Multiscale modeling of biomolecular systems: in serial and in parallel

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.     

Non-homogeneous Markov processes for biomedical data analysis

Some time ago, the Markov processes were introduced in biomedical sciences in order to study disease history events. Homogeneous and Non-homogeneous Markov processes are an important field of research into stochastic processes, especially when exact transition times are unknown and interval-censored observations are present in the analysis. Non-homogeneous Markov process should be used when the homogeneous assumption is too strong. However these sorts of models increase the complexity of the analysis and standard software is limited. In this paper, some methods for fitting non-homogeneous Markov models are reviewed and an algorithm is proposed for biomedical data analysis. The method has been applied to analyse breast cancer data. Specific software for this purpose has been implemented.     

Parameter inference for stochastic biochemical models from perturbation experiments parallelised at the single cell level

Understanding and characterising biochemical processes inside single cells requires experimental platforms that allow one to perturb and observe the dynamics of such processes as well as computational methods to build and parameterise models from the collected data. Recent progress with experimental platforms and optogenetics has made it possible to expose each cell in an experiment to an individualised input and automatically record cellular responses over days with fine time resolution. However, methods to infer parameters of stochastic kinetic models from single-cell longitudinal data have generally been developed under the assumption that experimental data is sparse and that responses of cells to at most a few different input perturbations can be observed. Here, we investigate and compare different approaches for calculating parameter likelihoods of single-cell longitudinal data based on approximations of the chemical master equation (CME) with a particular focus on coupling the linear noise approximation (LNA) or moment closure methods to a Kalman filter. We show that, as long as cells are measured sufficiently frequently, coupling the LNA to a Kalman filter allows one to accurately approximate likelihoods and to infer model parameters from data even in cases where the LNA provides poor approximations of the CME. Furthermore, the computational cost of filtering-based iterative likelihood evaluation scales advantageously in the number of measurement times and different input perturbations and is thus ideally suited for data obtained from modern experimental platforms. To demonstrate the practical usefulness of these results, we perform an experiment in which single cells, equipped with an optogenetic gene expression system, are exposed to various different light-input sequences and measured at several hundred time points and use parameter inference based on iterative likelihood evaluation to parameterise a stochastic model of the system.     

A novel approach to predicting human ingress motion using an artificial neural network

Due to the increased availability of digital human models, the need for knowing human movement is important in product design process. If the human motion is derived rapidly as design parameters change, a developer could determine the optimal parameters. For example, the optimal design of the door panel of an automobile can be obtained for a human operator to conduct the easiest ingress and egress motion. However, acquiring motion data from existing methods provides only unrealistic motion or requires a great amount of time. This not only leads to an increased time consumption for a product development, but also causes inefficiency of the overall design process. To solve such problems, this research proposes an algorithm to rapidly and accurately predict full-body human motion using an artificial neural network (ANN) and a motion database, as the design parameters are varied. To achieve this goal, this study refers to the processes behind human motor learning procedures. According to the previous research, human generate new motion based on past motion experience when they encounter new environments. Based on this principle, we constructed a motion capture database. To construct the database, motion capture experiments were performed in various environments using an optical motion capture system. To generate full-body human motion using this data, a generalized regression neural network (GRNN) was used. The proposed algorithm not only guarantees rapid and accurate results but also overcomes the ambiguity of the human motion objective function, which has been pointed out as a limitation of optimization-based research. Statistical criteria were utilized to confirm the similarity between the generated motion and actual human motion. Our research provides the basis for a rapid motion prediction algorithm that can include a variety of environmental variables. This research contributes to an increase in the usability of digital human models, and it can be applied to various research fields.     

Inference for nonlinear epidemiological models using genealogies and time series

Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses - increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data.     

