R nls function predicts data well but returned fitting coefficients are totally off

Question

I am trying to fit electrophysiological data with a Boltzmann functon. When using real data, the predicted values returned by the nls function nicely match the input data, however, the retuned fitting coefficients are totally off.

I first tested my function using simulated data. Doing so predicted values and fitting coefficients are acurate.

# generate sample data

V<-seq(-60,40,5)
Vhalf=-20
k=10
G<- (1/(1 + exp((Vhalf - V) / k)) + rnorm(length(V), sd = 0.05))

# normalization

normalize <- function(x, range = c(0, 1)) {
  if (!is.numeric(x)) {
    stop("Input x must be a numeric vector")
  }
  
  min_x <- min(x)
  max_x <- max(x)
  
  normalized_x <- (x - min_x) / (max_x - min_x)
  
  min_range <- range[1]
  max_range <- range[2]
  
  normalized_x * (max_range - min_range) + min_range
}

G <- normalize(G)

# fit function
boltzmann_eqn <- function(V, Vhalf, k) {
  (1 / (1 + exp((Vhalf - V) / k)))
}
  
# starting parameters and fit

start_Vhlaf=-10
start_k=10


fit <-  nls(
  G ~ boltzmann_eqn(V, Vhalf, k),
  start = list(Vhalf = start_Vhlaf, k = start_k),
  algorithm = "port",
  control = list(
    maxiter = 1000,
    tol = abs(min(V)) * 1e-05,
    minFactor = abs(min(V)) * 1e-05
  )
)

coef(fit)
predicted.value<-predict(fit)

#  plot actual and fitted values

library(ggplot2)

data<-data.frame(V,G,predicted.value)
ggplot(data,aes(x=V,y=G))+
  geom_point()+
  geom_line(aes(y=predicted.value))

however, if I now use real data, the fitting coefficients are totally off:

# real data for G
V<-seq(-60,40,5)
G <-
  c(
    2.886126e-10,
    2.299096e-10,
    3.479653e-10,
    3.854844e-10,
    5.786606e-10,
    6.859901e-10,
    9.479952e-10,
    1.107524e-09,
    1.569197e-09,
    1.685586e-09,
    2.163985e-09,
    2.231026e-09,
    3.036547e-09,
    3.402246e-09,
    3.396888e-09,
    4.070637e-09,
    4.297097e-09,
    4.218705e-09,
    4.651377e-09,
    5.019147e-09,
    5.336356e-09
  )

# normalization

normalize <- function(x, range = c(0, 1)) {
  if (!is.numeric(x)) {
    stop("Input x must be a numeric vector")
  }
  
  min_x <- min(x)
  max_x <- max(x)
  
  normalized_x <- (x - min_x) / (max_x - min_x)
  
  min_range <- range[1]
  max_range <- range[2]
  
  normalized_x * (max_range - min_range) + min_range
}

G <- normalize(G)

# fit function
boltzmann_eqn <- function(V, Vhalf, k) {
  (1 / (1 + exp((Vhalf - V) / k)))
}

# starting parameters and fit

start_Vhlaf=-10
start_k=10


fit <-  nls(
  G ~ boltzmann_eqn(V, Vhalf, k),
  start = list(Vhalf = start_Vhlaf, k = start_k),
  algorithm = "port",
  control = list(
    maxiter = 1000,
    tol = abs(min(V)) * 1e-05,
    minFactor = abs(min(V)) * 1e-05
  )
)

coef(fit)
predicted.value<-predict(fit)

#  plot actual and fitted values

library(ggplot2)

data<-data.frame(V,G,predicted.value)
ggplot(data,aes(x=V,y=G))+
  geom_point()+
  geom_line(aes(y=predicted.value))

I am not seeing any obvious difference between my simulated and the real data, possibly the real data doesnt fully saturate. However, I think that cant really explain why coefficients are off whil prediciton seems to work well. I was under the impression that both should be linked.

any suggestions are highly appreciated! Thanks for the help!