Abstract
In simulating realistic neuronal circuitry composed of diverse types of neurons, we need an elemental spiking neuron model that is capable of not only quantitatively reproducing spike times of biological neurons given in vivo-like fluctuating inputs, but also qualitatively representing a variety of firing responses to transient current inputs. Simplistic models based on leaky integrate-and-fire mechanisms have demonstrated the ability to adapt to biological neurons. In particular, the multi-timescale adaptive threshold (MAT) model reproduces and predicts precise spike times of regular-spiking, intrinsic-bursting, and fast-spiking neurons, under any fluctuating current; however, this model is incapable of reproducing such specific firing responses as inhibitory rebound spiking and resonate spiking. In this paper, we augment the MAT model by adding a voltage dependency term to the adaptive threshold so that the model can exhibit the full variety of firing responses to various transient current pulses while maintaining the high adaptability inherent in the original MAT model. Furthermore, with this addition, our model is actually able to better predict spike times. Despite the augmentation, the model has only four free parameters and is implementable in an efficient algorithm for large-scale simulation due to its linearity, serving as an element neuron model in the simulation of realistic neuronal circuitry.
Highlights
A mathematical model of a single-neuron that is capable of accurately reproducing diverse spiking behaviors of biological neurons is required for simulating real neuronal circuitry (Diesmann et al, 1999; Izhikevich, 2004; McIntyre et al, 2004; Markram, 2006; Brette et al, 2007; Gewaltig and Diesmann, 2007; Izhikevich and Edelman, 2008; Plesser and Diesmann, 2009; Rossant et al, 2011)
AUGMENTATION OF THE multi-timescale adaptive threshold (MAT) MODEL WITH VOLTAGE DEPENDENCY We have shown above that the MAT model is capable of exhibiting basic dynamic characteristics, such as type I/II excitability and burst firing, but we show that the original model is not sufficiently flexible to exhibit a richer variety of responses of biological neurons to transient input currents, summarized as Izhikevich’s table (Izhikevich, 2004)
REPRODUCING AND PREDICTING BIOLOGICAL NEURONAL RESPONSES TO FLUCTUATING CURRENTS In the preceding section, we showed that our augmented MAT model is capable of reproducing rebound spiking and a variety of responses induced by threshold variability
Summary
A mathematical model of a single-neuron that is capable of accurately reproducing diverse spiking behaviors of biological neurons is required for simulating real neuronal circuitry (Diesmann et al, 1999; Izhikevich, 2004; McIntyre et al, 2004; Markram, 2006; Brette et al, 2007; Gewaltig and Diesmann, 2007; Izhikevich and Edelman, 2008; Plesser and Diesmann, 2009; Rossant et al, 2011). AUGMENTATION OF THE MAT MODEL WITH VOLTAGE DEPENDENCY We have shown above that the MAT model is capable of exhibiting basic dynamic characteristics, such as type I/II excitability and burst firing, but we show that the original model is not sufficiently flexible to exhibit a richer variety of responses of biological neurons to transient input currents, summarized as Izhikevich’s table (Izhikevich, 2004).
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