Make the most of your samples : Bayes factor estimators for high-dimensional models of sequence evolution

Background: Accurate model comparison requires extensive computation times, especially for parameter-rich models of sequence evolution. In the Bayesian framework, model selection is typically performed through the evaluation of a Bayes factor, the ratio of two marginal likelihoods (one for each model). Recently introduced techniques to estimate (log) marginal likelihoods, such as path sampling and stepping-stone sampling, offer increased accuracy over the traditional harmonic mean estimator at an increased computational cost. Most often, each model's marginal likelihood will be estimated individually, which leads the resulting Bayes factor to suffer from errors associated with each of these independent estimation processes. Results: We here assess the original 'model-switch' path sampling approach for direct Bayes factor estimation in phylogenetics, as well as an extension that uses more samples, to construct a direct path between two competing models, thereby eliminating the need to calculate each model's marginal likelihood independently. Further, we provide a competing Bayes factor estimator using an adaptation of the recently introduced stepping-stone sampling algorithm and set out to determine appropriate settings for accurately calculating such Bayes factors, with context-dependent evolutionary models as an example. While we show that modest efforts are required to roughly identify the increase in model fit, only drastically increased computation times ensure the accuracy needed to detect more subtle details of the evolutionary process. Conclusions: We show that our adaptation of stepping-stone sampling for direct Bayes factor calculation outperforms the original path sampling approach as well as an extension that exploits more samples. Our proposed approach for Bayes factor estimation also has preferable statistical properties over the use of individual marginal likelihood estimates for both models under comparison. Assuming a sigmoid function to determine the path between two competing models, we provide evidence that a single well-chosen sigmoid shape value requires less computational efforts in order to approximate the true value of the (log) Bayes factor compared to the original approach. We show that the (log) Bayes factors calculated using path sampling and stepping-stone sampling differ drastically from those estimated using either of the harmonic mean estimators, supporting earlier claims that the latter systematically overestimate the performance of high-dimensional models, which we show can lead to erroneous conclusions. Based on our results, we argue that highly accurate estimation of differences in model fit for high-dimensional models requires much more computational effort than suggested in recent studies on marginal likelihood estimation

A Noise-Robust Fast Sparse Bayesian Learning Model

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. The hierarchical model structure in this Bayesian framework is designed such that the priors do not only penalize the unnecessary complexity of the model but will also be conditioned on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm which can achieve sparsity, low computational cost and faster learning process. We compare our methodology with two other popular learning models; the Relevance Vector Machine and the Bayesian Lasso. We test our model on examples involving both simulated and empirical data, and the results show that this approach has several performance advantages, such as being fast, sparse and also robust to the variance in random noise. In addition, our method can give out a more stable estimation of variance of random error, compared with the other methods in the study.Comment: 15 page

3D Ultrastructure of the Cochlear Outer Hair Cell Lateral Wall Revealed By Electron Tomography.

Outer Hair Cells (OHCs) in the mammalian cochlea display a unique type of voltage-induced mechanical movement termed electromotility, which amplifies auditory signals and contributes to the sensitivity and frequency selectivity of mammalian hearing. Electromotility occurs in the OHC lateral wall, but it is not fully understood how the supramolecular architecture of the lateral wall enables this unique form of cellular motility. Employing electron tomography of high-pressure frozen and freeze-substituted OHCs, we visualized the 3D structure and organization of the membrane and cytoskeletal components of the OHC lateral wall. The subsurface cisterna (SSC) is a highly prominent feature, and we report that the SSC membranes and lumen possess hexagonally ordered arrays of particles. We also find the SSC is tightly connected to adjacent actin filaments by short filamentous protein connections. Pillar proteins that join the plasma membrane to the cytoskeleton appear as variable structures considerably thinner than actin filaments and significantly more flexible than actin-SSC links. The structurally rich organization and rigidity of the SSC coupled with apparently weaker mechanical connections between the plasma membrane (PM) and cytoskeleton reveal that the membrane-cytoskeletal architecture of the OHC lateral wall is more complex than previously appreciated. These observations are important for our understanding of OHC mechanics and need to be considered in computational models of OHC electromotility that incorporate subcellular features

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na+ and K+ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin–Huxley model of the squid axon, optimizing the kinetics or number of Na+ and K+ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost

Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes. Here we show there are fundamental similarities between these two models. The implications are illustrated with two important sleep-wake phenomena. Firstly, we show that in the two-process model, transitions between different numbers of daily sleep episodes occur at grazing bifurcations.This provides the theoretical underpinning for numerical results showing that the sleep patterns of many mammals can be explained by the mutual inhibition model. Secondly, we show that when sleep deprivation disrupts the sleep-wake cycle, ostensibly different measures of sleepiness in the two models are closely related. The demonstration of the mathematical similarities of the two models is valuable because not only does it allow some features of the two-process model to be interpreted physiologically but it also means that knowledge gained from study of the two-process model can be used to inform understanding of the mutual inhibition model. This is important because the mutual inhibition model and its extensions are increasingly being used as a tool to understand a diverse range of sleep-wake phenomena such as the design of optimal shift-patterns, yet the values it uses for parameters associated with the circadian and homeostatic processes are very different from those that have been experimentally measured in the context of the two-process model

