Bayesian inference of causal effects from observational data in Gaussian graphical models

We assume that multivariate observational data are generated from a distribution whose conditional independencies are encoded in a Directed Acyclic Graph (DAG). For any given DAG, the causal effect of a variable onto another one can be evaluated through intervention calculus. A DAG is typically not identifiable from observational data alone. However, its Markov equivalence class (a collection of DAGs) can be estimated from the data. As a consequence, for the same intervention a set of causal effects, one for each DAG in the equivalence class, can be evaluated. In this paper, we propose a fully Bayesian methodology to make inference on the causal effects of any intervention in the system. Main features of our method are: (a) both uncertainty on the equivalence class and the causal effects are jointly modeled; (b) priors on the parameters of the modified Cholesky decomposition of the precision matrices across all DAG models are constructively assigned starting from a unique prior on the complete (unrestricted) DAG; (c) an efficient algorithm to sample from the posterior distribution on graph space is adopted; (d) an objective Bayes approach, requiring virtually no user specification, is used throughout. We demonstrate the merits of our methodology in simulation studies, wherein comparisons with current state‐of‐the‐art procedures turn out to be highly satisfactory. Finally we examine a real data set of gene expressions for Arabidopsis thaliana.     

多结构域酶的结构域进化关系

近年来随着生命科学新技术、新方法的涌现,酶蛋白结构和功能研究逐渐深入。具有多结构域的酶蛋白中各个结构域常具有独立的催化或结合底物的功能,在重组酶和组合生物合成研究中具有极大的研究和应用价值。这些结构域功能和组织方式的多样性,是研究分子进化的基础。对结构域进行进化分析对于研究多结构域酶的进化过程、功能相近酶之间的关系,以及对酶的分类鉴定等有重要意义。本文从结构域的重复性、结构域的水平基因转移和结构域的重组等方面出发,对多结构域酶中结构域之间进化关系的研究成果进行综述。     

Converting differential-equation models of biological systems to membrane computing

This paper presents a method to convert the deterministic, continuous representation of a biological system by ordinary differential equations into a non-deterministic, discrete membrane computation. The dynamics of the membrane computation is governed by rewrite rules operating at certain rates. That has the advantage of applying accurately to small systems, and to expressing rates of change that are determined locally, by region, but not necessary globally. Such spatial information augments the standard differentiable approach to provide a more realistic model. A biological case study of the ligand–receptor network of protein TGF-β is used to validate the effectiveness of the conversion method. It demonstrates the sense in which the behaviours and properties of the system are better preserved in the membrane computing model, suggesting that the proposed conversion method may prove useful for biological systems in particular.     

Testing the ability of species distribution models to infer variable importance

Models of species’ distributions and niches are frequently used to infer the importance of range- and niche-defining variables. However, the degree to which these models can reliably identify important variables and quantify their influence remains unknown. Here we use a series of simulations to explore how well models can 1) discriminate between variables with different influence and 2) calibrate the magnitude of influence relative to an ‘omniscient’ model. To quantify variable importance, we trained generalized additive models (GAMs), Maxent and boosted regression trees (BRTs) on simulated data and tested their sensitivity to permutations in each predictor. Importance was inferred by calculating the correlation between permuted and unpermuted predictions, and by comparing predictive accuracy of permuted and unpermuted predictions using AUC and the continuous Boyce index. In scenarios with one influential and one uninfluential variable, models failed to discriminate reliably between variables when training occurrences were < 8–64, prevalence was > 0.5, spatial extent was small, environmental data had coarse resolution and spatial autocorrelation was low, or when pairwise correlation between environmental variables was |r| > 0.7. When two variables influenced the distribution equally, importance was underestimated when species had narrow or intermediate niche breadth. Interactions between variables in how they shaped the niche did not affect inferences about their importance. When variables acted unequally, the effect of the stronger variable was overestimated. GAMs and Maxent discriminated between variables more reliably than BRTs, but no algorithm was consistently well-calibrated vis-à-vis the omniscient model. Algorithm-specific measures of importance like Maxent's change-in-gain metric were less robust than the permutation test. Overall, high predictive accuracy did not connote robust inferential capacity. As a result, requirements for reliably measuring variable importance are likely more stringent than for creating models with high predictive accuracy.     

