Inferring Neuronal Dynamics from Calcium Imaging Data Using Biophysical Models and Bayesian Inference

Calcium imaging has been used as a promising technique to monitor the dynamic activity of neuronal populations. However, the calcium trace is temporally smeared which restricts the extraction of quantities of interest such as spike trains of individual neurons. To address this issue, spike reconstruction algorithms have been introduced. One limitation of such reconstructions is that the underlying models are not informed about the biophysics of spike and burst generations. Such existing prior knowledge might be useful for constraining the possible solutions of spikes. Here we describe, in a novel Bayesian approach, how principled knowledge about neuronal dynamics can be employed to infer biophysical variables and parameters from fluorescence traces. By using both synthetic and in vitro recorded fluorescence traces, we demonstrate that the new approach is able to reconstruct different repetitive spiking and/or bursting patterns with accurate single spike resolution. Furthermore, we show that the high inference precision of the new approach is preserved even if the fluorescence trace is rather noisy or if the fluorescence transients show slow rise kinetics lasting several hundred milliseconds, and inhomogeneous rise and decay times. In addition, we discuss the use of the new approach for inferring parameter changes, e.g. due to a pharmacological intervention, as well as for inferring complex characteristics of immature neuronal circuits.     

Inferring Epidemiological Dynamics with Bayesian Coalescent Inference: The Merits of Deterministic and Stochastic Models

Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman’s coalescent theory. Here, we use recently described coalescent theory for epidemic dynamics to develop stochastic and deterministic coalescent susceptible–infected–removed (SIR) tree priors. We implement these in a Bayesian phylogenetic inference framework to permit joint estimation of SIR epidemic parameters and the sample genealogy. We assess the performance of the two coalescent models and also juxtapose results obtained with a recently published birth–death-sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. Additionally, we analyze influenza A (H1N1) sequence data sampled in the Canterbury region of New Zealand and HIV-1 sequence data obtained from known United Kingdom infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number R₀ and large population size S₀. Furthermore, we find that the stochastic variant generally outperforms its deterministic counterpart in terms of error, bias, and highest posterior density coverage, particularly for smaller R₀ and S₀. However, each of these inference models is shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R₀ close to one or with small effective susceptible populations.     

Inferring pathway activity toward precise disease classification

The advent of microarray technology has made it possible to classify disease states based on gene expression profiles of patients. Typically, marker genes are selected by measuring the power of their expression profiles to discriminate among patients of different disease states. However, expression-based classification can be challenging in complex diseases due to factors such as cellular heterogeneity within a tissue sample and genetic heterogeneity across patients. A promising technique for coping with these challenges is to incorporate pathway information into the disease classification procedure in order to classify disease based on the activity of entire signaling pathways or protein complexes rather than on the expression levels of individual genes or proteins. We propose a new classification method based on pathway activities inferred for each patient. For each pathway, an activity level is summarized from the gene expression levels of its condition-responsive genes (CORGs), defined as the subset of genes in the pathway whose combined expression delivers optimal discriminative power for the disease phenotype. We show that classifiers using pathway activity achieve better performance than classifiers based on individual gene expression, for both simple and complex case-control studies including differentiation of perturbed from non-perturbed cells and subtyping of several different kinds of cancer. Moreover, the new method outperforms several previous approaches that use a static (i.e., non-conditional) definition of pathways. Within a pathway, the identified CORGs may facilitate the development of better diagnostic markers and the discovery of core alterations in human disease.     

Inferring Adaptive Introgression Using Hidden Markov Models

Adaptive introgression—the flow of adaptive genetic variation between species or populations—has attracted significant interest in recent years and it has been implicated in a number of cases of adaptation, from pesticide resistance and immunity, to local adaptation. Despite this, methods for identification of adaptive introgression from population genomic data are lacking. Here, we present Ancestry_HMM-S, a hidden Markov model-based method for identifying genes undergoing adaptive introgression and quantifying the strength of selection acting on them. Through extensive validation, we show that this method performs well on moderately sized data sets for realistic population and selection parameters. We apply Ancestry_HMM-S to a data set of an admixed Drosophila melanogaster population from South Africa and we identify 17 loci which show signatures of adaptive introgression, four of which have previously been shown to confer resistance to insecticides. Ancestry_HMM-S provides a powerful method for inferring adaptive introgression in data sets that are typically collected when studying admixed populations. This method will enable powerful insights into the genetic consequences of admixture across diverse populations. Ancestry_HMM-S can be downloaded from https://github.com/jesvedberg/Ancestry_HMM-S/.     

