Synaptic communication is a natural Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. In particular, it features highly specialized mechanisms to enable inter-symbol interference (ISI)-free and energy efficient communication. The understanding of synaptic MC is furthermore critical for disruptive innovations in the context of brain-machine interfaces. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver arising from the competition of postsynaptic receptors for neurotransmitters. Saturation renders the system behavior nonlinear and is commonly neglected in existing analytical models. In this work, we propose a novel model for receptor saturation in terms of a nonlinear, state-dependent boundary condition for Fick's diffusion equation. We solve the resulting boundary-value problem using an eigenfunction expansion of the Laplace operator and the incorporation of the receiver memory as feedback system into the corresponding state-space description. The presented solution is numerically stable and computationally efficient. Furthermore, the proposed model is validated with particle-based stochastic computer simulations.

中文翻译：

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突触 DMC 的受体饱和建模

突触通信是一种自然的分子通信 (MC) 系统，可以作为合成 MC 系统设计的蓝图。特别是，它具有高度专业化的机制，可实现无符号间干扰 (ISI) 和节能的通信。此外，对突触 MC 的理解对于脑机接口背景下的颠覆性创新至关重要。然而，突触 MC 的物理建模由于突触后受体对神经递质的竞争而引起的分子受体可能饱和而变得复杂。饱和度使系统行为呈非线性，在现有的分析模型中通常被忽略。在这项工作中，我们根据 Fick' 的非线性、状态相关边界条件提出了一种新的受体饱和模型。s 扩散方程。我们使用拉普拉斯算子的本征函数展开和将接收器记忆作为反馈系统纳入相应的状态空间描述来解决由此产生的边界值问题。所提出的解决方案在数值上稳定且计算效率高。此外，所提出的模型通过基于粒子的随机计算机模拟进行了验证。