25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Vulnerability-Based Critical Neurons, Synapses, and Pathways in the <i>Caenorhabditis elegans</i> Connectome

<div><p>Determining the fundamental architectural design of complex nervous systems will lead to significant medical and technological advances. Yet it remains unclear how nervous systems evolved highly efficient networks with near optimal sharing of pathways that yet produce multiple distinct behaviors to reach the organism’s goals. To determine this, the nematode roundworm <i>Caenorhabditis elegans</i> is an attractive model system. Progress has been made in delineating the behavioral circuits of the <i>C</i>. <i>elegans</i>, however, many details are unclear, including the specific functions of every neuron and synapse, as well as the extent the behavioral circuits are separate and parallel versus integrative and serial. Network analysis provides a normative approach to help specify the network design. We investigated the vulnerability of the <i>Caenorhabditis elegans</i> connectome by performing computational experiments that (a) “attacked” 279 individual neurons and 2,990 weighted synaptic connections (composed of 6,393 chemical synapses and 890 electrical junctions) and (b) quantified the effects of each removal on global network properties that influence information processing. The analysis identified 12 critical neurons and 29 critical synapses for establishing fundamental network properties. These critical constituents were found to be control elements—i.e., those with the most influence over multiple underlying pathways. Additionally, the critical synapses formed into circuit-level pathways. These emergent pathways provide evidence for (a) the importance of backward locomotion, avoidance behavior, and social feeding behavior to the organism; (b) the potential roles of specific neurons whose functions have been unclear; and (c) both parallel and serial design elements in the connectome—i.e., specific evidence for a mixed architectural design.</p></div

Three main critical synapse pathways as determined by the Vulnerability analysis for average betweenness (<i>V</i>_<i>B</i>).

<p>Three main pathways for <i>V</i>_<i>B</i>: the AVA-based, the PVP-based, and the RMD (M) → OLL (S) pathways (S: Sensory neuron, I: Interneuron, M: Motor neuron). These three main pathways emerged from the critical synapse analysis and well capture the converged findings from both the critical neurons and synapse vulnerability analyses. (A) The first AVA-based pathway begins with RIB (I) → AVE (I) → AVA (I) and has two routes after this: (a) AVA (I) ←→ DA01 (M) → VD01 (M) (ending at VD01 since VD01 → DVC (I) is inhibitory); and (b) AVA (I) → PVC (I). For route (b) (RIB (I) to PVC (I)), we found that average network betweenness centrality (i.e., <i>X</i>_<i>B</i>(<i>i</i>,<i>j</i>)) actually increased with the AVAL/R (I) → PVCL (I) synapse removals (<i>V</i>_<i>B</i>(<i>i</i>,<i>j</i>) had negative values without taking the absolute values). This suggests that the loss of the AVA → PVC connection leaves greater differences among the remaining alternative routes to PVC, perhaps leaving the well-established forward locomotion circuit as the main throughway (i.e., AVB (I) → PVC (I)). (B) The second PVP-based pathway, begins with AQR (S) ←→ PVP (I) and has two routes after this: (a) AQR (S) ←→ PVP (I) ←→ DVC (I) → VD01 (M); and (b) AQR (S) ←→ PVP (I) → AVH (I). We also note that the inhibitory projection of VD01 (M) → DVC (I) suggests a separation of the AVA- and PVP-based pathways and a competitive relationship between them. (C) The RMD (M) → OLL (S) link was also identified as a critical pathway segment.</p

Vulnerability results for each network property and a visualization of critical neurons.

<p>(A-C) Sorted vulnerability values (red) for each network property (Clustering: <i>C</i>, Efficiency: <i>E</i>, and Betweenness: <i>B</i>) induced by 279 single neuronal attacks. Mean vulnerability value for 279 neurons are indicated by the solid black lines; black dashed lines indicate the threshold value (mean plus 3SDs). (D) Depiction of the 12 critical neurons with their connections to each other along the anterior-posterior body axis in the <i>C</i>. <i>elegans</i> body context. The network property for each neuron is shown (<i>C</i>, <i>E</i>, and <i>B</i>) with the critical grade in parenthesis; thickness of links indicates the weight grade of a link.</p

Vulnerability results for each network property and a visualization of critical synapses.

<p>(A-C) Sorted vulnerability values (red) for each network property (Clustering: <i>C</i>, Efficiency: <i>E</i>, and Betweenness: <i>B</i>) induced by all 2990 single synaptic attacks. Mean vulnerability values for 2990 synapses are indicated by the solid black lines; black dashed lines indicate the threshold value (mean plus 6SDs). (D) A depiction of the procedure used to determine the criterion for selecting critical synapses. The histogram of the distances of the highest <i>V</i>_<i>E</i>(<i>i</i>,<i>j</i>) values from the mean is shown. The intersection of the linear fitting of the blue bars (>6SD) and the linear fitting of the red bars (<6SD) reveals a change point at 6SD (y-intercepts were changed for clearer view). Because 6SD was the highest change point value among the three network properties, and thus the most conservative value, it was used as the criterion to identify critical synapses. (E) Depiction of the 12 critical neurons and 29 synapses along the anterior-posterior body axis in the <i>C</i>. <i>elegans</i> body context. The network property for each neuron is shown with the critical grade of a neuron in parenthesis; thickness of links indicates the critical grade of a link. For synapses, colors of links indicate network properties whose vulnerability value were over the threshold (6SDs) (black: <i>C</i>, red: <i>E</i>, and blue: <i>B</i>); if there were more than two critical measures for a synapse, each critical measure for the synapse was indicated with a separate colored link. Dashed shape indicates that the neuron is not critical but is connected with a critical neuron or critical synapse. For synapses, dashed lines indicate inhibitory synaptic connections (all others are excitatory).</p

Two critical pathways identified by the Vulnerability analysis for global efficiency (<i>V</i>_<i>E</i>), and intact network properties of the critical synapses compared with the rest of the nervous system.

<p>(A) The first critical pathway is also AVA-based, and starts with the AVE (I) → AVA (I) segment (S: Sensory neuron, I: Interneuron, and M: Motor neuron). Then there are four routes. The first three routes run from AVA to three different motor neurons: DA01 (same as <i>V</i>_<i>B</i>), VA08, and VA11. As with AVE and AVA, both DAn and VAn (dorsal and ventral) neurons participate in backward locomotor control. The fourth route is AVE (I) → AVA (I) → PVC (I) → DVA (I), with the latter link actually being the strongest with respect to SD size (14SDs). As was found for <i>V</i>_<i>B</i>, the <i>V</i>_<i>E</i> analysis shows the significance of the AVE (I) → AVA (I) → PVC (I) connection, and provides additional evidence for a relationship to DVA. DVA has been implicated in sensorimotor integration during locomotion, normally for avoidance behavior, and again suggests coordination of forward and backward locomotion (given its relationship to AVA). (B) The second critical pathway is PVP (I) ←→ DVC (I) ←→ VD01 (M), which was also identified by <i>V</i>_<i>B</i> as a component of the PVP-based pathway, and thus provides further evidence for a PVP, DVC, and VD01 relationship, and the importance of locomotor control. (C) The distributions (first, second, i.e., median, and third quartiles, and minimum to maximum) and statistical comparisons of critical and noncritical synapses for each network measure (Strength: <i>Str</i> and Edge Betweenness Centrality: <i>EBC</i>). The critical group has significantly higher <i>Str</i> and <i>EBC</i> values than the noncritical group.</p

The list of 12 critical neurons.

<p>The list of 12 critical neurons.</p