Inferring Bacterial Genome Flux While Considering Truncated Genes

Bacterial gene content variation during the course of evolution has been widely acknowledged and its pattern has been actively modeled in recent years. Gene truncation or gene pseudogenization also plays an important role in shaping bacterial genome content. Truncated genes could also arise from small-scale lateral gene transfer events. Unfortunately, the information of truncated genes has not been considered in any existing mathematical models on gene content variation. In this study, we developed a model to incorporate truncated genes. Maximum-likelihood estimates (MLEs) of the new model reveal fast rates of gene insertions/deletions on recent branches, suggesting a fast turnover of many recently transferred genes. The estimates also suggest that many truncated genes are in the process of being eliminated from the genome. Furthermore, we demonstrate that the ignorance of truncated genes in the estimation does not lead to a systematic bias but rather has a more complicated effect. Analysis using the new model not only provides more accurate estimates on gene gains/losses (or insertions/deletions), but also reduces any concern of a systematic bias from applying simplified models to bacterial genome evolution. Although not a primary purpose, the model incorporating truncated genes could be potentially used for phylogeny reconstruction using gene family content.GENE content variation as a key feature of bacterial genome evolution has been well recognized (Garcia-Vallvé et al. 2000; Ochman and Jones 2000; Snel et al. 2002; Welch et al. 2002; Kunin and Ouzounis 2003; Fraser-Liggett 2005; Tettelin et al. 2005) and gained increasing attention in recent years. Various methods have been employed to study the variation of gene content in the form of gene insertions/deletions (or gene gains/losses); there are studies of population dynamics (Nielsen and Townsend 2004), birth-and-death evolutionary models (Berg and Kurland 2002; Novozhilov et al. 2005), phylogeny-dependent studies including parsimony methods (Mirkin et al. 2003; Daubin et al. 2003a,b; Hao and Golding 2004), and maximum-likelihood methods (Hao and Golding 2006, 2008b; Cohen et al. 2008; Cohen and Pupko 2010; Spencer and Sangaralingam 2009). The pattern of gene presence/absence also contains phylogenetic signals (Fitz-Gibbon and House 1999; Snel et al. 1999; Tekaia et al. 1999) and has been used for phylogenetic reconstruction (Dutilh et al. 2004; Gu and Zhang 2004; Huson and Steel 2004; Zhang and Gu 2004; Spencer et al. 2007a,b). All these studies make use of the binary information of gene presence or absence and neglect the existence of gene segments or truncated genes.Bacterial genomes are known to harbor pseudogenes. An intracellular species Mycobacterium leprae is an extreme case for both the proportion and the number of pseudogenes: estimated as 40% of the 3.2-Mb genome and 1116 genes (Cole et al. 2001). In free-living bacteria, pseudogenes can make up to 8% of the annotated genes in the genome (Lerat and Ochman 2004). Many pseudogenes result from the degradation of native functional genes (Cole et al. 2001; Mira et al. 2001). Pseudogenes could also result from the degradation of transferred genes and might even be acquired directly via lateral gene transfer. For instance, in plant mitochondrial genomes, which have an α-proteobacterial ancestry, most, if not all, of the laterally transferred genes are pseudogenes (Richardson and Palmer 2007). Furthermore, evidence has been documented that gene transfer could take place at the subgenic level in a wide range of organisms, e.g., among bacteria (Miller et al. 2005; Choi and Kim 2007; Chan et al. 2009), between ancient duplicates in archaea (Archibald and Roger 2002), between different organelles (Hao and Palmer 2009; Hao 2010), and between eukaryotes (Keeling and Palmer 2001). A large fraction of pseudogenes have been shown to arise from failed lateral transfer events (Liu et al. 2004) and most of them are transient in bacterial genomes (Lerat and Ochman 2005). Zhaxybayeva et al. (2007) reported that genomes with truncated homologs might erroneously lead to false inferences of “gene gain” rather than multiple instances of “gene loss.” This raises the question of how a false diagnosis of gene absence affects the estimation of insertion/deletion rates. Recently, we showed that the effect of a false diagnosis of gene absence on estimation of insertion/deletion rates is not systematic, but rather more complicated (Hao and Golding 2008a). To further address the problem, a study incorporating the information of truncated genes is highly desirable. This will not only yield more accurate estimates of the rates of gene insertions/deletions, but also provide a quantitative view of the effect of truncated genes on rate estimation, which has been understudied in bacterial genome evolution.In this study, we developed a model that considers the information of truncated genes and makes use of a parameter-rich time-reversible rate matrix. Rate variation among genes is allowed in the model by incorporating a discrete Γ-distribution. We also allow rates to vary on different parts of the phylogeny (external branches vs. internal branches). Consistent with previous studies, the rates of gene insertions/deletions are comparable to or larger than the rates of nucleotide substitution and the rates of gene insertions/deletions are further inflated in closely related groups and on external branches, suggesting high rates of gene turnover of recently transferred genes. The results from the new model also suggest that many recently truncated genes are in the process of being rapidly deleted from the genome. Some other interesting estimates in the model are also presented and discussed. One implication of the study, though not primary, is that the state of truncated genes could serve as an additional phylogenetic character for phylogenetic reconstruction using gene family content.     

