Computational network models for molecular, neuronal and brain data in the presence of long range dependence
Keywords: network science
long range dependence
non-parametric methods
hidden markov models

Standard parametric statistical approaches based on comparison to global activity tend to perform poorly when this activity varies over multiple scales. Such multiscale variation, termed long range dependence, is a well-documented features of many biological and neurological data sets. We provide evidence from the literature as well as from data that demonstrates long range dependence across three contexts in: protein, brain and neuronal data. We propose novel non-parametric statistical approaches that account for these dependencies using network models.
In networks of annotated proteins (nodes) connected by their physical interactions (edges), communities of functionally related proteins can provide possible novel drug targets. However, this guilt by association approach is vulnerable to potential bias in protein annotations. By restricted random-walk-based ranking of communities, our method, CommFinedWalker, preserves protein co-expression within well-ranked communities (suggesting functional conservation). The method provides novel drug target candidates that add to the diversity of interesting proteins and potential drug targets for research. As proof of concept, we explore a case study of a community that contains proteins involved in a rare genetic disorder. These results also serve as inspiration for novel methods to rank interesting communities in other contexts including brain state networks.
Brain states have previously been studied across many conditions, including sleep and disorders of consciousness using a variety of models. However, brain state has not yet been studied in pharmacologically-induced unconsciousness. We define a new subclass of models, Hidden Markov Graph Models, to study brain states and communities of brain regions in fMRI data from subjects in both wakefulness and anaesthesia-induced unconsciousness. The framework draws on principles of free energy minimisation and entropy maximisation. We show evidence of characteristic resting state network activity in wakefulness as well as states of reduced temporal and functional complexity that are unique to anaesthesia-induced unconsciousness. These states further relate to established EEG markers of unconsciousness and long range dependent slow waves with implications for effective anaesthesia concentration in surgery.
Lastly, we propose a pipeline to guide experimentation and perform automated detection of synaptic calcium events from single neuron light sheet microscopy data. This pipeline iteratively combines experimentation with experimentally informed simulation to improve experimental outcomes. The model fitting framework we provide draws on the free energy principle, and detection and smoothing methods that account for long range dependence and non-stationary activity present in the microscopy background. Through simulated results we empirically show that our methods can provide consistent estimates of actual experimental conditions that could be used to inform future experimentation.