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Fit binding models to dose-response data

Source: R/fit.R
mst_fit.Rd

Fits the binding models used by MO.Affinity Analysis by non-linear least squares, with stats::nls().

Usage

mst_fit(
  data,
  model = c("kd", "hill"),
  concentration = ligand_concentration,
  response = response,
  target_concentration = NULL,
  .by = NULL
)

Arguments

data

A data frame with a row for each concentration, such as from read_mst_dose_response() or mst_fnorm(). If data is grouped with dplyr::group_by(), each group is fitted separately.

model

The model to fit, "kd" or "hill". See the Models section.

concentration, response

<data-masking> The columns of ligand concentration (molar) and response.

target_concentration

For the Kd model, the target concentration in molar. If NULL, the default, it is estimated along with the other parameters, as MO.Affinity Analysis can do. If it is known, fixing it gives a more stable fit.

.by

<tidy-select> Columns to group by, fitting each group separately. An alternative to grouping data.

Value

A tibble with one row per group, with the grouping columns and:

  • model: the model fitted.

  • n: the number of points fitted.

  • sigma: the residual standard deviation.

  • fit: the fitted model, used by mst_coefs(), mst_curve() and mst_normalise(). NULL if the fit failed.

Models

The Kd model describes 1:1 binding of a ligand to a target, accounting for depletion of free ligand:

$$f = \frac{c + c_T + K_d - \sqrt{(c + c_T + K_d)^2 - 4 c c_T}}{2 c_T}$$

$$y = U + (B - U) f$$

where \(c\) is the ligand concentration, \(c_T\) the target concentration, \(f\) the fraction of target bound, and \(U\) and \(B\) the responses of the unbound and bound states.

The Hill model describes cooperative binding:

$$y = U + \frac{B - U}{1 + (EC_{50} / c)^n}$$

Examples

doses <- read_mst_dose_response(
  tidymst_example("dppr10-cy5_dose-response-flat.xlsx")
)
fits <- mst_fit(doses, .by = target)
fits
#> # A tibble: 1 × 5
#>   target  model     n sigma fit       
#>   <chr>   <chr> <int> <dbl> <list>    
#> 1 atpH-fl kd       48 0.107 <mst_bnd_>

mst_coefs(fits)
#> # A tibble: 4 × 7
#>   target  model term                 estimate     std_error conf_low conf_high
#>   <chr>   <chr> <chr>                   <dbl>         <dbl>    <dbl>     <dbl>
#> 1 atpH-fl kd    unbound               1.09e+3 2.44           1.09e+3   1.10e+3
#> 2 atpH-fl kd    bound                 8.51e+2 3.98           8.43e+2   8.59e+2
#> 3 atpH-fl kd    kd                    1.47e-8 0.00000000557  6.88e-9   3.16e-8
#> 4 atpH-fl kd    target_concentration  1.13e-7 0.0000000138   8.86e-8   1.45e-7

# Fix the target concentration at its nominal value
mst_fit(doses, target_concentration = 50e-9, .by = target)
#> # A tibble: 1 × 5
#>   target  model     n sigma fit       
#>   <chr>   <chr> <int> <dbl> <list>    
#> 1 atpH-fl kd       48 0.120 <mst_bnd_>