Correction: Experimentally-Based Computational Investigation into Beat-To-Beat Variability in Ventricular Repolarization and Its Response to Ionic Current Inhibition.

[This corrects the article DOI: 10.1371/journal.pone.0151461.].

Sampling methods for exploring between-subject variability in cardiac electrophysiology experiments.

Between-subject and within-subject variability is ubiquitous in biology and physiology, and understanding and dealing with this is one of the biggest challenges in medicine. At the same time, it is difficult to investigate this variability by experiments alone. A recent modelling and simulation approach, known as population of models (POM), allows this exploration to take place by building a mathematical model consisting of multiple parameter sets calibrated against experimental data. However, finding such sets within a high-dimensional parameter space of complex electrophysiological models is computationally challenging. By placing the POM approach within a statistical framework, we develop a novel and efficient algorithm based on sequential Monte Carlo (SMC). We compare the SMC approach with Latin hypercube sampling (LHS), a method commonly adopted in the literature for obtaining the POM, in terms of efficiency and output variability in the presence of a drug block through an in-depth investigation via the Beeler-Reuter cardiac electrophysiological model. We show improved efficiency for SMC that produces similar responses to LHS when making out-of-sample predictions in the presence of a simulated drug block. Finally, we show the performance of our approach on a complex atrial electrophysiological model, namely the Courtemanche-Ramirez-Nattel model.

Experimentally-Based Computational Investigation into Beat-To-Beat Variability in Ventricular Repolarization and Its Response to Ionic Current Inhibition.

Beat-to-beat variability in repolarization (BVR) has been proposed as an arrhythmic risk marker for disease and pharmacological action. The mechanisms are unclear but BVR is thought to be a cell level manifestation of ion channel stochasticity, modulated by cell-to-cell differences in ionic conductances. In this study, we describe the construction of an experimentally-calibrated set of stochastic cardiac cell models that captures both BVR and cell-to-cell differences in BVR displayed in isolated canine action potential measurements using pharmacological agents. Simulated and experimental ranges of BVR are compared in control and under pharmacological inhibition, and the key ionic currents determining BVR under physiological and pharmacological conditions are identified. Results show that the 4-aminopyridine-sensitive transient outward potassium current, Ito1, is a fundamental driver of BVR in control and upon complete inhibition of the slow delayed rectifier potassium current, IKs. In contrast, IKs and the L-type calcium current, ICaL, become the major contributors to BVR upon inhibition of the fast delayed rectifier potassium current, IKr. This highlights both IKs and Ito1 as key contributors to repolarization reserve. Partial correlation analysis identifies the distribution of Ito1 channel numbers as an important independent determinant of the magnitude of BVR and drug-induced change in BVR in control and under pharmacological inhibition of ionic currents. Distributions in the number of IKs and ICaL channels only become independent determinants of the magnitude of BVR upon complete inhibition of IKr. These findings provide quantitative insights into the ionic causes of BVR as a marker for repolarization reserve, both under control condition and pharmacological inhibition.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem.

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via calculation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases, the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN: decoys are able to block binding sites on PTEN mRNAs, thereby reducing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations.

Anomalous diffusion and multifractional Brownian motion: simulating molecular crowding and physical obstacles in systems biology.

There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our sample data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.

The systems biology approach to drug development: application to toxicity assessment of cardiac drugs.

Side effects account for most of the instances of failure of candidate drugs at late stages of development. These development failures contribute to the exorbitant cost of bringing new compounds to market: a single withdrawal can represent a loss of more than $1 billion. Many unwanted actions of drugs affect the heart, resulting in potentially proarrhythmic alteration of ion channel function. Because these can be fatal, potential electrophysiological cardiotoxicity is among the most stringent exclusion criteria in the licensing process.

Atypical mycobacterial cervical lymphadenitis with extensive local spread: a surgical disease.

Atypical (nontuberculous) mycobacterium is an uncommon cause of cervical lymphadenitis in immunocompetent children. Rarely, this disease progresses to locoregional destruction of the deep structures of the neck including salivary glands. Recent reports suggest medical monotherapy as an effective treatment of this disease. We report three cases of children who experienced progression to locoregional disease while on appropriate antibiotics. We suggest that the patient population to benefit from medical monotherapy has yet to be adequately defined. In our experience, surgical therapy is the only effective treatment for locoregional disease.

Stochastic approaches for modelling in vivo reactions.

In recent years, stochastic modelling has emerged as a physically more realistic alternative for modelling in vivo reactions. There are numerous stochastic approaches available in the literature; most of these assume that observed random fluctuations are a consequence of the small number of reacting molecules. We review some important developments of the stochastic approach and consider its suitability for modelling intracellular reactions. We then describe recent efforts to include the fluctuation effects caused by the structural organisation of the cytoplasm and the limited diffusion of molecules due to macromolecular crowding.

Computer simulation of magnetic resonance spectra employing homotopy.

Multidimensional homotopy provides an efficient method for accurately tracing energy levels and hence transitions in the presence of energy level anticrossings and looping transitions. Herein we describe the application and implementation of homotopy to the analysis of continuous wave electron paramagnetic resonance spectra. The method can also be applied to electron nuclear double resonance, electron spin echo envelope modulation, solid-state nuclear magnetic resonance, and nuclear quadrupole resonance spectra.

Inhibition of metastatic spread by I.C.R.F. 159: selective deletion of a malignant characteristic.

Treatment with I.C.R.F. 159 completely inhibited metastasis formation in mice implanted with Lewis lung carcinoma at doses having little influence on the rate of growth of the primary implant. This inhibition was due to the effect of I.C.R.F. 159 on the development of blood vessels of the invading margins of the primary tumour. So far as is known, this is the first time a drug has induced a specific loss of the malignant characteristic of blood-borne tumour cell dissemination.