Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.     

Molecular Filters for Noise Reduction

Living systems are inherently stochastic and operate in a noisy environment, yet despite all these uncertainties, they perform their functions in a surprisingly reliable way. The biochemical mechanisms used by natural systems to tolerate and control noise are still not fully understood, and this issue also limits our capacity to engineer reliable, quantitative synthetic biological circuits. We study how representative models of biochemical systems propagate and attenuate noise, accounting for intrinsic as well as extrinsic noise. We investigate three molecular noise-filtering mechanisms, study their noise-reduction capabilities and limitations, and show that nonlinear dynamics such as complex formation are necessary for efficient noise reduction. We further suggest that the derived molecular filters are widespread in gene expression and regulation and, particularly, that microRNAs can serve as such noise filters. To our knowledge, our results provide new insight into how biochemical networks control noise and could be useful to build robust synthetic circuits.     

Noise Management by Molecular Networks

Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise.     

Integrative Multi-omics Module Network Inference with Lemon-Tree

Module network inference is an established statistical method to reconstruct co-expression modules and their upstream regulatory programs from integrated multi-omics datasets measuring the activity levels of various cellular components across different individuals, experimental conditions or time points of a dynamic process. We have developed Lemon-Tree, an open-source, platform-independent, modular, extensible software package implementing state-of-the-art ensemble methods for module network inference. We benchmarked Lemon-Tree using large-scale tumor datasets and showed that Lemon-Tree algorithms compare favorably with state-of-the-art module network inference software. We also analyzed a large dataset of somatic copy-number alterations and gene expression levels measured in glioblastoma samples from The Cancer Genome Atlas and found that Lemon-Tree correctly identifies known glioblastoma oncogenes and tumor suppressors as master regulators in the inferred module network. Novel candidate driver genes predicted by Lemon-Tree were validated using tumor pathway and survival analyses. Lemon-Tree is available from http://lemon-tree.googlecode.com under the GNU General Public License version 2.0.

This is a PLOS Computational Biology Software Article

     

SEBINI: Software Environment for BIological Network Inference

The Software Environment for BIological Network Inference (SEBINI) has been created to provide an interactive environment for the deployment and evaluation of algorithms used to reconstruct the structure of biological regulatory and interaction networks. SEBINI can be used to compare and train network inference methods on artificial networks and simulated gene expression perturbation data. It also allows the analysis within the same framework of experimental high-throughput expression data using the suite of (trained) inference methods; hence SEBINI should be useful to software developers wishing to evaluate, compare, refine or combine inference techniques, and to bioinformaticians analyzing experimental data. SEBINI provides a platform that aids in more accurate reconstruction of biological networks, with less effort, in less time. AVAILABILITY: A demonstration website is located at https://www.emsl.pnl.gov/NIT/NIT.html. The Java source code and PostgreSQL database schema are available freely for non-commercial use.     

A Full Bayesian Approach for Boolean Genetic Network Inference

Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.     

Discovering Main Genetic Interactions with LABNet LAsso-Based Network Inference

Genome-wide association studies can potentially unravel the mechanisms behind complex traits and common genetic diseases. Despite the valuable results produced thus far, many questions remain unanswered. For instance, which specific genetic compounds are linked to the risk of the disease under investigation; what biological mechanism do they act through; or how do they interact with environmental and other external factors? The driving force of computational biology is the constantly growing amount of big data generated by high-throughput technologies. A practical framework that can deal with this abundance of information and that consent to discovering genetic associations and interactions is provided by means of networks. Unfortunately, high dimensionality, the presence of noise and the geometry of data can make the aforementioned problem extremely challenging. We propose a penalised linear regression approach that can deal with the aforementioned issues that affect genetic data. We analyse the gene expression profiles of individuals with a common trait to infer the network structure of interactions among genes. The permutation-based approach leads to more stable and reliable networks inferred from synthetic microarray data. We show that a higher number of permutations determines the number of predicted edges, improves the overall sensitivity and controls the number of false positives.     

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.     

贝叶斯推论及其在百合目分子系统学中的应用

贝叶斯推论作为进化生物学的最新进展,在适用复杂模型、大型数据集、计算速度和结果容易解释等方面明显优于其它算法。本文简要介绍了贝叶斯推论原理及其在分子进化和系统发育研究中的重要性,并使用该方法对百合目主要类群的系统发育关系进行了重建。结果显示,百合目rbcL基因最适合的DNA进化模型为GTR I G,贝叶斯法与距离法和最大简约法构建的系统发育树拓扑结构相似,没有显著差异,但是分辨率和支持率明显比后者高。贝叶斯分析结果显示,百合目内划分的7个科,除Smilacaceae科外,其余各科均为高后验概率(PP=1·0)支持的单系类群;文中作者还对各科间的系统关系进行了探讨。     

