Centrosome radius determination using gaussian function

Centrosome radius determination for a typical mitotic spindle

This script is used to call a pre-written library script that computes the Gaussian fit function on a histogram plot of microtubules minus end distance to the centre of each spindle pole (centriole). The aim is to determine the radius of the centrosome, which corresponds with the second value ($x2$) on the x-axis intercept with the y-axis when the value on the y-axis is at half the maximum peak height of the Gaussian peak.

The Gaussian function is computed using the following equation:

$f(x) = Ae^{\frac{-(x - x0)^2}{2σ^2}}$

Amplitude (A): This is the peak height of the Gaussian curve.

The amplitude indicates the maximum value of the density function. In the context of a histogram fitted by a Gaussian curve, it represents the height of the curve at its peak. A higher amplitude means a higher peak, suggesting more data points are concentrated around the mean.

Mean (x0): This is the position of the center of the peak.

The mean is the average or expected value of the distribution. It indicates where the center of the data distribution is located along the x-axis. In a perfectly symmetric Gaussian distribution, this is also the point of symmetry.

Standard Deviation (σ): This measures the width of the peak.

The standard deviation is a key measure of the spread or dispersion of the data around the mean. A smaller σ indicates that the data points are clustered closely around the mean, resulting in a narrower peak. Conversely, a larger σ suggests a wider spread of data, leading to a broader peak. It essentially describes how much variation or "dispersion" there is from the average (mean).

Instruction on how to run this script

To run this notebook successfully, this notebook must be in the same folder as the Python file called MTGaussianFitting.py

The file input and output folder(s) should be defined in the second cell of this notebook. Also, the name of the input .csv file should be added correctly in the third cell of this notebook. It is important to know that all the imported libraries used in this code should be correctly installed in a created Python environment. The following lines can be used to install the required libraries to run this notebook:

• Jupyter lab conda install -c conda-forge jupyterlab

• Pandas pip install pandas

• Numpy conda install -c conda-forge numpy

• Matplotlib conda install -c conda-forge matplotlib

• Scipy conda install -c conda-forge scipy

Bins size estimation

To optimally estimate the bins size of the histogram plot, Freedman Diaconis Estimator function was used in the code. For more detail, see link (Freedman Diaconis Estimator)

$h = 2 \frac{IQR}{n^{\frac{1}{3}}}$

• $h$: Freedman Diaconis Estimator
• $n$: number or length of data
• $IQR$: Interquartile Range See link (Freedman Diaconis Estimator)

The binwidth is proportional to the interquartile range (IQR) and inversely proportional to cube root of data.size. Can be too conservative for small datasets, but is quite good for large datasets. The IQR is very robust to outliers.