Computational and experimental modulation of a noisy chaotic neuronal system.

In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed.

Multimodal sensory information is represented by a combinatorial code in a sensorimotor system.

A ubiquitous feature of the nervous system is the processing of simultaneously arriving sensory inputs from different modalities. Yet, because of the difficulties of monitoring large populations of neurons with the single resolution required to determine their sensory responses, the cellular mechanisms of how populations of neurons encode different sensory modalities often remain enigmatic. We studied multimodal information encoding in a small sensorimotor system of the crustacean stomatogastric nervous system that drives rhythmic motor activity for the processing of food. This system is experimentally advantageous, as it produces a fictive behavioral output in vitro, and distinct sensory modalities can be selectively activated. It has the additional advantage that all sensory information is routed through a hub ganglion, the commissural ganglion, a structure with fewer than 220 neurons. Using optical imaging of a population of commissural neurons to track each individual neuron's response across sensory modalities, we provide evidence that multimodal information is encoded via a combinatorial code of recruited neurons. By selectively stimulating chemosensory and mechanosensory inputs that are functionally important for processing of food, we find that these two modalities were processed in a distributed network comprising the majority of commissural neurons imaged. In a total of 12 commissural ganglia, we show that 98% of all imaged neurons were involved in sensory processing, with the two modalities being processed by a highly overlapping set of neurons. Of these, 80% were multimodal, 18% were unimodal, and only 2% of the neurons did not respond to either modality. Differences between modalities were represented by the identities of the neurons participating in each sensory condition and by differences in response sign (excitation versus inhibition), with 46% changing their responses in the other modality. Consistent with the hypothesis that the commissural network encodes different sensory conditions in the combination of activated neurons, a new combination of excitation and inhibition was found when both pathways were activated simultaneously. The responses to this bimodal condition were distinct from either unimodal condition, and for 30% of the neurons, they were not predictive from the individual unimodal responses. Thus, in a sensorimotor network, different sensory modalities are encoded using a combinatorial code of neurons that are activated or inhibited. This provides motor networks with the ability to differentially respond to categorically different sensory conditions and may serve as a model to understand higher-level processing of multimodal information.

Predicting slow and fast neuronal dynamics with machine learning.

In this work, we employ reservoir computing, a recently developed machine learning technique, to predict the time evolution of neuronal activity produced by the Hindmarsh-Rose neuronal model. Our results show accurate short- and long-term predictions for periodic (tonic and bursting) neuronal behaviors, but only short-term accurate predictions for chaotic neuronal states. However, after the accuracy of the short-term predictability deteriorates in the chaotic regime, the predicted output continues to display similarities with the actual neuronal behavior. This is reinforced by a striking resemblance between the bifurcation diagrams of the actual and of the predicted outputs. Error analyses of the reservoir's performance are consistent with standard results previously obtained.

Synchronous tonic-to-bursting transitions in a neuronal hub motif.

We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.

Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach.

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.

Quantitative description of neuronal calcium dynamics in C. elegans' thermoreception.

The dynamical mechanisms underlying thermoreception in the nematode C. elegans are studied with a mathematical model for the amphid finger-like ciliated (AFD) neurons. The equations, equipped with Arrhenius temperature factors, account for the worm's thermotaxis when seeking environments at its cultivation temperature, and for the AFD's calcium dynamics when exposed to both linearly ramping and oscillatory temperature stimuli. Calculations of the peak time for calcium responses during simulations of pulse-like temperature inputs are consistent with known behavioral time scales of C. elegans.

Temperature effects on neuronal firing rates and tonic-to-bursting transitions.

Temperature fluctuations can affect neurological processes at a variety of levels, with the overall output that higher temperatures in general increase neuronal activity. While variations in firing rates can happen with the neuronal system maintaining its homeostatic firing pattern of tonic firing, or bursting, changes in firing rates can also be associated with transitions between the two patterns of firing. Our computer simulations suggest a possible mechanism directly related to the shortening of the duration of the action potential for higher firing rates with temperature increase. Increased temperatures also shorten the period doubling cascade and chaos transition between tonic and burting regimes.