Inference or Enaction? The Impact of Genre on the Narrative Processing of Other Minds

Do narratives shape how humans process other minds or do they presuppose an existing theory of mind? This study experimentally investigated this problem by assessing subject responses to systematic alterations in the genre, levels of intentionality, and linguistic complexity of narratives. It showed that the interaction of genre and intentionality level are crucial in determining how narratives are cognitively processed. Specifically, genres that deployed evolutionarily familiar scenarios (relationship stories) were rated as being higher in quality when levels of intentionality were increased; conversely, stories that lacked evolutionary familiarity (espionage stories) were rated as being lower in quality with increases in intentionality level. Overall, the study showed that narrative is not solely either the origin or the product of our intuitions about other minds; instead, different genres will have different—even opposite—effects on how we understand the mind states of others.     

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.     

Inference of Network Dynamics and Metabolic Interactions in the Gut Microbiome

We present a novel methodology to construct a Boolean dynamic model from time series metagenomic information and integrate this modeling with genome-scale metabolic network reconstructions to identify metabolic underpinnings for microbial interactions. We apply this in the context of a critical health issue: clindamycin antibiotic treatment and opportunistic Clostridium difficile infection. Our model recapitulates known dynamics of clindamycin antibiotic treatment and C. difficile infection and predicts therapeutic probiotic interventions to suppress C. difficile infection. Genome-scale metabolic network reconstructions reveal metabolic differences between community members and are used to explore the role of metabolism in the observed microbial interactions. In vitro experimental data validate a key result of our computational model, that B. intestinihominis can in fact slow C. difficile growth.     

Data Identification for Improving Gene Network Inference using Computational Algebra

Identification of models of gene regulatory networks is sensitive to the amount of data used as input. Considering the substantial costs in conducting experiments, it is of value to have an estimate of the amount of data required to infer the network structure. To minimize wasted resources, it is also beneficial to know which data are necessary to identify the network. Knowledge of the data and knowledge of the terms in polynomial models are often required a priori in model identification. In applications, it is unlikely that the structure of a polynomial model will be known, which may force data sets to be unnecessarily large in order to identify a model. Furthermore, none of the known results provides any strategy for constructing data sets to uniquely identify a model. We provide a specialization of an existing criterion for deciding when a set of data points identifies a minimal polynomial model when its monomial terms have been specified. Then, we relax the requirement of the knowledge of the monomials and present results for model identification given only the data. Finally, we present a method for constructing data sets that identify minimal polynomial models.     

