Neural codes have been postulated to build efficient representations of the external world. The hippocampus, an encoding system, employs neuronal firing rates and spike phases to encode external space. Although the biophysical origin of such codes is at a single neuronal level, the role of neural components in efficient coding is not understood. The complexity of this problem lies in the dimensionality of the parametric space encompassing neural components, and is amplified by the enormous biological heterogeneity observed in each parameter. A central question that spans encoding systems therefore is how neurons arrive at efficient codes in the face of widespread biological heterogeneities. To answer this, we developed a conductance-based spiking model for phase precession, a phase code of external space exhibited by hippocampal place cells. Our model accounted for several experimental observations on place cell firing and electrophysiology: the emergence of phase precession from exact spike timings of conductance-based models with neuron-specific ion channels and receptors; biological heterogeneities in neural components and excitability; the emergence of subthreshold voltage ramp, increased firing rate, enhanced theta power within the place field; a signature reduction in extracellular theta frequency compared to its intracellular counterpart; and experience-dependent asymmetry in firing-rate profile. We formulated phase-coding efficiency, using Shannon's information theory, as an information maximization problem with spike phase as the response and external space within a single place field as the stimulus. We employed an unbiased stochastic search spanning an 11-dimensional neural space, involving thousands of iterations that accounted for the biophysical richness and neuron-to-neuron heterogeneities. We found a small subset of models that exhibited efficient spatial information transfer through the phase code, and investigated the distinguishing features of this subpopulation at the parametric and functional scales. At the parametric scale, which spans the molecular components that defined the neuron, several nonunique parametric combinations with weak pairwise correlations yielded models with similar high phase-coding efficiency. Importantly, placing additional constraints on these models in terms of matching other aspects of hippocampal neural responses did not hamper parametric degeneracy. We provide quantitative evidence demonstrating this parametric degeneracy to be a consequence of a many-to-one relationship between the different parameters and phase-coding efficiency. At the functional scale, involving the cellular-scale neural properties, our analyses revealed an important higher-order constraint that was exclusive to models exhibiting efficient phase coding. Specifically, we found a counterbalancing negative correlation between neuronal gain and the strength of external synaptic inputs as a critical functional constraint for the emergence of efficient phase coding. These observations implicate intrinsic neural properties as important contributors in effectuating such counterbalance, which can be achieved by recruiting nonunique parametric combinations. Finally, we show that a change in afferent statistics, manifesting as input asymmetry onto these neuronal models, induced an adaptive shift in the phase code that preserved its efficiency. Together, our analyses unveil parametric degeneracy as a mechanism to harness widespread neuron-to-neuron heterogeneity towards accomplishing stable and efficient encoding, provided specific higher-order functional constraints on the relationship of neural gain to external inputs are satisfied.

中文翻译：

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海马区细胞中的有效相位编码

假设使用神经密码来建立对外部世界的有效表示。海马是一种编码系统，它利用神经元放电速率和突波相位来编码外部空间。尽管此类代码的生物物理起源是在单个神经元水平上，但尚不清楚神经成分在有效编码中的作用。这个问题的复杂性在于包含神经成分的参数空间的维数，并且在每个参数中观察到的巨大的生物异质性进一步放大了这一问题。因此，跨越编码系统的中心问题是面对广泛的生物异质性，神经元如何到达有效的编码。为了回答这个问题，我们开发了一种基于电导的峰值旋律模型，用于相位进动，这是海马体细胞显示的外部空间的相位代码。我们的模型考虑了关于位置细胞放电和电生理学的一些实验观察结果：相位进动的出现是基于具有神经元特异性离子通道和受体的基于电导的模型的精确尖峰定时。神经成分和兴奋性方面的生物异质性；亚阈值电压斜坡的出现，提高的点火速率，在位场中增强的theta功率；与胞内对应物相比，胞外theta频率明显降低；和点火速率曲线中与经验有关的不对称性。我们使用香农的信息理论，将相位编码效率公式化为一个信息最大化问题，其中尖峰相位作为响应，单个场所内的外部空间作为激励。我们采用了跨越11维神经空间的无偏随机搜索，涉及成千上万次迭代，这解释了生物物理丰富度和神经元至神经元异质性。我们发现了一小部分模型，这些模型通过相位代码展示了有效的空间信息传递，并在参数和功能尺度上研究了该亚群的显着特征。在跨越定义神经元的分子成分的参数尺度上，几种具有成对相关性较弱的非唯一参数组合产生了具有相似的高相位编码效率的模型。重要的是，在匹配海马神经反应的其他方面方面，在这些模型上施加了额外的约束，并不妨碍参数退化。我们提供定量证据，证明此参数简并性是不同参数与相位编码效率之间多对一关系的结果。在功能范围内，涉及细胞范围的神经特性，我们的分析显示出重要的高阶约束，而该约束是展现有效相位编码的模型所独有的。具体来说，我们发现神经元增益和外部突触输入强度之间的负相关负平衡是有效相位编码出现的关键功能约束。这些观察暗示内在神经属性是实现这种平衡的重要因素，这可以通过募集非唯一的参数组合来实现。最后，我们证明传入统计的变化，在这些神经元模型上表现为输入不对称时，会在相位代码中引起自适应移位，从而保持其效率。总之，我们的分析揭示了参数简并性是一种机制，可以利用广泛的神经元到神经元异质性来完成稳定和有效的编码，只要满足对神经增益与外部输入的关系的特定高阶功能约束即可。