Modeling DNA methylation dynamics with approaches from phylogenetics

Methylation of CpG dinucleotides is a prevalent epigenetic modification that is required for proper development in vertebrates, and changes in CpG methylation are essential to cellular differentiation. Genome-wide DNA methylation assays have become increasingly common, and recently distinct stages across differentiating cellular lineages have been assayed. How- ever, current methods for modeling methylation dynamics do not account for the dependency structure between precursor and dependent cell types. We developed a continuous-time Markov chain approach, based on the observation that changes in methylation state over tissue differentiation can be modeled similarly to DNA nucleotide changes over evolutionary time. This model explicitly takes precursor to descendant relationships into account and enables inference of CpG methylation dynamics. To illustrate our method, we analyzed a high-resolution methylation map of the differentiation of mouse stem cells into several blood cell types. Our model can successfully infer unobserved CpG methylation states from observations at the same sites in related cell types (90% correct), and this approach more accurately reconstructs missing data than imputation based on neighboring CpGs (84% correct). Additionally, the single CpG resolution of our methylation dynamics estimates enabled us to show that DNA sequence context of CpG sites is informative about methylation dynamics across tissue differentiation. Finally, we identified genomic regions with clusters of highly dynamic CpGs and present a likely functional example. Our work establishes a framework for inference and modeling that is well-suited to DNA methylation data, and our success suggests that other methods for analyzing DNA nucleotide substitutions will also translate to the modeling of epigenetic phenomena.Comment: 8 pages, 5 figure

Real-Time Anisotropic Diffusion using Space-Variant Vision

Many computer and robot vision applications require multi-scale image analysis. Classically, this has been accomplished through the use of a linear scale-space, which is constructed by convolution of visual input with Gaussian kernels of varying size (scale). This has been shown to be equivalent to the solution of a linear diffusion equation on an infinite domain, as the Gaussian is the Green's function of such a system (Koenderink, 1984). Recently, much work has been focused on the use of a variable conductance function resulting in anisotropic diffusion described by a nonlinear partial differential equation (PDF). The use of anisotropic diffusion with a conductance coefficient which is a decreasing function of the gradient magnitude has been shown to enhance edges, while decreasing some types of noise (Perona and Malik, 1987). Unfortunately, the solution of the anisotropic diffusion equation requires the numerical integration of a nonlinear PDF which is a costly process when carried out on a fixed mesh such as a typical image. In this paper we show that the complex log transformation, variants of which are universally used in mammalian retino-cortical systems, allows the nonlinear diffusion equation to be integrated at exponentially enhanced rates due to the non-uniform mesh spacing inherent in the log domain. The enhanced integration rates, coupled with the intrinsic compression of the complex log transformation, yields a seed increase of between two and three orders of magnitude, providing a means of performing real-time image enhancement using anisotropic diffusion.Office of Naval Research (N00014-95-I-0409

How informative are spatial CA3 representations established by the dentate gyrus?

In the mammalian hippocampus, the dentate gyrus (DG) is characterized by sparse and powerful unidirectional projections to CA3 pyramidal cells, the so-called mossy fibers. Mossy fiber synapses appear to duplicate, in terms of the information they convey, what CA3 cells already receive from entorhinal cortex layer II cells, which project both to the dentate gyrus and to CA3. Computational models of episodic memory have hypothesized that the function of the mossy fibers is to enforce a new, well separated pattern of activity onto CA3 cells, to represent a new memory, prevailing over the interference produced by the traces of older memories already stored on CA3 recurrent collateral connections. Can this hypothesis apply also to spatial representations, as described by recent neurophysiological recordings in rats? To address this issue quantitatively, we estimate the amount of information DG can impart on a new CA3 pattern of spatial activity, using both mathematical analysis and computer simulations of a simplified model. We confirm that, also in the spatial case, the observed sparse connectivity and level of activity are most appropriate for driving memory storage and not to initiate retrieval. Surprisingly, the model also indicates that even when DG codes just for space, much of the information it passes on to CA3 acquires a non-spatial and episodic character, akin to that of a random number generator. It is suggested that further hippocampal processing is required to make full spatial use of DG inputs.Comment: 19 pages, 11 figures, 1 table, submitte

Session 5: Development, Neuroscience and Evolutionary Psychology

Proceedings of the Pittsburgh Workshop in History and Philosophy of Biology, Center for Philosophy of Science, University of Pittsburgh, March 23-24 2001 Session 5: Development, Neuroscience and Evolutionary Psycholog