Our model serves three main purposes:
Our model is divided into four interconnected parts, representing the inhalation of muscone, its binding to receptors, intracellular signal transduction and lactic acid secretion triggered by receptor activation, and the absorption of lactic acid. These models provide a comprehensive understanding of the project and yield valuable computational results.
The main focus of our project is the use of muscone as a signaling molecule to activate engineered bacteria in the gut for therapeutic purposes. Therefore, it is crucial to provide a quantitative description and computational support for the diffusion of muscone in the body. This model describes the entire process from the inhalation of muscone to its increased concentration in the intestinal tract. We will establish a multi-compartment model that includes the following main processes:
TODO:Insert design diagram
Corresponding to the above processes, five compartments need to be established for simulation, where $t$ represents the time variable:
At \(t=0\), the amount of muscone in all compartments is \(0\).
Assuming that the total amount of inhaled muscone is \(Q_{\text{inhale}}\) (\(\text{mg}\)), which is assumed to be \(100\text{mg}\). Only \(0.5\%\) of muscone enters the systemic circulation through adhesion. In this model, since muscone only acts as a signaling molecule to activate yeast to synthesize lactic acid, we only consider the metabolism and excretion of muscone in the systemic circulation. We only focus on the short-term process of muscone appearing in the intestine from scratch, and the subsequent process of reaching a certain concentration can be ignored.
\( V_{\text{inhale}}(t) =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \)
Explanation:This describes the rate equation for inhaling muscone over five seconds, where the total amount \( Q \) remains constant. The function \( u(t) \) is a step function, which takes the value of \( \frac{Q_{\text{inhale}}}{5} \) from \( t=0s \) to \( t=5s \), and is \( 0 \) otherwise, simulating the scenario of resting human respiration.
\( \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) - \left( k_{\text{exhale}} + k_{\text{perm}} \right) Q_A(t) \)
Explanation: The amount of muscone in the alveoli increases through inhalation and decreases due to exhalation, adhesion to the respiratory mucosa, and permeation into the alveolar capillaries.
Parameters:
\( \frac{dQ_M(t)}{dt} = 0.0005 \cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t) \)
Explanation: The increase in muscone on the mucosa comes from adhesion in the alveoli, and the decrease is due to diffusion into the systemic circulation.
Parameters:
\( \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \)
Explanation: The increase in muscone in the alveolar capillaries comes from permeation in the alveoli, and the decrease is due to diffusion into the systemic circulation.
Parameters:
\( \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}} Q_C(t) - k_{\text{excrete}} Q_C(t) \)
Explanation: The increase in muscone in the systemic circulation comes from the input of mucosa and alveolar capillaries, and the decrease is due to distribution to the intestinal mesenteric microvascular network and excretion through various routes.
Parameters:
\( \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t) - k_{move}Q_I(t) \)
Explanation: The increase in muscone in the intestine comes from the distribution of the systemic circulation, and the decrease is due to metabolism and excretion through intestinal fluid and peristalsis.
\( k_{\text{dist}} \): Same as above
\( k_{move} \): The metabolism and excretion of muscone in the intestine, taken as \( 0.02 \
\text{min}^{-1} \)
In summary, we can write a system of ordinary differential equations and import it into MATLAB for simulation:
\( Q_{\text{inhale}}(t)=100(mg)(Assumption) \)
\( V_{\text{inhale}}(t) =\frac{Q_{\text{inhale}}}{5}(u(t)-u(t-5)) \)
\( \frac{dQ_A(t)}{dt} = V_{\text{inhale}}(t) -\left( k_{\text{exhale}} + k_{\text{perm}} \right) Q_A(t) \)
\( \frac{dQ_L(t)}{dt} = k_{\text{perm}} Q_A(t) - k_{\text{diffLC}} Q_L(t) \)
\( \frac{dQ_M(t)}{dt} = 0.0005\cdot k_{\text{adh}} V_{\text{inhale}}(t) - k_{\text{diffMC}} Q_M(t) \)
\( \frac{dQ_C(t)}{dt} = k_{\text{diffMC}} Q_M(t) + k_{\text{diffLC}} Q_L(t) - k_{\text{dist}} Q_C(t) - k_{\text{excrete}} Q_C(t) \)
\( \frac{dQ_I(t)}{dt} = k_{\text{dist}} Q_C(t)-k_{move}Q_I(t) \)
TODO:插入结果图
We simulated the distribution of muscone in the systemic circulation and obtained the concentration change curve of muscone in the systemic circulation. According to the model, after one breath, traces of muskone can spread into the intestine, similarly, the concentration change caused by continuous muskone is simulated by changing the inhalation equation, and the concentration of muskone in the intestine can be obtained in combination with experimental determination. Because there is no animal experimental support, the data are manually drafted, and the calculation method is more meaningful than the calculation results.
