Emergent stochastic oscillations and signal detection in tree networks of excitable elements

Kromer, Justus A.; Khaledi-Nasab, Ali; Schimansky‐Geier, Lutz; Neiman, Alexander

doi:10.1038/s41598-017-04193-8

Cited by 15 publications

(25 citation statements)

References 58 publications

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“…Ottoson and Shepherd (1970) proposed that the radially branched myelinated terminals of afferents at vertebrate muscle spindles undergo synchronous spiking, consistent with the high regularity of background afferent firing (Matthews and Stein, 1969). A model for radially symmetrical star networks proposed that spike initiation at multiple distal SIZs may be coherent due to strong coupling via myelinated dendrites (Kromer et al, 2016(Kromer et al, , 2017.…”

Section: Radial Myelinated Treesmentioning

confidence: 86%

Large-Scale Convergence of Receptor Cell Arrays Onto Afferent Terminal Arbors in the Lorenzinian Electroreceptors of Polyodon

et al. 2020

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Certain sensory receptors contain many transducers, converging onto few afferents. Convergence creates star-topology neural networks, of iterative parallel organization, that may yield special functional properties. We quantitated large-scale convergence in electroreceptors on the rostrum of preadult paddlefish, Polyodon spathula (Acipenseriforme vertebrates), and analyzed the afferent terminal branching underlying the convergence. From neurophysiological mapping, a recorded afferent innervated 23.3 ± 9.1 (range 6-45) ampullary organs, and innervated every ampullary organ within the receptive field's sharp boundary. Ampullary organs each contained ∼665 Lorenzinian receptor cells, from imaging and modeling. We imaged three serial types of afferent branching at electroreceptors, after immunofluorescent labeling for neurite filaments, glial sheaths, or nodal ion channels, or by DiI tracing. (i) Myelinated tree: Each of 3.08 ± 0.51 (2-4) parallel afferents from a cranial nerve (ALLn) entered a receptive field from deeper tissue, then branched into a laminar tree of large myelinated dendrites, parallel to the skin, that branched radially until ∼9 extremities with heminodes, which were candidate sites of spike encoders. (ii) Inline transition: Each myelinated extremity led distally into local unmyelinated arbors originating at inline branching structures covered by terminal (satellite) glia. The unmyelinated transition zones included globular afferent modules, 4-6 microns wide, from which erupted fine fascicles of parallel submicron neurites, a possibly novel type of neuronal branching. The neurite fascicles formed loose bundles projecting ∼105 microns distally to innervate local groups of ∼3 adjacent ampullary organs. (iii) Radial arbors: Receptor cells in an electrosensory neuroepithelium covering the basal pole of each ampullary organ were innervated by bouton endings of radial neurites, unmyelinated and submicron, forming a thin curviplanar lamina distal to the lectin+ basal lamina. The profuse radial neurites diverged from thicker (∼2 micron) basolateral trunks. Overall, an average Polyodon electroreceptor formed a star topology array of ∼9 sensor groups. Total convergence ratios were 15,495 ± 6,052 parallel receptor cells per afferent per mean receptive field,

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Section: Radial Myelinated Treesmentioning

confidence: 86%

Large-Scale Convergence of Receptor Cell Arrays Onto Afferent Terminal Arbors in the Lorenzinian Electroreceptors of Polyodon

et al. 2020

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“…We documented that sites of reduced NEFH ir or reduced DiI emission can serve as markers for node loci. Myelinated afferent branches with nodes and nodal branch points can be considered within the contexts of active neuronal dendrites or strongly coupled oscillators [30] [31].…”

Section: Discussionmentioning

confidence: 99%

Nonbinary branching of myelinated dendrites at nodal networks on afferent terminal arbors in paddlefish electroreceptors

Russell

Rogers

Neiman

2019

Matters

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The branching of vertebrate neuronal processes, axons or dendrites, is predominantly binary, where a proximal neuronal process bifurcates into two distal progeny. Here, we illustrate counterexamples where neuronal processes branched into more than 2, up to 6, progeny branches, in one step. These were branch points of myelinated dendrites in the peripheral terminals of ALLn cranial nerve afferents innervating the Lorenziniantype ampullary electroreceptors on the rostrum of paddlefish, Polyodon spathula. We imaged afferent terminals fluorescently (in widefield stacks, with deconvolution) after immunolabling of afferent terminals for neuronal cytoplasmic neurofilament-H (NEFH), myelin markers (MBP, P0), or nodal ion channels (Nav1.x, Kv1.1), or after migration of DiI in dendrite membranes. Branched afferent terminals formed a laminar radial radiation beneath a receptive field, parallel to the skin surface, with two serial stages: (1) Starting at each afferent's centric first branchpoint, each of a small group of 2-4 (most often 3) afferents branched radially into 2-4 (usually 3) generations of myelinated dendrites, whose internodes were covered by sheaths immunoreactive for antigenic markers of myelin (MBP+/P0+), ending distally at~15 heminode presumed spike initiation zones. (2) From the latter, bundles of unmyelinated (MBP-/P0-) sensory neuron (NEFH+) processes projected distally to innervate electrosensory neuroepithelia of adjacent ampullary organs. The nonbinary branch points that we imaged were in stage-1, on myelinated dendrites. Branch points always coincided with composite systems of nodes, in which each progeny dendrite started at a narrowed nodal segment expressing voltage gated sodium ion channels at high density. These narrowed nodal segments of multiple progeny branched in parallel from a parent's blunt distal end. Hence the branch point nodal complexes formed multisite excitable systems, likely strongly coupled due to proximity. 1 + 2 where N varies from 1.5 to 2 corresponding to symmetrical d/D ratios of 0.63-0.71 [2].

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“…In the following, we use a Hodgkin-Huxley type (HH) model for the ionic currents of nodes of Ranvier, which is a simplified version of the model used in [38]. Ionic currents are represented by Na + and leak currents, I ion = I Na + I L , [35,36]. The Na + current is I Na = g Na m 3 h(V − V Na ), where g Na = 1100 mS/cm 2 is the maximal value of the sodium conductance and V Na = 50 mV is the Na + reversal potential.…”

Section: A Hodgkin-huxley Type Modelmentioning

confidence: 99%

“…The nodal ionic current, I ion [V k , m k , h k ], and the gating variables, m k and h k , are given by the same equations as for the network model in Sec. II A. Equations for J eff,k (t) for regular trees were derived in [36]. In Appendix C, we extend their approach to random trees and obtain, Here J and S are the constant current and the noise intensity, respectively.…”

Section: B Strong Coupling Approximationmentioning

confidence: 99%

Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements

Khaledi-Nasab

Kromer

Schimansky‐Geier

et al. 2018

Preprint

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We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, exciting the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree network and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong coupling limit in which the entire tree network can be represented by an effective single element.

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Emergent stochastic oscillations and signal detection in tree networks of excitable elements

Cited by 15 publications

References 58 publications

Large-Scale Convergence of Receptor Cell Arrays Onto Afferent Terminal Arbors in the Lorenzinian Electroreceptors of Polyodon

Large-Scale Convergence of Receptor Cell Arrays Onto Afferent Terminal Arbors in the Lorenzinian Electroreceptors of Polyodon

Nonbinary branching of myelinated dendrites at nodal networks on afferent terminal arbors in paddlefish electroreceptors

Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements

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