MATLAB As a newly hired engineer for Amgen you have been tas

MATLAB As a newly hired engineer for Amgen, you have been tasked with scaling up the process for the production of a new cancer therapy drug Auximab (Amab) similar to Rituximab, an anti-cancer antibody drug produced by your competitors. Your new drug is produced by the enzymatically catalyzed coupling of a small toxic molecule (D) onto an antibody similar to Rituximab (U). The kinetics of this reaction result in a rate of production that depends on both the concentrations of D and U as follows. T_Amab = 3.0 [D][U]^0.7/(1 + [D]^0.95 + [U]^3 To proceed, write and print out a functional, well-commented script based on the provided template. Please note: if your output does not seem to match your script you must provide an electronic version of your script upon request. Once you have a working script,

Solution

% (1) Use Matlab to create a surface plot of rDmab as a function of both

% [D] and [U] concentrations from 0 M to 3 M.

% (2) Determine the concentrations that maximize the rate of production of

% Dmab.

% Clear command window and all variables

________

________

% Create two vectors, D and U, which represent the concentrations of D and

% U we want to use to make our plot. \"linspace\" is a useful command that

% allows us to divide a specified range, in this case 0 to 3, into an

% specific number of numerical steps. Here we have arbitrarily selected

% 100.

D = linspace(________);

U = linspace(________);

% Create an initial minimum value of rmax for future comparisons

rmax = ________;

% Now use nested ________________ to cycle through all values of the

% vectors D and U. At each value of D, the inside for loop will go through

% all the values in U. In this way, all pairs of D and U values

% will be considered in the rate equation

for i = 1:length(D)

for j = ________

% This is the rate equation expression. Note that the values D(i)

% and U(j) are scalars, and represent the values of D and U in the

% i-th and j-th position of those respective vectors.

r = ________________________________________________________;

% Each time the rate expression calulates a new value, we need to

% record it. Previously we were able to record all values into a

% vector, as we only had one variable changing. Now there are 2 (U

% and D). This requires we save them into an array.

________________ = r;

% Here we are using a comparison technique for capturing the

% largest or maximum rate (rmax) that is obtained for the various

% D and U combinations. The values of D and U which give this

% maximum rate are recorded in dmax and umax, respectively.

if r > rmax

rmax = r;

dmax = ________________;

umax = ________________;

end % end of ________ block

end % end of ________ loop

end % end of ________ loop

% The following plot command creates a surface plot with U and D along the

% x and y axes, and the rate (rDmab) on the z axes: NOTE the positions of

% the U and D vectors relative to there order in the array. It is OPPOSITE

% what you might expect. To make sure you have it right, make D and U

% vectors different lengths. If your order is incorrect, you will get a

% dimensions related error in \"surf\". If you have D and U the same size,

% and you have them reversed, you might never know it!

surf(________________________)

title(‘________________________________’)

xlabel(‘________________’)

ylabel(________________________)

zlabel(________________________)

% This next step takes the maximum (umax, dmax, rmax) and adds it to the

% plot. The next command then adds a label to that point

hold on

scatter3(________, ________, ________,‘k.’)

s=strcat(‘maximum at’,‘(‘,num2str(________),‘,’,num2str(________),‘,’,num2str(________),‘)’);

text(umax,dmax,1.1*rmax,s)

hold off

% Output the maximum rate and the corresponding D and U values to the

% Command window.

fprintf(‘n The maximum rate is %6.4f mol/s and it ‘, ________)

fprintf(‘n occurs at [D] = ________ M and [U] = ________ M.n’, dmax, umax)

% end of program