Determination of Dynamic Brain Connectivity via Spectral Analysis.

Spectral analysis based on neural field theory is used to analyze dynamic connectivity via methods based on the physical eigenmodes that are the building blocks of brain dynamics. These approaches integrate over space instead of averaging over time and thereby greatly reduce or remove the temporal averaging effects, windowing artifacts, and noise at fine spatial scales that have bedeviled the analysis of dynamical functional connectivity (FC). The dependences of FC on dynamics at various timescales, and on windowing, are clarified and the results are demonstrated on simple test cases, demonstrating how modes provide directly interpretable insights that can be related to brain structure and function. It is shown that FC is dynamic even when the brain structure and effective connectivity are fixed, and that the observed patterns of FC are dominated by relatively few eigenmodes. Common artifacts introduced by statistical analyses that do not incorporate the physical nature of the brain are discussed and it is shown that these are avoided by spectral analysis using eigenmodes. Unlike most published artificially discretized "resting state networks" and other statistically-derived patterns, eigenmodes overlap, with every mode extending across the whole brain and every region participating in every mode-just like the vibrations that give rise to notes of a musical instrument. Despite this, modes are independent and do not interact in the linear limit. It is argued that for many purposes the intrinsic limitations of covariance-based FC instead favor the alternative of tracking eigenmode coefficients vs. time, which provide a compact representation that is directly related to biophysical brain dynamics.

Brain dynamics and structure-function relationships via spectral factorization and the transfer function.

It is shown how the brain's linear transfer function provides a means to systematically analyze brain connectivity and dynamics, and to infer connectivity, eigenmodes, and activity measures such as spectra, evoked responses, coherence, and causality, all of which are widely used in brain monitoring. In particular, the Wilson spectral factorization algorithm is outlined and used to efficiently obtain linear transfer functions from experimental two-point correlation functions. The algorithm is tested on a series of brain-like structures of increasing complexity which include time delays, asymmetry, two-dimensionality, and complex network connectivity. These tests are used to verify the algorithm is suitable for application to brain dynamics, specify sampling requirements for experimental time series, and to verify that its runtime is short enough to obtain accurate results for systems of similar size to current experiments. The results can equally well be applied to inference of the transfer function in complex linear systems other than brains.

Functional mechanisms underlie the emergence of a diverse range of plasticity phenomena.

Diverse plasticity mechanisms are orchestrated to shape the spatiotemporal dynamics underlying brain functions. However, why these plasticity rules emerge and how their dynamics interact with neural activity to give rise to complex neural circuit dynamics remains largely unknown. Here we show that both Hebbian and homeostatic plasticity rules emerge from a functional perspective of neuronal dynamics whereby each neuron learns to encode its own activity in the population activity, so that the activity of the presynaptic neuron can be decoded from the activity of its postsynaptic neurons. We explain how a range of experimentally observed plasticity phenomena with widely separated time scales emerge from learning this encoding function, including STDP and its frequency dependence, and metaplasticity. We show that when implemented in neural circuits, these plasticity rules naturally give rise to essential neural response properties, including variable neural dynamics with balanced excitation and inhibition, and approximately log-normal distributions of synaptic strengths, while simultaneously encoding a complex real-world visual stimulus. These findings establish a novel function-based account of diverse plasticity mechanisms, providing a unifying framework relating plasticity, dynamics and neural computation.

Design and Synthesis of a Novel Series of Orally Bioavailable, CNS-Penetrant, Isoform Selective Phosphoinositide 3-Kinase γ (PI3Kγ) Inhibitors with Potential for the Treatment of Multiple Sclerosis (MS).

The lipid kinase phosphoinositide 3-kinase γ (PI3Kγ) has attracted attention as a potential target to treat a variety of autoimmune disorders, including multiple sclerosis, due to its role in immune modulation and microglial activation. By minimizing the number of hydrogen bond donors while targeting a previously uncovered selectivity pocket adjacent to the ATP binding site of PI3Kγ, we discovered a series of azaisoindolinones as selective, brain penetrant inhibitors of PI3Kγ. This ultimately led to the discovery of 16, an orally bioavailable compound that showed efficacy in murine experimental autoimmune encephalomyelitis (EAE), a preclinical model of multiple sclerosis.