In‐line monitoring of amino acids in mammalian cell cultures using raman spectroscopy and multivariate chemometrics models

The application of PAT for in‐line monitoring of biopharmaceutical manufacturing operations has a central role in developing more robust and consistent processes. Various spectroscopic techniques have been applied for collecting real‐time data from cell culture processes. Among these, Raman spectroscopy has been shown to have advantages over other spectroscopic techniques, especially in aqueous culture solutions. Measurements of several process parameters such as glucose, lactate, glutamine, glutamate, ammonium, osmolality and VCD using Raman‐based chemometrics models have been reported in literature. The application of Raman spectroscopy, coupled with calibration models for amino acid measurement in cell cultures, has been assessed. The developed models cover four amino acids important for cell growth and production: tyrosine, tryptophan, phenylalanine and methionine. The chemometrics models based on Raman spectroscopy data demonstrate the significant potential for the quantification of tyrosine, tryptophan and phenylalanine. The model for methionine would have to be further refined to improve quantification.     

Predicting in vitro drug sensitivity using Random Forests

MOTIVATION: Panels of cell lines such as the NCI-60 have long been used to test drug candidates for their ability to inhibit proliferation. Predictive models of in vitro drug sensitivity have previously been constructed using gene expression signatures generated from gene expression microarrays. These statistical models allow the prediction of drug response for cell lines not in the original NCI-60. We improve on existing techniques by developing a novel multistep algorithm that builds regression models of drug response using Random Forest, an ensemble approach based on classification and regression trees (CART). RESULTS: This method proved successful in predicting drug response for both a panel of 19 Breast Cancer and 7 Glioma cell lines, outperformed other methods based on differential gene expression, and has general utility for any application that seeks to relate gene expression data to a continuous output variable. Implementation: Software was written in the R language and will be available together with associated gene expression and drug response data as the package ivDrug at http://r-forge.r-project.org.     

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data.     

Joint modelling of repeated transitions in follow-up data--a case study on breast cancer data

In longitudinal studies where time to a final event is the ultimate outcome often information is available about intermediate events the individuals may experience during the observation period. Even though many extensions of the Cox proportional hazards model have been proposed to model such multivariate time-to-event data these approaches are still very rarely applied to real datasets. The aim of this paper is to illustrate the application of extended Cox models for multiple time-to-event data and to show their implementation in popular statistical software packages. We demonstrate a systematic way of jointly modelling similar or repeated transitions in follow-up data by analysing an event-history dataset consisting of 270 breast cancer patients, that were followed-up for different clinical events during treatment in metastatic disease. First, we show how this methodology can also be applied to non Markovian stochastic processes by representing these processes as "conditional" Markov processes. Secondly, we compare the application of different Cox-related approaches to the breast cancer data by varying their key model components (i.e. analysis time scale, risk set and baseline hazard function). Our study showed that extended Cox models are a powerful tool for analysing complex event history datasets since the approach can address many dynamic data features such as multiple time scales, dynamic risk sets, time-varying covariates, transition by covariate interactions, autoregressive dependence or intra-subject correlation.     

Random Walk Models for Bayesian Clustering of Gene Expression Profiles

The analysis of gene expression temporal profiles is a topic of increasing interest in functional genomics. Model-based clustering methods are particularly interesting because they are able to capture the dynamic nature of these data and to identify the optimal number of clusters. We have defined a new Bayesian method that allows us to cope with some important issues that remain unsolved in the currently available approaches: the presence of time dislocations in gene expression, the non-stationarity of the processes generating the data, and the presence of data collected on an irregular temporal grid. Our method, which is based on random walk models, requires only mild a priori assumptions about the nature of the processes generating the data and explicitly models inter-gene variability within each cluster. It has first been validated on simulated datasets and then employed for the analysis of a dataset relative to serum-stimulated fibroblasts. In all cases, the results have been promising, showing that the method can be helpful in functional genomics research.     

A Simple Regression-Based Method to Map Quantitative Trait Loci Underlying Function-Valued Phenotypes

Most statistical methods for quantitative trait loci (QTL) mapping focus on a single phenotype. However, multiple phenotypes are commonly measured, and recent technological advances have greatly simplified the automated acquisition of numerous phenotypes, including function-valued phenotypes, such as growth measured over time. While methods exist for QTL mapping with function-valued phenotypes, they are generally computationally intensive and focus on single-QTL models. We propose two simple, fast methods that maintain high power and precision and are amenable to extensions with multiple-QTL models using a penalized likelihood approach. After identifying multiple QTL by these approaches, we can view the function-valued QTL effects to provide a deeper understanding of the underlying processes. Our methods have been implemented as a package for R, funqtl.     