Using biological assemblage composition to infer the values of covarying environmental factors

1. Observations of different organisms can often be used to infer environmental conditions at a site. These inferences may be useful for diagnosing the causes of degradation in streams and rivers. 2. When used for diagnosis, biological inferences must not only provide accurate, unbiased predictions of environmental conditions, but also pairs of inferred environmental variables must covary no more strongly than actual measurements of those same environmental variables. 3. Mathematical analysis of the relationship between the measured and inferred values of different environmental variables provides an approach for comparing the covariance between measurements with the covariance between inferences. Then, simulated and field‐collected data are used to assess the performance of weighted average and maximum likelihood inference methods. 4. Weighted average inferences became less accurate as covariance in the calibration data increased, whereas maximum likelihood inferences were unaffected by covariance in the calibration data. In contrast, the accuracy of weighted average inferences was unaffected by changes in measurement error, whilst the accuracy of maximum likelihood inferences decreased as measurement error increased. Weighted average inferences artificially increased the covariance of environmental variables beyond what was expected from measurements, whereas maximum likelihood inference methods more accurately reproduced the expected covariances. 5. Multivariate maximum likelihood inference methods can potentially provide more useful diagnostic information than single variable inference models.     

Assessing the components of the eIF3 complex and their phosphorylation status

The eukaryotic initiation factor 3 (eIF3) is an essential, highly conserved multiprotein complex that is a key component in the recruitment and assembly of the translation initiation machinery. To better understand the molecular function of eIF3, we examined its composition and phosphorylation status in Saccharomyces cerevisiae. The yeast eIF3 complex contains five core components: Rpg1, Nip1, Prt1, Tif34, and Tif35. 2-D LC-MS/MS analysis of affinity purified eIF3 complexes showed that several other initiation factors (Fun12, Tif5, Sui3, Pab1, Hcr1, and Sui1) and the casein kinase 2 complex (CK2) copurify. In Vivo metabolic labeling of proteins with (32)P revealed that Nip1 is phosphorylated. Using 2-D LC-MS/MS analysis of eIF3 complexes, we identified Prt1 phosphopeptides indicating phosphorylation at S22 and T707 and a Tif5 phosphopeptide with phosphorylation at T191. Additionally, we used immobilized metal affinity chromatography (IMAC) to enrich for eIF3 phosphopeptides and tandem mass spectrometry to identify phosphorylated residues. We found that three CK2 consensus sequences in Nip1 are phosphorylated: S98, S99, and S103. Using in vitro kinase assays, we showed that CK2 phophorylates Nip1 and that a synthetic Nip1 peptide containing S98, S99, and S103 competitively inhibits the reaction. Replacement of these three Nip1 serines with alanines causes a slow growth phenotype.     

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures—most of which are variants of Granger causality—with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger’s original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.     

Phylogenetic utility of different types of molecular data used to infer evolutionary relationships among stalk-eyed flies (Diopsidae)

A phylogenetic hypothesis of relationships among 33 species of stalk-eyed flies was generated from a molecular data set comprising three mitochondrial and three nuclear gene regions. A combined analysis of all the data equally weighted produced a single most-parsimonious cladogram with relatively strong support at the majority of nodes. The phylogenetic utility of different classes of molecular data was also examined. In particular, using a number of different measures of utility in both a combined and separate analysis framework, we focused on the distinction between mitochondrial and nuclear genes and between faster-evolving characters and slower-evolving characters. For the first comparison, by nearly any measure of utility, the nuclear genes are substantially more informative for resolving diopsid relationships than are the mitochondrial genes. The nuclear genes exhibit less homoplasy, are less incongruent with one another and with the combined data, and contribute more support to the combined analysis topology than do the mitochondrial genes. Results from the second comparison, however, provide little evidence of a clear difference in utility. Despite indications of rapid divergence and saturation, faster-evolving characters in both the nuclear and mitochondrial data sets still provide substantial phylogenetic signal. In general, inclusion of the more rapidly evolving data consistently improves the congruence among partitions.     

