Dataset Information

Synchrotron imaging and Markov Chain Monte Carlo reveal tooth mineralization patterns.

ABSTRACT: The progressive character of tooth formation records aspects of mammalian life history, diet, seasonal behavior and climate. Tooth mineralization occurs in two stages: secretion and maturation, which overlap to some degree. Despite decades of study, the spatial and temporal pattern of elemental incorporation during enamel mineralization remains poorly characterized. Here we use synchrotron X-ray microtomography and Markov Chain Monte Carlo sampling to estimate mineralization patterns from an ontogenetic series of sheep molars (n = 45 M1s, 18 M2s). We adopt a Bayesian approach that posits a general pattern of maturation estimated from individual- and population-level mineral density variation over time. This approach converts static images of mineral density into a dynamic model of mineralization, and demonstrates that enamel secretion and maturation waves advance at nonlinear rates with distinct geometries. While enamel secretion is ordered, maturation geometry varies within a population and appears to be driven by diffusive processes. Our model yields concrete expectations for the integration of physiological and environmental signals, which is of particular significance for paleoseasonality research. This study also provides an avenue for characterizing mineralization patterns in other taxa. Our synchrotron imaging data and model are available for application to multiple disciplines, including health, material science, and paleontological research.

SUBMITTER: Green DR

PROVIDER: S-EPMC5648163 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Synchrotron imaging and Markov Chain Monte Carlo reveal tooth mineralization patterns.

Green Daniel R DR Green Gregory M GM Colman Albert S AS Bidlack Felicitas B FB Tafforeau Paul P Smith Tanya M TM

PloS one 20171019 10

The progressive character of tooth formation records aspects of mammalian life history, diet, seasonal behavior and climate. Tooth mineralization occurs in two stages: secretion and maturation, which overlap to some degree. Despite decades of study, the spatial and temporal pattern of elemental incorporation during enamel mineralization remains poorly characterized. Here we use synchrotron X-ray microtomography and Markov Chain Monte Carlo sampling to estimate mineralization patterns from an ont ...[more]

PMID: 29049333

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Project description:BackgroundIn quantitative biology, mathematical models are used to describe and analyze biological processes. The parameters of these models are usually unknown and need to be estimated from experimental data using statistical methods. In particular, Markov chain Monte Carlo (MCMC) methods have become increasingly popular as they allow for a rigorous analysis of parameter and prediction uncertainties without the need for assuming parameter identifiability or removing non-identifiable parameters. A broad spectrum of MCMC algorithms have been proposed, including single- and multi-chain approaches. However, selecting and tuning sampling algorithms suited for a given problem remains challenging and a comprehensive comparison of different methods is so far not available.ResultsWe present the results of a thorough benchmarking of state-of-the-art single- and multi-chain sampling methods, including Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering and Parallel Hierarchical Sampling. Different initialization and adaptation schemes are considered. To ensure a comprehensive and fair comparison, we consider problems with a range of features such as bifurcations, periodical orbits, multistability of steady-state solutions and chaotic regimes. These problem properties give rise to various posterior distributions including uni- and multi-modal distributions and non-normally distributed mode tails. For an objective comparison, we developed a pipeline for the semi-automatic comparison of sampling results.ConclusionThe comparison of MCMC algorithms, initialization and adaptation schemes revealed that overall multi-chain algorithms perform better than single-chain algorithms. In some cases this performance can be further increased by using a preceding multi-start local optimization scheme. These results can inform the selection of sampling methods and the benchmark collection can serve for the evaluation of new algorithms. Furthermore, our results confirm the need to address exploration quality of MCMC chains before applying the commonly used quality measure of effective sample size to prevent false analysis conclusions.

Dataset Information

Synchrotron imaging and Markov Chain Monte Carlo reveal tooth mineralization patterns.

Publications

Synchrotron imaging and Markov Chain Monte Carlo reveal tooth mineralization patterns.

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