Fit Surface Plasmon Resonance (SPR) data in ggplot - r

Question

I am trying to fit association-dissociation SPR kinetics data for a protein and small molecule for two concentrations using ggplot2. The data is here.
The time variable indicates the time in seconds, the sample variable indicates the two concentrations (32nM and 8nM), and the values variable is the readout.
I have imported the data and running the following code to plot:
# LINE PLOT
ggplot(data) +
geom_point(aes(x = time, y = values), size = 1, color = "black") +
geom_smooth(aes(x = time, y = values, color = sample), method = "loess", se = F) +
scale_x_continuous(expand = c(0, 0), limits = c(0, NA)) +
#scale_y_continuous(expand = c(0, 0), limits = c(0, 60)) +
scale_color_npg(breaks = c("2nM", "4nM", "8nM", "16nM", "32nM")) +
theme_linedraw() +
labs(x = "Time (seconds)",
y = "Response Units") +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
Here is the plot:
As you can see that the fit did not work using method = "loess". I need something like this(there are 5 concentrations here):
The fitting requires 1:1 Langmuir model but I am not sure how I can do that in ggplot. Can someone please help me?
Here is the equation:
This is from the pbm package that fits this kind of plots.

Answer 1

Your data are smooth enough that you need only use geom_line, not geom_smooth:
df %>%
ggplot(aes(time, values, color = sample)) +
geom_line(size = 2, na.rm = TRUE) +
geom_point(color = 'black', size = 1) +
theme_linedraw(base_size = 16) +
xlim(c(0, 400))
Edit
It is possible to fit the results to the data using non-linear least squares, employing the binding1to1 function from pbm, but it requires a bit of method tweaking to get the model to fit. It would probably be better to create a model then plot the predictions rather than using geom_smooth. However, if you really wanted to, you could do:
df %>%
ggplot(aes(time, values, color = sample)) +
geom_smooth(method = nls, se = FALSE, n = 1000,
formula = y ~ binding1to1(x, 123, 32e-9, kon, koff, rmax),
method.args = list(
start = list(kon = 2000, koff = 0.02, rmax = 2e4),
control = nls.control(minFactor = 1e-6, maxiter = 1000)
),
data = df[df$time > 0 & df$sample == "32nM",]) +
geom_smooth(method = nls, se = FALSE, n = 1000,
formula = y ~ binding1to1(x, 123, 8e-9, kon, koff, rmax),
method.args = list(
start = list(kon = 3000, koff = 0.02, rmax = 2e4),
control = nls.control(minFactor = 1e-9, maxiter = 10000)
),
data = df[df$time > 0 & df$sample == "8nM",]) +
geom_point(color = 'black', size = 1) +
theme_linedraw(base_size = 16) +
xlim(c(0, 400))
If you want to actually fit a model from which to extract the parameters and plot, you can do:
library(tidyverse)
library(pbm)
df <- read.csv("SPR.csv") %>%
filter(time >= 0) %>%
mutate(sample = as.numeric(gsub("\\D+", "", sample)) * 1e-9,
values = values * 1e-3) %>%
group_by(sample) %>%
mutate(tmax = time[which.max(values)])
fit_fun <- function(time, tmax, sample, kon, koff, rmax) {
unlist(Map(function(time, tmax, sample) {
binding1to1(time, tmax, sample, kon, koff, rmax)
}, time, tmax, sample))
}
mod <- nls(values ~ fit_fun(time, tmax, sample, kon, koff, rmax),
data = df,
start = list(kon = 3000, koff = 0.02, rmax = 2),
control = nls.control(minFactor = 1e-9, maxiter = 10000))
This gives us a model with the best fitting values for the various parameters:
mod
#> Nonlinear regression model
#> model: values ~ fit_fun(time, tmax, sample, kon, koff, rmax)
#> data: df
#> kon koff rmax
#> 8.925e+05 2.521e-03 5.445e-02
#> residual sum-of-squares: 5.219e-05
#>
#> Number of iterations to convergence: 536
#> Achieved convergence tolerance: 5.155e-07
We can then predict the output of the model over the range of our input variables:
pred_df <- expand.grid(time = 0:400, sample = c(8, 32) * 1e-9,
tmax = df$tmax[1])
pred_df$values <- predict(mod, pred_df)
And we can plot it like this:
df %>%
ggplot(aes(time, values, color = factor(sample))) +
geom_line(data = pred_df, size = 1) +
geom_point(color = 'black', size = 1) +
theme_linedraw(base_size = 16) +
xlim(c(0, 400))