Dynamics of Bacterial Swarming

When vegetative bacteria that can swim are grown in a rich medium on an agar surface, they become multinucleate, elongate, synthesize large numbers of flagella, produce wetting agents, and move across the surface in coordinated packs: they swarm. We examined the motion of swarming Escherichia coli, comparing the motion of individual cells to their motion during swimming. Swarming cells' speeds are comparable to bulk swimming speeds, but very broadly distributed. Their speeds and orientations are correlated over a short distance (several cell lengths), but this correlation is not isotropic. We observe the swirling that is conspicuous in many swarming systems, probably due to increasingly long-lived correlations among cells that associate into groups. The normal run-tumble behavior seen in swimming chemotaxis is largely suppressed, instead, cells are continually reoriented by random jostling by their neighbors, randomizing their directions in a few tenths of a second. At the edge of the swarm, cells often pause, then swim back toward the center of the swarm or along its edge. Local alignment among cells, a necessary condition of many flocking theories, is accomplished by cell body collisions and/or short-range hydrodynamic interactions.     

Inferring the Dynamics of Diversification: A Coalescent Approach

Recent analyses of the fossil record and molecular phylogenies suggest that there are fundamental limits to biodiversity, possibly arising from constraints in the availability of space, resources, or ecological niches. Under this hypothesis, speciation rates decay over time and biodiversity eventually saturates, with new species emerging only when others are driven to extinction. This view of macro-evolution contradicts an alternative hypothesis that biodiversity is unbounded, with species ever accumulating as they find new niches to occupy. These contrasting theories of biodiversity dynamics yield fundamentally different explanations for the disparity in species richness across taxa and regions. Here, we test whether speciation rates have decayed or remained constant over time, and whether biodiversity is saturated or still expanding. We first derive a general likelihood expression for internode distances in a phylogeny, based on the well-known coalescent process from population genetics. This expression accounts for either time-constant or time-variable rates, time-constant or time-variable diversity, and completely or incompletely sampled phylogenies. We then compare the performance of different diversification scenarios in explaining a set of 289 phylogenies representing amphibians, arthropods, birds, mammals, mollusks, and flowering plants. Our results indicate that speciation rates typically decay over time, but that diversity is still expanding at present. The evidence for expanding-diversity models suggests that an upper limit to biodiversity has not yet been reached, or that no such limit exists.     

Dynamics of Immunological Models

We analyse the effect of the regulatory T cells (Tregs) in the local control of the immune responses by T cells. We obtain an explicit formula for the level of antigenic stimulation of T cells as a function of the concentration of T cells and the parameters of the model. The relation between the concentration of the T cells and the antigenic stimulation of T cells is an hysteresis, that is unfold for some parameter values. We study the appearance of autoimmunity from cross-reactivity between a pathogen and a self antigen or from bystander proliferation. We also study an asymmetry in the death rates. With this asymmetry we show that the antigenic stimulation of the Tregs is able to control locally the population size of Tregs. Other effects of this asymmetry are a faster immune response and an improvement in the simulations of the bystander proliferation. The rate of variation of the levels of antigenic stimulation determines if the outcome is an immune response or if Tregs are able to maintain control due to the presence of a transcritical bifurcation for some tuning between the antigenic stimuli of T cells and Tregs. This behavior is explained by the presence of a transcritical bifurcation.     

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins.     

Inferring Tree Causal Models of Cancer Progression with Probability Raising

Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel theoretical framework called CAPRESE (CAncer PRogression Extraction with Single Edges) to reconstruct such models based on the notion of probabilistic causation defined by Suppes. We consider a general reconstruction setting complicated by the presence of noise in the data due to biological variation, as well as experimental or measurement errors. To improve tolerance to noise we define and use a shrinkage-like estimator. We prove the correctness of our algorithm by showing asymptotic convergence to the correct tree under mild constraints on the level of noise. Moreover, on synthetic data, we show that our approach outperforms the state-of-the-art, that it is efficient even with a relatively small number of samples and that its performance quickly converges to its asymptote as the number of samples increases. For real cancer datasets obtained with different technologies, we highlight biologically significant differences in the progressions inferred with respect to other competing techniques and we also show how to validate conjectured biological relations with progression models.     

