弱耦合双房室神经元模型中基于稀疏胞体监督的树突记录胞体动力学物理约束推断

中文摘要 AI 辅助

胞体膜电位是神经元输出的主要决定因素，然而在许多仅能获得树突记录的实验设置中，胞体膜电位无法直接获取。从远端测量重建胞体动力学是一个具有挑战性的逆问题，尤其是在胞体与树突弱耦合的情况下，因为树突信号是胞体活动的滤波且衰减版本。为解决此问题，我们使用受双房室Hodgkin-Huxley模型约束的物理信息神经网络（PINN）。该网络在密集的树突电压记录和已知的注入电流上进行训练，并辅以少量胞体电压样本（最多占时间点的5%），从而重建完整的胞体轨迹，同时调整一组选定的胞体最大电导。在四种刺激协议的合成数据上，我们量化了重建对胞体监督量的依赖。在没有胞体样本的情况下，当前公式返回一条平滑轨迹，其中动作电位缺失且阈下水平有偏，均方根误差为10-14 mV；1%的胞体时间点足以恢复每个尖峰；5%的胞体时间点可将均方根误差降至约2 mV（含尖峰），钠电导和延迟整流电导的相对误差低于0.1%。我们还将PINN与受相同模型约束并同化相同观测的无迹卡尔曼滤波器进行比较，并评估了对测量噪声和随机初始化的鲁棒性。因此，本文报告的重建依赖于稀疏的胞体锚定以及树突记录。结果界定了在这种合成、弱监督双房室设置中可以推断的内容，并确定了当前公式所需的胞体信息量。

英文摘要

Somatic membrane potential is the primary determinant of neuronal output, yet it remains inaccessible in many experimental setups where only dendritic recordings are available. Reconstructing somatic dynamics from distal measurements is a challenging inverse problem, particularly when the soma and dendrites are weakly coupled, as dendritic signals represent a filtered and attenuated version of somatic activity. To address this, we use a physics-informed neural network (PINN) constrained by a two-compartment Hodgkin--Huxley model. The network is trained on dense dendritic voltage recordings and the known injected current, complemented by a small number of somatic voltage samples (at most 5\% of the time points), and it reconstructs the full somatic trajectory while adjusting a selected set of somatic maximal conductances. On synthetic data from four stimulation protocols, we quantify how the reconstruction depends on the amount of somatic supervision. Without somatic samples, the present formulation returns a smooth trajectory in which the action potentials are absent and the subthreshold level is biased, with a root-mean-square error of 10--14~mV; 1\% of the somatic time points is enough to recover every spike; and 5\% brings the root-mean-square error to about 2~mV, spikes included, with relative errors below 0.1\% on the sodium and delayed-rectifier conductances. We also compare the PINN with an unscented Kalman filter constrained by the same model and assimilating the same observations, and we assess robustness to measurement noise and to random initialization. The reconstructions reported here therefore rely on sparse somatic anchoring in addition to the dendritic recordings. The results delimit what can be inferred in this synthetic, weakly supervised two-compartment setting and identify the amount of somatic information required by the present formulation.

发表机构

• Université Le Havre Normandie（勒阿弗尔诺曼底大学）
• The Hudson School of Mathematics（哈德森数学学院）

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