Department of Mathematics, UCI

© 2015 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved. Despite an extensive body of reported information about peripheral and central mechanisms involved in the pathophysiology of IBS symptoms, no comprehensive disease model has emerged that would guide the development of novel, effective therapies. In this Review, we will first describe novel insights into some key components of brain–gut interactions, starting with the emerging findings of distinct functional and structural brain signatures of IBS. We will then point out emerging correlations between these brain networks and genomic, gastrointestinal, immune and gut-microbiome-related parameters. We will incorporate this new information, as well as the reported extensive literature on various peripheral mechanisms, into a systems-based disease model of IBS, and discuss the implications of such a model for improved understanding of the disorder, and for the development of more-effective treatment approaches in the future.

The use of evolutionary profiles to predict protein secondary structure, as well as other protein structural features, has been standard practice since the 1990s. Using profiles in the input of such predictors, in place or in addition to the sequence itself, leads to significantly more accurate predictions. While profiles can enhance structural signals, their role remains somewhat surprising as proteins do not use profiles when folding in vivo. Furthermore, the same sequence-based redundancy reduction protocols initially derived to train and evaluate sequence-based predictors, have been applied to train and evaluate profile-based predictors. This can lead to unfair comparisons since profiles may facilitate the bleeding of information between training and test sets. Here we use the extensively studied problem of secondary structure prediction to better evaluate the role of profiles and show that: (1) high levels of profile similarity between training and test proteins are observed when using standard sequence-based redundancy protocols; (2) the gain in accuracy for profile-based predictors, over sequence-based predictors, strongly relies on these high levels of profile similarity between training and test proteins; and (3) the overall accuracy of a profile-based predictor on a given protein dataset provides a biased measure when trying to estimate the actual accuracy of the predictor, or when comparing it to other predictors. We show, however, that this bias can be mitigated by implementing a new protocol (EVALpro) which evaluates the accuracy of profile-based predictors as a function of the profile similarity between training and test proteins. Such a protocol not only allows for a fair comparison of the predictors on equally hard or easy examples, but also reduces the impact of choosing a given similarity cutoff when selecting test proteins. The EVALpro program is available in the SCRATCH suite ( www.scratch.proteomics.ics.uci.edu) and can be downloaded at: www.download.igb.uci.edu/#evalpro.

Theoretical and empirical comparisons have been made to assess the expressive power and performance of invariant and equivariant GNNs. However, there is currently no theoretical result comparing the expressive power of k-hop invariant GNNs and equivariant GNNs. Additionally, little is understood about whether the performance of equivariant GNNs, employing steerable features up to type-L, increases as L grows - especially when the feature dimension is held constant. In this study, we introduce a key lemma that allows us to analyze steerable features by examining their corresponding invariant features. The lemma facilitates us in understanding the limitations of k-hop invariant GNNs, which fail to capture the global geometric structure due to the loss of geometric information between local structures. Furthermore, we analyze the ability of steerable features to carry information by studying their corresponding invariant features. In particular, we establish that when the input spatial embedding has full rank, the information-carrying ability of steerable features is characterized by their dimension and remains independent of the feature types. This suggests that when the feature dimension is constant, increasing L does not lead to essentially improved performance in equivariant GNNs employing steerable features up to type-L. We substantiate our theoretical insights with numerical evidence.