The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches

Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth–death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle’s study of a susceptible–infected–recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.     

Using phylochronology to reveal cryptic population histories: review and synthesis of 29 ancient DNA studies

The evolutionary history of a population involves changes in size, movements and selection pressures through time. Reconstruction of population history based on modern genetic data tends to be averaged over time or to be biased by generally reflecting only recent or extreme events, leaving many population historic processes undetected. Temporal genetic data present opportunities to reveal more complex population histories and provide important insights into what processes have influenced modern genetic diversity. Here we provide a synopsis of methods available for the analysis of ancient genetic data. We review 29 ancient DNA studies, summarizing the analytical methods and general conclusions for each study. Using the serial coalescent and a model-testing approach, we then re-analyse data from two species represented by these data sets in a common interpretive framework. Our analyses show that phylochronologic data can reveal more about population history than modern data alone, thus revealing 'cryptic' population processes, and enable us to determine whether simple or complex models best explain the data. Our re-analyses point to the need for novel methods that consider gene flow, multiple populations and population size in reconstruction of population history. We conclude that population genetic samples over large temporal and geographical scales, when analysed using more complex models and the serial coalescent, are critical to understand past population dynamics and provide important tools for reconstructing the evolutionary process.     

Semi‐Markov Models with Phase‐Type Sojourn Distributions

Summary Continuous‐time multistate models are widely used for categorical response data, particularly in the modeling of chronic diseases. However, inference is difficult when the process is only observed at discrete time points, with no information about the times or types of events between observation times, unless a Markov assumption is made. This assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state. Such a formulation results in a semi‐Markov model. We show that the computational problems associated with fitting semi‐Markov models to panel‐observed data can be alleviated by considering a class of semi‐Markov models with phase‐type sojourn distributions. This allows methods for hidden Markov models to be applied. In addition, extensions to models where observed states are subject to classification error are given. The methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post‐lung‐transplantation patients.     

Joint analysis of panel count and interval-censored data using distribution-free frailty analysis

We propose a joint analysis of recurrent and nonrecurrent event data subject to general types of interval censoring. The proposed analysis allows for general semiparametric models, including the Box–Cox transformation and inverse Box–Cox transformation models for the recurrent and nonrecurrent events, respectively. A frailty variable is used to account for the potential dependence between the recurrent and nonrecurrent event processes, while leaving the distribution of the frailty unspecified. We apply the pseudolikelihood for interval-censored recurrent event data, usually termed as panel count data, and the sufficient likelihood for interval-censored nonrecurrent event data by conditioning on the sufficient statistic for the frailty and using the working assumption of independence over examination times. Large sample theory and a computation procedure for the proposed analysis are established. We illustrate the proposed methodology by a joint analysis of the numbers of occurrences of basal cell carcinoma over time and time to the first recurrence of squamous cell carcinoma based on a skin cancer dataset, as well as a joint analysis of the numbers of adverse events and time to premature withdrawal from study medication based on a scleroderma lung disease dataset.     

Modeling progression in radiation-induced lung adenocarcinomas

Quantitative multistage carcinogenesis models are used in radiobiology to estimate cancer risks and latency periods (time from exposure to clinical cancer). Steps such as initiation, promotion and transformation have been modeled in detail. However, progression, a later step during which malignant cells can develop into clinical symptomatic cancer, has often been approximated simply as a fixed lag time. This approach discounts important stochastic mechanisms in progression and evidence on the high prevalence of dormant tumors. Modeling progression more accurately is therefore important for risk assessment. Unlike models of earlier steps, progression models can readily utilize not only experimental and epidemiological data but also clinical data such as the results of modern screening and imaging. Here, a stochastic progression model is presented. We describe, with minimal parameterization: the initial growth or extinction of a malignant clone after formation of a malignant cell; the likely dormancy caused, for example, by nutrient and oxygen deprivation; and possible escape from dormancy resulting in a clinical cancer. It is shown, using cohort simulations with parameters appropriate for lung adenocarcinomas, that incorporating such processes can dramatically lengthen predicted latency periods. Such long latency periods together with data on timing of radiation-induced cancers suggest that radiation may influence progression itself.     