Tsinghua University engages in extensive research and offers 51 bachelor's degree programs, 139 master's degree programs, and 107 doctoral programs through 20 colleges and 57 departments covering a broad range of subjects, including science, engineering, arts and literature, social sciences, law, medicine. Along with its membership in the C9 League, Tsinghua University affiliations include the Association of Pacific Rim Universities, a group of 50 leading Asian and American universities, Washington University in St. Louis's McDonnell International Scholars Academy, a group of 35 premier global universities, and the Association of East Asian Research Universities, a 17-member research collaboration network of top regional institutions. Tsinghua is an associate member of the Consortium Linking Universities of Science and Technology for Education and Research (CLUSTER). Tsinghua is a member of a Low Carbon Energy University Alliance (LCEUA), together with the University of Cambridge and the Massachusetts Institute of Technology (MIT).
School of Life Sciences was first established in 1926 under the name Department of Biology. Botanist Qian Chongshu took up the first dean.During the nationwide reorganization of universities in the early 1950s, the Department of Biology was merged into other universities, namely Peking University etc., resulting in a vacancy in the field of biological research in Tsinghua for almost 30 years.In June 1984, decisions were made about the reestablishment of the Department of Biology, and the department officially reopened in September. During the reestablishment the Department of Biology of Peking University, the Institute of Biophysics of Chinese Academy of Sciences, and many other institutes as well as biologists provided valuable support and help. The department changed its name to the current name in September 2009. As of 2013, structural biologist and foreign associate of National Academy of Sciences of United States Dr. Wang Hongwei (王宏伟) is the current dean of School of Life Sciences. The school currently has 129 professors and employees, around 600 undergraduates (including the candidates of Tsinghua University – Peking Union Medical College joint MD program).
Admission to Tsinghua for both undergraduate and graduate schools is extremely competitive. Undergraduate admissions for domestic students is decided through the gaokao, the Chinese national college entrance exam, which allows students to list Tsinghua University among their preferred college choices. While selectivity varies by province, the sheer number of high school students applying for college each year has resulted in overall acceptance rates far lower than 0.1% of all test takers. Admission to Tsinghua's graduate schools is also very competitive. Only about 16% of MBA applicants are admitted each year.
Department of Mathematical Sciences The Department of Mathematical Sciences (DMS) was established in 1927. In 1952, Tsinghua DMS was merged with the Peking University Department of Mathematical Sciences. Then in 1979 it was renamed "Department of Applied Mathematics", and renamed again in 1999 to its current title. Tsinghua DMS has three institutes at present, the institute of Pure Mathematics which has 27 faculty members, the Institute of Applied Mathematics and Probability and Statistics which has 27 faculty members, and the Institute of Computational Mathematics and Operations Research which has 20 faculty members. There are currently about 400 undergraduate students and 200 graduate students.
Tsinghua University is consistently ranked among the top universities in the Asia-Pacific according to major international university rankings. Tsinghua University ranked No. 1 in China, the whole of Asia-Oceania region and emerging countries according to the Times Higher Education, with its industry income, research, and teaching performance indicator placed at 1st, 4th and 9th respectively in the world. Internationally, Tsinghua was regarded as the most reputable Chinese university by the Times Higher Education World Reputation Rankings where, it has ranked 8th globally and 1st in the Asia-Pacific.
The Engineering Research Center for Navigation Technology is a relatively young institute in the Department of Precision Instrument which was established in 2000, with the intention to "[pursue] excellence in the research and development in the field of high-accuracy inertial instruments and navigation technology, as well as in MEMS inertial sensor fields, and to provide advanced training for future scientists and engineers in the field of inertial technology." Its research interests cover high-accuracy inertial instruments and navigation technology, MEMS inertial sensors and systems, and precise electro-mechanical control systems and their application. As of 2012, the area of the center is 2900 square meters, including approximately 550 square meters of clean rooms. Equipment and instruments in this center are worth over 50 million RMB (US$7.56 million).