Dynamics of Epidemiological Models

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation.     

Inferring Pairwise Interactions from Biological Data Using Maximum-Entropy Probability Models

Maximum entropy-based inference methods have been successfully used to infer direct interactions from biological datasets such as gene expression data or sequence ensembles. Here, we review undirected pairwise maximum-entropy probability models in two categories of data types, those with continuous and categorical random variables. As a concrete example, we present recently developed inference methods from the field of protein contact prediction and show that a basic set of assumptions leads to similar solution strategies for inferring the model parameters in both variable types. These parameters reflect interactive couplings between observables, which can be used to predict global properties of the biological system. Such methods are applicable to the important problems of protein 3-D structure prediction and association of gene–gene networks, and they enable potential applications to the analysis of gene alteration patterns and to protein design.     

Inferring Adaptive Codon Preference to Understand Sources of Selection Shaping Codon Usage Bias

Alternative synonymous codons are often used at unequal frequencies. Classically, studies of such codon usage bias (CUB) attempted to separate the impact of neutral from selective forces by assuming that deviations from a predicted neutral equilibrium capture selection. However, GC-biased gene conversion (gBGC) can also cause deviation from a neutral null. Alternatively, selection has been inferred from CUB in highly expressed genes, but the accuracy of this approach has not been extensively tested, and gBGC can interfere with such extrapolations (e.g., if expression and gene conversion rates covary). It is therefore critical to examine deviations from a mutational null in a species with no gBGC. To achieve this goal, we implement such an analysis in the highly AT rich genome of Dictyostelium discoideum, where we find no evidence of gBGC. We infer neutral CUB under mutational equilibrium to quantify “adaptive codon preference,” a nontautologous genome wide quantitative measure of the relative selection strength driving CUB. We observe signatures of purifying selection consistent with selection favoring adaptive codon preference. Preferred codons are not GC rich, underscoring the independence from gBGC. Expression-associated “preference” largely matches adaptive codon preference but does not wholly capture the influence of selection shaping patterns across all genes, suggesting selective constraints associated specifically with high expression. We observe patterns consistent with effects on mRNA translation and stability shaping adaptive codon preference. Thus, our approach to quantifying adaptive codon preference provides a framework for inferring the sources of selection that shape CUB across different contexts within the genome.     

Mucin Dynamics in Intestinal Bacterial Infection

Background

Bacterial gastroenteritis causes morbidity and mortality in humans worldwide. Murine Citrobacter rodentium infection is a model for gastroenteritis caused by the human pathogens enteropathogenic Escherichia coli and enterohaemorrhagic E. coli. Mucin glycoproteins are the main component of the first barrier that bacteria encounter in the intestinal tract.

Methodology/Principal Findings

Using Immunohistochemistry, we investigated intestinal expression of mucins (Alcian blue/PAS, Muc1, Muc2, Muc4, Muc5AC, Muc13 and Muc3/17) in healthy and C. rodentium infected mice. The majority of the C. rodentium infected mice developed systemic infection and colitis in the mid and distal colon by day 12. C. rodentium bound to the major secreted mucin, Muc2, in vitro, and high numbers of bacteria were found in secreted MUC2 in infected animals in vivo, indicating that mucins may limit bacterial access to the epithelial surface. In the small intestine, caecum and proximal colon, the mucin expression was similar in infected and non-infected animals. In the distal colonic epithelium, all secreted and cell surface mucins decreased with the exception of the Muc1 cell surface mucin which increased after infection (p<0.05). Similarly, during human infection Salmonella St Paul, Campylobacter jejuni and Clostridium difficile induced MUC1 in the colon.

Conclusion

Major changes in both the cell-surface and secreted mucins occur in response to intestinal infection.     

森林动态模型概论

讨论了模拟森林林分动态变化的模型,并把模型分为森林生长模型和演替模型。森林生长模型包括：全林分模型、林分级模型和单木模型;演替模型包括马尔可夫类模型和林窗模型。文中给出了演替模型的基本原理和适用性,在比较早期和最新发展的林窗模型后,叙述了林窗模型的新进展。生长和演替模型的结构和数据要求不同决定了它们的在时间和空间上的适应性,最后指出模型将向综合总体方向发展。