Modeling markers of disease progression by a hidden Markov process: application to characterizing CD4 cell decline

Multistate models have been increasingly used to model natural history of many diseases as well as to characterize the follow-up of patients under varied clinical protocols. This modeling allows describing disease evolution, estimating the transition rates, and evaluating the therapy effects on progression. In many cases, the staging is defined on the basis of a discretization of the values of continuous markers (CD4 cell count for HIV application) that are subject to great variability due mainly to short time-scale noise (intraindividual variability) and measurement errors. This led us to formulate a Bayesian hierarchical model where, at a first level, a disease process (Markov model on the true states, which are unobserved) is introduced and, at a second level, the measurement process making the link between the true states and the observed marker values is modeled. This hierarchical formulation allows joint estimation of the parameters of both processes. Estimation of the quantities of interest is performed via stochastic algorithms of the family of Markov chain Monte Carlo methods. The flexibility of this approach is illustrated by analyzing the CD4 data on HIV patients of the Concorde clinical trial.     

关于极限定理的一个新结果

设{X_n,n≥0}是可列非齐次马氏链,S_n(i_1,…,i_m,w)表示m元状态序组(i_1,…,i_m)在序列(X_1,…,X_m),(X_2,…,X_m 1)…,(X_n,…,X_n m-1)中出现的次数．本文通过利用{X_n,n≥O}在Wiener概率空间的一种实现,给出了关于S_n(i_1,…,i_m,w)的一个对任意可列非齐次马氏链普遍成立的强级限定理．     

The use of ubiquitin lysine mutants to characterize E2–E3 linkage specificity: Mass spectrometry offers a cautionary “tail”

Oligomeric ubiquitin structures (i.e. ubiquitin “chains”) may be formed through any of seven different lysine residues in the polypeptide, or via the amine group of Met 1. Different types of ubiquitin chains can confer very different biological outcomes to a protein substrate, yet the structural characteristics of E2s and E3s that determine ubiquitin linkage specificity remain poorly understood. In vitro autoubiquitylation assays combined with ubiquitin protein variants bearing individually mutated lysine residues (“K‐to‐R” mutants) have thus been widely used to characterize E2–E3 linkage specificity. However, how this type of assay compares to direct identification of ubiquitin linkage types using mass spectrometry (MS) has not been rigorously tested. Here, we characterize the linkage specificity of 12 different E2–E3 combinations using both approaches. The simple MS‐based method described here is more robust, requires less material and is less prone to bias introduced by, e.g. the use of mutant proteins with unknown effects on E1, E2 or E3 recognition, antibodies with uncharacterized epitopes, the low dynamic range of X‐ray film, and additional sources of experimental error. Indeed, our results suggest that the K‐to‐R assay be approached with some caution.     

Hydrothermal treatment and iodine binding provide insights into the organization of glucan chains within the semi‐crystalline lamellae of corn starch granules

The importance of glucan chains that pass through both the amorphous and crystalline lamellae (tie chains) in the organization of corn starch granules was studied using heat‐moisture treatment (HMT), annealing (ANN), and iodine binding. Molecular structural analysis showed that hylon starches (HV, HVII, and HVIII) contained higher proportion of intermediate glucan chains (HVIII > HVII > HV) than normal corn (CN) starch. Wide angle X‐ray scattering revealed that on HMT, the extent of polymorphic transition in hylon starches decreased with increasing proportion of intermediate and long chains. Iodine treated hylon starches exhibited increased order in the V‐type polymorphism as evidenced by the intense peak at 20° 2θ and the strong reflection intensity at 7.5° 2θ and the extent of the change depended on the type of hylon starch. DSC results showed that the gelatinization enthalpy of CN and waxy corn starch (CW) remained unchanged after ANN. However, hylon starches showed a significant increase in enthalpy with more distinct endotherms after ANN. It can be concluded that tie chains influence the organization of crystalline lamellae in amylose extender mutant starches. © 2014 Wiley Periodicals, Inc. Biopolymers 101: 871–885, 2014.     

Catastrophe Bond and Risk Modeling: A Review and Calibration Using Chinese Earthquake Loss Data

Earthquake risks are attracting increased attention as a result of recent catastrophic events such as the Wenchuan earthquake in China. This article aims to select, tailor, and develop loss modeling methods for catastrophic insurance. We review the state-of-the-art approaches in modeling catastrophe losses for catastrophe bonds’ modeling and pricing. The methods are applied to the 1966–2008 losses resulted from the earthquakes in China. Various error measures are proposed for validating catastrophe modeling. Results suggest that the double exponential jump-diffusion model fits the data well.     

