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A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universität Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus

Network behavior depending on the gap weight g. (A) The average spike rate ν and (B) the synchrony χ (Equation 10) of the neurons in the network, depending on the gap weight. The results for the iterative method with cubic interpolation are shown as solid curves (step size 0.05 ms) and for the single-step method with dashed (step size 0.05 ms) and dotted (step size 0.001 ms) curves. Two different synaptic amplitudes JI = −50 pA and JI = −25 pA were used, as indicated by the figure legend. The prelim_tol was chosen as 10−5 and the maximum number of iterations was not used as a stopping criterion. The simulation duration was 100 s (JI = −25 pA), respectively 180 s (JI = −50 pA) of biological time. The inset of (A) shows the difference between the results of the iterative method (step size 0.05 ms) and the results of the single-step method for different step sizes h measured by the RMSE. The dotted vertical lines correspond to the panels of Figure 9.
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Figure 10: Network behavior depending on the gap weight g. (A) The average spike rate ν and (B) the synchrony χ (Equation 10) of the neurons in the network, depending on the gap weight. The results for the iterative method with cubic interpolation are shown as solid curves (step size 0.05 ms) and for the single-step method with dashed (step size 0.05 ms) and dotted (step size 0.001 ms) curves. Two different synaptic amplitudes JI = −50 pA and JI = −25 pA were used, as indicated by the figure legend. The prelim_tol was chosen as 10−5 and the maximum number of iterations was not used as a stopping criterion. The simulation duration was 100 s (JI = −25 pA), respectively 180 s (JI = −50 pA) of biological time. The inset of (A) shows the difference between the results of the iterative method (step size 0.05 ms) and the results of the single-step method for different step sizes h measured by the RMSE. The dotted vertical lines correspond to the panels of Figure 9.

Mentions: Figure 9 shows the spiking behavior of the employed network for different choices of the gap weight g. For a lower gap weight g = 0.3 nS the network remains in an asynchronous state. In panel B (g = 0.54 nS) the network switches randomly between the asynchronous to the synchronous state, while for the highest gap weight g = 0.7 nS a stable synchronous state is reached. The exact transition between these two states as a function of the gap weight and depending on the employed integration method is visualized in Figure 10. To overcome statistical fluctuations caused by the random transitions between the asynchronous and the synchronous state, which can be observed in Figure 9B, the system needs to be simulated for prolonged time to obtain smooth transition curves. The transition is investigated for two different choices of the synaptic weight of the inhibitory synapses to demonstrate the influence of the chemical synapses on the location of the transition. The shift of the transition point between both choices of JI guarantees the influence of the chemical synapses on the global network dynamics, which is needed in order to show the correctness of the new iterative method for networks with chemical synapses and gap junctions.


A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations.

Hahne J, Helias M, Kunkel S, Igarashi J, Bolten M, Frommer A, Diesmann M - Front Neuroinform (2015)

Network behavior depending on the gap weight g. (A) The average spike rate ν and (B) the synchrony χ (Equation 10) of the neurons in the network, depending on the gap weight. The results for the iterative method with cubic interpolation are shown as solid curves (step size 0.05 ms) and for the single-step method with dashed (step size 0.05 ms) and dotted (step size 0.001 ms) curves. Two different synaptic amplitudes JI = −50 pA and JI = −25 pA were used, as indicated by the figure legend. The prelim_tol was chosen as 10−5 and the maximum number of iterations was not used as a stopping criterion. The simulation duration was 100 s (JI = −25 pA), respectively 180 s (JI = −50 pA) of biological time. The inset of (A) shows the difference between the results of the iterative method (step size 0.05 ms) and the results of the single-step method for different step sizes h measured by the RMSE. The dotted vertical lines correspond to the panels of Figure 9.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4563270&req=5

Figure 10: Network behavior depending on the gap weight g. (A) The average spike rate ν and (B) the synchrony χ (Equation 10) of the neurons in the network, depending on the gap weight. The results for the iterative method with cubic interpolation are shown as solid curves (step size 0.05 ms) and for the single-step method with dashed (step size 0.05 ms) and dotted (step size 0.001 ms) curves. Two different synaptic amplitudes JI = −50 pA and JI = −25 pA were used, as indicated by the figure legend. The prelim_tol was chosen as 10−5 and the maximum number of iterations was not used as a stopping criterion. The simulation duration was 100 s (JI = −25 pA), respectively 180 s (JI = −50 pA) of biological time. The inset of (A) shows the difference between the results of the iterative method (step size 0.05 ms) and the results of the single-step method for different step sizes h measured by the RMSE. The dotted vertical lines correspond to the panels of Figure 9.
Mentions: Figure 9 shows the spiking behavior of the employed network for different choices of the gap weight g. For a lower gap weight g = 0.3 nS the network remains in an asynchronous state. In panel B (g = 0.54 nS) the network switches randomly between the asynchronous to the synchronous state, while for the highest gap weight g = 0.7 nS a stable synchronous state is reached. The exact transition between these two states as a function of the gap weight and depending on the employed integration method is visualized in Figure 10. To overcome statistical fluctuations caused by the random transitions between the asynchronous and the synchronous state, which can be observed in Figure 9B, the system needs to be simulated for prolonged time to obtain smooth transition curves. The transition is investigated for two different choices of the synaptic weight of the inhibitory synapses to demonstrate the influence of the chemical synapses on the location of the transition. The shift of the transition point between both choices of JI guarantees the influence of the chemical synapses on the global network dynamics, which is needed in order to show the correctness of the new iterative method for networks with chemical synapses and gap junctions.

Bottom Line: This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions.To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers.Finally, we discuss limitations of the novel technology.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Science, Bergische Universität Wuppertal Wuppertal, Germany.

ABSTRACT
Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

No MeSH data available.


Related in: MedlinePlus