Spatial distribution of intermingling pools of projection neurons with distinct targets: A 3D analysis of the commissural ganglia in Cancer borealis.

Projection neurons play a key role in carrying long-distance information between spatially distant areas of the nervous system and in controlling motor circuits. Little is known about how projection neurons with distinct anatomical targets are organized, and few studies have addressed their spatial organization at the level of individual cells. In the paired commissural ganglia (CoGs) of the stomatogastric nervous system of the crab Cancer borealis, projection neurons convey sensory, motor, and modulatory information to several distinct anatomical regions. While the functions of descending projection neurons (dPNs) which control downstream motor circuits in the stomatogastric ganglion are well characterized, their anatomical distribution as well as that of neurons projecting to the labrum, brain, and thoracic ganglion have received less attention. Using cell membrane staining, we investigated the spatial distribution of CoG projection neurons in relation to all CoG neurons. Retrograde tracing revealed that somata associated with different axonal projection pathways were not completely spatially segregated, but had distinct preferences within the ganglion. Identified dPNs had diameters larger than 70% of CoG somata and were restricted to the most medial and anterior 25% of the ganglion. They were contained within a cluster of motor neurons projecting through the same nerve to innervate the labrum, indicating that soma position was independent of function and target area. Rather, our findings suggest that CoG neurons projecting to a variety of locations follow a generalized rule: for all nerve pathway origins, the soma cluster centroids in closest proximity are those whose axons project down that pathway.

Bifurcation transitions in gap-junction-coupled neurons.

Here we investigate transitions occurring in the dynamical states of pairs of distinct neurons electrically coupled, with one neuron tonic and the other bursting. Depending on the dynamics of the individual neurons, and for strong enough coupling, they synchronize either in a tonic or a bursting regime, or initially tonic transitioning to bursting via a period doubling cascade. Certain intrinsic properties of the individual neurons such as minimum firing rates are carried over into the dynamics of the coupled neurons affecting their ultimate synchronous state.

Dynamics of signal propagation and collision in axons.

Long-range communication in the nervous system is usually carried out with the propagation of action potentials along the axon of nerve cells. While typically thought of as being unidirectional, it is not uncommon for axonal propagation of action potentials to happen in both directions. This is the case because action potentials can be initiated at multiple "ectopic" positions along the axon. Two ectopic action potentials generated at distinct sites, and traveling toward each other, will collide. As neuronal information is encoded in the frequency of action potentials, action potential collision and annihilation may affect the way in which neuronal information is received, processed, and transmitted. We investigate action potential propagation and collision using an axonal multicompartment model based on the Hodgkin-Huxley equations. We characterize propagation speed, refractory period, excitability, and action potential collision for slow (type I) and fast (type II) axons. In addition, our studies include experimental measurements of action potential propagation in axons of two biological systems. Both computational and experimental results unequivocally indicate that colliding action potentials do not pass each other; they are reciprocally annihilated.

Phase Oscillatory Network and Visual Pattern Recognition.

We explore a properly interconnected set of Kuramoto type oscillators that results in a new associative-memory network configuration, which includes second- and third-order additional terms in the Fourier expansion of the network's coupling. Investigation of the response of the network to different external stimuli indicates an increase in the network capability for coding and information retrieval. Comparison of the network output with that of an equivalent experiment with subjects, for recognizing perturbed binary patterns, shows comparable results between the two approaches. We also discuss the enhanced storage capacity of the network.

Phase detection of chaos.

A technique, first introduced in the context of pseudoperiodic sound waves, is here applied to the problem of detecting the phase of phase coherent and also phase noncoherent chaotic oscillators. The approach is based on finding sinusoidal fits to segments of the signal, therefore obtaining, for each segment, an appropriate frequency from which a phase can be derived. Central to the method is a judicious choice for the size of a sliding window and for the frequency range, as well as for the window advancing step. The approach is robust against moderate noise levels and three cases are presented for demonstrating the applicability of the method.