Bayesian classification of OXPHOS deficient skeletal myofibres

Abstract

Mitochondria are organelles in most human cells which release the energy required for cells to function. Oxidative phosphorylation (OXPHOS) is a key biochemical process within mitochondria required for energy production and requires a range of proteins and protein complexes. Mitochondria contain multiple copies of their own genome (mtDNA), which codes for some of the proteins and ribonucleic acids required for mitochondrial function and assembly. Pathology arises from genetic defects in mtDNA and can reduce cellular abundance of OXPHOS proteins, affecting mitochondrial function. Due to the continuous turn-over of mtDNA, pathology is random and neighbouring cells can possess different OXPHOS protein abundance. Estimating the proportion of cells where OXPHOS protein abundance is too low to maintain normal function is critical to understanding disease severity and predicting disease progression. Currently, one method to classify single cells as being OXPHOS deficient is prevalent in the literature. The method compares a patient's OXPHOS protein abundance to that of a small number of healthy control subjects. If the patient's cell displays an abundance which differs from the abundance of the controls then it is deemed deficient. However, due to the natural variation between subjects and the low number of control subjects typically available, this method is inflexible and often results in a large proportion of patient cells being misclassified. These misclassifications have significant consequences for the clinical interpretation of these data. We propose a single-cell classification method using a Bayesian hierarchical mixture model, which allows for inter-subject OXPHOS protein abundance variation. The model accurately classifies an example dataset of OXPHOS protein abundances in skeletal muscle fibres (myofibres). When comparing the proposed and existing model classifications to manual classifications performed by experts, the proposed model results in estimates of the proportion of deficient myofibres that are consistent with expert manual classifications.

Fig 1. Random, mosaic pattern of single skeletal muscle fibres OXPHOS protein abundance within a cross-section.

Pseudo image of approximately 130 skeletal muscle fibre cross-sections captured by imaging mass cytometry after needle biopsy of a patient (P05) with a nuclear DNA variant causing multiple deletions in mtDNA. Yellow shows the level of VDAC (mitochondrial mass surrogate), red shows the level of MTCO1 (OXPHOS protein), and white shows the level of DMD (cell membrane marker).

Fig 2. Single-myofibre OXPHOS protein abundances split into two populations; like-control and not-like-control.

Single-fibre protein abundances were collected by Imaging Mass Cytometry (IMC) from skeletal muscle myofibres from four healthy control subjects (grey, 1,155 myofibres) and one patient, P09, (pink, 571 myofibres).

Fig 3. Frequentist classification arbitrarily splits healthy myofibre populations.

(top) Frequentist model’s 95% predictive interval and classifications for all three OXPHOS proteins in P09 with 571 myofibres (coloured points). Control myofibres are shown in grey (1,155 from four healthy subjects). Patient myofibres are coloured blue or red, depending if the model classified them as like-control or not-like-control respectively. The 95% predictive interval and fitted values for the model are shown in green. The manually classified not-like-control myofibres are shown with a small yellow dot within the myofibre’s point.

Fig 4. Bayesian model correctly identifies the majority of like-control patient myofibres.

Model posterior and classifications for three OXPHOS proteins for P09 with 571 myofibres (coloured points). Control myofibres are shown in grey (1,155 myofibres from four healthy subjects). Patient myofibres are shown on a scale of blue to red, depending on their probability of being not-like-control. The 95% posterior predictive interval and fitted values for the healthy patient (log) OXPHOS abundance and shown in green.

Fig 5. Marginal prior and posterior densities for all parameters after classifying myofibres from P09 by NDUFB8.

Kernel density estimates of 20,000 draws from prior (pink) and posterior (green) distributions. Posterior densities of patient slope and intercept are thick, solid green. The control posteriors are shown as transparent green. Dotted lines indicate the population marginal densities of the population-level distributions of the slope and intercept, $\text{N}\left({\mu }_m,{\tau }_m^{-1}\right)$ and $\text{N}\left({\mu }_c,{\tau }_c^{-1}\right)$.

Fig 6. Difference between Bayesian model and manual classification is minimised at γ = 0 . 0001.

The mean absolute difference (MAD) between the Bayesian proportion of difference and the manual classification calculated across all samples and proteins within the dataset was calculated for varying values of γ.

Fig 7. The difference between the frequentist and manual estimates of the proportion of not-like-control is larger than that of the Bayesian and manual estimates.

The differences between the manual and frequentist classifications are point estimates and are shown as triangles. The difference between the Bayesian and manual classifications is distributions summarised by 5,000 posterior draws. Each posterior sample of the difference distribution is shown as a small transparent circle. The dashed line is zero. Therefore, the distance between the dashed line and the points is the difference in the estimated proportion of not-like control myofibres from the two methods models and the manual classification.