本文選題：生化反應(yīng)系統(tǒng) + 隨機(jī)性　； 參考：《清華大學(xué)》2016年博士論文

【摘要】：精密而復(fù)雜的生化反應(yīng)網(wǎng)絡(luò)調(diào)控著各種各樣的生命活動(dòng),研究模擬生命系統(tǒng)的反應(yīng)動(dòng)力學(xué)行為無疑是了解生命活動(dòng)的重要途徑。生命活動(dòng)的基本單元是細(xì)胞,傳統(tǒng)的確定性反應(yīng)速率方程不再能夠描述細(xì)胞這種介觀體系。如何準(zhǔn)確描述隨機(jī)生化反應(yīng)系統(tǒng)的動(dòng)力學(xué)過程是當(dāng)前研究的熱點(diǎn)之一。信息以動(dòng)作電位的形式編碼并在神經(jīng)網(wǎng)絡(luò)中傳遞,動(dòng)作電位的產(chǎn)生和傳播都是電流通過細(xì)胞膜上的離子通道實(shí)現(xiàn)的。HH模型給出動(dòng)作電位的演化方程。而由于通道噪聲、突觸噪聲的存在,這種確定性的描述需要做進(jìn)一步修正。隨機(jī)生化反應(yīng)系統(tǒng)以及HH神經(jīng)元通道的隨機(jī)動(dòng)力學(xué)過程均是馬爾可夫過程,這種過程可以由描述系統(tǒng)狀態(tài)概率分布演化的主方程準(zhǔn)確描述。Gillespie算法是一種常用的能精確求解它的蒙特卡洛模擬方法,但對(duì)于很多復(fù)雜系統(tǒng)而言,Gillespie算法需要的計(jì)算量過大。本文介紹生成函數(shù)法,將由極多的常微分方程(ODE)組成的主方程改寫為由一個(gè)決定概率分布演化的波動(dòng)方程的量子場論(QFT)形式,并等價(jià)轉(zhuǎn)換為生成函數(shù)的描述方式。我們將生成函數(shù)法應(yīng)用到非線性的雙元反應(yīng)系統(tǒng)中,并給出不同的嘗試解,利用變分法將生成函數(shù)滿足的偏微分方程(PDE)近似為有限個(gè)ODEs。在不同的反應(yīng)參數(shù)條件下,無論分子數(shù)多少,都能和Gillespie算法符合得非常好。而且,由于這種方法僅僅計(jì)算有限個(gè)ODEs,且計(jì)算時(shí)間和分子數(shù)多少無關(guān),算法高效。我們利用生成函數(shù)法對(duì)神經(jīng)元?jiǎng)幼麟娢贿M(jìn)行隨機(jī)模擬。通道打開關(guān)閉的過程是一個(gè)典型的馬爾可夫過程,可以用主方程描述。由于電壓的含時(shí)演化只和通道打開數(shù)有關(guān),我們同時(shí)提出了只需對(duì)通道打開數(shù)進(jìn)行取樣的兩種加速算法。計(jì)算結(jié)果表明,除了計(jì)算效率高之外,生成函數(shù)法均能提供與準(zhǔn)確的Gillespie算法相近的結(jié)果,然而大多數(shù)Langevin方法差距較大。生成函數(shù)法為動(dòng)作電位在軸突乃至整個(gè)神經(jīng)網(wǎng)絡(luò)中的傳播提供一種新的途徑。
[Abstract]:Precise and complex biochemical reaction networks regulate all kinds of life activities. It is undoubtedly an important way to understand life activities to study the dynamic behavior of simulated life systems. The basic unit of life activity is cell, and the traditional deterministic reaction rate equation can no longer describe the mesoscopic system of cell. How to accurately describe the dynamic process of stochastic biochemical reaction system is one of the hot research topics at present. The information is encoded in the form of action potential and transmitted in the neural network. The generation and propagation of action potential are all realized by the current through the ion channel on the cell membrane. The evolution equation of action potential is given by using the. HH model. Due to the presence of channel noise and synaptic noise, this deterministic description needs to be further modified. The stochastic biochemical reaction system and the stochastic dynamics of HH neuronal channel are all Markov processes. This process can be accurately described by the master equation describing the evolution of the system state probability distribution. The Gillespie algorithm is a common Monte Carlo simulation method that can accurately solve it, but for many complex systems, the Gillespie algorithm requires too much computation. In this paper, the method of generating function is introduced. The main equation, which consists of a lot of ordinary differential equations (ODEs), is rewritten into the quantum field theory (QFTT) form of a wave equation which determines the evolution of the probability distribution, and is equivalent to the description of the generating function. In this paper, we apply the generating function method to the nonlinear binary reaction system, and give different solutions. By using the variational method, we approximate the PDE of the generating function to a finite number of ODEs. Under different reaction parameters, no matter the number of molecules, it can agree well with the Gillespie algorithm. Moreover, the algorithm is efficient because only a finite number of ODEs is calculated, and the calculation time is independent of the number of molecules. We use the generating function method to simulate the action potential of neurons at random. The process of opening and closing the channel is a typical Markov process, which can be described by the master equation. Since the time-dependent evolution of voltage is only related to the number of open channels, we also propose two acceleration algorithms that only need to sample the number of open channels. The results show that except for the high computational efficiency, the generative function method can provide the same results as the accurate Gillespie algorithm. However, most of the Langevin methods are far behind each other. The method of generating function provides a new way for the propagation of action potential in axon and even the whole neural network.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：Q61;O241.8

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