$A + L \overset{k_{on}}{\underset{k_{off}}\rightleftarrows} AL\;\; (K_d = k_{off}/K_{on})$
Below is the rate equation:
${d[AL] \over dt} = k_{on} [A] [L] - k_{off} [AL]$
other forms:
${dy \over dt} = k_{on} [conc] (R_{max} - R) - k_{off} y$
${dy \over dt} = k_{on} [conc] R_{max} - (k_{on} [conc] + k_{off}) y$
${dy \over dt} = k_{on} C R_{max} - (k_{on} C + k_{off}) R$
Parameters:
knitr::opts_chunk$set(fig.width=6.5, fig.height = 4) require(reshape2); require(ggplot2); require(grid) require(pldfit)
# simulate the data use the following parameters par = list(kon = 2e2, koff = 1e-2, rmax = 1, concs = 1e-5 * (2^(0:5)), time = seq(0, 300, length.out = 1501), t2 = 150) # simulation model = "simple1to1" xySimulated <- kinsim(par = par, model = model, noise = 0.01) # plot the simulation # ySimulated$Time = time; xy <-reshape2::melt(data = xySimulated, id.vars = "Time", measure.vars = rev(1:6), variable.name = "Conc") g <- ggplot() + xlab("Time (sec)") + ylab("Response (nm)") + labs(linetype= 'title') + ylim(-0.025,1) + theme_classic() + theme(legend.position=c(0.9, 0.65), legend.text=element_text(size = rel(1)), legend.key.size=unit(0.9,"line")); g <- g + geom_line(data = xy, aes(x = Time, y = value, color = Conc)); print(g)
# init initPar_test = list(kon =1, koff = 1, rmax = 1) lower = list(kon =1e-04, koff=1e-04, rmax = 0.01); upper = list(kon =1e04, koff=1e04, rmax = 10); t2 = par$t2 # t2 is the beginning of the diassociation. concs = par$concs dat = xySimulated # Fit fit <- kinfit(par = initPar_test, lower = lower, upper = upper, dat = dat, concs = concs, t2 = t2, model = "simple1to1") names(fit) class(fit) par[1:3] # simulation parameters fit$par[1:3] # paramenters after fitting cbind(simulation= par, init = initPar_test, fitting = fit$par) #prodict and plot predFit <- predict(fit, concs) predFit <- reshape2::melt(predFit, id.vars = "Time") g + geom_line(data=predFit, aes(x = Time, y = value, group = variable) )
# dat = xySimulated concs = par$concs scale = 1e3 fit <- ssgfit(datF = dat, concs = concs * scale, start = list(Rmax = 0.5, Kd=1), width = 5, t2 = 149.5, model = "simple1to1") coef(fit) with(par, koff/kon *scale) plot(fit$datF[1:2]) par$concs * scale lines(fit$predict, lty = 2) class(fit) plot(fit)
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