Data from: Input-dependent frequency modulation of cortical gamma oscillations shapes spatial synchronization and enables phase coding

Fine-scale temporal organization of cortical activity in the gamma range (~25–80Hz) may play a significant role in information processing, for example by neural grouping (‘binding’) and phase coding. Recent experimental studies have shown that the precise frequency of gamma oscillations varies with input drive (e.g. visual contrast) and that it can differ among nearby cortical locations. This has challenged theories assuming widespread gamma synchronization at a fixed common frequency. In the present study, we investigated which principles govern gamma synchronization in the presence of input-dependent frequency modulations and whether they are detrimental for meaningful input-dependent gamma-mediated temporal organization. To this aim, we constructed a biophysically realistic excitatory-inhibitory network able to express different oscillation frequencies at nearby spatial locations. Similarly to cortical networks, the model was topographically organized with spatially local connectivity and spatially-varying input drive. We analyzed gamma synchronization with respect to phase-locking, phase-relations and frequency differences, and quantified the stimulus-related information represented by gamma phase and frequency. By stepwise simplification of our models, we found that the gamma-mediated temporal organization could be reduced to basic synchronization principles of weakly coupled oscillators, where input drive determines the intrinsic (natural) frequency of oscillators. The gamma phase-locking, the precise phase relation and the emergent (measurable) frequencies were determined by two principal factors: the detuning (intrinsic frequency difference, i.e. local input difference) and the coupling strength. In addition to frequency coding, gamma phase contained complementary stimulus information. Crucially, the phase code reflected input differences, but not the absolute input level. This property of relative input-to-phase conversion, contrasting with latency codes or slower oscillation phase codes, may resolve conflicting experimental observations on gamma phase coding. Our modeling results offer clear testable experimental predictions. We conclude that input-dependency of gamma frequencies could be essential rather than detrimental for meaningful gamma-mediated temporal organization of cortical activity.大脑皮层活动在伽马频段（gamma range，~25–80Hz）的精细时间组织，或许在信息处理中发挥关键作用，例如通过神经集群（neural grouping，或称“绑定”‘binding’）与相位编码（phase coding）完成信息处理。近期实验研究显示，伽马振荡（gamma oscillations）的精确频率会随输入驱动（input drive）发生改变（例如视觉对比度（visual contrast）），且邻近皮层区域的伽马振荡频率可能存在差异。这一发现挑战了此前认为伽马振荡会在固定公共频率下广泛同步的理论。在本研究中，我们探究了在输入依赖的频率调制下，支配伽马同步的核心原则是什么，以及这类调制是否会破坏具备生物学意义的、由伽马振荡介导的时间组织。为此，我们构建了一个具有生物物理真实性的兴奋-抑制网络（biophysically realistic excitatory-inhibitory network），该网络可在邻近空间位置产生不同的振荡频率。与大脑皮层网络类似，该模型采用拓扑组织（topographically organized）架构，包含空间局部连接（spatially local connectivity）与空间变化的输入驱动（spatially-varying input drive）。我们从锁相（phase-locking）、相位关系（phase-relations）与频率差异三个维度分析了伽马同步，并量化了由伽马相位与频率所表征的刺激相关信息。通过逐步简化模型，我们发现由伽马振荡介导的时间组织可被简化为弱耦合振子（weakly coupled oscillators）的基本同步原则，其中输入驱动决定振子的固有（自然）频率（intrinsic (natural) frequency）。伽马锁相、精确相位关系以及涌现（可观测）频率由两个核心因素决定：频率失谐（detuning，即固有频率差异，也就是局部输入差异）与耦合强度（coupling strength）。除频率编码外，伽马相位还包含互补的刺激信息。至关重要的是，该相位编码反映的是输入差异，而非绝对输入水平。这种相对输入-相位转换的特性，与潜伏期编码（latency codes）或慢速振荡相位编码形成鲜明对比，或可解决此前关于伽马相位编码的诸多矛盾实验观测结果。我们的建模研究结果提供了明确且可验证的实验预测。我们最终得出结论：伽马频率的输入依赖性，对于构建具备生物学意义的、由伽马振荡介导的大脑皮层活动时间组织而言，或许是至关重要的，而非有害的。