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Mechanisms Leading to Rhythm Cessation in the Respiratory PreBötzinger Complex Due to Piecewise Cumulative Neuronal Deletions(1,2,3).

Song H, Hayes JA, Vann NC, Drew LaMar M, Del Negro CA - eNeuro (2015)

Bottom Line: When the recruitment rate drops below 1 neuron/ms the network stops spontaneous rhythmic activity.Neurons that play pre-eminent roles in rhythmogenesis include those that commence spiking during the quiescent phase between respiratory bursts and those with a high number of incoming synapses, which both play key roles in recruitment, i.e., recurrent excitation leading to network bursts.This study provides a theoretical framework for the operating mechanism of mammalian central pattern generator networks and their susceptibility to loss-of-function in the case of disease or neurodegeneration.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Applied Science, The College of William & Mary , Williamsburg, Virginia 23187-8795.

ABSTRACT
The mammalian breathing rhythm putatively originates from Dbx1-derived interneurons in the preBötzinger complex (preBötC) of the ventral medulla. Cumulative deletion of ∼15% of Dbx1 preBötC neurons in an in vitro breathing model stops rhythmic bursts of respiratory-related motor output. Here we assemble in silico models of preBötC networks using random graphs for structure, and ordinary differential equations for dynamics, to examine the mechanisms responsible for the loss of spontaneous respiratory rhythm and motor output measured experimentally in vitro. Model networks subjected to cellular ablations similarly discontinue functionality. However, our analyses indicate that model preBötC networks remain topologically intact even after rhythm cessation, suggesting that dynamics coupled with structural properties of the underlying network are responsible for rhythm cessation. Simulations show that cumulative cellular ablations diminish the number of neurons that can be recruited to spike per unit time. When the recruitment rate drops below 1 neuron/ms the network stops spontaneous rhythmic activity. Neurons that play pre-eminent roles in rhythmogenesis include those that commence spiking during the quiescent phase between respiratory bursts and those with a high number of incoming synapses, which both play key roles in recruitment, i.e., recurrent excitation leading to network bursts. Selectively ablating neurons with many incoming synapses impairs recurrent excitation and stops spontaneous rhythmic activity and motor output with lower ablation tallies compared with random deletions. This study provides a theoretical framework for the operating mechanism of mammalian central pattern generator networks and their susceptibility to loss-of-function in the case of disease or neurodegeneration.

No MeSH data available.


Cumulative cellular ablations in the model preBötC network. Running time spike histogram (top, red) and plots of rhythmic burst frequency and six discrete network metrics (global and local). The simulated experiment where a total of 100 neurons were deleted (one per 25 simulated seconds) in sequence was repeated 15 times. The running time spike histogram is shown for one representative simulation. The top trace shows inspiratory-like burst frequency (Hz) for all 15 simulations. The abscissa (percentage of total cellular ablations) is the same for frequency and all discrete network metrics. LCC, CC, and BC are plotted for each neuron in the deletion sequence. The number of SCCs, K-core and in-degree are plotted for neurons in the remaining network during the ablation sequence. Blue symbols show the average metric (for 15 simulations) during the deletion sequence; these quantities were no longer computed after the 100th ablation. Red symbols show the scattered data points for all individual 15 simulations.
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Figure 2: Cumulative cellular ablations in the model preBötC network. Running time spike histogram (top, red) and plots of rhythmic burst frequency and six discrete network metrics (global and local). The simulated experiment where a total of 100 neurons were deleted (one per 25 simulated seconds) in sequence was repeated 15 times. The running time spike histogram is shown for one representative simulation. The top trace shows inspiratory-like burst frequency (Hz) for all 15 simulations. The abscissa (percentage of total cellular ablations) is the same for frequency and all discrete network metrics. LCC, CC, and BC are plotted for each neuron in the deletion sequence. The number of SCCs, K-core and in-degree are plotted for neurons in the remaining network during the ablation sequence. Blue symbols show the average metric (for 15 simulations) during the deletion sequence; these quantities were no longer computed after the 100th ablation. Red symbols show the scattered data points for all individual 15 simulations.

Mentions: Previously, we reported canonical local and global measures of topology for the underlying graph G(n,p) at the start of a simulation and after piecewise cellular deletions stopped the rhythm (Wang et al., 2014, their supplemental file 2). Here, we provide more detail by tracking the state of network topology as a function of cumulative percentage of total ablations (Fig. 2). During progressive ablation sequences, there were no major changes in measures of local connectivity, i.e., local metrics, such as local cluster coefficient (LCC), closeness centrality (CC), and betweenness centrality (BC). A network is strongly connected if a directed path exists between any two constituent nodes, which can be quantified by the number of strongly connected components (SCC). Cumulative deletion sequences at no point caused SCC to depart from unity (a fully connected graph). Other global connectivity metrics, such as the K-core and the average in-degree, showed linear declines. Whereas network burst frequency declined to zero in each simulation, K-core remained >12 and the average in-degree remained >28. These data indicate that the model networks remain fully connected for the entire duration of cumulative cellular ablation simulations that invariably stop rhythmic function.


