突触DMC中的饱和受体和受体竞争：确定性和统计信号模型
Saturating Receiver and Receptor Competition in Synaptic DMC: Deterministic and Statistical Signal Models
摘要：
突触通讯是基于生物分子通讯（MC）系统，它可以作为设计合成MC系统的蓝图。然而，突触MC的物理建模是复杂的可能饱和的分子受体所造成的神经递质（NT）的竞争突触后受体。接收器饱和使得系统行为在释放NT的数量上是非线性的，并且在现有的分析模型中通常被忽略。此外，由于配体对受体的竞争（反之亦然），分子接收器处的个体结合事件通常是统计依赖性的，并且接收信号的统计的二项式模型不适用。在这项工作中，我们提出了一种新的确定性模型受体饱和度的状态空间描述的基础上的本征函数扩展的菲克扩散方程。所提出的解决方案是数值稳定和计算效率。采用所提出的确定性模型，我们表明，在分子接收器的饱和度降低了预期的接收信号的峰值和加速清除NT相比，当受体占用被忽略的情况下。我们进一步推导出一个统计模型的接收信号的超几何分布，占竞争的NT的受体和竞争的NT的受体。所提出的统计模型揭示了信号统计是如何形成的数量释放的NT，受体的数量，和受体的结合动力学，分别在竞争的存在下。我们表明，这些参数对信号方差的影响取决于NT和受体的相对数量。基于粒子的计算机模拟验证了所提出的确定性和统计模型的准确性。
英文摘要：
Synaptic communication is based on a biological Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver caused by the competition of neurotransmitters (NTs) for postsynaptic receptors. Receiver saturation renders the system behavior nonlinear in the number of released NTs and is commonly neglected in existing analytical models. Furthermore, due to the ligands' competition for receptors (and vice versa), the individual binding events at the molecular receiver are in general statistically dependent and the binomial model for the statistics of the received signal does not apply. In this work, we propose a novel deterministic model for receptor saturation in terms of a state-space description based on an eigenfunction expansion of Fick's diffusion equation. The presented solution is numerically stable and computationally efficient. Employing the proposed deterministic model, we show that saturation at the molecular receiver reduces the peak-value of the expected received signal and accelerates the clearance of NTs as compared to the case when receptor occupancy is neglected. We further derive a statistical model for the received signal in terms of the hypergeometric distribution which accounts for the competition of NTs for receptors and the competition of receptors for NTs. The proposed statistical model reveals how the signal statistics are shaped by the number of released NTs, the number of receptors, and the binding kinetics of the receptors, respectively, in the presence of competition. We show that the impact of these parameters on the signal variance depends on the relative numbers of NTs and receptors. The accuracy of the proposed deterministic and statistical models is verified by particle-based computer simulations.
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