Local dendritic voltage provides a reliable read-out of global synaptic activity

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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 in to the many ways dendrites provide a space for complex computations at the single neuron level. References [1] Chklovskii, D. (2004). Synaptic Connectivity and Neuronal Morphology. Neuron, 43(5), 609-617. doi: 10.1016/j.neuron.2004.08.012[2] Cuntz, H., Bird, A., Mittag, M., Beining, M., Schneider, M., Mediavilla, L., Hoffmann, F., Deller, T., & Jedlicka, P. (2021). A general principle of dendritic constancy: A neuron's size- and shape-invariant excitability. Neuron, 109(22), 3647-3662.e7. doi: 10.1016/j.neuron.2021.08.028[3] Bird, A., Jedlicka, P., & Cuntz, H. (2021). Dendritic normalisation improves learning in sparsely connected artificial neural networks. PLOS Computational Biology, 17(8), e1009202. doi: 10.1371/journal.pcbi.1009202[4] Rall, W. (1962). Theory of Physiological Properties of Dendrites. Annals of the New York Academy of Sciences, 96(4), 1071-1092. doi: 10.1111/j.1749-6632.1962.tb54120.x[5] Cuntz, H., Forstner, F., Borst, A., & Häusser, M. (2010). One Rule to Grow Them All: A General Theory of Neuronal Branching and Its Practical Application. PLoS Computational Biology, 6(8), e1000877. doi: 10.1371/journal.pcbi.1000877[6] Beining, M., Mongiat, L., Schwarzacher, S., Cuntz, H., & Jedlicka, P. (2017). T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells. eLife, 6. doi: 10.7554/eLife.26517[7] Hines, M., & Carnevale, N. (1997). Neural Computation, 9(6), 1179–1209[8] Bienenstock, E., Cooper, L., & Munro, P. (1982). Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. The Journal of Neuroscience, 2(1), 32-48. doi: 10.1523/JNEUROSCI.02-01-00032.1982[9] Oja, E. (1982). Simplified neuron model as a principal component analyzer. Journal of Mathematical Biology, 15(3), 267-273. doi: 10.1007/BF00275687

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