Probability models of the neuromuscular junction synapse

The objective of this thesis is to develop the probability model enabling to compute the probability of the acetylcholine release in neuromuscular junction synapse under different physiological conditions. The main accomplishment is the construction of the Inverse Pólya process model for the probability of the acetylcholine release when the neuromuscular synapse is vulnerable to a chemical attack. To achieve the goals that have been set, it is required to solve the following targets. First, establish a method of estimation for the number of the acetylcholine vesicles. Then, derive a formula for the probability of the acetylcholine vesicle release in neuromuscular synapse under different conditions. After that, formulate the axioms for the construction of the Inverse Pólya process model. Most importantly, prove the theorem about the probability distribution that satisfy the introduced axioms. For the case of the chemical effect, a new model, so-called Inverse Pólya process was suggested. A differential equation for happening k events in the Inverse Pólya process was derived. Due to this differential equation, we obtain the formula for the probability of happening exactly k events over time t. Finally, we derive the density function of the random time of k-th event.

本论文的研究目的为构建概率模型，以计算不同生理条件下神经肌肉接头突触（neuromuscular junction synapse）内乙酰胆碱（acetylcholine）的释放概率。本研究的核心成果为，针对神经肌肉突触易受化学攻击的场景，构建了用于描述乙酰胆碱释放概率的逆波利亚过程（Inverse Pólya process）模型。为达成既定研究目标，需完成以下研究任务：其一，建立乙酰胆碱囊泡（acetylcholine vesicles）数量的估计方法；其二，推导不同条件下神经肌肉突触内乙酰胆碱囊泡释放概率的计算公式；其三，为逆波利亚过程模型的构建确立公理体系；尤为关键的是，证明满足所引入公理的概率分布相关定理。针对化学效应场景，本研究提出了一种新型模型——逆波利亚过程，推导了逆波利亚过程中发生k次事件的微分方程，借此得到时长t内恰好发生k次事件的概率公式，最终推导得到第k次事件发生的随机时间的密度函数。