The Regulation of Cellular Systems

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