HIV with contact-tracing: a case study in Approximate Bayesian Computation

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%

Inference on periodicity of circadian time series

Estimation of the period length of time-course data from cyclical biological processes, such as those driven by the circadian pacemaker, is crucial for inferring the properties of the biological clock found in many living organisms. We propose a methodology for period estimation based on spectrum resampling (SR) techniques. Simulation studies show that SR is superior and more robust to non-sinusoidal and noisy cycles than a currently used routine based on Fourier approximations. In addition, a simple fit to the oscillations using linear least squares is available, together with a non-parametric test for detecting changes in period length which allows for period estimates with different variances, as frequently encountered in practice. The proposed methods are motivated by and applied to various data examples from chronobiology

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Planning for the next influenza H1N1 season: a modelling study

<p>Abstract</p> <p>Background</p> <p>The level of herd immunity before and after the first 2009 pandemic season is not precisely known, and predicting the shape of the next pandemic H1N1 season is a difficult challenge.</p> <p>Methods</p> <p>This was a modelling study based on data on medical visits for influenza-like illness collected by the French General Practitioner Sentinel network, as well as pandemic H1N1 vaccination coverage rates, and an individual-centred model devoted to influenza. We estimated infection attack rates during the first 2009 pandemic H1N1 season in France, and the rates of pre- and post-exposure immunity. We then simulated various scenarios in which a pandemic influenza H1N1 virus would be reintroduced into a population with varying levels of protective cross-immunity, and considered the impact of extending influenza vaccination.</p> <p>Results</p> <p>During the first pandemic season in France, the proportion of infected persons was 18.1% overall, 38.3% among children, 14.8% among younger adults and 1.6% among the elderly. The rates of pre-exposure immunity required to fit data collected during the first pandemic season were 36% in younger adults and 85% in the elderly. We estimated that the rate of post-exposure immunity was 57.3% (95% Confidence Interval (95%CI) 49.6%-65.0%) overall, 44.6% (95%CI 35.5%-53.6%) in children, 53.8% (95%CI 44.5%-63.1%) in younger adults, and 87.4% (95%CI 82.0%-92.8%) in the elderly.</p> <p>The shape of a second season would depend on the degree of persistent protective cross-immunity to descendants of the 2009 H1N1 viruses. A cross-protection rate of 70% would imply that only a small proportion of the population would be affected. With a cross-protection rate of 50%, the second season would have a disease burden similar to the first, while vaccination of 50% of the entire population, in addition to the population vaccinated during the first pandemic season, would halve this burden. With a cross-protection rate of 30%, the second season could be more substantial, and vaccination would not provide a significant benefit.</p> <p>Conclusions</p> <p>These model-based findings should help to prepare for a second pandemic season, and highlight the need for studies of the different components of immune protection.</p

Modeling of negative Poisson’s ratio (auxetic) crystalline cellulose Iβ

Energy minimizations for unstretched and stretched cellulose models using an all-atom empirical force field (Molecular Mechanics) have been performed to investigate the mechanism for auxetic (negative Poisson’s ratio) response in crystalline cellulose Iβ from kraft cooked Norway spruce. An initial investigation to identify an appropriate force field led to a study of the structure and elastic constants from models employing the CVFF force field. Negative values of on-axis Poisson’s ratios nu31 and nu13 in the x1-x3 plane containing the chain direction (x3) were realized in energy minimizations employing a stress perpendicular to the hydrogen-bonded cellobiose sheets to simulate swelling in this direction due to the kraft cooking process. Energy minimizations of structural evolution due to stretching along the x3 chain direction of the ‘swollen’ (kraft cooked) model identified chain rotation about the chain axis combined with inextensible secondary bonds as the most likely mechanism for auxetic response

Filtering and inference for stochastic oscillators with distributed delays

Motivation The time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here. Results We develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus. Availability and implementation Programmes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD

Scalable Bayesian inference for coupled hidden Markov and semi-Markov models

Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyse models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of Escherichia coli O157:H7 in cattle

Extracting fluorescent reporter time courses of cell lineages from high-throughput microscopy at low temporal resolution

The extraction of fluorescence time course data is a major bottleneck in high-throughput live-cell microscopy. Here we present an extendible framework based on the open-source image analysis software ImageJ, which aims in particular at analyzing the expression of fluorescent reporters through cell divisions. The ability to track individual cell lineages is essential for the analysis of gene regulatory factors involved in the control of cell fate and identity decisions. In our approach, cell nuclei are identified using Hoechst, and a characteristic drop in Hoechst fluorescence helps to detect dividing cells. We first compare the efficiency and accuracy of different segmentation methods and then present a statistical scoring algorithm for cell tracking, which draws on the combination of various features, such as nuclear intensity, area or shape, and importantly, dynamic changes thereof. Principal component analysis is used to determine the most significant features, and a global parameter search is performed to determine the weighting of individual features. Our algorithm has been optimized to cope with large cell movements, and we were able to semi-automatically extract cell trajectories across three cell generations. Based on the MTrackJ plugin for ImageJ, we have developed tools to efficiently validate tracks and manually correct them by connecting broken trajectories and reassigning falsely connected cell positions. A gold standard consisting of two time-series with 15,000 validated positions will be released as a valuable resource for benchmarking. We demonstrate how our method can be applied to analyze fluorescence distributions generated from mouse stem cells transfected with reporter constructs containing transcriptional control elements of the Msx1 gene, a regulator of pluripotency, in mother and daughter cells. Furthermore, we show by tracking zebrafish PAC2 cells expressing FUCCI cell cycle markers, our framework can be easily adapted to different cell types and fluorescent markers