.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/applications/plot_colocalization_metrics.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_applications_plot_colocalization_metrics.py: ====================== 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? .. GENERATED FROM PYTHON SOURCE LINES 17-28 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. .. GENERATED FROM PYTHON SOURCE LINES 28-84 .. code-block:: default import matplotlib.pyplot as plt import numpy as np from matplotlib.colors import LinearSegmentedColormap from scipy import ndimage as ndi from skimage import data, filters, measure, segmentation rng = np.random.default_rng() # segment nucleus nucleus = data.protein_transport()[0, 0, :, :180] smooth = filters.gaussian(nucleus, sigma=1.5) thresh = smooth > filters.threshold_otsu(smooth) fill = ndi.binary_fill_holes(thresh) nucleus_seg = 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 = data.binary_blobs(180, blob_size_fraction=0.5, volume_fraction=(50/(180**2)), rng=blob_seed) blobs_image = 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() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_001.png :alt: Nucleus, Nucleus segmentation, Protein A, Protein A segmentation, Protein A with nucleus overlaid, Protein A segmentation with nucleus overlaid :srcset: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 85-91 Intersection coefficient ======================== After segmenting both the nucleus and the protein of interest, we can determine what fraction of the protein A segmentation overlaps with the nucleus segmentation. .. GENERATED FROM PYTHON SOURCE LINES 91-94 .. code-block:: default measure.intersection_coeff(proteinA_seg, nucleus_seg) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.22 .. GENERATED FROM PYTHON SOURCE LINES 95-110 Manders' Colocalization Coefficient (MCC) ========================================= The overlap coefficient assumes that the area of protein segmentation corresponds to the concentration of that protein - with larger areas indicating more protein. As the resolution of images are usually too small to make out individual proteins, they can clump together within one pixel, making the intensity of that pixel brighter. So, to better capture the protein concentration, we may choose to determine what proportion of the *intensity* of the protein channel is inside the nucleus. This metric is known as Manders' Colocalization Coefficient. In this image, while there are a lot of protein A spots within the nucleus they are dim compared to some of the spots outside the nucleus, so the MCC is much lower than the overlap coefficient. .. GENERATED FROM PYTHON SOURCE LINES 110-113 .. code-block:: default measure.manders_coloc_coeff(proteinA, nucleus_seg) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.1837270538071842 .. GENERATED FROM PYTHON SOURCE LINES 114-122 After choosing a co-occurence metric, we can apply the same process to control images. If no control images are available, the Costes method could be used to compare the MCC value of the original image with that of the randomly scrambled image. Information about this method is given in [1]_. .. [1] J. S. Aaron, A. B. Taylor and T.-L. Chew, Image co-localization – co-occurrence versus correlation. J Cell Sci 1 February 2018 131 (3): jcs211847. doi: https://doi.org/10.1242/jcs.211847 .. GENERATED FROM PYTHON SOURCE LINES 124-131 Correlation: association of two proteins ======================================== Now, imagine that we want to know how closely related two proteins are. First, we will generate protein B and plot intensities of the two proteins in every pixel to see the relationship between them. .. GENERATED FROM PYTHON SOURCE LINES 131-155 .. code-block:: default # generating protein B data that is correlated to protein A for demo proteinB = proteinA + rng.normal(loc=100, scale=10, size=proteinA.shape) # plot images fig, ax = plt.subplots(1, 2, figsize=(8, 8), sharey=True) ax[0].imshow(proteinA, cmap=black_magenta) ax[0].set_title('Protein A') black_cyan = LinearSegmentedColormap.from_list("", ["black", "cyan"]) ax[1].imshow(proteinB, cmap=black_cyan) ax[1].set_title('Protein B') for a in ax.ravel(): a.set_axis_off() # plot pixel intensity scatter plt.figure() plt.scatter(proteinA, proteinB) plt.title('Pixel intensity') plt.xlabel('Protein A intensity') plt.ylabel('Protein B intensity') .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_002.png :alt: Protein A, Protein B :srcset: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_002.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_003.png :alt: Pixel intensity :srcset: /auto_examples/applications/images/sphx_glr_plot_colocalization_metrics_003.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(38.347222222222214, 0.5, 'Protein B intensity') .. GENERATED FROM PYTHON SOURCE LINES 156-158 The intensities look linearly correlated so Pearson's Correlation Coefficient would give us a good measure of how strong the association is. .. GENERATED FROM PYTHON SOURCE LINES 158-162 .. code-block:: default pcc, pval = measure.pearson_corr_coeff(proteinA, proteinB) print(f"PCC: {pcc:0.3g}, p-val: {pval:0.3g}") .. rst-class:: sphx-glr-script-out .. code-block:: none PCC: 0.816, p-val: 0 .. GENERATED FROM PYTHON SOURCE LINES 163-168 Sometimes the intensities are correlated but not in a linear way. A rank-based correlation coefficient like `Spearman's `_ might give a more accurate measure of the non-linear relationship in that case. .. GENERATED FROM PYTHON SOURCE LINES 168-169 .. code-block:: default plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.784 seconds) .. _sphx_glr_download_auto_examples_applications_plot_colocalization_metrics.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-image/scikit-image/v0.21.x?filepath=notebooks/auto_examples/applications/plot_colocalization_metrics.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_colocalization_metrics.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_colocalization_metrics.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_