Identification of key ionic channel contributors to the overall dynamics of a neuron is an important problem in experimental neuroscience. Such a problem is challenging since even in the best cases, identification relies on noisy recordings of membrane potential only, and strict inversion to the constituent channel dynamics is mathematically ill-posed. In this work, we develop a biophysically interpretable, learning-based strategy for data-driven inference of neuronal dynamics. In particular, we propose two optimization frameworks to learn and approximate neural dynamics from an observed voltage trajectory. In both the proposed strategies, the membrane potential dynamics are approximated as a weighted sum of ionic currents. In the first strategy, the ionic currents are represented using voltage dependent channel conductances and membrane potential in a parametric form, while in the second strategy, the currents are represented as a linear combination of generic basis functions. A library of channel activation/inactivation and time-constant curves describing prototypical channel kinetics are used to provide estimates of the channel variables to approximate the ionic currents. Finally, a linear optimization problem is solved to infer the weights/scaling variables in the membrane-potential dynamics. In the first strategy, the weights can be used to recover the channel conductances, and the reversal potentials while in the second strategy, using the estimated weights, active channels can be inferred and the trajectory of the gating variables are recovered, allowing for biophysically salient inference. Our results suggest that the complex nonlinear behavior of the neural dynamics over a range of temporal scales can be efficiently inferred in a data-driven manner from noisy membrane potential recordings.

中文翻译：

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单个神经元动力学的生物物理学解释。

识别关键离子通道贡献者的神经元的整体动力学是实验神经科学中的重要问题。由于即使在最佳情况下，识别也仅依赖于膜电位的嘈杂记录，并且严格逆转组成通道动力学在数学上是不合适的，因此该问题具有挑战性。在这项工作中，我们为数据驱动的神经元动力学推断开发了一种基于生物学的解释性，基于学习的策略。特别是，我们提出了两个优化框架，以从观察到的电压轨迹中学习和近似神经动力学。在这两种建议的策略中，膜电势动力学都近似为离子电流的加权和。在第一个策略中 离子电流使用电压依赖性通道电导和膜电势以参数形式表示，而在第二种策略中，电流表示为通用基函数的线性组合。描述原型通道动力学的通道激活/失活和时间常数曲线库用于提供通道变量的估计值，以近似离子电流。最后，解决了线性优化问题，以推断膜电位动力学中的权重/缩放比例变量。在第一种策略中，可以使用权重来恢复通道电导和反转电位，而在第二种策略中，可以使用估计的权重来推断活动通道并恢复选通变量的轨迹，允许进行生物学上的显着推断。我们的结果表明，可以从嘈杂的膜电位记录中以数据驱动的方式有效地推断出一系列时间尺度上神经动力学的复杂非线性行为。