Dynamical patterns underlying response properties of cortical circuits.

Recent experimental studies show cortical circuit responses to external stimuli display varied dynamical properties. These include stimulus strength-dependent population response patterns, a shift from synchronous to asynchronous states and a decline in neural variability. To elucidate the mechanisms underlying these response properties and explore how they are mechanistically related, we develop a neural circuit model that incorporates two essential features widely observed in the cerebral cortex. The first feature is a balance between excitatory and inhibitory inputs to individual neurons; the second feature is distance-dependent connectivity. We show that applying a weak external stimulus to the model evokes a wave pattern propagating along lateral connections, but a strong external stimulus triggers a localized pattern; these stimulus strength-dependent population response patterns are quantitatively comparable with those measured in experimental studies. We identify network mechanisms underlying this population response, and demonstrate that the dynamics of population-level response patterns can explain a range of prominent features in neural responses, including changes to the dynamics of neurons' membrane potentials and synaptic inputs that characterize the shift of cortical states, and the stimulus-evoked decline in neuron response variability. Our study provides a unified population activity pattern-based view of diverse cortical response properties, thus shedding new insights into cortical processing.

Inference of direct and multistep effective connectivities from functional connectivity of the brain and of relationships to cortical geometry.

BACKGROUND: The problem of inferring effective brain connectivity from functional connectivity is under active investigation, and connectivity via multistep paths is poorly understood. NEW METHOD: A method is presented to calculate the direct effective connection matrix (deCM), which embodies direct connection strengths between brain regions, from functional CMs (fCMs) by minimizing the difference between an experimental fCM and one calculated via neural field theory from an ansatz deCM based on an experimental anatomical CM. RESULTS: The best match between fCMs occurs close to a critical point, consistent with independent published stability estimates. Residual mismatch between fCMs is identified to be largely due to interhemispheric connections that are poorly estimated in an initial ansatz deCM due to experimental limitations; improved ansatzes substantially reduce the mismatch and enable interhemispheric connections to be estimated. Various levels of significant multistep connections are then imaged via the neural field theory (NFT) result that these correspond to powers of the deCM; these are shown to be predictable from geometric distances between regions. COMPARISON WITH EXISTING METHODS: This method gives insight into direct and multistep effective connectivity from fCMs and relating to physiology and brain geometry. This contrasts with other methods, which progressively adjust connections without an overarching physiologically based framework to deal with multistep or poorly estimated connections. CONCLUSIONS: deCMs can be usefully estimated using this method and the results enable multistep connections to be investigated systematically.

Synthesis and evaluation of NS5A inhibitors containing diverse heteroaromatic cores.

Inhibitors of the HCV NS5A nonstructural protein are showing promising clinical potential in the treatment of hepatitis C when used in combination with other direct-acting antiviral agents. Current NS5A clinical candidates such as daclatasvir, ledipasvir, and ombitasvir share a common pharmacophore that features a pair of (S)-methoxycarbonylvaline capped pyrrolidines linked to various cores by amides, imidazoles and/or benzimidazoles. In this Letter, we describe the evaluation of NS5A inhibitors which contain alternative heteroaromatic replacements for these amide mimetics. The SAR knowledge gleaned in the optimization of scaffolds containing benzoxazoles was parlayed toward the identification of potent NS5A inhibitors containing other heteroaromatic replacements such as indoles and imidazopyridines.

Benzimidazole-containing HCV NS5A inhibitors: effect of 4-substituted pyrrolidines in balancing genotype 1a and 1b potency.

