Calculation of the divergence rate

Inferring the divergence rate between orthologs as a function of divergence time or protein distance

1. Define t and y vectors to fit divergence model. For each pair of orthologs, values in t are the divergence time between species expressed in billions of years, values in y are the percent sequence identity between corresponding orthologs.

   
   

2. Use the fitnlm function in matlab (or an alternative nonlinear regression method) to fit equation 3 from Konate et al. and retrieve the values for the R₀ and alpha parameters. (relevant matlab code shown below).

   

   model3=@(b,x)100.*((b(1).*x/b(2))+1).^-b(2)

   beta=[1,0.5];

   fit=fitnlm(t,y,model3,beta);

   [R0,alpha]=fit.Coefficients.Estimate;

   
   

3.  Use the obtained R₀ and alpha parameters in equation 5 from Konate et al. to determine the divergence rate (dy/dt) at an arbitrary t expressed in billions of years.

   
   

4. Alternatively, use the obtained R₀ and alpha parameters in equation 4 from Konate et al. to determine the divergence rate an arbitrary protein distance expressed as a fraction (i.e. 1 – percent identity/100)