Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are “sloppy,” i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher information matrix, which is interpreted as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. The manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.

Accumulating evidence suggests that the brain can efficiently process both external and internal information. The processing of internal information is a distinct “offline” cognitive mode that requires not only spontaneously generated mental activity; it has also been hypothesized to require a decoupling of attention from perception in order to separate competing streams of internal and external information. This process of decoupling is potentially adaptive because it could prevent unimportant external events from disrupting an internal train of thought. Here, we use measurements of pupil diameter (PD) to provide concrete evidence for the role of decoupling during spontaneous cognitive activity. First, during periods conducive to offline thought but not during periods of task focus, PD exhibited spontaneous activity decoupled from task events. Second, periods requiring external task focus were characterized by large task evoked changes in PD; in contrast, encoding failures were preceded by episodes of high spontaneous baseline PD activity. Finally, high spontaneous PD activity also occurred prior to only the slowest 20% of correct responses, suggesting high baseline PD indexes a distinct mode of cognitive functioning. Together, these data are consistent with the decoupling hypothesis, which suggests that the capacity for spontaneous cognitive activity depends upon minimizing disruptions from the external world.

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Herein, the synthesis of 1,2,3,4‐tetrasubstituted benzenoid rings, motifs found in pharmaceutical, agrochemical, and natural products, is described.^[1] In the past, the regioselective syntheses of such compounds have been a significant challenge. This work reports a method using substituted arynes derived from aryl(Mes)iodonium salts to access a range of densely functionalized 1,2,3,4‐tetrasubstituted benzenoid rings. Significantly, it was found that halide substituents are compatible under these conditions, enabling post‐synthetic elaboration via palladium‐catalyzed coupling. This concise strategy is predicated on two regioselective events: 1) ortho‐ deprotonation of aryl(Mes)iodonium salts to generate a substituted aryne intermediate, and 2) regioselective trapping of said arynes, thereby improving previously reported reaction conditions to generate arynes at room temperature and in shorter reaction times. Density functional theory (DFT) computations and linear free energy relationship (LFER) analysis suggest the regioselectivity of deprotonation is influenced by both proximal and distal ring substituents on the aryne precursor. A competition experiment further reveals the role of arene substituents on relative reactivity of aryl(Mes)iodoniums as aryne precursors.

Correlated amino acid substitution algorithms attempt to discover groups of residues that co-fluctuate due to either structural or functional constraints. Although these algorithms could inform both ab initio protein folding calculations and evolutionary studies, their utility for these purposes has been hindered by a lack of confidence in their predictions due to hard to control sources of error. To complicate matters further, naive users are confronted with a multitude of methods to choose from, in addition to the mechanics of assembling and pruning a dataset. We first introduce a new pair scoring method, called ZNMI (Z-scored-product Normalized Mutual Information), which drastically improves the performance of mutual information for co-fluctuating residue prediction. Second and more important, we recast the process of finding coevolving residues in proteins as a data-processing pipeline inspired by the medical imaging literature. We construct an ensemble of alignment partitions that can be used in a cross-validation scheme to assess the effects of choices made during the procedure on the resulting predictions. This pipeline sensitivity study gives a measure of reproducibility (how similar are the predictions given perturbations to the pipeline?) and accuracy (are residue pairs with large couplings on average close in tertiary structure?). We choose a handful of published methods, along with ZNMI, and compare their reproducibility and accuracy on three diverse protein families. We find that (i) of the algorithms tested, while none appear to be both highly reproducible and accurate, ZNMI is one of the most accurate by far and (ii) while users should be wary of predictions drawn from a single alignment, considering an ensemble of sub-alignments can help to determine both highly accurate and reproducible couplings. Our cross-validation approach should be of interest both to developers and end users of algorithms that try to detect correlated amino acid substitutions.