The treatment of HCV with highly efficacious, well-tolerated, interferon-free regimens is a compelling clinical goal. Trials employing combinations of direct-acting antivirals that include NS5A inhibitors have shown significant promise in meeting this challenge. Herein, we describe our efforts to identify inhibitors of NS5A and report on the discovery of benzimidazole-containing analogs with subnanomolar potency against genotype 1a and 1b replicons. Our SAR exploration of 4-substituted pyrrolidines revealed that the subtle inclusion of a 4-methyl group could profoundly increase genotype 1a potency in multiple scaffold classes.

Discovery of thienoimidazole-based HCV NS5A inhibitors. Part 1: C2-symmetric inhibitors with diyne and biphenyl linkers.

The discovery of C2-symmetric bis-thienoimidazoles HCV NS5A inhibitors is herein reported. Two straightforward approaches to access the requisite diyne and biphenyl linker moieties are described. This study revealed the paramount importance of the aromatic character of the linker to achieve high genotype 1a potency.

Discovery of thienoimidazole-based HCV NS5A inhibitors. Part 2: non-symmetric inhibitors with potent activity against genotype 1a and 1b.

The discovery of non-symmetric thienoimidazole-containing HCV NS5A inhibitors is described. The inhibitors herein reported display high potencies against both genotype 1a and 1b. In this follow-up manuscript, we discuss the importance of the linker aromaticity to achieve high potency, particularly against genotype 1a.

Discovery of Thienoimidazole-Based HCV NS5A Genotype 1a and 1b Inhibitors.

The discovery of potent thienoimidazole-based HCV NS5A inhibitors is herein reported. A novel method to access the thienoimidazole [5,5]-bicyclic system is disclosed. This method gave access to a common key intermediate (6) that was engaged in Suzuki or Sonogashira reactions with coupling partners bearing different linkers. A detailed study of the structure-activity relationship (SAR) of the linkers revealed that aromatic linkers with linear topologies are required to achieve high potency for both 1a and 1b HCV genotypes. Compound 20, with a para-phenyl linker, was identified as a potential lead displaying potencies of 17 and 8 pM against genotype 1a and 1b replicons, respectively.

Spectral Characterization of Hierarchical Modularity in Product Architectures.

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

Relations between the geometry of cortical gyrification and white-matter network architecture.

A geometrically based network model of cortico-cortical white-matter connectivity is used in combination with diffusion spectrum MRI (DSI) data to show that white-matter cortical network architecture is founded on a homogeneous, isotropic geometric connection principle. No other special information about single connections or groups of connections is required to generate networks very similar to experimental ones. This model provides excellent agreement with experimental DSI frequency distributions of network measures-degree, clustering coefficient, path length, and betweenness centrality. In the model, these distributions are a result of geometrically induced spatial variations in the values of these measures with deep nodes having more hublike properties than superficial nodes. This leads to experimentally testable predictions of corresponding variations in real cortexes. The convoluted geometry of the cortex is also found to introduce weak modularity, similar to the lobe structure of the cortex, with the boundaries between modules having hublike properties. These findings mean that some putative discoveries regarding the structure of white-matter cortical networks are simply artifacts and/or consequences of geometry. This model may help provide insight into diseases associated with differences in gyrification as well as evolutionary development of the cortex.

Spectral characterization of hierarchical network modularity and limits of modularity detection.

Many real world networks are reported to have hierarchically modular organization. However, there exists no algorithm-independent metric to characterize hierarchical modularity in a complex system. The main results of the paper are a set of methods to address this problem. First, classical results from random matrix theory are used to derive the spectrum of a typical stochastic block model hierarchical modular network form. Second, it is shown that hierarchical modularity can be fingerprinted using the spectrum of its largest eigenvalues and gaps between clusters of closely spaced eigenvalues that are well separated from the bulk distribution of eigenvalues around the origin. Third, some well-known results on fingerprinting non-hierarchical modularity in networks automatically follow as special cases, threreby unifying these previously fragmented results. Finally, using these spectral results, it is found that the limits of detection of modularity can be empirically established by studying the mean values of the largest eigenvalues and the limits of the bulk distribution of eigenvalues for an ensemble of networks. It is shown that even when modularity and hierarchical modularity are present in a weak form in the network, they are impossible to detect, because some of the leading eigenvalues fall within the bulk distribution. This provides a threshold for the detection of modularity. Eigenvalue distributions of some technological, social, and biological networks are studied, and the implications of detecting hierarchical modularity in real world networks are discussed.