Mechanisms Leading to Rhythm Cessation in the Respiratory PreBötzinger Complex Due to Piecewise Cumulative Neuronal Deletions(1,2,3).

Song H, Hayes JA, Vann NC, Drew LaMar M, Del Negro CA - eNeuro (2015)

Cumulative cellular ablations in the model preBötC network. Running time spike histogram (top, red) and plots of rhythmic burst frequency and six discrete network metrics (global and local). The simulated experiment where a total of 100 neurons were deleted (one per 25 simulated seconds) in sequence was repeated 15 times. The running time spike histogram is shown for one representative simulation. The top trace shows inspiratory-like burst frequency (Hz) for all 15 simulations. The abscissa (percentage of total cellular ablations) is the same for frequency and all discrete network metrics. LCC, CC, and BC are plotted for each neuron in the deletion sequence. The number of SCCs, K-core and in-degree are plotted for neurons in the remaining network during the ablation sequence. Blue symbols show the average metric (for 15 simulations) during the deletion sequence; these quantities were no longer computed after the 100th ablation. Red symbols show the scattered data points for all individual 15 simulations.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4596029&req=5

Figure 2: Cumulative cellular ablations in the model preBötC network. Running time spike histogram (top, red) and plots of rhythmic burst frequency and six discrete network metrics (global and local). The simulated experiment where a total of 100 neurons were deleted (one per 25 simulated seconds) in sequence was repeated 15 times. The running time spike histogram is shown for one representative simulation. The top trace shows inspiratory-like burst frequency (Hz) for all 15 simulations. The abscissa (percentage of total cellular ablations) is the same for frequency and all discrete network metrics. LCC, CC, and BC are plotted for each neuron in the deletion sequence. The number of SCCs, K-core and in-degree are plotted for neurons in the remaining network during the ablation sequence. Blue symbols show the average metric (for 15 simulations) during the deletion sequence; these quantities were no longer computed after the 100th ablation. Red symbols show the scattered data points for all individual 15 simulations.
Mentions: Previously, we reported canonical local and global measures of topology for the underlying graph G(n,p) at the start of a simulation and after piecewise cellular deletions stopped the rhythm (Wang et al., 2014, their supplemental file 2). Here, we provide more detail by tracking the state of network topology as a function of cumulative percentage of total ablations (Fig. 2). During progressive ablation sequences, there were no major changes in measures of local connectivity, i.e., local metrics, such as local cluster coefficient (LCC), closeness centrality (CC), and betweenness centrality (BC). A network is strongly connected if a directed path exists between any two constituent nodes, which can be quantified by the number of strongly connected components (SCC). Cumulative deletion sequences at no point caused SCC to depart from unity (a fully connected graph). Other global connectivity metrics, such as the K-core and the average in-degree, showed linear declines. Whereas network burst frequency declined to zero in each simulation, K-core remained >12 and the average in-degree remained >28. These data indicate that the model networks remain fully connected for the entire duration of cumulative cellular ablation simulations that invariably stop rhythmic function.

Bottom Line: When the recruitment rate drops below 1 neuron/ms the network stops spontaneous rhythmic activity.Neurons that play pre-eminent roles in rhythmogenesis include those that commence spiking during the quiescent phase between respiratory bursts and those with a high number of incoming synapses, which both play key roles in recruitment, i.e., recurrent excitation leading to network bursts.This study provides a theoretical framework for the operating mechanism of mammalian central pattern generator networks and their susceptibility to loss-of-function in the case of disease or neurodegeneration.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Applied Science, The College of William & Mary , Williamsburg, Virginia 23187-8795.

ABSTRACT
The mammalian breathing rhythm putatively originates from Dbx1-derived interneurons in the preBötzinger complex (preBötC) of the ventral medulla. Cumulative deletion of ∼15% of Dbx1 preBötC neurons in an in vitro breathing model stops rhythmic bursts of respiratory-related motor output. Here we assemble in silico models of preBötC networks using random graphs for structure, and ordinary differential equations for dynamics, to examine the mechanisms responsible for the loss of spontaneous respiratory rhythm and motor output measured experimentally in vitro. Model networks subjected to cellular ablations similarly discontinue functionality. However, our analyses indicate that model preBötC networks remain topologically intact even after rhythm cessation, suggesting that dynamics coupled with structural properties of the underlying network are responsible for rhythm cessation. Simulations show that cumulative cellular ablations diminish the number of neurons that can be recruited to spike per unit time. When the recruitment rate drops below 1 neuron/ms the network stops spontaneous rhythmic activity. Neurons that play pre-eminent roles in rhythmogenesis include those that commence spiking during the quiescent phase between respiratory bursts and those with a high number of incoming synapses, which both play key roles in recruitment, i.e., recurrent excitation leading to network bursts. Selectively ablating neurons with many incoming synapses impairs recurrent excitation and stops spontaneous rhythmic activity and motor output with lower ablation tallies compared with random deletions. This study provides a theoretical framework for the operating mechanism of mammalian central pattern generator networks and their susceptibility to loss-of-function in the case of disease or neurodegeneration.

No MeSH data available.