1 function [ PoPSans ] = Fluoro2( matrix, matrix2, DNA, modeldata )
 2 %Fluoro 2: This function takes in a matrix of titrations and determines
 3 %both the possible percentage for bound mRNA as well as the actual
 4 %fluorescent mRNA concentration from fluorescent input values.
 5 
 6 
 7 controlc = matrix(end,:); %concentration and fluorescence of the control
 8 controlconc = controlc(1); %concentration of dye for the control
 9 controldat = controlc(1:end); %fluorescence of the control
10 maxc = max(controldat);
11 concs = matrix(:,1); %concentrations of the dye in the wells
12 concs1 = concs(1:(end - 2));
13 controlmax = maxc;
14 
15 Rf = [];
16 
17 for i = 2:size(matrix, 2);
18     fluordat = matrix(:,i); %fluoroscence data at some time point
19     fluordat1 = fluordat(1:(end - 2));
20     s = fitoptions('Method', 'NonlinearLeastSquares', 'Startpoint',...
21     [fluordat1(end), 1/(controlconc)]);
22     g = fittype('a * (1 - exp(b * (-x)))', 'coefficients', {'a', 'b'},...
23     'options', s);
24     h = fit(concs1, fluordat1, g);
25     coeffvals = coeffvalues(h);
26     %figure(i);
27     %plot(h, concs1, fluordat1)
28     factorScale = coeffvals(1) / controlmax;
29                 %scaling factor from in vitro to in vivo
30     for j = 1:size(concs1);
31         if abs(h(concs1(j)) - h(1)) <= (.2 * h(1));
32             Rf(i - 1) = concs1(j) * factorScale;
33             break
34         end
35     end
36 
37 end
38 time = matrix(1,:);
39 fluortime = time(2:size(matrix, 2));
40 
41 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
42 %Section for Transcriptional Efficiency      %
43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
44 
45 Rt = FluoroLR(Rf, fluortime);
46 
47 
48 alpha2 = Degradation(modeldata);
49 
50 ETF = mRNAexpress(fluortime, DNA, Rt, alpha2);
51 %ETF = mean(ETF);
52 
53 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
54 %Section for Translational Efficiency        %
55 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
56 
57 Pt = ProteinFunctions(matrix2);
58 
59 beta2 = DegradationP(modeldata);
60 
61 Tl = proteinexpress(DNA, Pt, ETF, alpha2, beta2);
62 
63 %Tl = proteinexpress(DNA, 1.6, ETF, alpha2, beta2)
64 
65 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
66 %Section for Polymerase per Second           %
67 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
68 
69 PoPSans = PoPS(alpha2, beta2, Pt, Tl);
70 
71 end

 1 function [ alpha2 ] = Degradation ( modeldata )
 2 dRi = modeldata(:,3);
 3 time = modeldata(:,1);
 4 %dRi(length(dRi),:) = [];
 5 C = max(dRi);
 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 7 %Differential Equation: dRi./dt = alpha * Rt%
 8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 9 
10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
11 %dRi is the fluorescence measurements of RNA during degradation only%
12 %alpha is the desired result, so we solve the diff eq               %
13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
14 
15 for i = 1:(length(dRi));
16     if dRi(i) ~= 0 && time(i) ~= 0
17         alpha(i) = log(dRi(i) ./ C) ./ time(i);
18     else
19         alpha(i) = log(dRi(2) ./ C) ./ time(2);
20     end
21 end
22 alpha;
23 alpha2 = -mean(alpha);
24 %Rdegra = Rt * alpha2;
25 
26 end

 1 function [ beta2 ] = DegradationP ( modeldata )
 2 %DegradationP
 3 
 4 dPi = modeldata(:,6);
 5 timeP = modeldata(:,1);
 6 %dRi ./ dt = alpha * Ri, solution: R = Ce^(alpha t) ./ alpha
 7 C1 = max(dPi);
 8 %ln(Ri ./ C) ./ t = alpha
 9 for i = 1:length(dPi)
10     if dPi(i) ~= 0 && timeP(i) ~= 0
11         beta(i) = log(dPi(i) ./ C1) ./ timeP(i);
12     else
13         beta(i) = log(dPi(2) ./ C1) ./ timeP(2);
14     end
15 end
16 
17 beta2 = -mean(beta);
18 %Pdegra = beta2 * Pt;
19 end

 1 function [ Pt ] = ProteinFunctions( matrix)
 2 %UNTITLED Summary of this function goes here
 3 %   Detailed explanation goes here
 4 
 5 controlc = matrix(end,:); %concentration and fluorescence of the control
 6 controlconc = controlc(1); %concentration of dye for the control
 7 controldat = controlc(1:end); %fluorescence of the control
 8 maxc = max(controldat);
 9 concs = matrix(:,1); %concentrations of the dye in the wells
10 concs1 = concs(1:(end - 2));
11 controlmax = maxc;
12 
13 Pf = [];
14 
15 for i = 2:size(matrix, 2);
16     fluordat = matrix(:,i); %fluoroscence data at some time point
17     fluordat1 = fluordat(1:(end - 2));
18 
19     s = fitoptions('Method', 'NonlinearLeastSquares', 'Startpoint',...
20     [fluordat1(end), 1/(controlconc)]);
21 
22     g = fittype('a * (1 - exp(b * (-x)))', 'coefficients', {'a', 'b'},...
23     'options', s);
24 
25     h = fit(concs1, fluordat1, g);
26     coeffvals = coeffvalues(h);
27     %figure(i);
28     %plot(h, concs1, fluordat1)
29     factorScale = coeffvals(1) / controlmax;...
30         %scaling factor from in vitro to in vivo
31     for j = 1:size(concs1);
32         if abs(h(concs1(j)) - h(1)) <= (.2 * h(1));
33             Pf(i - 1) = concs1(j) * factorScale;
34             break
35         end
36     end
37 
38 end
39 time = matrix(1,:);
40 fluortime = time(2:size(matrix, 2));
41 
42 Pt = FluoroLP (Pf, fluortime);
43 
44 end
45 

