Borisyuk Alla, Semple Malcolm N, Rinzel John
Courant Institute of Mathematical Sciences, New York University, New York 10012, USA.
J Neurophysiol. 2002 Oct;88(4):2134-46. doi: 10.1152/jn.2002.88.4.2134.
A mathematical model was developed for exploring the sensitivity of low-frequency inferior colliculus (IC) neurons to interaural phase disparity (IPD). The formulation involves a firing-rate-type model that does not include spikes per se. The model IC neuron receives IPD-tuned excitatory and inhibitory inputs (viewed as the output of a collection of cells in the medial superior olive). The model cell possesses cellular properties of firing rate adaptation and postinhibitory rebound (PIR). The descriptions of these mechanisms are biophysically reasonable, but only semi-quantitative. We seek to explain within a minimal model the experimentally observed mismatch between responses to IPD stimuli delivered dynamically and those delivered statically (McAlpine et al. 2000; Spitzer and Semple 1993). The model reproduces many features of the responses to static IPD presentations, binaural beat, and partial range sweep stimuli. These features include differences in responses to a stimulus presented in static or dynamic context: sharper tuning and phase shifts in response to binaural beats, and hysteresis and "rise-from-nowhere" in response to partial range sweeps. Our results suggest that dynamic response features are due to the structure of inputs and the presence of firing rate adaptation and PIR mechanism in IC cells, but do not depend on a specific biophysical mechanism. We demonstrate how the model's various components contribute to shaping the observed phenomena. For example, adaptation, PIR, and transmission delay shape phase advances and delays in responses to binaural beats, adaptation and PIR shape hysteresis in different ranges of IPD, and tuned inhibition underlies asymmetry in dynamic tuning properties. We also suggest experiments to test our modeling predictions: in vitro simulation of the binaural beat (phase advance at low beat frequencies, its dependence on firing rate), in vivo partial range sweep experiments (dependence of the hysteresis curve on parameters), and inhibition blocking experiments (to study inhibitory tuning properties by observation of phase shifts).
我们构建了一个数学模型，用于探究低频下丘（IC）神经元对双耳相位差（IPD）的敏感性。该模型公式涉及一种不包含单个脉冲本身的发放率类型模型。模型中的IC神经元接收经IPD调谐的兴奋性和抑制性输入（可视为内侧上橄榄核中一组细胞的输出）。模型细胞具有发放率适应和抑制后反弹（PIR）的细胞特性。对这些机制的描述在生物物理学上是合理的，但只是半定量的。我们试图在一个最小模型中解释实验观察到的动态呈现IPD刺激与静态呈现IPD刺激时反应之间的不匹配现象（McAlpine等人，2000年；Spitzer和Semple，1993年）。该模型再现了对静态IPD呈现、双耳节拍和部分范围扫描刺激反应的许多特征。这些特征包括在静态或动态环境中呈现刺激时反应的差异：对双耳节拍反应时调谐更尖锐和相位偏移，以及对部分范围扫描反应时的滞后和“无中生有”现象。我们的结果表明，动态反应特征归因于输入结构以及IC细胞中发放率适应和PIR机制的存在，但不依赖于特定的生物物理机制。我们展示了模型的各个组成部分如何对所观察到的现象产生影响。例如，适应、PIR和传输延迟塑造了对双耳节拍反应中的相位提前和延迟，适应和PIR在不同IPD范围内塑造滞后现象，而调谐抑制是动态调谐特性不对称的基础。我们还提出了实验来检验我们的建模预测：双耳节拍的体外模拟（低频节拍时的相位提前及其对发放率的依赖性）、体内部分范围扫描实验（滞后曲线对参数的依赖性）以及抑制阻断实验（通过观察相位偏移来研究抑制性调谐特性）。
