$A + B \overset{k_{on}}{\underset{k_{off}}\rightleftarrows} AB \; (Kd_1)$
$\frac{d[AB]}{dt} = k_{on} [A] [B] - k_{off} [AL]$
$\Rightarrow$
$\frac{dy}{dt} = k_{on} [A] (R_{max} - R) - k_{off} * R$ ( Called "simple 1:1 model" )
$\Rightarrow$
$\frac{dy}{dt} = k_{on} \frac{-Kd_2+\sqrt{Kd_2^2+8Kd_2*[At]}}{4} (R_{max} - R) - k_{off} * R$
Where $Kd_{2} = \frac{k_{off}}{k_{on}}$, assuming $Kd_1 = Kd_2$.
require(reshape2); require(ggplot2); require(grid) knitr::opts_chunk$set(fig.height = 4, fig.width = 4) require(pldfit)
# simulate the data use the following parameters # simulate the data use the following parameters par = list(kon = 2e2, koff = 1e-2, rmax = 1, concs = 1e-5 * (2^(0:5)), time = seq(0, 300, length.out = 2501), t2 = 150) # simulation model = "dimer" xySimulated <- kinsim(par = par, model = model, noise = 0.01) # plot the simulation # ySimulated$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); concs = par$concs t2 = par$t2 # t2 is the beginning of the diassociation. dat = xySimulated # Fit model = "dimer" fit <- kinfit(par = initPar_test, dat = dat, concs = concs, t2 = t2, lower = lower, upper = upper, model = "dimer") names(fit) cbind(simulation= par, init = initPar_test, fitting = fit$par) #prodict and plot predFit = kinsim(par = fit$par, model = model, noise = 0) predFit <- reshape2::melt(predFit, id.vars = "Time") g + geom_line(data=predFit, aes(x = Time, y = value, group = variable) )
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.