Quantifying the distribution of probes between subcellular locations using unsupervised pattern unmixing

Abstract

Motivation: Proteins exhibit complex subcellular distributions, which may include localizing in more than one organelle and varying in location depending on the cell physiology. Estimating the amount of protein distributed in each subcellular location is essential for quantitative understanding and modeling of protein dynamics and how they affect cell behaviors. We have previously described automated methods using fluorescent microscope images to determine the fractions of protein fluorescence in various subcellular locations when the basic locations in which a protein can be present are known. As this set of basic locations may be unknown (especially for studies on a proteome-wide scale), we here describe unsupervised methods to identify the fundamental patterns from images of mixed patterns and estimate the fractional composition of them.

Methods: We developed two approaches to the problem, both based on identifying types of objects present in images and representing patterns by frequencies of those object types. One is a basis pursuit method (which is based on a linear mixture model), and the other is based on latent Dirichlet allocation (LDA). For testing both approaches, we used images previously acquired for testing supervised unmixing methods. These images were of cells labeled with various combinations of two organelle-specific probes that had the same fluorescent properties to simulate mixed patterns of subcellular location.

Results: We achieved 0.80 and 0.91 correlation between estimated and underlying fractions of the two probes (fundamental patterns) with basis pursuit and LDA approaches, respectively, indicating that our methods can unmix the complex subcellular distribution with reasonably high accuracy.

Availability: http://murphylab.web.cmu.edu/software.

Fig. 1.

Overview of unmixing methods. (a) The algorithms use a collection of images as input in which various concentrations of two probes are present (the concentrations of the Mitotracker and Lysotracker probes are shown by increasing intensity of red and green, respectively). Example images are shown from wells containing only Mitotracker (b), only Lysotracker (c) and a mixture of the two probes (d). (e) Objects with different size and shapes are extracted and object features are calculated. (f) Objects are clustered into groups in feature space, shown with different colors. (g) Fundamental patterns are identified and the fractions they contribute to each image are estimated.

Fig. 2.

LDA for unmixing. α represents the prior on the topics, θ is the topic mixture parameter (one for each of M images), z represents the particular object topic which is combined with β, the topic distributions to generate an object of type w.

Fig. 3.

Average squared reconstruction error as a function of the number of patterns B for basis pursuit. This is the value of ∑_i ‖ε‖² in (2). For B = 0, we show the total variance, i.e.

Fig. 4.

Log likelihood as a function of the number of fundamental patterns.

Fig. 5.

Comparison of results for different unmixing methods. The inferred fraction of pattern 1 is displayed as different intensities of gray (black corresponding to pure pattern 1). The design matrix, which was kept hidden from the algorithms is shown on the top left, for comparison; the other three panels are results of computation.

Fig. 6.

Estimated concentration as a function of the underlying relative probe concentration. Perfect result would be along the dashed diagonal. In LDA unmixing with 3 fundamental patterns, fractions of the two major patterns are normalized and plotted over ground-truth.