Gap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics. To obtain insight into the modulatory role of gap junctions in tuning networks of resonant dendritic trees, we generalise the "sum-over-trips" formalism for calculating the response function of a single branching dendrite to a gap junctionally coupled network. Each cell in the network is modelled by a soma connected to an arbitrary structure of dendrites with resonant membrane. The network is treated as a single extended tree structure with dendro-dendritic gap junction coupling. We present the generalised "sum-over-trips" rules for constructing the network response function in terms of a set of coefficients defined at special branching, somatic and gap-junctional nodes. Applying this framework to a two-cell network, we construct compact closed form solutions for the network response function in the Laplace (frequency) domain and study how a preferred frequency in each soma depends on the location and strength of the gap junction.

中文翻译：

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间隙连接、树突和共振：调整网络动力学的秘诀。

间隙连接，也称为电突触，沿着整个中枢神经系统表达，在调节正常和病理状态下的各种脑节律方面很重要。这些连接可以在单个细胞的树突树之间形成。许多树突表达膜通道，赋予它们一种亚阈值共振动力学形式。为了深入了解间隙连接在谐振树突树的调谐网络中的调节作用，我们将用于计算单个分支树突到间隙连接耦合网络的响应函数的“sum-over-trips”形式化。网络中的每个细胞都由连接到具有共振膜的树突的任意结构的胞体建模。该网络被视为具有树突-树突间隙连接耦合的单个扩展树结构。我们根据在特殊分支、体细胞和间隙连接节点处定义的一组系数，提出了用于构建网络响应函数的广义“总和过行程”规则。将此框架应用于双细胞网络，我们为拉普拉斯（频率）域中的网络响应函数构建紧凑的封闭形式解决方案，并研究每个体中的首选频率如何取决于间隙连接的位置和强度。