Nonlinear multiplicative dendritic integration in neuron and network models

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.

The influence of sensory afferent input on local motor cortical excitatory circuitry in humans

“…Previous studies have suggested that the pharmacological profile of MEP inhibition mediated by SAI is most compatible with that of basket cells which, like SAI, are sensitive to drugs acting on GABA A -α1 subtype and acetylcholine receptors. These synapse at the perisomatic region of pyramidal cells and thus have a privileged position in blocking the propagation of dendritic spikes and shunting cell firing (Di Lazzaro et al 2006Spruston, 2008;Teo et al 2009;Zhang et al 2013). Indeed there is evidence from human Alkondon et al 2000) and rodent cortex (Kimura, 2000;Alkondon & Albuquerque, 2001) of cholinergically modulated GABAergic input at the soma including circuitry models that would be compatible with the interactions reported here between SAI and SICF and previously between SAI and SICI (Alle et al 2009).…”

Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling

“…5(b)]. Equations (31) are equivalent to the order-parameter equations of the conventional Hopfield model with threshold ϑ. For Θ > 0, we may therefore conclude that the dendritic branches reduce the neuronal threshold to ϑ ≤ Θ and thereby improve the critical storage capacity α c of the network.…”

“…References [28][29][30] proposed that NMDA-receptordependent dendritic nonlinearities play a crucial role in working memory, i.e., in the formation of persistent activity in unstructured networks. Nonlinear, multiplicative dendritic processing arising from spatial summation of input across the dendritic arbor was similarly shown to enable spontaneous and persistent network activity [31]. Dendritic spikes were suggested to work as coincidence detectors and provide a neuronal basis for temporal and spatial contexts in biological networks [32,33].…”

A new computing rule for neuromorphic engineering

“…This error analysis indicates that there should exist some other items besides the simple linear superposition of the EPSP and IPSP inputs. In fact, some recent experimental research [7,8] reveal that indeed the soma integration of the simultaneous excitatory and inhibitory inputs could be well described in a multiplicative form: (2) where is factor determining the strength of the nonlinear product item. Based on the good agreement of this experimental description and the above conclusions derived from the error analysis of the linear computing model, we introduce a nonlinear LIF neuron model [8] into the neuromorphic engineering: Fig.…”

“…To this end, we introduce a new computing rule in neuron block, especially for the soma integration. In our implementation, the membrane potential not only depends on the linear superposition of the excitatory post-synaptic potential (EPSP) and the inhibitory post-synaptic potential (IPSP), but also depends on their product item [7,8]. Based on this bio-plausible model, we give a heuristic design in crossbar structure based neuromorphic system to deliver this kind of nonlinear behavior.…”