Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators.

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.

Post-Processing of MCMC.

Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to approximate the posterior and derived quantities of interest. Despite this, the issue of how the output from a Markov chain is post-processed and reported is often overlooked. Convergence diagnostics can be used to control bias via burn-in removal, but these do not account for (common) situations where a limited computational budget engenders a bias-variance trade-off. The aim of this article is to review state-of-the-art techniques for post-processing Markov chain output. Our review covers methods based on discrepancy minimisation, which directly address the bias-variance trade-off, as well as general-purpose control variate methods for approximating expected quantities of interest.

Causal Learning via Manifold Regularization.

This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as 'labels' and to exploit available data on the variables of interest to provide features for the labelling task. Background scientific knowledge or any available interventional data provide labels on some causal relationships and the remainder are treated as unlabelled. To illustrate the key ideas, we develop a distance-based approach (based on bivariate histograms) within a manifold regularization framework. We present empirical results on three different biological data sets (including examples where causal effects can be verified by experimental intervention), that together demonstrate the efficacy and general nature of the approach as well as its simplicity from a user's point of view.

Repair of Partly Misspecified Causal Diagrams.

Errors in causal diagrams elicited from experts can lead to the omission of important confounding variables from adjustment sets and render causal inferences invalid. In this report, a novel method is presented that repairs a misspecified causal diagram through the addition of edges. These edges are determined using a data-driven approach designed to provide improved statistical efficiency relative to de novo structure learning methods. Our main assumption is that the expert is "directionally informed," meaning that "false" edges provided by the expert would not create cycles if added to the "true" causal diagram. The overall procedure is cast as a preprocessing technique that is agnostic to subsequent causal inferences. Results based on simulated data and data derived from an observational cohort illustrate the potential for data-assisted elicitation in epidemiologic applications. See video abstract at, http://links.lww.com/EDE/B208.

RNA editing generates cellular subsets with diverse sequence within populations.

RNA editing is a mutational mechanism that specifically alters the nucleotide content in transcribed RNA. However, editing rates vary widely, and could result from equivalent editing amongst individual cells, or represent an average of variable editing within a population. Here we present a hierarchical Bayesian model that quantifies the variance of editing rates at specific sites using RNA-seq data from both single cells, and a cognate bulk sample to distinguish between these two possibilities. The model predicts high variance for specific edited sites in murine macrophages and dendritic cells, findings that we validated experimentally by using targeted amplification of specific editable transcripts from single cells. The model also predicts changes in variance in editing rates for specific sites in dendritic cells during the course of LPS stimulation. Our data demonstrate substantial variance in editing signatures amongst single cells, supporting the notion that RNA editing generates diversity within cellular populations.

Causal network inference using biochemical kinetics.

MOTIVATION: Networks are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of biochemical systems are generally non-linear, suggesting that suitable non-linear formulations may offer gains with respect to causal network inference and aid in associated prediction problems. RESULTS: We present a general framework for network inference and dynamical prediction using time course data that is rooted in non-linear biochemical kinetics. This is achieved by considering a dynamical system based on a chemical reaction graph with associated kinetic parameters. Both the graph and kinetic parameters are treated as unknown; inference is carried out within a Bayesian framework. This allows prediction of dynamical behavior even when the underlying reaction graph itself is unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that non-linear formulations can yield gains in causal network inference and permit dynamical prediction and uncertainty quantification in the challenging setting where the reaction graph is unknown. AVAILABILITY AND IMPLEMENTATION: MATLAB R2014a software is available to download from warwick.ac.uk/chrisoates. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Quantifying the multi-scale performance of network inference algorithms.

Graphical models are widely used to study complex multivariate biological systems. Network inference algorithms aim to reverse-engineer such models from noisy experimental data. It is common to assess such algorithms using techniques from classifier analysis. These metrics, based on ability to correctly infer individual edges, possess a number of appealing features including invariance to rank-preserving transformation. However, regulation in biological systems occurs on multiple scales and existing metrics do not take into account the correctness of higher-order network structure. In this paper novel performance scores are presented that share the appealing properties of existing scores, whilst capturing ability to uncover regulation on multiple scales. Theoretical results confirm that performance of a network inference algorithm depends crucially on the scale at which inferences are to be made; in particular strong local performance does not guarantee accurate reconstruction of higher-order topology. Applying these scores to a large corpus of data from the DREAM5 challenge, we undertake a data-driven assessment of estimator performance. We find that the "wisdom of crowds" network, that demonstrated superior local performance in the DREAM5 challenge, is also among the best performing methodologies for inference of regulation on multiple length scales.

Single-cell states in the estrogen response of breast cancer cell lines.

Estrogen responsive breast cancer cell lines have been extensively studied to characterize transcriptional patterns in hormone-responsive tumors. Nevertheless, due to current technological limitations, genome-wide studies have typically been limited to population averaged data. Here we obtain, for the first time, a characterization at the single-cell level of the states and expression signatures of a hormone-starved MCF-7 cell system responding to estrogen. To do so, we employ a recently proposed model that allows for dissecting single-cell states from time-course microarray data. We show that within 32 hours following stimulation, MCF-7 cells traverse, most likely, six states, with a faster early response followed by a progressive deceleration. We also derive the genome-wide transcriptional profiles of such single-cell states and their functional characterization. Our results support a scenario where estrogen promotes cell cycle progression by controlling multiple, sequential regulatory steps, whose single-cell events are here identified.

A stochastic model dissects cell states in biological transition processes.

Many biological processes, including differentiation, reprogramming, and disease transformations, involve transitions of cells through distinct states. Direct, unbiased investigation of cell states and their transitions is challenging due to several factors, including limitations of single-cell assays. Here we present a stochastic model of cellular transitions that allows underlying single-cell information, including cell-state-specific parameters and rates governing transitions between states, to be estimated from genome-wide, population-averaged time-course data. The key novelty of our approach lies in specifying latent stochastic models at the single-cell level, and then aggregating these models to give a likelihood that links parameters at the single-cell level to observables at the population level. We apply our approach in the context of reprogramming to pluripotency. This yields new insights, including profiles of two intermediate cell states, that are supported by independent single-cell studies. Our model provides a general conceptual framework for the study of cell transitions, including epigenetic transformations.

Network inference using steady-state data and Goldbeter-Koshland kinetics. [corrected].

MOTIVATION: Network inference approaches are widely used to shed light on regulatory interplay between molecular players such as genes and proteins. Biochemical processes underlying networks of interest (e.g. gene regulatory or protein signalling networks) are generally nonlinear. In many settings, knowledge is available concerning relevant chemical kinetics. However, existing network inference methods for continuous, steady-state data are typically rooted in statistical formulations, which do not exploit chemical kinetics to guide inference. RESULTS: Herein, we present an approach to network inference for steady-state data that is rooted in non-linear descriptions of biochemical mechanism. We use equilibrium analysis of chemical kinetics to obtain functional forms that are in turn used to infer networks using steady-state data. The approach we propose is directly applicable to conventional steady-state gene expression or proteomic data and does not require knowledge of either network topology or any kinetic parameters. We illustrate the approach in the context of protein phosphorylation networks, using data simulated from a recent mechanistic model and proteomic data from cancer cell lines. In the former, the true network is known and used for assessment, whereas in the latter, results are compared against known biochemistry. We find that the proposed methodology is more effective at estimating network topology than methods based on linear models. AVAILABILITY: mukherjeelab.nki.nl/CODE/GK_Kinetics.zip CONTACT: c.j.oates@warwick.ac.uk; s.mukherjee@nki.nl SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.