中国森林凋落物不同组分异速比例关系

森林凋落物(litterfall)是森林植物在其生长发育过程中新陈代谢的产物, 在物质循环和能量流动方面起着重要作用。该文利用已发表的我国主要森林凋落物的研究数据, 分析了不同组分(叶、枝和繁殖器官)凋落物量之间及其与总凋落物量之间的异速比例关系。结果表明: 我国森林叶、枝和繁殖器官的平均凋落物量分别为3 810.34、1 019.07和767.95 kg·hm^-2·a^-1; 温度、降水量、林龄对森林凋落物量均有一定程度的影响, 其中温度对各组分凋落物量的影响最大。叶凋落物量(L_L)与总凋落物量(L_T)之间呈等速生长关系(L_L ∝ L_T^0.96), 繁殖器官和枝的凋落物量(分别为L_P和L_B)与L_T之间呈异速比例关系, 分别为L_P ∝ L_T^1.84和L_B ∝ L_T^1.61。不同组分凋落物量之间具有显著的异速比例关系, 其异速指数均小于1.0。不同林型(常绿林和落叶林)各组分凋落物量之间的异速比例关系无显著差异。了解不同组分凋落物量与总凋落物量之间的异速比例关系可以为更加精确地估算森林生产力提供理论依据。     

Topology-based abstraction of complex biological systems: application to the Golgi apparatus

Many complex cellular processes involve major changes in topology and geometry. We have developed a method using topology-based geometric modelling in which the edge labels of an n-dimensional generalized map (a subclass of graphs) represent the relations between neighbouring biological compartments. We illustrate our method using two topological models of the Golgi apparatus. These models can be animated using transformation rules, which depend on geometric and/or biochemical data and which modify both these data and the topology. Both models constitute plausible topological representations of the Golgi apparatus, but only the model based on a recent hypothesis about the Golgi apparatus is fully compatible with data from electron microscopy. Finally, we outline how our method may help biologists to choose between different hypotheses.     

Measuring complexity to infer changes in the dynamics of ecological systems under stress

Despite advances in our mechanistic understanding of ecological processes, the inherent complexity of real-world ecosystems still limits our ability in predicting ecological dynamics especially in the face of on-going environmental stress. Developing a model is frequently challenged by structure uncertainty, unknown parameters, and limited data for exploring out-of-sample predictions. One way to address this challenge is to look for patterns in the data themselves in order to infer the underlying processes of an ecological system rather than to build system-specific models. For example, it has been recently suggested that statistical changes in ecological dynamics can be used to infer changes in the stability of ecosystems as they approach tipping points. For computer scientists such inference is similar to the notion of a Turing machine: a computational device that could execute a program (the process) to produce the observed data (the pattern). Here, we make use of such basic computational ideas introduced by Alan Turing to recognize changing patterns in ecological dynamics in ecosystems under stress. To do this, we use the concept of Kolmogorov algorithmic complexity that is a measure of randomness. In particular, we estimate an approximation to Kolmogorov complexity based on the Block Decomposition Method (BDM). We apply BDM to identify changes in complexity in simulated time-series and spatial datasets from ecosystems that experience different types of ecological transitions. We find that in all cases, K_BDM complexity decreased before all ecological transitions both in time-series and spatial datasets. These trends indicate that loss of stability in the ecological models we explored is characterized by loss of complexity and the emergence of a regular and computable underlying structure. Our results suggest that Kolmogorov complexity may serve as tool for revealing changes in the dynamics of ecosystems close to ecological transitions.     

