Abstract
Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.
Highlights
For information processing, a neuron receives and integrates thousands of synaptic inputs from its dendrites and induces the change of its membrane potential at the soma
We demonstrate that our bilinear integration rule is more general than that in Ref. [3]: (i) our rule holds for a pair of excitatory and inhibitory inputs that can arrive at different times; (ii) our rule is valid at any time and is not limited to the peak time of the excitatory postsynaptic potential (EPSP); (iii) our rule is general for all types of paired synaptic input integration, including excitatory-inhibitory, excitatory-excitatory and inhibitory-inhibitory inputs
We first analytically derive the bilinear integration rule from the twocompartment passive cable model, and validate the bilinear integration rule using the realistic model of a pyramidal neuron with both active channels and dendritic branches; we further validate the bilinear integration rule in electrophysiological experiments in rat CA1 pyramidal neurons
Summary
A neuron receives and integrates thousands of synaptic inputs from its dendrites and induces the change of its membrane potential at the soma. The integration of excitatory and inhibitory inputs has been found to enhance motion detection [5], regularize spiking patterns [6], and achieve optimal information coding [7] in many sensory systems. They have been suggested to be able to fine tune information processing within the brain, such as the modulation of frequency [8] and the improvement of the robustness [9] of gamma oscillations. In order to understand how information is processed in neuronal networks in the brain, it is important to understand the computational rules that govern the dendritic integration of synaptic inputs
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