CNS*2026 Halifax

Introduction
Neurons receive synaptic inputs across a spatially extended dendritic tree [1]. Recent work has shown that neuronal excitability is independent of the size of the dendritic tree when distributed dendritic, instead of somatic, inputs are considered [2]. Such dendritic normalisation has also been shown to improve the speed and robustness of learning [3]. The question remains, however, whether the same principle applies to local dendritic voltages across the entire neuron, and whether this might be computationally useful.

Methods
We derive analytical results using the cable equation [4] in passive dendritic structures, and validate our results using simulations of passive and active cells, including detailed and biophysically validated multicompartmental models, in the Matlab Trees Toolbox package [5], T2N [6], and the NEURON environment [7].

Results
We first show analytically that the steady state voltage response of a dendritic cable receiving distributed inputs is completely independent of dendrite size and measurement location; a dendrite acts like a ‘bucket’ filling with synaptic ‘water’. We investigate how far perturbations due to stochastic inputs impact the ‘bucketness’ of a cell, and find that the local dendritic voltage at every location in the dendrite typically reflects the strength of global inputs. We confirm that calcium concentrations are much longer-lived and more local than voltages. We finally show that the interaction between calcium and voltage could provide a substrate for robust learning by reinterpreting long-term plasticity rules [8,9].

Discussion
Dendritic voltages are surprisingly global and quickly equalise deviations in synaptic inputs. In contrast, calcium transients can provide a long-lived record of local afferents. The interplay between these two indicators provides a continuous, biophysically grounded, learning signal at every point in a dendritic tree. Our results provide a foundation for further studies into the many ways dendrites provide a space for complex computations at the single neuron level.

References
1.\tChklovskii D. Neuron. 2004;43(5):609–17. 10.1016/j.neuron.2004.08.012
2.\tCuntz H, Bird A, et al. Neuron. 2021;109(22):3647-3662.e7. 10.1016/j.neuron.2021.08.028 PMID: 34555313.
3.\tBird AD, Jedlicka P, Cuntz H. PLOS Comp Bio. 2021;17(8):e1009202. 10.1371/journal.pcbi.1009202
4.\tRall W. Ann NY Acad Sci. 1962;96(4):1071–92. 10.1111/j.1749-6632.1962.tb54120.x
5.\tCuntz H, Forstner F, et al. PLOS Comp Bio. 2010;6(8):e1000877. 10.1371/journal.pcbi.1000877
6.\tBeining M, Mongiat L, et al. eLife. 2017;6:e26517. 10.7554/eLife.26517
7.\tHines M, Carnevale N. Neural Comput. 1997;9(6):1179–209. PMID: 9248061.
8.\tBienenstock EL, Cooper LN, Munro PW. J Neurosci. 1982;2(1):32–48. 10.1523/JNEUROSCI.02-01-00032.1982 PMID: 7054394.
9.\tOja E. J Math Biology. 1982;15(3):267–73. 10.1007/BF00275687

Acknowledgement
None.