function [p,K]=rate_matrix(beta, x) %------------------- LineShapeKin RATE_MATRIX ----------------------------- %-- version 3.0 % % 3/17/08 % Written by Evgenii Kovrigin, Medical College of Wisconsin % % This function builds a rate (K) matrix for the spin exchange between the % sites corresponding to the equation: % P+L=PL, Kd=k2/k1, where k1=kon*[L], k2=Koff % % NOTES: this is a version with fixed preset Kd (only koff and scaling factor % are variable parameters. global B_vector Model X_columns %--- extract fixed (preset) values %- use fixed preset Kd Kd = Model.Kd; %-- extract variable parameters koff=beta(B_vector.Koff); %-- extract experimental parameters: Ptot = x(X_columns.Ptotal); Ltot = Ptot*x(X_columns.LPratio); %% Analytical solution for [L] out of % % Kd = [P][L]/[PL] % a=1; b=-(Ptot+Ltot+Kd); c=Ptot*Ltot; sola=-b/(2*a); solb=sqrt(b^2-(4*a*c))/(2*a); sol1=[(sola+solb) (sola-solb)]; Peq=max(Ptot-sol1); %-- get positive solution PLeq=Ptot-Peq; Leq=Ltot-PLeq; % Equilibrium mole fractions of species containting P p=[Peq/Ptot,PLeq/Ptot]; %-- relationships of true constants kon=koff/Kd; % K matrix elements kab=kon*Leq; kba=koff; K=[-kab,kba;kab,-kba]; %-- prepare relaxation rates and frequencies for the individual species R2=[x(i,4),x(i,5)]; % R2free, R2bound v0=[x(i,6),x(i,7)]; % v0free, v0bound