Introduction The spatial distribution of parallel fiber (PF) synaptic inputs to a Purkinje cell (PC) induces complex intracellular dynamics along the dendrites, enabling nonlinear pattern discrimination [1]. However, the relationship between PC morphology and memory capacity remains unclear. Although simulations of biophysical neuron models incorporating morphology are effective for such investigations, current models lack long-term depression (LTD) implementation. Therefore, we propose a learning-rule-independent method to evaluate memory capacity. In this study, we apply the "Survival Game [2]" from machine learning to biophysical models to evaluate neuronal memory capacity without explicit learning rules.
Methods To evaluate the PC model\'s memory capacity, we presented input patterns by activating 30 of 100 dendritic PF synapses, using the following procedure: (1) 50,000 PC models were prepared with 100 random PF synaptic weights. (2) 30 synapses were randomly activated for current injection, and a teacher label was randomly assigned. (3) Models whose outputs (firing or not) matched the label "survived"; others were eliminated. (4) All models received the same 30 inputs to determine survival. (5) Steps (2)-(4) were repeated until all models were eliminated. Theoretically, with a sufficiently large number of models, the number of rounds corresponds to the memory capacity.
Results We constructed the PC model using morphology data [3] and ion channel data [4], and performed simulations on the supercomputer "Fugaku." First, the simulation results showed that the PC model memorized an average of 6.7 patterns (SD 1.9) when selecting 30 active synapses out of 100. Next, as the number of PF synapses increased from 100 to 400, the memory capacity increased in proportion to the input dimension. This trend follows the theoretical predictions in [2], validating our evaluation method. Furthermore, evaluating memory capacity using a random subset of 500 models yielded results nearly identical to the full-scale simulation of 50,000 models.
Discussion Our proposed method offers two primary advantages. First, it is independent of specific neuronal learning rules. While biophysical simulations are effective, the realistic implementation of diverse learning rules (e.g., Hebbian, STDP, LTP/LTD, or dopaminergic modulation) for different neuron types is difficult. Our method bypasses that complexity, allowing for a direct evaluation of the fundamental relationship between neuronal morphology and memory capacity. Second, the memory capacity for complex tasks, such as the 30-out-of-100 synapse activation, can be estimated with hundreds of simulations. Using parallel simulators and GPUs, these simulations can be completed within several hours without requiring a supercomputer.
References [1] Tamura, K., et al. (2023). Discrimination and learning of temporal input sequences in a cerebellar Purkinje cell model. Front. Cell. Neurosci.17:1075005. [2] Okada, M. (2005). [Statistical mechanics of ensemble learning]. Ansanburu gakushu no toukei rikigaku (in Japanese). Watanabe, S. (Eds). [Theory and implementation of learning systems] Gakushu shisutemu no riron to jitsugen (pp. 132-159). Morikita Publishing Co., Ltd. [3] Nedelescu, H., et al. (2018). Regional differences in Purkinje cell morphology in the cerebellar vermis of male mice. Neurosci. Res.96:1476–1489. [4] Masoli, S., et al. (2024). Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity. Commun. Biol.7:5.
Acknowledgement This research was supported by AMED under Grant Number JP25wm0625418h0001.