Synthesis of alcohols from m-fluorophenylsulfones and dialkylboranes: application to the C14-C35 building block of E7389.

The reaction of m-fluorophenylsulfone anions with dialkylboranes, followed by alkaline hydroperoxide oxidation, yields alcohols in high yields. Optimization of the process, scope and limitation, and application to the synthesis of one of the C14-C35 building blocks of E7389, a right half analogue of halichondrin B, are reported.

Dramatic improvement in catalyst loadings and molar ratios of coupling partners for Ni/Cr-mediated coupling reactions: heterobimetallic catalysts.

Two new ligands 1a,b are reported. Upon treatment with 1 equiv of NiCl(2) x (MeOCH(2))(2), 1a,b give the corresponding Ni complexes. X-ray analysis of 1a x NiCl(2) established that the NiCl(2) is selectively coordinated to the phenanthroline nitrogens. Ni/Cr heterobimetallic catalysts 1a,b x CrCl(2)/NiCl(2), prepared from 1a,b x NiCl(2), have been shown to behave exceptionally well in catalytic asymmetric Ni/Cr-mediated couplings, with highlights including the following: (1) 1-2 mol % catalyst is sufficient to complete the coupling; (2) only negligible amounts of the dimers, byproducts formed through the alkenyl Ni species, are observed; (3) the coupling goes to completion even with a 1:1 molar ratio of the coupling partners; and (4) the asymmetric induction is practically identical with that obtained from the coupling with the Cr catalysts prepared from (S)-sulfonamides 2a,b. The scope of the new Ni/Cr heterobimetallic catalysts was briefly studied using four additional aldehydes. The applicability of the new catalysts to polyfunctional substrates was demonstrated by two C-C bond formations chosen from the halichondrin/E7389 synthesis as examples.

New syntheses of E7389 C14-C35 and halichondrin C14-C38 building blocks: reductive cyclization and oxy-Michael cyclization approaches.

Cr-mediated coupling reactions are usually achieved with a slight excess of a given nucleophile. To develop a cost-effective use of this process, two different approaches have been studied. The first approach depends on two consecutive catalytic asymmetric Cr-mediated couplings, with use of coupling partners purposely being of unbalanced molecular size and complexity. The second approach rests on the success in identifying the nucleophile, which allows us to achieve the coupling satisfactorily with a 1:1 molar ratio of the coupling partners. The C23-O bond is stereospecifically constructed via reductive cyclization of the oxonium ion, or oxy-Michael cyclization. Both syntheses have a high overall efficiency: E7389 C14-C35 and halichondrin C14-C38 building blocks have been synthesized from the corresponding C27-C35 and C27-C38 aldehydes, respectively, in high overall yields with an excellent stereoselectivity. Because of operational simplicity, the synthesis outlined herein appears to be well suited for scaling.

The N-acetylmannosamine transferase catalyzes the first committed step of teichoic acid assembly in Bacillus subtilis and Staphylococcus aureus.

There have been considerable strides made in the characterization of the dispensability of teichoic acid biosynthesis genes in recent years. A notable omission thus far has been an early gene in teichoic acid synthesis encoding the N-acetylmannosamine transferase (tagA in Bacillus subtilis; tarA in Staphylococcus aureus), which adds N-acetylmannosamine to complete the synthesis of undecaprenol pyrophosphate-linked disaccharide. Here, we show that the N-acetylmannosamine transferases are dispensable for growth in vitro, making this biosynthetic enzyme the last dispensable gene in the pathway, suggesting that tagA (or tarA) encodes the first committed step in wall teichoic acid synthesis.