 1 function [Rt] = FluoroLR (Rf, concentrations)
 2 %DFHBI = 1*10^(-9); %concentration of dye
 3 %Rfmax = 1*10^(-10);%max concentration of the mRNA
 4 KD = 464*10^(-9);
 5 
 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 7 %Relates the mRNA fluorescence levels with the total mRNA levels%
 8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 9 
10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
11 %fluorescence is measured, Rf is the fluorescent mRNA concentration%
12 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
13 
14 %a = max(fluorescence) ./ Rfmax;
15 %Rf = zeros(length(fluorescence) - 1, 1);
16 %for i = 1:(length(fluorescence) - 1)
17 %    Rf(i) = fluorescence(i) ./ a;    
18 %end
19 
20 %%%%%%%%%%%%%%%%%%%%%%
21 %Rt is the total mRNA%
22 %%%%%%%%%%%%%%%%%%%%%%
23 
24 Rt = [];
25 for j = 1:(length(Rf))
26     Rt(j) = Rf(j) * (1 + KD ./ (concentrations(j) - Rf(j)));
27 end
28 
29 end

 1 function [Pt] = FluoroLP (Pf, concentrationsP)
 2 MAG = 1*10^(-9); %concentration of dye
 3 Pfmax = 1*10^(-10);  %max concentration of the protein
 4 KD2 = 464*10^(-9);
 5 
 6 
 7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 8 %Relates the protein fluorescence levels with the total protein levels%
 9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
10 
11 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
12 %fluorescence is measured, Pf is the fluorescent protein concentration%
13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
14 
15 %b = max(fluorescenceP) ./ Pfmax;
16 %Pf = zeros(length(fluorescenceP), 1);
17 %for i = 1:(length(fluorescenceP))
18 %    Pf(i) = fluorescenceP(i) ./ b;
19 %end
20 
21 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
22 %Pt is the total protein concentration%
23 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
24 
25 Pt = [];
26 for j = 1:(length(concentrationsP))
27     Pt(j) = Pf(j) * (1 + KD2 ./ (concentrationsP(j) - Pf(j)));
28 end
29 end

 1 function [ ETF ] = mRNAexpress ( fluortime, DNA, Rt, alpha2 )
 2 %mRNA expression model
 3 
 4 %%%%%%%%%%%%%%%%%
 5 %DNA is measured%
 6 %%%%%%%%%%%%%%%%%
 7 
 8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 9 %ET is the transcriptional efficiency, ETF is the average%
10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
11 
12 for k = 1:(length(Rt))
13     if fluortime(k) ~= 0
14         ET(k) = Rt(k) * alpha2 ./ DNA ./(1 - exp(-alpha2 * (fluortime(k))));
15     else
16         ET(k) = Rt(k) * alpha2 ./ DNA ./(1 - exp(-alpha2 * (.2)));
17     end
18 end
19 ET;
20 ET = ET(2:end);
21 ETF = mean(ET);
22 %ETF = ET;
23 end

 1 function [ Tl ] = proteinexpress (DNA, Pt, ETF, alpha2, beta2)
 2 %proteinexpress
 3 
 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 5 %differential equation comes from: dP./dt = Trans * RNA - beta * P%
 6 %want to solve for Trans, the translational efficiency            %
 7 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 8 
 9 for k = 1:length(Pt)
10     Trans(k) = Pt(k) ./ (ETF * DNA ./ (alpha2 * beta2) *...
11     (1 - exp(-beta2 * (k - 1))) - ETF * DNA ./ (alpha2 *...
12     (-alpha2 + beta2)) * (exp(-alpha2 * (k - 1)) - exp(-beta2 * (k - 1))));
13 end
14 
15 %for k = 1:length(ETF)
16 %    Pt(k) = Trans * (ETF(k) * DNA ./ (alpha2 * beta2) * (1 -...
17 %    exp(-beta2 * (k - 1))) - ETF(k) * DNA ./ (alpha2 *...
18 %    (-alpha2 + beta2)) * (exp(-alpha2 * (k - 1)) - ...
19 %    exp(-beta2 * (k - 1))));
20 %    
21 %end
22 
23 Tl = mean(Trans);
24 end

1 function [ PoPS ] = PoPS( alpha2, beta2, Pt, Tl )
2 %This function calculates Polymerase per second given a few parameters
3 %This equation is valid at steady state.
4 
5 n = 1;
6 PoPS = alpha2 * beta2 * Pt ./ (n * Tl);
7 
8 end