Exploring voltage-dependent ion channels in silico by hysteretic conductance

Kinetic models of voltage-dependent ion channels are normally inferred from time records of macroscopic current relaxation or microscopic single channel data. A complementary explorative approach is outlined. Hysteretic conductance refers to conductance delays in response to voltage changes, delays at either macroscopic or microscopic levels of observation. It enables complementary assessments of model assumptions and gating schemes of voltage-dependent channels, e.g. independent versus cooperative gating, and multiple gating modes. Under the Hodgkin-Huxley condition of independent gating, and under ideal measurement conditions, hysteretic conductance makes it also possible to estimate voltage-dependent rate functions. The argument is mainly theoretical, based on experimental observations, and illustrated by simulations of Markov kinetic models.     

A Markov chain Monte Carlo strategy for sampling from the joint posterior distribution of pedigrees and population parameters under a Fisher-Wright model with partial selfing

A simple population genetic model is presented for a hermaphrodite annual species, allowing both selfing and outcrossing. Those male gametes (pollen) responsible for outcrossing are assumed to disperse much further than seeds. Under this model, the pedigree of a sample from a single locality is loop-free. A novel Markov chain Monte Carlo strategy is presented for sampling from the joint posterior distribution of the pedigree of such a sample and the parameters of the population genetic model (including the selfing rate) given the genotypes of the sampled individuals at unlinked marker loci. The computational costs of this Markov chain Monte Carlo strategy scale well with the number of individuals in the sample, and the number of marker loci, but increase exponentially with the age (time since colonisation from the source population) of the local population. Consequently, this strategy is particularly suited to situations where the sample has been collected from a population which is the result of a recent colonisation process.     

Coevolutionary Patterns in Cytochrome c Oxidase Subunit I Depend on Structural and Functional Context

The strength and pattern of coevolution between amino acid residues vary depending on their structural and functional environment. This context dependence, along with differences in analytical technique, is responsible for the different results among coevolutionary analyses of different proteins. It is thus important to perform detailed study of individual proteins to gain better insight into how context dependence can affect coevolutionary patterns even within individual proteins, and to unravel the details of context dependence with respect to structure and function. Here we extend our previous study by presenting further analysis of residue coevolution in cytochrome c oxidase subunit I sequences from 231 vertebrates using a statistically robust phylogeny-based maximum likelihood ratio method. As in previous studies, a strong overall coevolutionary signal was detected, and coevolution within structural regions was significantly related to the C_α distances between residues. While the strong selection for adjacent residues among predicted coevolving pairs in the surface region indicates that the statistical method is highly selective for biologically relevant interactions, the coevolutionary signal was strongest in the transmembrane region, although the distances between coevolving residues were greater. This indicates that coevolution may act to maintain more global structural and functional constraints in the transmembrane region. In the transmembrane region, sites that coevolved according to polarity and hydrophobicity rather than volume had a greater tendency to colocalize with just one of the predicted proton channels (channel H). Thus, the details of coevolution in cytochrome c oxidase subunit I depend greatly on domain structure and residue physicochemical characteristics, but proximity to function appears to play a critical role. We hypothesize that coevolution is indicative of a more important functional role for this channel. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Bayesian flux balance analysis applied to a skeletal muscle metabolic model

In this article, the steady state condition for the multi-compartment models for cellular metabolism is considered. The problem is to estimate the reaction and transport fluxes, as well as the concentrations in venous blood when the stoichiometry and bound constraints for the fluxes and the concentrations are given. The problem has been addressed previously by a number of authors, and optimization-based approaches as well as extreme pathway analysis have been proposed. These approaches are briefly discussed here. The main emphasis of this work is a Bayesian statistical approach to the flux balance analysis (FBA). We show how the bound constraints and optimality conditions such as maximizing the oxidative phosphorylation flux can be incorporated into the model in the Bayesian framework by proper construction of the prior densities. We propose an effective Markov chain Monte Carlo (MCMC) scheme to explore the posterior densities, and compare the results with those obtained via the previously studied linear programming (LP) approach. The proposed methodology, which is applied here to a two-compartment model for skeletal muscle metabolism, can be extended to more complex models.