Information processing in neural populations is inherently constrained by metabolic resource limits and noise properties, with dynamics that are not accurately described by existing mathematical models. Recent data, for example, shows that neurons in mouse visual cortex go into a "low power mode" in which they maintain firing rate homeostasis while expending less energy. This adaptation leads to increased neuronal noise and tuning curve flattening in response to metabolic stress. We have developed a theoretical population coding framework that captures this behavior using two novel, surprisingly simple constraints: an approximation of firing rate homeostasis and an energy limit tied to noise levels via biophysical simulation. A key feature of our contribution is an energy budget model directly connecting adenosine triphosphate (ATP) use in cells to a fully explainable mathematical framework that generalizes existing optimal population codes. Specifically, our simulation provides an energy-dependent dispersed Poisson noise model, based on the assumption that the cell will follow an optimal decay path to produce the least-noisy spike rate that is possible at a given cellular energy budget. Each state along this optimal path is associated with properties (resting potential and leak conductance) which can be measured in electrophysiology experiments and have been shown to change under prolonged caloric deprivation. We analytically derive the optimal coding strategy for neurons under varying energy budgets and coding goals, and show how our method uniquely captures how populations of tuning curves adapt while maintaining homeostasis, as has been observed empirically.

翻译：神经群体的信息处理本质上受到代谢资源限制和噪声特性的约束，其动态特性无法被现有数学模型准确描述。例如，近期数据显示，小鼠视觉皮层神经元会进入"低功耗模式"，在维持放电率稳态的同时消耗更少能量。这种适应机制导致神经元噪声增加和调谐曲线平坦化，以应对代谢应激。我们开发了一个理论群体编码框架，通过两个新颖且异常简单的约束条件来捕捉这种行为：放电率稳态的近似表示，以及通过生物物理模拟将能量限制与噪声水平相关联的模型。我们贡献的一个关键特征是能量预算模型，该模型直接将细胞中三磷酸腺苷（ATP）的消耗与一个完全可解释的数学框架相连接，该框架推广了现有的最优群体编码理论。具体而言，我们的模拟提供了一个能量依赖的分散泊松噪声模型，其基于以下假设：细胞将遵循最优衰减路径，在给定细胞能量预算下产生可能的最低噪声尖峰发放率。沿着这条最优路径的每个状态都具有可通过电生理实验测量的特性（静息电位和漏电导），这些特性已被证明在长期热量剥夺条件下会发生改变。我们通过解析方法推导出不同能量预算和编码目标下神经元的最优编码策略，并证明我们的方法能独特地捕捉到调谐曲线群体在维持稳态过程中的适应机制，这与实验观测结果一致。