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Abstract Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25–51, 2015; Lyttle et al. in Biol Cybern 111(1):25–47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701–744, 2021. https://doi.org/10.1137/20M1344974 ) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia , and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties. 

Abstract Deep brain stimulation (DBS) is a promising neuromodulation therapy, but the neurophysiological mechanisms of DBS remain unclear. In awake mice, we performed high-speed membrane voltage fluorescence imaging of individual hippocampal CA1 neurons during DBS delivered at 40 Hz or 140 Hz, free of electrical interference. DBS powerfully depolarized somatic membrane potentials without suppressing spike rate, especially at 140 Hz. Further, DBS paced membrane voltage and spike timing at the stimulation frequency and reduced timed spiking output in response to hippocampal network theta-rhythmic (3–12 Hz) activity patterns. To determine whether DBS directly impacts cellular processing of inputs, we optogenetically evoked theta-rhythmic membrane depolarization at the soma. We found that DBS-evoked membrane depolarization was correlated with DBS-mediated suppression of neuronal responses to optogenetic inputs. These results demonstrate that DBS produces powerful membrane depolarization that interferes with the ability of individual neurons to respond to inputs, creating an informational lesion. 

During early mammalian embryo development, a small number of cells make robust fate decisions at particular spatial locations in a tight time window to form inner cell mass (ICM), and later epiblast (Epi) and primitive endoderm (PE). While recent single-cell transcriptomics data allows scrutinization of heterogeneity of individual cells, consistent spatial and temporal mechanisms the early embryo utilize to robustly form the Epi/PE layers from ICM remain elusive. Here we build a multiscale three-dimensional model for mammalian embryo to recapitulate the observed patterning process from zygote to late blastocyst. By integrating the spatiotemporal information reconstructed from multiple single-cell transcriptomic datasets, the data-informed modeling analysis suggests two major processes critical to the formation of Epi/PE layers: a selective cell-cell adhesion mechanism (via EphA4/EphrinB2) for fate-location coordination and a temporal attenuation mechanism of cell signaling (via Fgf). Spatial imaging data and distinct subsets of single-cell gene expression data are then used to validate the predictions. Together, our study provides a multiscale framework that incorporates single-cell gene expression datasets to analyze gene regulations, cell-cell communications, and physical interactions among cells in complex geometries at single-cell resolution, with direct application to late-stage development of embryogenesis. 

This work explores a method for analytically computing the infinites-imal phase response curves (iPRCs) of a synthetic nervous system (SNS) for a hybrid exoskeleton. Phase changes, in response to perturbations, revealed by the iPRCs, could assist in tuning the strength and locations of sensory pathways. We model the SNS exoskeleton controller in a reduced form using a state-space rep-resentation that interfaces neural and motor dynamics. The neural dynamics are modeled after non-spiking neurons configured as a central pattern generator (CPG), while the motor dynamics model a power unit for the hip joint of the exoskeleton. Within the dynamics are piecewise functions and hard boundaries (i.e. “sliding conditions”), which cause discontinuities in the vector field at their boundaries. The analytical methods for computing the iPRCs used in this work apply the adjoint equation method with jump conditions that are able to account for these discontinuities. To show the accuracy and speed provided by these methods, we compare the analytical and brute-force solutions.