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  1. The preBötzinger Complex (preBötC) encodes inspiratory time as rhythmic bursts of activity underlying each breath. Spike synchronization throughout a sparsely connected preBötC microcircuit initiates bursts that ultimately drive the inspiratory motor patterns. Using minimal microcircuit models to explore burst initiation dynamics, we examined the variability in probability and latency to burst following exogenous stimulation of a small subset of neurons, mimicking experiments. Among various physiologically plausible graphs of 1000 excitatory neurons constructed using experimentally determined synaptic and connectivity parameters, directed Erdős-Rényi graphs with a broad (lognormal) distribution of synaptic weights best captured the experimentally observed dynamics. preBötC synchronization leading to bursts was regulated by the efferent connectivity of spiking neurons that are optimally tuned to amplify modest preinspiratory activity through input convergence. Using graph-theoretic and machine learning-based analyses, we found that input convergence of efferent connectivity at the next-nearest neighbor order was a strong predictor of incipient synchronization. Our analyses revealed a crucial role of synaptic heterogeneity in imparting exceptionally robust yet flexible preBötC attractor dynamics. Given the pervasiveness of lognormally distributed synaptic strengths throughout the nervous system, we postulate that these mechanisms represent a ubiquitous template for temporal processing and decision-making computational motifs.

    SIGNIFICANCE STATEMENTMammalian breathing is robust, virtually continuous throughout life, yet is inherently labile: to adapt to rapid metabolic shifts (e.g., fleeing a predator or chasing prey); for airway reflexes; and to enable nonventilatory behaviors (e.g., vocalization, breathholding, laughing). Canonical theoretical frameworks—based on pacemakers and intrinsic bursting—cannot account for the observed robustness and flexibility of the preBötzinger Complex rhythm. Experiments reveal that network synchronization is the key to initiate inspiratory bursts in each breathing cycle. We investigated preBötC synchronization dynamics using network models constructed with experimentally determined neuronal and synaptic parameters. We discovered that a fat-tailed (non-Gaussian) synaptic weight distribution—a manifestation of synaptic heterogeneity—augments neuronal synchronization and attractor dynamics in this vital rhythmogenic network, contributing to its extraordinary reliability and responsiveness.

     
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  2. null (Ed.)
    Understanding force propagation through the fibrous extracellular matrix can elucidate how cells interact mechanically with their surrounding tissue. Presumably, due to elastic nonlinearities of the constituent filaments and their random connection topology, force propagation in fiber networks is quite complex, and the basic problem of force propagation in structurally heterogeneous networks remains unsolved. We report on a new technique to detect displacements through such networks in response to a localized force, using a fibrin hydrogel as an example. By studying the displacements of fibers surrounding a two-micron bead that is driven sinusoidally by optical tweezers, we develop maps of displacements in the network. Fiber movement is measured by fluorescence intensity fluctuations recorded by a laser scanning confocal microscope. We find that the Fourier magnitude of these intensity fluctuations at the drive frequency identifies fibers that are mechanically coupled to the driven bead. By examining the phase relation between the drive and the displacements, we show that the fiber displacements are, indeed, due to elastic couplings within the network. Both the Fourier magnitude and phase depend on the direction of the drive force, such that displacements typically propagate farther, but not exclusively, along the drive direction. This technique may be used to characterize the local mechanical response in 3-D tissue cultures, and to address fundamental questions about force propagation within fiber networks. 
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  3. null (Ed.)
    We consider the propagation of tension along specific filaments of a semiflexible filament network in response to the application of a point force using a combination of numerical simulations and analytic theory. We find the distribution of force within the network is highly heterogeneous, with a small number of fibers supporting a significant fraction of the applied load over distances of multiple mesh sizes surrounding the point of force application. We suggest that these structures may be thought of as tensile force chains, whose structure we explore via simulation. We develop self-consistent calculations of the point-force response function and introduce a transfer matrix approach to explore the decay of tension (into bending) energy and the branching of tensile force chains in the network. 
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  4. Despite the ubiquitous importance of cell contact guidance, the signal-inducing contact guidance of mammalian cells in an aligned fibril network has defied elucidation. This is due to multiple interdependent signals that an aligned fibril network presents to cells, including, at least, anisotropy of adhesion, porosity, and mechanical resistance. By forming aligned fibrin gels with the same alignment strength, but cross-linked to different extents, the anisotropic mechanical resistance hypothesis of contact guidance was tested for human dermal fibroblasts. The cross-linking was shown to increase the mechanical resistance anisotropy, without detectable change in network microstructure and without change in cell adhesion to the cross-linked fibrin gel. This methodology thus isolated anisotropic mechanical resistance as a variable for fixed anisotropy of adhesion and porosity. The mechanical resistance anisotropy |Y*|−1− |X*|−1increased over fourfold in terms of the Fourier magnitudes of microbead displacement |X*| and |Y*| at the drive frequency with respect to alignment directionYobtained by optical forces in active microrheology. Cells were found to exhibit stronger contact guidance in the cross-linked gels possessing greater mechanical resistance anisotropy: the cell anisotropy index based on the tensor of cell orientation, which has a range 0 to 1, increased by 18% with the fourfold increase in mechanical resistance anisotropy. We also show that modulation of adhesion via function-blocking antibodies can modulate the guidance response, suggesting a concomitant role of cell adhesion. These results indicate that fibroblasts can exhibit contact guidance in aligned fibril networks by sensing anisotropy of network mechanical resistance.

     
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  5. We study the change in the size and shape of the mean limit cycle of a stochastically driven nonlinear oscillator as a function of noise amplitude. Such dynamics occur in a variety of nonequilibrium systems, including the spontaneous oscillations of hair cells of the inner ear. The noise-induced distortion of the limit cycle generically leads to its rounding through the elimination of sharp (high-curvature) features through a process we call corner cutting. We provide a criterion that may be used to identify limit cycle regions most susceptible to such noise-induced distortions. By using this criterion, one may obtain more meaningful parametric fits of nonlinear dynamical models from noisy experimental data, such as those coming from spontaneously oscillating hair cells. 
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