A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity

Abstract

A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.’s (J Comput Neurosci 10:281–302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.

Appendices

Appendix 1: Group classification algorithm

Pseudocode

For each simulated model do

• (A) assign label to each of the two neurons corresponding to their activity type;

• (B) assign label group based on both neurons’ activity type;

end for;

Step 1—Activity type level

• for both neurons of a model do

  • if a neuron doesn’t have a spiking file created, assign channelType = ‘silent’;

  • else parse its spiking file

    • if the neuron doesn’t show any burst, assign channelType = ‘spiking’;

    • else assign channelType = ‘bursting activity’;

  end for;

• assign to the model its group label

  • if its neuron labels are different, assign systType = ‘asymmetric activity’; done.

  • else

    • assign systType = {‘spiking’, ‘silent’} if the labels of both neurons are channelType = {‘spiking’, ‘silent’}, respectively; done.

    • or assign systType = {‘bursting activity’} if its neuron labels are channelType = ‘bursting activity’; go to Step 2;

Step 2—Spike type level

• for each neuron of a model labeled ‘bursting activity’ do

  • for each of its bursts, check

    • if a burst is plateau, then re-assign channelType = ‘plateau’;

    • else if a burst has irregular spikes, then re-assign channelType = ‘irregular spikes’;

    end for (burst checking);

  • if neuron’s label is neither ‘plateau’ nor ‘irregular spikes’, then re-assign channelType = ‘normal spikes’;

  end for;

• assign to the model its group label

  • if its neurons’ labels are different, re-assign systType = ‘asymmetric bursting’; done.

  • else

    • re-assign systType = {‘plateau’, ‘irregular spikes’} if the labels of both neurons are channelType = {‘plateau’, ‘irregular spikes’}, respectively; done.

    • or re-assign systType = {‘normal spikes’} if its neuron labels are channelType = ‘normal spikes’; go to Step 3;

Step 3—Number of bursts level

• for each neuron of a model labeled ‘normal spikes’ check its number of bursts

  • if number_of_bursts = 1, re-assign channelType = ‘one burst’;

  • else re-assign channelType = ‘repeated bursts’;

  end for;

• assign to the model its group label

  • if its neurons’ labels are ‘repeated bursts’, then re-assign systType = {‘repeated bursts’}; go to Step 4;

  • else re-assign systType = {‘one burst’}; done.

Step 4—Period regularity level

• for each neuron of a model labeled ‘repeated bursts’ check the coefficient of variation (cv) of its period

  • if cv > = 0.05, re-assign channelType = ‘irregular period’;

  • else re-assign channelType = ‘regular period’;

  end for;

• assign to the model its group label

  • if both its neurons’ labels are ‘regular period’, then re-assign systType = {‘regular period’}; go to Step 5;

  • else re-assign systType = {‘irregular period’}; done.

Step 5—Phase level

• for each neuron of a model labeled ‘regular period’ check its phase range

  • if phase in [0.45, 0.55], re-assign channelType = ‘functional’;

  • else re-assign channelType = ‘unbalanced’;

  end for;

• assign to the model its group label

  • if both its neurons’ labels are ‘functional’, then re-assign systType = {‘functional’}; done.

  • else re-assign systType = {‘unbalanced’}; done.

Appendix 2: SQL query

SELECT

• eo1. ‘simNo’ as simNo_1, eo1. ‘simParPer_gBarSynS’ as synS_1, eo1. ‘simParPer_gBarSynG’ as synG_1, eo2. ‘simNo’ as simNo_2, eo2. ‘simParPer_gBarSynS’ as synS_2, eo2. ‘simParPer_gBarSynG’ as synG_2

• FROM EO_db AS eo1 INNER JOIN EO_db AS eo2 USING (‘simPar_EleakVal’, ‘simParPer_gBarP’, ‘simParPer_gBarK2’, ‘simParPer_gBarLeak’, ‘simParPer_gBarCaS’, ‘simParPer_gBarh’)

• WHERE ((eo1. ‘simParPer_gBarSynG’ < > 0 or eo1. ‘simParPer_gBarSynS’ < > 0) AND (eo2. ‘simParPer_gBarSynG’ = 0 or eo2. ‘simParPer_gBarSynS’ = 0))

Appendix 3: Activity characteristics

Our classification method split the HCO models into seven terminal groups at three different tree levels (Fig. 2): at level 1 spiking, silent, and asymmetric activity; at level 2 plateau, irregular spikes, and asymmetric bursting; at level 3 one burst. The repeated bursts HCOs group resulting from level 3 parsing was further split employing electrophysiological criteria into three terminal groups: at level 4 irregular period; at level 5 unbalanced and functional to obtain the functional HCOs group, which correspond to activity observed in the living system. In summary, during this classification process, there were eight activity characteristics used as follows:

• 1. Any spiking activity present or not (threshold of −20 mV) to obtain the silent and non-silent HCOs

• 2. Number of spikes—presence of minimum three spikes to define a burst or not

• 3. Presence of a minimum inter-burst interval of 1 s to differentiate between spiking and bursting activities

• 4. The value of the voltage trace at the end point of the burst (greater than −35 mV) to obtain the plateaus

• 5. Coefficient of variation of the amplitudes of the spikes in the burst (≤0.07) to obtain the irregular spikes and normal spikes HCO models

• 6. The number of bursts per neuron in 100 s of simulation time to obtain the one burst models and the repeated bursts HCOs; the next two criteria were used to split the repeated bursts HCOs

• 7. Coefficient of variation of the period (<0.05) to obtain the irregular period and regular period models

• 8. Mean phase (in the range of 0.45–0.55) to obtain the unbalanced and functional models

Appendix 4: Synaptic components for each HCO group

Table 3 Terminal groups for all HCO models broken down by the synaptic components present

Appendix 5: The number of model neurons that fall into each intrinsic activity group

Table 4 The number of the HCO models with at least one synaptic component and, in parentheses, the number of their unique corresponding isolated neuron models for each terminal group (with the same non-synaptic parameters). Levels corresponding to Fig. 2 are indicated for the HCO models and implied by gray vertical columns for the isolated neuron models. The divergence ratio in the last row is the number of corresponding functional HCO models divided by the number of unique isolated neuron models in each terminal group