordingly.

Task 1

The differential equation of a first order chemical reaction is:

dC/dt = -kC = r

where, r = rate of reaction 

C = concentration of the reactant

t = time  

k = koexp(-Ea/RT) = reaction rate constant

Solving the equation, we have,

C             = Cin exp(-kt)

where, Cin = initial concentration

Task 2

Now, it has been given that,

Cin = 6M

K = 0.0015/sec

In-flow rate of H2O2 = 0.5 litres/sec

Thus, the required flow rate is,

Flow rate = ((0.5x6)/4)exp(-0.0015t)

Thus, we see that this flow rate is a function of time.

Task 3

 

Line Number

Function

1

Description of the program

2-3

Clear/close all previous variables and figures

4-5

Declaration of variables

6-7

Declaration of constants

8-9

Function and integration LHS

10-11

Function and integration of RHS

12

Solution of the equation

13

Print result

14

Actual molar concentration

15

Print Result

16

Molar Outflow

17

Rate of decomposition expression

18-27

Plotting of the functions

28

Calculation of time taken to reach 90% of target

 

The code snippet has been attached below:

%Concentration Analysis

clear all %clear all variables

close all %close all figures

syms t; %declaration of variable

syms C; %declaration of variable

Ci = 6; %initial concentration

k = 0.0015; %rate in sec^-1

f1 = 1/C; %LHS of function

g1 = int(f1,C); %integration of LHS

f2 = -k; %RHS of Function

g2 = int(f2,t); %integration of RHS

C = Ci*exp(g2); %Concentration solution

C %print result

Cn = ((Ci*0.5)/4)*exp(g2); %actual concentration in molar form

Cn

Cout = C - Cn %Molar flow out of the tank to maintain the concentration

rate = -k*C %Rate of decomposition of hydrogen peroxide

%plotting

figure %to start a figure

subplot(4,1,1) %to plot multiple graph in one figure

ezplot(C,[0 10]);xlabel('Time:s');ylabel('Concentration:M');legend('Molar flow into Tank');

subplot(4,1,2)

ezplot(Cn,[0 10]);xlabel('Time:s');ylabel('Concentration:M');legend('Actual conc. in Tank');

subplot(4,1,3)

ezplot(Cout,[0 10]);xlabel('Time:s');ylabel('Concentration:M');legend('Molar Flow out of Tank');

subplot(4,1,4)

ezplot(rate,[0 10]);xlabel('Time:s');ylabel('Rate:M/s');legend('Rate of Decomposition');

time = - (log((0.9*4)/6))/0.0015 %time taken to reach 90% of target concentration

The time received from the function is: 340.5504 sec

Fig. Plot of the functions obtained

 

References

Kenneth A. Connors Chemical Kinetics, the study of reaction rates in solution, 1991, VCH Publishers.

Heinrich, R. and Schuster, S. (1996) The regulation of cellular systems. Chapman & Hall, New York.

Quarteroni, Alfio; Saleri, Fausto (2006). Scientific Computing with MATLAB and Octave. Springer.

Iglesias, P.A. and Ingalls, B.P. (2010) Control theory and systems biology. MIT Press Cambridge.

"System Requirements and Platform Availability". MathWorks.

"Create Symbolic Variables and Expressions". Symbolic Math Toolbox. MathWorks.

"Generate Field Names from Variables". MathWorks.

"Application Programming Interfaces to MATLAB". MathWorks.

Gilat, Amos (2004). MATLAB: An Introduction with Applications 2nd Edition. John Wiley & Sons.

Ferreira, A.J.M. (2009). MATLAB Codes for Finite Element Analysis. Springer.

Lynch, Stephen (2004). Dynamical Systems with Applications using MATLAB. Birkhäuser.

Physical Modeling in MATLAB by Allen B. Downey, Green Tea Press, An introduction to MATLAB.

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