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Abstract
Neurons receive inputs from thousands of synapses distributed across dendritic trees of complex morphology. It is known that dendritic integration of excitatory and inhibitory synapses can be highly non-linear in reality and can heavily depend on the exact location and spatial arrangement of inhibitory and excitatory synapses on the dendrite. Despite this known fact, most neuron models used in artificial neural networks today still only describe the voltage potential of a single somatic compartment and assume a simple linear summation of all individual synaptic inputs. We here suggest a new biophysical motivated derivation of a single compartment model that integrates the non-linear effects of shunting inhibition, where an inhibitory input on the route of an excitatory input to the soma cancels or “shunts” the excitatory potential. In particular, our integration of non-linear dendritic processing into the neuron model follows a simple multiplicative rule, suggested recently by experiments, and allows for strict mathematical treatment of network effects. Using our new formulation, we further devised a spiking network model where inhibitory neurons act as global shunting gates, and show that the network exhibits persistent activity in a low firing regime.
Highlights
A hallmark of neural computations is the interaction of excitatory and inhibitory drives (Wilson and Cowan, 1972; Brunel, 2000; Herz et al, 2006; Vogels and Abbott, 2009)
To get an intuitive idea of the non-linearity involved in integrating two synaptic inputs, let us first consider a conductance-based neuron model which receives a pair of excitatory and inhibitory inputs at the soma
We show that the model captures well the non-linear integration of excitatory and inhibitory inputs at the soma with an arithmetic rule, where the shunting effect is expressed as a product between the contributions of excitatory and inhibitory inputs, as was suggested by recent experimental finding (Hao et al, 2009)
Summary
A hallmark of neural computations is the interaction of excitatory and inhibitory drives (Wilson and Cowan, 1972; Brunel, 2000; Herz et al, 2006; Vogels and Abbott, 2009). While the theoretical basis for the effect of shunting inhibition has been laid out several decades ago by analyzing passive electric membrane properties of dendrites (Barrett and Crill, 1974; Blomfield, 1974; Rall, 2011; Koch, 2004), neural network models today still often rely on single compartment models (point models), such as (quadratic) integrate-and-fire model (Gerstner and Kistler, 2002; Izhikevich, 2006), and ignore this potentially important non-linear integration of synaptic inputs (McLaughlin et al, 2000; Wang, 2002; Vogels and Abbott, 2009; Rasch et al, 2011). Parts of the results were previously presented on a conference (Zhang et al, 2011)
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