Colocalization metrics

In this example, we demonstrate the use of different metrics to assess the colocalization of two different image channels.

Colocalization can be split into two different concepts: 1. Co-occurence: What proportion of a substance is localized to a particular area? 2. Correlation: What is the relationship in intensity between two substances?

Co-occurence: subcellular localization

Imagine that we are trying to determine the subcellular localization of a protein - is it located more in the nucleus or cytoplasm compared to a control?

We begin by segmenting the nucleus of a sample image as described in another example and assume that whatever is not in the nucleus is in the cytoplasm. The protein, “protein A”, will be simulated as blobs and segmented.

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.colors import LinearSegmentedColormap
from scipy import ndimage as ndi
import skimage as ski

rng = np.random.default_rng()

# segment nucleus
nucleus = ski.data.protein_transport()[0, 0, :, :180]
smooth = ski.filters.gaussian(nucleus, sigma=1.5)
thresh = smooth > ski.filters.threshold_otsu(smooth)
fill = ndi.binary_fill_holes(thresh)
nucleus_seg = ski.segmentation.clear_border(fill)

# protein blobs of varying intensity
proteinA = np.zeros_like(nucleus, dtype="float64")
proteinA_seg = np.zeros_like(nucleus, dtype="float64")

for blob_seed in range(10):
    blobs = ski.data.binary_blobs(
        180, blob_size_fraction=0.5, volume_fraction=(50 / (180**2)), rng=blob_seed
    )
    blobs_image = ski.filters.gaussian(blobs, sigma=1.5) * rng.integers(50, 256)
    proteinA += blobs_image
    proteinA_seg += blobs

# plot data
fig, ax = plt.subplots(3, 2, figsize=(8, 12), sharey=True)
ax[0, 0].imshow(nucleus, cmap=plt.cm.gray)
ax[0, 0].set_title('Nucleus')

ax[0, 1].imshow(nucleus_seg, cmap=plt.cm.gray)
ax[0, 1].set_title('Nucleus segmentation')

black_magenta = LinearSegmentedColormap.from_list("", ["black", "magenta"])
ax[1, 0].imshow(proteinA, cmap=black_magenta)
ax[1, 0].set_title('Protein A')

ax[1, 1].imshow(proteinA_seg, cmap=black_magenta)
ax[1, 1].set_title('Protein A segmentation')

ax[2, 0].imshow(proteinA, cmap=black_magenta)
ax[2, 0].imshow(nucleus_seg, cmap=plt.cm.gray, alpha=0.2)
ax[2, 0].set_title('Protein A\nwith nucleus overlaid')

ax[2, 1].imshow(proteinA_seg, cmap=black_magenta)
ax[2, 1].imshow(nucleus_seg, cmap=plt.cm.gray, alpha=0.2)
ax[2, 1].set_title('Protein A segmentation\nwith nucleus overlaid')

for a in ax.ravel():
    a.set_axis_off()