Interactions among the components of the interleukin-10 receptor complex

We used fluorescence resonance energy transfer previously to show that the interferon-gamma (IFN-gamma) receptor complex is a preformed entity mediated by constitutive interactions between the IFN-gammaR2 and IFN-gammaR1 chains, and that this preassembled entity changes its structure after the treatment of cells with IFN-gamma. We applied this technique to determine the structure of the interleukin-10 (IL-10) receptor complex and whether it undergoes a similar conformational change after treatment of cells with IL-10. We report that, like the IFN-gamma receptor complex, the IL-10 receptor complex is preassembled: constitutive but weaker interactions occur between the IL-10R1 and IL-10R2 chains, and between two IL-10R2 chains. The IL-10 receptor complex undergoes no major conformational changes when cells are treated with cellular or Epstein-Barr viral IL-10. Receptor complex preassembly may be an inherent feature of Class 2 cytokine receptor complexes.     

AFLP markers resolve intra-specific relationships and infer genetic structure among lineages of the canyon treefrog, Hyla arenicolor

The canyon treefrog, Hyla arenicolor, is a wide-ranging hylid found from southwestern US into southern Mexico. Recent studies have shown this species to have a complex evolutionary history, with several phylogeographically distinct lineages, a probable cryptic species, and multiple episodes of mitochondrial introgression with the sister group, the H. eximia complex. We aimed to use genome wide AFLP markers to better resolve relationships within this group. As in other studies, our inferred phylogeny not only provides evidence for repeated mitochondrial introgression between H. arenicolor lineages and H. eximia/H. wrightorum, but it also affords more resolution within the main H. arenicolor clade than was previously achieved with sequence data. However, as with a previous study, the placement of a lineage of H. arenicolor whose distribution is centered in the Balsas Basin of Mexico remains poorly resolved, perhaps due to past hybridization with the H. eximia complex. Furthermore, the AFLP data set shows no differentiation among lineages from the Grand Canyon and Colorado Plateau despite their large mitochondrial sequence divergence. Finally, our results infer a well-supported sister relationship between this combined Colorado Plateau/Grand Canyon lineage and the Sonoran Desert lineage, a relationship that strongly contradicts conclusions drawn from the mtDNA evidence. Our study provides a basis for further behavioral and ecological speciation studies of this system and highlights the importance of multi-taxon (species) sampling in phylogenetic and phylogeographic studies.     

Template-based intervention in Boolean network models of biological systems

Motivation

A grand challenge in the modeling of biological systems is the identification of key variables which can act as targets for intervention. Boolean networks are among the simplest of models, yet they have been shown to adequately model many of the complex dynamics of biological systems. In our recent work, we utilized a logic minimization approach to identify quality single variable targets for intervention from the state space of a Boolean network. However, as the number of variables in a network increases, the more likely it is that a successful intervention strategy will require multiple variables. Thus, for larger networks, such an approach is required in order to identify more complex intervention strategies while working within the limited view of the network’s state space. Specifically, we address three primary challenges for the large network arena: the first challenge is how to consider many subsets of variables, the second is to design clear methods and measures to identify the best targets for intervention in a systematic way, and the third is to work with an intractable state space through sampling.

Results

We introduce a multiple variable intervention target called a template and show through simulation studies of random networks that these templates are able to identify top intervention targets in increasingly large Boolean networks. We first show that, when other methods show drastic loss in performance, template methods show no significant performance loss between fully explored and partially sampled Boolean state spaces. We also show that, when other methods show a complete inability to produce viable intervention targets in sampled Boolean state spaces, template methods maintain significantly consistent success rates even as state space sizes increase exponentially with larger networks. Finally, we show the utility of the template approach on a real-world Boolean network modeling T-LGL leukemia.

Conclusions

Overall, these results demonstrate how template-based approaches now effectively take over for our previous single variable approaches and produce quality intervention targets in larger networks requiring sampled state spaces.