The performance of modularity maximization in practical contexts

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q_max for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.Comment: 20 pages, 14 figures, 6 appendices; code available at http://www.santafe.edu/~aaronc/modularity

Genetic Diversity in the Interference Selection Limit

Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, similar to models of quantitative genetics, molecular evolution is determined by the variance in fitness within the population, defined over an effectively asexual segment of the genome (a “linkage block”). We exploit this insensitivity in a new “coarse-grained” coalescent framework, which approximates the effects of many weakly selected mutations with a smaller number of strongly selected mutations that create the same variance in fitness. This approximation generates accurate and efficient predictions for silent site variability when interference is common. However, these results suggest that there is reduced power to resolve individual selection pressures when interference is sufficiently widespread, since a broad range of parameters possess nearly identical patterns of silent site variability

Beyond ‘significance’:Principles and practice of the analysis of credibility

The inferential inadequacies of statistical significance testing are now widely recognized. There is, however, no consensus on how to move research into a ‘post p < 0.05’ era. We present a potential route forward via the Analysis of Credibility, a novel methodology that allows researchers to go beyond the simplistic dichotomy of significance testing and extract more insight from new findings. Using standard summary statistics, AnCred assesses the credibility of significant and non-significant findings on the basis of their evidential weight, and in the context of existing knowledge. The outcome is expressed in quantitative terms of direct relevance to the substantive research question, providing greater protection against misinterpretation. Worked examples are given to illustrate how AnCred extracts additional insight from the outcome of typical research study designs. Its ability to cast light on the use of p-values, the interpretation of non-significant findings and the so-called ‘replication crisis’ is also discussed

Dietary DHA supplementation causes selective changes in phospholipids from different brain regions in both wild type mice and the Tg2576 mouse model of Alzheimer's disease

Alzheimer's disease (AD) is of major concern in ageing populations and we have used the Tg2576 mouse model to understand connections between brain lipids and amyloid pathology. Because dietary docosahexaenoic acid (DHA) has been identified as beneficial, we compared mice fed with a DHA-supplemented diet to those on a nutritionally-sufficient diet. Major phospholipids from cortex, hippocampus and cerebellum were separated and analysed. Each phosphoglyceride had a characteristic fatty acid composition which was similar in cortex and hippocampus but different in the cerebellum. The biggest changes on DHA-supplementation were within ethanolamine phospholipids which, together with phosphatidylserine, had the highest proportions of DHA. Reciprocal alterations in DHA and arachidonate were found. The main diet-induced alterations were found in ethanolamine phospholipids, (and included their ether derivatives), as were the changes observed due to genotype. Tg mice appeared more sensitive to diet with generally lower DHA percentages when on the standard diet and higher relative proportions of DHA when the diet was supplemented. All four major phosphoglycerides analysed showed age-dependent decreases in polyunsaturated fatty acid contents. These data provide, for the first time, a detailed evaluation of phospholipids in different brain areas previously shown to be relevant to behaviour in the Tg2576 mouse model for AD. The lipid changes observed with genotype are consistent with the subtle alterations found in AD patients, especially for the ethanolamine phospholipid molecular species. They also emphasise the contrasting changes in fatty acid content induced by DHA supplementation within individual phospholipid classes

Discovery and Validation of a New Class of Small Molecule Toll-Like Receptor 4 (TLR4) Inhibitors

Many inflammatory diseases may be linked to pathologically elevated signaling via the receptor for lipopolysaccharide (LPS), toll-like receptor 4 (TLR4). There has thus been great interest in the discovery of TLR4 inhibitors as potential anti-inflammatory agents. Recently, the structure of TLR4 bound to the inhibitor E5564 was solved, raising the possibility that novel TLR4 inhibitors that target the E5564-binding domain could be designed. We utilized a similarity search algorithm in conjunction with a limited screening approach of small molecule libraries to identify compounds that bind to the E5564 site and inhibit TLR4. Our lead compound, C34, is a 2-acetamidopyranoside (MW 389) with the formula C17H27NO9, which inhibited TLR4 in enterocytes and macrophages in vitro, and reduced systemic inflammation in mouse models of endotoxemia and necrotizing enterocolitis. Molecular docking of C34 to the hydrophobic internal pocket of the TLR4 co-receptor MD-2 demonstrated a tight fit, embedding the pyran ring deep inside the pocket. Strikingly, C34 inhibited LPS signaling ex-vivo in human ileum that was resected from infants with necrotizing enterocolitis. These findings identify C34 and the β-anomeric cyclohexyl analog C35 as novel leads for small molecule TLR4 inhibitors that have potential therapeutic benefit for TLR4-mediated inflammatory diseases. © 2013 Neal et al