In the auditory streaming paradigm alternating sequences of pure tones can be perceived as a single galloping rhythm (integration) or as two sequences with separated low and high tones (segregation). Although studied for decades, the neural mechanisms underlining this perceptual grouping of sound remains a mystery. With the aim of identifying a plausible minimal neural circuit that captures this phenomenon, we propose a firing rate model with two periodically forced neural populations coupled by fast direct excitation and slow delayed inhibition. By analyzing the model in a non-smooth, slow-fast regime we analytically prove the existence of a rich repertoire of dynamical states and of their parameter dependent transitions. We impose plausible parameter restrictions and link all states with perceptual interpretations. Regions of stimulus parameters occupied by states linked with each percept matches those found in behavioral experiments. Our model suggests that slow inhibition masks the perception of subsequent tones during segregation (forward masking), while fast excitation enables integration for large pitch differences between the two tones.
We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stable swimming and synchrony. We show that swimming is stable in a significantly larger range of parameters, and can be initiated more robustly, than synchrony. Our results can explain the appearance of long-lasting synchrony bouts seen in experiments at the start of a swimming episode.
Although, in most animals, brain connectivity varies between individuals, behaviour is often similar across a species. What fundamental structural properties are shared across individual networks that define this behaviour? We describe a probabilistic model of connectivity in the hatchling Xenopus tadpole spinal cord which, when combined with a spiking model, reliably produces rhythmic activity corresponding to swimming. The probabilistic model allows calculation of structural characteristics that reflect common network properties, independent of individual network realisations. We use the structural characteristics to study examples of neuronal dynamics, in the complete network and various sub-networks, and this allows us to explain the basis for key experimental findings, and make predictions for experiments. We also study how structural and functional features differ between detailed anatomical connectomes and those generated by our new, simpler, model (meta-model).
Abstract Ambiguous sensory information can lead to spontaneous alternations between perceptual states, recently shown to extend to tactile perception. The authors recently proposed a simplified form of tactile rivalry which evokes two competing percepts for a fixed difference in input amplitudes across antiphase, pulsatile stimulation of the left and right fingers. This study addresses the need for a tactile rivalry model that captures the dynamics of perceptual alternations and that incorporates the structure of the somatosensory system. The model features hierarchical processing with two stages. The first and the second stages of model could be located at the secondary somatosensory cortex (area S2), or in higher areas driven by S2. The model captures dynamical features specific to the tactile rivalry percepts and produces general characteristics of perceptual rivalry: input strength dependence of dominance times (Levelt’s proposition II), short-tailed skewness of dominance time distributions and the ratio of distribution moments. The presented modelling work leads to experimentally testable predictions. The same hierarchical model could generalise to account for percept formation, competition and alternations for bistable stimuli that involve pulsatile inputs from the visual and auditory domains.
Abstract This study introduces a novel neuromechanical model employing a detailed spiking neural network to explore the role of axial proprioceptive sensory feedback, namely stretch feedback, in salamander locomotion. Unlike previous studies that often oversimplified the dynamics of the locomotor networks, our model includes detailed simulations of the classes of neurons that are considered responsible for generating movement patterns. The locomotor circuits, modeled as a spiking neural network of adaptive leaky integrate-and-fire neurons, are coupled to a three-dimensional mechanical model of a salamander with realistic physical parameters and simulated muscles. In open-loop simulations (i.e., without sensory feedback), the model replicates locomotor patterns observed in-vitro and in-vivo for swimming and trotting gaits. Additionally, a modular descending reticulospinal drive to the central pattern generation network allows to accurately control the activation, frequency and phase relationship of the different sections of the limb and axial circuits. In closed-loop swimming simulations (i.e. including axial stretch feedback), systematic evaluations reveal that intermediate values of feedback strength increase the tail beat frequency and reduce the intersegmental phase lag, contributing to a more coordinated, faster and energy-efficient locomotion. Interestingly, the result is conserved across different feedback topologies (ascending or descending, excitatory or inhibitory), suggesting that it may be an inherent property of axial proprioception. Moreover, intermediate feedback strengths expand the stability region of the network, enhancing its tolerance to a wider range of descending drives, internal parameters’ modifications and noise levels. Conversely, high values of feedback strength lead to a loss of controllability of the network and a degradation of its locomotor performance. Overall, this study highlights the beneficial role of proprioception in generating, modulating and stabilizing locomotion patterns, provided that it does not excessively override centrally-generated locomotor rhythms. This work also underscores the critical role of detailed, biologically-realistic neural networks to improve our understanding of vertebrate locomotion. Author summary In this paper, we developed a computational model to investigate how salamanders move, both while swimming and walking. Unlike previous studies that often oversimplified the dynamics of these complex neural networks, our model includes detailed simulations of the classes of neurons that are considered responsible for generating movement patterns. The locomotor circuits, modeled as a spiking neural network, are coupled to a three-dimensional mechanical model of a salamander with realistic physical parameters and simulated muscles. The neural model integrates axial proprioceptive sensory feedback from the body’s movements to modulate the locomotor gaits. Our simulations suggest that this sensory feedback plays a major role in controlling the rhythm and coordination of movements. This has implications for understanding not only how salamanders move but also provides insights into the evolution of locomotion in vertebrates. By investigating how central and sensory mechanisms interact to produce efficient and adaptable movement, our work contributes to the broader field of neuroscience and robotics, offering potential strategies for designing more effective biomimetic robots.