The Impact of Biosampling Procedures on Molecular Data Interpretation

The separation between biological and technical variation without extensive use of technical replicates is often challenging, particularly in the context of different forms of protein and peptide modifications. Biosampling procedures in the research laboratory are easier to conduct within a shorter time frame and under controlled conditions as compared with clinical sampling, with the latter often having issues of reproducibility. But is the research laboratory biosampling really less variable? Biosampling introduces within minutes rapid tissue-specific changes in the cellular microenvironment, thus inducing a range of different pathways associated with cell survival. Biosampling involves hypoxia and, depending on the circumstances, hypothermia, circumstances for which there are evolutionarily conserved defense strategies in the range of species and also are relevant for the range of biomedical conditions. It remains unclear to what extent such adaptive processes are reflected in different biosampling procedures or how important they are for the definition of sample quality. Lately, an increasing number of comparative studies on different biosampling approaches, post-mortem effects and pre-sampling biological state, have investigated such immediate early biosampling effects. Commonalities between biosampling effects and a range of ischemia/reperfusion- and hypometabolism/anoxia-associated biological phenomena indicate that even small variations in post-sampling time intervals are likely to introduce a set of nonrandom and tissue-specific effects of experimental importance (both in vivo and in vitro). This review integrates the information provided by these comparative studies and discusses how an adaptive biological perspective in biosampling procedures may be relevant for sample quality issues.The understanding of how specific observations at the molecular level relate to properties of the entire living organism is one of the greatest challenges in biomedical research. Observations can be influenced significantly by both the methodologies used and the manner in which data are interpreted and shared. Biosampling, here defined as encompassing the collection of biosamples, is therefore central to any study investigating either molecular mechanisms or biomarkers. Biosampling methods differ in their usefulness, and no single method has universal applicability, making the choice of biosampling approach an important part of experimental design.Despite extensive investment in biomarker research for clinical diseases, modern molecular biology has largely failed to deliver any substantial improvements in the biomarker field (1), a failure often blamed on the lack of standardization in biosampling procedures. Studies on phosphoproteins in clinical tissues 20–30 min post-extraction and later have demonstrated that cells in such biosamples exhibit a range of adaptive processes (2). But in an era that aims at an ever more high resolution understanding of molecular processes, is functional molecular research that operates within a much shorter post-sampling time frame much better? Most discussions and attempts at standardization have been focused on the quality of analytical data, which have resulted in standard operating procedures and/or minimum standard protocols such as MIAME and MIAPE. Yet beyond minimal analytical variance, a more exact definition of what constitutes good sample quality or an approach to differentiate subtle biological effects from technical noise is generally lacking.All forms of biosampling, whether post-mortem or ante-mortem, in vivo or in vitro, deprive biological systems of oxygen and nutrients, an extreme event to which biological systems are likely to respond in an adaptive manner even within the very short time frames encountered in the research laboratory. When investigating immediate post-biosampling effects on the molecular level, it is very difficult to separate what can be called the cellular homeostatic adaptive processes (“biological processes”) and reactive sample degradation as both types intersect and change during the post-sampling time period before the samples are inactivated. It should be noted that adaptive in this context does not necessarily equate with protective, only that cellular systems initiate responses, however futile, within their scope of capabilities, toward extreme stress. The increase of protein degradation fragments initiated directly after sampling is nominally a nonadaptive biological process, although it has yet to be proven that all the resulting fragments from such degradation are devoid of any biological functionality or biomarker usefulness (see below). Sample preparation-dependent modifications (such as chemical modifications dependent on sample buffer composition and oxidations) are clear reactive processes.Such adaptive processes depend both on the adaptive systems inherent in the organism in question and the exact conditions of the pre-sampling state of the organism. In animal research, there are major differences in euthanasia protocols both with regard to methodology (such as asphyxiation, terminal anesthesia, or decapitation in the case of smaller rodents such as mice) and the time required for their performance. Yet, there is little discussion as to what extent adaptive biological reactions occur during different forms of biosampling and how they might influence the interpretability of results and/or extrapolation between experiments. Biological evolution has resulted in a range of different life strategies (3). An animal can be resuscitated after a short period of global ischemia, rapidly adapting to the reduced oxygen levels, and yet become unable to handle the sudden reintroduction of oxygen. Intriguingly, such damage can sometimes be ameliorated by therapeutic hypothermia, a result that is likely to depend on more than just the consequences of a reduced metabolism. A reduction of core temperature in rats correlates with a drop of ∼5%/°C in the cerebral metabolic rate of oxygen (4), meaning that the observed protection in animals, and possibly humans, at 4–5°C reduction, occurs at a metabolic reduction of only 20–25%. The neuroprotective effects invoked by anesthesia against ischemia/reperfusion damage (5, 6) also indicate that cells initially try to adapt to the hypometabolism and/or hypothermia associated with biosampling. The mechanisms underlying such physiological changes need to have an extremely short response time and are therefore heavily dependent on enzymatic processes, singling out the proteome as being particularly sensitive to the choice of both sampling methodology and type of tissue (7–12). A few minutes difference in sampling time can, for instance, have profound effects on the peptidome (here defined as all proteins <10 kDa) (13, 14), yet it easily remains within the acceptable time frame for sampling in most biomedical research. In contrast, some peptidomics biomarker signatures are dependent on protease activity induced during post-sampling handling rather than pre-sampling levels (15). Choosing whether to heat or freeze a sample can result in ∼30% difference (8) in results at the proteome level (here defined as all proteins >10 kDa) (Fig. 1, A and B). This brings into question our definition of sample quality, the nature of these biosampling differences, and their implications for research methodology and data interpretation, especially when investigating the molecular mechanisms underlying tissue-protective processes.

Table I

Survival strategies and anoxia sensitivity

A Multi-Method Approach for Proteomic Network Inference in 11 Human Cancers

Protein expression and post-translational modification levels are tightly regulated in neoplastic cells to maintain cellular processes known as ‘cancer hallmarks’. The first Pan-Cancer initiative of The Cancer Genome Atlas (TCGA) Research Network has aggregated protein expression profiles for 3,467 patient samples from 11 tumor types using the antibody based reverse phase protein array (RPPA) technology. The resultant proteomic data can be utilized to computationally infer protein-protein interaction (PPI) networks and to study the commonalities and differences across tumor types. In this study, we compare the performance of 13 established network inference methods in their capacity to retrieve the curated Pathway Commons interactions from RPPA data. We observe that no single method has the best performance in all tumor types, but a group of six methods, including diverse techniques such as correlation, mutual information, and regression, consistently rank highly among the tested methods. We utilize the high performing methods to obtain a consensus network; and identify four robust and densely connected modules that reveal biological processes as well as suggest antibody–related technical biases. Mapping the consensus network interactions to Reactome gene lists confirms the pan-cancer importance of signal transduction pathways, innate and adaptive immune signaling, cell cycle, metabolism, and DNA repair; and also suggests several biological processes that may be specific to a subset of tumor types. Our results illustrate the utility of the RPPA platform as a tool to study proteomic networks in cancer.