%An example of RNAP/sigma factor competition among the genome of promoters

%Restricted to two sigma factors: Sigma70 and SigmaS as an example

range = linspace(1,1000,1001);

for i=1:length(range) %Incrementing the copy number from 1 to 1000 in steps of 1

%Plasmid / chromosome copy number
copynumber = range(i);

%Conversion factors & constants
molec2uM = 0.00166057788110;
RT = 1.987e-3*310;

%Constant Concentrations
Sigma70 = 4700;  %Measured experimentally
SigmaS = 100; %Measured experimentally
RNAP = 2600; %Measured experimentally

Promoters = copynumber;
Other_Sigma70_Promoters = 10500; %Estimated from E. coli genome
Other_SigmaS_Promoters = 5000; %A completely arbitrary estimate
Random_DNA = 1e6; %E. coli genome size in base pairs

%Competing random DNA
dG_NonSpecific = -4.5; %Estimated

%Thermodynamic Parameters [kcal/mol]
%Target Promoter
dG_Sigma70 =  -9.3 - dG_NonSpecific; %A medium strength Sigma70 promoter
dG_SigmaS = -5 - dG_NonSpecific; %Estimated

%All other competing promoters (average)
dG_Sigma_OtherPromoters = -8 - dG_NonSpecific; %Estimated

%Equilibrium Statements
%Competition between RNAP and different sigma factors. Assumes each sigma
%factor binds to RNAP with equal affinity.
TotalSigma = Sigma70 + SigmaS;
Total_RNAP_Sigma70 = RNAP * Sigma70 / TotalSigma;
Total_RNAP_SigmaS = RNAP * SigmaS / TotalSigma;

%Competition between RNAP/sigma and every promoter in the genome. We assume
%that there is an average dG of binding for the non-target (other)
%promoters in the genome.
Sigma70_PromoterCompetition = Promoters * exp(-dG_Sigma70/RT) / (Promoters * exp(-dG_Sigma70/RT) + Other_Sigma70_Promoters*exp(-dG_Sigma_OtherPromoters/RT));
SigmaS_PromoterCompetition = Promoters * exp(-dG_SigmaS/RT) / (Promoters * exp(-dG_SigmaS/RT) + Other_SigmaS_Promoters*exp(-dG_Sigma_OtherPromoters/RT));

RNAP_Sigma70(i) = Total_RNAP_Sigma70 * Sigma70_PromoterCompetition;
RNAP_SigmaS(i) = Total_RNAP_SigmaS * SigmaS_PromoterCompetition;

end

semilogy(range,RNAP_Sigma70,range,RNAP_SigmaS,'LineWidth',2)
xlabel('Copy number of Target Promoter');
ylabel('Molecules of RNAP/ \sigma factor')
legend('RNAP/ \sigma^7^0','RNAP/ \sigma^S','Location','SouthEast');