A Theory of Rate Coding Control by Intrinsic Plasticity Effects

Intrinsic plasticity (IP) is a ubiquitous activity-dependent process regulating neuronal excitability and a cellular correlate of behavioral learning and neuronal homeostasis. Because IP is induced rapidly and maintained long-term, it likely represents a major determinant of adaptive collective neuronal dynamics. However, assessing the exact impact of IP has remained elusive. Indeed, it is extremely difficult disentangling the complex non-linear interaction between IP effects, by which conductance changes alter neuronal activity, and IP rules, whereby activity modifies conductance via signaling pathways. Moreover, the two major IP effects on firing rate, threshold and gain modulation, remain unknown in their very mechanisms. Here, using extensive simulations and sensitivity analysis of Hodgkin-Huxley models, we show that threshold and gain modulation are accounted for by maximal conductance plasticity of conductance that situate in two separate domains of the parameter space corresponding to sub- and supra-threshold conductance (i.e. activating below or above the spike onset threshold potential). Analyzing equivalent integrate-and-fire models, we provide formal expressions of sensitivities relating to conductance parameters, unraveling unprecedented mechanisms governing IP effects. Our results generalize to the IP of other conductance parameters and allow strong inference for calcium-gated conductance, yielding a general picture that accounts for a large repertoire of experimental observations. The expressions we provide can be combined with IP rules in rate or spiking models, offering a general framework to systematically assess the computational consequences of IP of pharmacologically identified conductance with both fine grain description and mathematical tractability. We provide an example of such IP loop model addressing the important issue of the homeostatic regulation of spontaneous discharge. Because we do not formulate any assumptions on modification rules, the present theory is also relevant to other neural processes involving excitability changes, such as neuromodulation, development, aging and neural disorders.

固有可塑性（Intrinsic plasticity，IP）是一种普遍存在的活动依赖性过程，可调控神经元兴奋性，同时是行为学习与神经元稳态的细胞水平相关标志物。由于固有可塑性可被快速诱导并长期维持，其大概率是适应性神经元集体动力学的核心决定因素之一。然而，精准评估固有可塑性的确切影响始终颇具挑战。事实上，要厘清固有可塑性效应（即电导变化如何改变神经元活动）与固有可塑性规则（即活动如何通过信号通路调控电导）之间复杂的非线性相互作用，难度极高。此外，固有可塑性对神经元放电频率、阈值及增益调制的两大核心效应，其具体机制至今仍未明确。本研究通过对霍奇金-赫胥黎模型（Hodgkin-Huxley model）开展大规模仿真与敏感性分析，证实阈值与增益调制可由两类分别位于参数空间不同区域的电导的最大电导可塑性介导，这两类电导对应阈下与阈上门电导（即激活电位分别低于或高于动作电位起始阈值电位）。本研究通过分析等效的积分-放电模型（Integrate-and-Fire model），推导得到与电导参数相关的敏感性解析表达式，揭示了调控固有可塑性效应的全新机制。本研究结果可推广至其他电导参数的固有可塑性，并可用于对钙门控电导开展可靠推断，由此构建了能够解释大量多样实验观测结果的统一理论图景。我们推导得到的表达式可与放电率或脉冲发放模型中的固有可塑性规则相结合，为系统性评估经药理学鉴定的电导的固有可塑性所带来的计算效应提供了兼具精细化描述与数学可处理性的通用框架。本研究还提供了这类固有可塑性环路模型的示例，用于解决自发放电稳态调控这一重要科学问题。由于本研究未对修饰规则作出任何假设，因此该理论同样适用于其他涉及兴奋性改变的神经过程，例如神经调制、发育、衰老以及神经疾病。