MOTIVATION: Accumulation models, where a system progressively acquires binary features over time, are common in the study of cancer progression, evolutionary biology, and other fields. Many approaches have been developed to infer the accumulation pathways by which features (e.g. mutations) are acquired over time. However, most of these approaches do not support reversibility: the loss of a feature once it has been acquired (e.g. the clearing of a mutation from a tumor or population). RESULTS: Here, we demonstrate how the well-established Mk model from evolutionary biology, embedded on a hypercubic transition graph, can be used to infer the dynamics of accumulation processes, including the possibility of reversible transitions, from data which may be uncertain and cross-sectional, longitudinal, or phylogenetically/phylogenomically embedded. Positive and negative interactions between arbitrary sets of features (not limited to pairwise interactions) are supported. We demonstrate this approach with synthetic datasets and real data on bacterial drug resistance and cancer progression. While this implementation is limited in the number of features that can be considered, we discuss how this limitation may be relaxed to deal with larger systems. AVAILABILITY AND IMPLEMENTATION: The code implementing this setup in R is freely available at https://github.com/StochasticBiology/hypermk.

Accumulation processes, where many potentially coupled features are acquired over time, occur throughout the sciences from evolutionary biology to disease progression, and particularly in the study of cancer progression. Existing methods for learning the dynamics of such systems typically assume limited (often pairwise) relationships between feature subsets, cross-sectional or untimed observations, small feature sets, or discrete orderings of events. Here we introduce HyperTraPS-CT (Hypercubic Transition Path Sampling in Continuous Time) to compute posterior distributions on continuous-time dynamics of many, arbitrarily coupled, traits in unrestricted state spaces, accounting for uncertainty in observations and their timings. We demonstrate the capacity of HyperTraPS-CT to deal with cross-sectional, longitudinal, and phylogenetic data, which may have no, uncertain, or precisely specified sampling times. HyperTraPS-CT allows positive and negative interactions between arbitrary subsets of features (not limited to pairwise interactions), supporting Bayesian and maximum-likelihood inference approaches to identify these interactions, consequent pathways, and predictions of future and unobserved features. We also introduce a range of visualisations for the inferred outputs of these processes and demonstrate model selection and regularisation for feature interactions. We apply this approach to case studies on the accumulation of mutations in cancer progression and the acquisition of anti-microbial resistance genes in tuberculosis, demonstrating its flexibility and capacity to produce predictions aligned with applied priorities.

MOTIVATION: The evolution of bacterial drug resistance and other features in biology, the progression of cancer and other diseases and a wide range of broader questions can often be viewed as the sequential stochastic acquisition of binary traits (e.g. genetic changes, symptoms or characters). Using potentially noisy or incomplete data to learn the sequences by which such traits are acquired is a problem of general interest. The problem is complicated for large numbers of traits, which may, individually or synergistically, influence the probability of further acquisitions both positively and negatively. Hypercubic inference approaches, based on hidden Markov models on a hypercubic transition network, address these complications, but previous Bayesian instances can consume substantial time for converged results, limiting their practical use. RESULTS: Here, we introduce HyperHMM, an adapted Baum-Welch (expectation-maximization) algorithm for hypercubic inference with resampling to quantify uncertainty, and show that it allows orders-of-magnitude faster inference while making few practical sacrifices compared to previous hypercubic inference approaches. We show that HyperHMM allows any combination of traits to exert arbitrary positive or negative influence on the acquisition of other traits, relaxing a common limitation of only independent trait influences. We apply this approach to synthetic and biological datasets and discuss its more general application in learning evolutionary and progressive pathways. AVAILABILITY AND IMPLEMENTATION: Code for inference and visualization, and data for example cases, is freely available at https://github.com/StochasticBiology/hypercube-hmm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Mitochondria are highly dynamic organelles, containing vital populations of mitochondrial DNA (mtDNA) distributed throughout the cell. Mitochondria form diverse physical structures in different cells, from cell-wide reticulated networks to fragmented individual organelles. These physical structures are known to influence the genetic makeup of mtDNA populations between cell divisions, but their influence on the inheritance of mtDNA at divisions remains less understood. Here, we use statistical and computational models of mtDNA content inside and outside the reticulated network to quantify how mitochondrial network structure can control the variances of inherited mtDNA copy number and mutant load. We assess the use of moment-based approximations to describe heteroplasmy variance and identify several cases where such an approach has shortcomings. We show that biased inclusion of one mtDNA type in the network can substantially increase heteroplasmy variance (acting as a genetic bottleneck), and controlled distribution of network mass and mtDNA through the cell can conversely reduce heteroplasmy variance below a binomial inheritance picture. Network structure also allows the generation of heteroplasmy variance while controlling copy number inheritance to sub-binomial levels, reconciling several observations from the experimental literature. Overall, different network structures and mtDNA arrangements within them can control the variances of key variables to suit a palette of different inheritance priorities.

The dynamics of the cellular proportion of mutant mtDNA molecules is crucial for mitochondrial diseases. Cellular populations of mitochondria are under homeostatic control, but the details of the control mechanisms involved remain elusive. Here, we use stochastic modelling to derive general results for the impact of cellular control on mtDNA populations, the cost to the cell of different mtDNA states, and the optimisation of therapeutic control of mtDNA populations. This formalism yields a wealth of biological results, including that an increasing mtDNA variance can increase the energetic cost of maintaining a tissue, that intermediate levels of heteroplasmy can be more detrimental than homoplasmy even for a dysfunctional mutant, that heteroplasmy distribution (not mean alone) is crucial for the success of gene therapies, and that long-term rather than short intense gene therapies are more likely to beneficially impact mtDNA populations.

We present a study investigating the role of mitochondrial variability in generating noise in eukaryotic cells. Noise in cellular physiology plays an important role in many fundamental cellular processes, including transcription, translation, stem cell differentiation and response to medication, but the specific random influences that affect these processes have yet to be clearly elucidated. Here we present a mechanism by which variability in mitochondrial volume and functionality, along with cell cycle dynamics, is linked to variability in transcription rate and hence has a profound effect on downstream cellular processes. Our model mechanism is supported by an appreciable volume of recent experimental evidence, and we present the results of several new experiments with which our model is also consistent. We find that noise due to mitochondrial variability can sometimes dominate over other extrinsic noise sources (such as cell cycle asynchronicity) and can significantly affect large-scale observable properties such as cell cycle length and gene expression levels. We also explore two recent regulatory network-based models for stem cell differentiation, and find that extrinsic noise in transcription rate causes appreciable variability in the behaviour of these model systems. These results suggest that mitochondrial and transcriptional variability may be an important mechanism influencing a large variety of cellular processes and properties.