The Hill equation is defined as follows:

y = bottom + ((top - bottom) * x^nH) / (EC50^nH+ x^nH)

where bottom is the minimum activity; top is maximum activity; EC50 is the half-maximum effective dose; and nH is the Hill coefficient. The variables x & y are the stimuli dose and the cellular or tissue response. The hillfit module applies this biological equation, and is available with the MIT License.

The following command are executed in a command prompt/terminal environment:

pip install hillfit

The data environment, in a Python IDE, is defined:

import hillfit
hf = hillfit.HillFit(x_data, y_data)

• x_data & y_data list or ndarray: specifies the x-values & y-values, respectively, of the raw data that will be fitted with the Hill equation.
• bottom_param bool: specifies whether the accessory bottom parameter of the Hill equation will be employed in the regression.

The parameterized data is fitted to the Hill equation, with the following arguments and their default values:

hf.fitting(x_label = 'x', y_label = 'y', title = 'Fitted Hill equation', sigfigs = 6,
           log_x = False, bottom_param = True, print_r_sqr = True, view_figure = True)

• x_label & y_label str: specifies the x-axis & y-axis labels, respectively, that will be applied to the regression plot for the raw data points and the fitted Hill equation.
• title str: specifies the title of the regression plot for the raw data points and the fitted Hill equation.
• sigfigs int: specifies the number of significant figures that will be used in printed instances of the fitted Hill equation.
• log_x bool: specifies whether the x-axis of the regression plot will be converted into a logarithmic scale.
• view_figure bool: specifies whether the regression plot will be printed in the Python environment.
• print_r_sqr bool: specifies whether the coefficient of determination (R²) regression plot will be printed in the Python environment.

Many data sets and exported components of the fitted information are accessible through the hillfit model object.

• top, bottom, ec50, & nH float: The fitted parameters of the Hill equation are accessible via hf.top, hf.bottom, hf.ec50, & hf.nH, respectively.
• R²float: The coefficient of determination of the regression figure is available via hf.r_2.
• fitted_xs & fitted_ys list: The x- and y-values of the fitted Hill equation are accessible via hf.x_fit & hf.y_fit, respectively.
• fitted_equation str: The fitted Hill equation, in an amenable string format for the eval() built-in function of Python that allows the user to directly execute the string as a function for an "x" variable, is accessible via hf.equation.
• figure & ax matplotlib.figure: The fig and ax objects of the regression figure are available via hf.figure & hf.ax, respectively. This allows users to edit the figures after the simulation is conducted.
• x_data & y_data ndarray: The arrays of original data are available via hf.x_data & hf.y_data, respectively.

The fitted Hill equation, with its data points and parameters, and the regression information are exported to a designated folder through the following syntax and arguments:

hf.export(export_directory = None, export_name = None)

• export_directory str: optionally specifies a path to where the content will be exported, where None selects the current working directory.
• export_name str: optionally specifies a name for the folder of exported content, where None enables the code to design a unique folder name for the information.

Hillfit is executed through the following sequence of the aforementioned functions, which is exemplified in the example Notebook of our GitHub repository:

import hillfit
hf = hillfit.HillFit(x_data, y_data)
hf.fitting(x_label = 'test_x', y_label = 'test_y', title = 'Fitted Hill equation', sigfigs = 6, log_x = False, view_figure = True, print_r_sqr = True)
hf.export(export_directory = None, export_name = None)