Phenomenological Incorporation of Nonlinear Dendritic Integration Using Integrate-and-Fire Neuronal Frameworks

Abstract

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as , where , and are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.

Nonlinear multiplicative dendritic integration in neuron and network models

“…Thus, κ on tends to have a larger value if inhibitory inputs are at a distal site of a dendrite in comparison to inputs at a proximal site, agreeing with experimental observations (Hao et al, 2009). Moreover, in contrast to earlier two-port analysis (Koch et al, 1983; Hao et al, 2009; Zhou et al, 2013), our approximation of κ on does not depend on the transfer conductance between E and I, therefore the shunting strength is approximately constant when the excitatory synapse location is increasingly distal but the inhibitory location is fixed. This again agrees well with experimental findings (Hao et al, 2009).…”

“…In contrast to the approach of Zhou et al (2013), in our neuron model (Equation 11) the shunting strength κ on is explicitly given in biophysical terms. From Equation (14) it can be seen that the shunting strength will be particular prominent if the resting potential and the inhibitory reversal potentials are similar E L ≈ E I , in agreement with experimental and early theoretical findings (Koch, 2004; Hao et al, 2009).…”

“…In summary, we derived a new formulation of the sub-threshold dynamics of an integrate-and-fire model with integrated dendritic processing [Equation (11); note that our form of the single compartment model is different from the formulation of Zhou et al (2013)]. Our model incorporates effects of shunting inhibition of two synaptic inputs with on-path configuration.…”

“…Given the good experimental agreement of this description, a follow-up study tried to incorporate this abstract formulation of shunting inhibition into a simple single-compartment neuron model (Zhou et al, 2013), which the authors called the “DIF”-model (dendritic integrate-and-fire). In fact, incorporating non-linear effects of shunting inhibition into simple neuron models would make neural network simulations based on point models more realistic while keeping the formulation and simulation simple and efficient: there would be no need to simulate complex multi-compartment neuron models instead where effects of shunting inhibition are very well understood (Hao et al, 2009).…”

“…However, in the study (Zhou et al, 2013), the derivation was based on phenomenological arguments to describe the effects of shunting as observed in experiments. Here we suggest a different derivation of a single compartment model starting from a biophysical more realistic conductance-based three-compartment model.…”