Limits...
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 Universit├Ąt 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

Artefactual shift when using the single-step method. The black curve shows the reference time course of the membrane potential of a Hodgkin-Huxley point-neuron model subject to a constant input current of 200 pA after simulating 1 s of biological time. The other curves indicate the time course of the membrane potential of the same neuron with the same input for the case that the neuron is coupled by a gap junction to a second model neuron with exactly the same properties and the simulation is carried out with the single-step approach using a Runge-Kutta-Fehlberg solver with an adaptive step-size control to cover the interval of one computation time step h. The orange curve displays the result for a step size of h = 0.1 ms and the blue curve for 0.02 ms.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4563270&req=5

Figure 1: Artefactual shift when using the single-step method. The black curve shows the reference time course of the membrane potential of a Hodgkin-Huxley point-neuron model subject to a constant input current of 200 pA after simulating 1 s of biological time. The other curves indicate the time course of the membrane potential of the same neuron with the same input for the case that the neuron is coupled by a gap junction to a second model neuron with exactly the same properties and the simulation is carried out with the single-step approach using a Runge-Kutta-Fehlberg solver with an adaptive step-size control to cover the interval of one computation time step h. The orange curve displays the result for a step size of h = 0.1 ms and the blue curve for 0.02 ms.

Mentions: At present time-driven simulators supporting gap junctions implement the instantaneous interaction with a simplification effectively decoupling the neurons for the duration of the computation time step h: the membrane potentials of gap-junction coupled neurons are communicated at the beginning of each time step and for the purpose of integration are assumed to be constant for the duration of the time step (for NEURON simulation software see Hines et al., 2008). There is no communication for the duration of the computation time step and no repeated communication of improved membrane potential values for a given point on the computation-time grid. In the following, we will refer to this approach as the single-step method. Note that in this framework a solver may still use adaptive step-size control to cover the interval h. The single-step method has two major disadvantages: Firstly communication is needed in every time step instead of in intervals of the minimal delay, which can slow down the simulation due to the latency of the employed MPI communication. Secondly the step size of the approach needs to be small. Otherwise the error results in a systematic shift of the membrane potential time course. This can be easily demonstrated by a two-neuron network: Two identical model neurons that are coupled by a gap junction should behave exactly the same as an uncoupled pair since Igap = 0 holds at all times. However, Figure 1 shows that the single-step approach produces a significant shift within only 1 s of biological time, even when simulated with a step size that is already small compared to the time constants of the model neuron. To yield accurate results the time step would have to be exceedingly small, requiring even more communication and thereby further slowing down the simulation.


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)

Artefactual shift when using the single-step method. The black curve shows the reference time course of the membrane potential of a Hodgkin-Huxley point-neuron model subject to a constant input current of 200 pA after simulating 1 s of biological time. The other curves indicate the time course of the membrane potential of the same neuron with the same input for the case that the neuron is coupled by a gap junction to a second model neuron with exactly the same properties and the simulation is carried out with the single-step approach using a Runge-Kutta-Fehlberg solver with an adaptive step-size control to cover the interval of one computation time step h. The orange curve displays the result for a step size of h = 0.1 ms and the blue curve for 0.02 ms.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4563270&req=5

Figure 1: Artefactual shift when using the single-step method. The black curve shows the reference time course of the membrane potential of a Hodgkin-Huxley point-neuron model subject to a constant input current of 200 pA after simulating 1 s of biological time. The other curves indicate the time course of the membrane potential of the same neuron with the same input for the case that the neuron is coupled by a gap junction to a second model neuron with exactly the same properties and the simulation is carried out with the single-step approach using a Runge-Kutta-Fehlberg solver with an adaptive step-size control to cover the interval of one computation time step h. The orange curve displays the result for a step size of h = 0.1 ms and the blue curve for 0.02 ms.
Mentions: At present time-driven simulators supporting gap junctions implement the instantaneous interaction with a simplification effectively decoupling the neurons for the duration of the computation time step h: the membrane potentials of gap-junction coupled neurons are communicated at the beginning of each time step and for the purpose of integration are assumed to be constant for the duration of the time step (for NEURON simulation software see Hines et al., 2008). There is no communication for the duration of the computation time step and no repeated communication of improved membrane potential values for a given point on the computation-time grid. In the following, we will refer to this approach as the single-step method. Note that in this framework a solver may still use adaptive step-size control to cover the interval h. The single-step method has two major disadvantages: Firstly communication is needed in every time step instead of in intervals of the minimal delay, which can slow down the simulation due to the latency of the employed MPI communication. Secondly the step size of the approach needs to be small. Otherwise the error results in a systematic shift of the membrane potential time course. This can be easily demonstrated by a two-neuron network: Two identical model neurons that are coupled by a gap junction should behave exactly the same as an uncoupled pair since Igap = 0 holds at all times. However, Figure 1 shows that the single-step approach produces a significant shift within only 1 s of biological time, even when simulated with a step size that is already small compared to the time constants of the model neuron. To yield accurate results the time step would have to be exceedingly small, requiring even more communication and thereby further slowing down the simulation.

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 Universit├Ąt 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