Panel semiparametric quantile regression neural network for electricity consumption forecasting

Addressing the forecasting issues is one of the core objectives of developing and restructuring of electric power industry in China. However, there are not enough efforts that have been made to develop an accurate electricity consumption forecasting procedure. In this paper, a panel semiparametric quantile regression neural network (PSQRNN) is developed by combining an artificial neural network and semiparametric quantile regression for panel data. By embedding penalized quantile regression with least absolute shrinkage and selection operator (LASSO), ridge regression and backpropagation, PSQRNN keeps the flexibility of nonparametric models and the interpretability of parametric models simultaneously. The prediction accuracy is evaluated based on China's electricity consumption data set, and the results indicate that PSQRNN performs better compared with three benchmark methods including BP neural network (BP), Support Vector Machine (SVM) and Quantile Regression Neural Network (QRNN).     

Usefulness of single nucleotide polymorphism data for estimating population parameters

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the scaled product of effective population size and per-site mutation rate), which is related to the branch lengths of the reconstructed genealogy. With infinite amounts of data, ML models using SNP data are expected to produce consistent estimates of Theta. With finite amounts of data the estimates are accurate when Theta is high, but tend to be biased upward when Theta is low. If recombination is present and not allowed for in the analysis, the results are additionally biased upward, but this effect can be removed by incorporating recombination into the analysis. SNPs defined as sites that are polymorphic in the actual sample under consideration (sample SNPs) are somewhat more accurate for estimation of Theta than SNPs defined by their polymorphism in a panel chosen from the same population (panel SNPs). Misrepresenting panel SNPs as sample SNPs leads to large errors in the maximum likelihood estimate of Theta. Researchers collecting SNPs should collect and preserve information about the method of ascertainment so that the data can be accurately analyzed.     

A statistical approach to quasi-extinction forecasting

Forecasting population decline to a certain critical threshold (the quasi-extinction risk) is one of the central objectives of population viability analysis (PVA), and such predictions figure prominently in the decisions of major conservation organizations. In this paper, we argue that accurate forecasting of a population's quasi-extinction risk does not necessarily require knowledge of the underlying biological mechanisms. Because of the stochastic and multiplicative nature of population growth, the ensemble behaviour of population trajectories converges to common statistical forms across a wide variety of stochastic population processes. This paper provides a theoretical basis for this argument. We show that the quasi-extinction surfaces of a variety of complex stochastic population processes (including age-structured, density-dependent and spatially structured populations) can be modelled by a simple stochastic approximation: the stochastic exponential growth process overlaid with Gaussian errors. Using simulated and real data, we show that this model can be estimated with 20-30 years of data and can provide relatively unbiased quasi-extinction risk with confidence intervals considerably smaller than (0,1). This was found to be true even for simulated data derived from some of the noisiest population processes (density-dependent feedback, species interactions and strong age-structure cycling). A key advantage of statistical models is that their parameters and the uncertainty of those parameters can be estimated from time series data using standard statistical methods. In contrast for most species of conservation concern, biologically realistic models must often be specified rather than estimated because of the limited data available for all the various parameters. Biologically realistic models will always have a prominent place in PVA for evaluating specific management options which affect a single segment of a population, a single demographic rate, or different geographic areas. However, for forecasting quasi-extinction risk, statistical models that are based on the convergent statistical properties of population processes offer many advantages over biologically realistic models.     

An application of statistical models in mental health research

Two statistical models are presented to describe the admission-discharge process of a psychiatric unit. Both models have the form of Markov processes. Common statistical terms such as length of stay in hospital, time off books, patients on books, and number of admissions are related to characteristics of the models. The models permit an assessment of the effect of studying statistical data based on cohorts of individuals rather than individuals considered separately. In addition, with refinement, it is expected that these models will permit the use of more sophisticated statistical methods in psychiatric research problems. The authors wish to acknowledge the continuing support of the Psychiatric Services Branch, Saskatchewan Department of Health and National Health Grant 607-7-129.