This study introduces a novel neuromechanical model employing a detailed spiking neural network to explore the role of axial proprioceptive sensory feedback, namely stretch feedback, in salamander locomotion. Unlike previous studies that often oversimplified the dynamics of the locomotor networks, our model includes detailed simulations of the classes of neurons that are considered responsible for generating movement patterns. The locomotor circuits, modeled as a spiking neural network of adaptive leaky integrate-and-fire neurons, are coupled to a three-dimensional mechanical model of a salamander with realistic physical parameters and simulated muscles. In open-loop simulations (i.e., without sensory feedback), the model replicates locomotor patterns observed in-vitro and in-vivo for swimming and trotting gaits. Additionally, a modular descending reticulospinal drive to the central pattern generation network allows to accurately control the activation, frequency and phase relationship of the different sections of the limb and axial circuits. In closed-loop swimming simulations (i.e. including axial stretch feedback), systematic evaluations reveal that intermediate values of feedback strength increase the tail beat frequency and reduce the intersegmental phase lag, contributing to a more coordinated, faster and energy-efficient locomotion. Interestingly, the result is conserved across different feedback topologies (ascending or descending, excitatory or inhibitory), suggesting that it may be an inherent property of axial proprioception. Moreover, intermediate feedback strengths expand the stability region of the network, enhancing its tolerance to a wider range of descending drives, internal parameters’ modifications and noise levels. Conversely, high values of feedback strength lead to a loss of controllability of the network and a degradation of its locomotor performance. Overall, this study highlights the beneficial role of proprioception in generating, modulating and stabilizing locomotion patterns, provided that it does not excessively override centrally-generated locomotor rhythms. This work also underscores the critical role of detailed, biologically-realistic neural networks to improve our understanding of vertebrate locomotion.
We analyse periodic solutions in a system of four delayed differential equations forced by periodic inputs representing two competing neural populations connected with fast mutual excitation and slow delayed inhibition. The combination of mechanisms generates a rich dynamical structure that we are able to characterize using slow-fast dissection and a binary classification of states. We previously proved the existence conditions of all possible states 1:1 locked to the inputs and applied this analysis to the tracking of the rhythms perceived when listening to alternating sequences of low and high tones. Here we extend this analysis using analytical and computational tools by proving the existence a set of n:1 periodically locked states and their location in parameter space. Firstly we examine cycle skipping states and find that they accumulate in an infinite cascade of period-incrementing bifurcations with increasing periods for decreasing values of the local input strength. Secondly we analyse periodic solutions that alternate between 1:1 locked states that repeat after an integer multiple of the input period (swapping states). We show that such states accumulate in similar bifurcation cascades with decreasing values of the lateral input strength. We report a parameter-dependent scaling constant for the ratio of widths of successive regions in the cascades, which generalises across cycle skipping and swapping states. The periodic states reported here - emergent behaviours in the model - can be linked to known phenomena in auditory perception that are beyond the original scope of the model’s design.
In the auditory streaming paradigm alternating sequences of pure tones can be perceived as a single galloping rhythm (integration) or as two sequences with separated low and high tones (segregation). Although studied for decades, the neural mechanisms underlining this perceptual grouping of sound remains a mystery. With the aim of identifying a plausible minimal neural circuit that captures this phenomenon, we propose a firing rate model with two periodically forced neural populations coupled by fast direct excitation and slow delayed inhibition. By analyzing the model in a non-smooth, slow-fast regime we analytically prove the existence of a rich repertoire of dynamical states and of their parameter dependent transitions. We impose plausible parameter restrictions and link all states with perceptual interpretations. Regions of stimulus parameters occupied by states linked with each percept matches those found in behavioral experiments. Our model suggests that slow inhibition masks the perception of subsequent tones during segregation (forward masking), while fast excitation enables integration for large pitch differences between the two tones.
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