Bilinearity in Spatiotemporal Integration of Synaptic Inputs

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.

Dendritic computations captured by an effective point neuron model

“…In particular, the spatial dependence of kEI measured at the time when the EPSP reaches its peak value exhibits the feature of spatial asymmetry: when the location of the I input is fixed on the dendritic trunk and the E input is located between the soma and the I input site, kEI increases as the distance between the E input and the soma increases; when the E input is located farther away from the soma than the I input site, kEI remains constant with further increase in the distance between the E input site and the soma. The bilinear rule of dendritic integration has also been observed for the integration of a pair of E inputs, a pair of I inputs, and a mixture of multiple E and I inputs in both experiments and realistic neuron simulations (24).…”

“…Our point neuron model with the synaptic integration current incorporated is capable of capturing a bilinear rule of dendritic integration discovered in recent experiments (21, 24). In the experiments (21, 24), given a pair of glutamatergic E input and GABAergic I input simultaneously to a hippocampal CA1 pyramidal neuron, the SSP measured at the soma denoted by VS can be well characterized by a bilinear rule as VS=VE+VI+kEI⋅VEVI, where VE and VI are the EPSP and IPSP measured at the soma when the E or I input is given alone, respectively, and kEI is the shunting coefficient, which depends on the dendritic locations and arrival times of the E and I inputs but not the strengths of the inputs. In particular, the spatial dependence of kEI measured at the time when the EPSP reaches its peak value exhibits the feature of spatial asymmetry: when the location of the I input is fixed on the dendritic trunk and the E input is located between the soma and the I input site, kEI increases as the distance between the E input and the soma increases; when the E input is located farther away from the soma than the I input site, kEI remains constant with further increase in the distance between the E input site and the soma.…”

“…Model details can be found in refs. 21, 24, and 25. ( B ) A set of simulated individual EPSP, individual IPSP, and SSP induced by both E and I inputs.…”

“…We adapted the multicompartment neuron model used in our previous studies (21, 24, 25) for our realistic pyramidal neuron simulation. The morphology of the reconstructed pyramidal neuron, which includes 200 compartments, was obtained from the Duke–Southampton Archive of Neuronal Morphology (36).…”

PNP: What's in a Name?

“…Some of those nonlinearities are emergent properties that exist (i.e., emerge) only on scales much larger than a channel. Many nonlinearities arise on the cellular scale of neurons and dendrites [81,82]. Some nonlinear properties arise on the molecular scale of proteins.…”