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1、Construction of Networks And Mathematical Description - ODE EquationsWe based on the Michealis-Menten Equation and Hill Equation to describe the kinetics of gene regulatory networks. The M-M Equation and Hill Equation describe the relationship between the production rate of products and the concentr
2、ation of substrate. M-M Equations of activation (monotone-increasing) and inhibition (monotone-decreasing) are defined as:Hill Equations of activation (monotone-increasing) and inhibition (monotone-decreasing) are defined as: (C is a constant, K is called half maximal effective concentration and n i
3、s called hill coefficient.) In our project, we aimed at all three-node network structures, and each contains 4 nodes (1 input node, 2 regulatory nodes and 1 output node) and vast possible regulatory edges among them. So we formed ODE equation sets to describe the mutual relationships and form networ
4、ks. The ODE equation sets involve two 4*4 matrices to respectively bring in the activating effect and inhibitive effect, and a column vector for self-decomposition. In our wet lab part, we synthetized network and constructed plasmids transferred into Hela cells, and we made some adjustment in our de
5、sign for a better realization in experiment: We assumed that input (I) is not regulated by the network and remains constant. We fixed two certain edges (I inhibits A, A inhibits O), because when constructing the system, the components to function as inducers are quite few. So we tend to use 2 repres
6、sors to substitute it. We limited the maximum number of regulatory nodes to 2 to restrict the problem to an acceptable scale. We chose relative parameters close to the actual experiments in our simulation. According to previous research, we guaranteed that most parameters are within the already conf
7、irmed range, such as reaction rate. Basic Function Analysis - Massive Parallel Data ProcessingThe ideal network in our project must be sensitive to the input signal and be able to distinguish the low input and high input from each other. So we expected that the target structure should have a low-inp
8、ut-low-output and high-input-high-output character. Besides, it should avoid ambiguous interim region between low input and high input. We firstly raised two basic indexes, High-low Ratio and Interim Slope to evaluate the performance of all three-node network structures. To each structure, we scanne
9、d the value of input ranging from 1 to 1000 and recorded the corresponding output. Then we enumerated all possible network structures and illustrated the filtering result in a 2D map. The X-axis represents High-low Ratio and the Y-axis represents Interim Slope, and there are 19683 three-node structu
10、res illustrated as docs in grids in the map. According to our target, only networks with high High-low Ratio and high Interim Slope can achieve the required function. In other words, only networks located in the top-right corner of the map are acceptable. Finally we screened 476 three-node network s
11、tructures out of 19683 network structures in total, which can achieve the high High-low Ratio and high Interim Slope. The whole process involved massive calculation and parallel data processing. Especially, it requires serious computing power to solve all the ODE equations of 19683 networks and comp
12、uter cluster is a powerful tool. Computer cluster connects a group of incompact computers which collaborate together to offer stronger processor power and larger space. We finished the first round of screening with the help of High Performance Computing Cluster (HPCC) in Tsinghua University. Adaptat
13、ion to Copy Number - Decision Based on Probability DistributionIn order to obtain an ideal and robust network which is adaptive to DNA template abundance (copy number), we firstly did parameter scan analysis and made comparisons among all the selected 476 structures intuitively. We changed the range
14、 of reaction rate to represent the change of copy number (proportional relationship), and expected to get a cluster of input-output curves (when copy number changes). Besides, we analyzed the correlativity between copy number and output, and expected the curve to be saturated.Since the target networ
15、k structure is supposed to robustly distinguish different cells with either low or high endogenous input signal, there needs to be a saturated tendency to copy number. In other words, the output shouldnt infinitely increase when the value of copy number increases, especially when the input is low. O
16、therwise, the network would wrongly regard the low-input kind of cell as the high-input kind when copy number is at high level. According to our simulation, we selected 111 network structures that tend to be saturated out of 476 structures. Considering that the actual number of DNA templates that may be transferred into cells is not certain but rather follows a certain distribution in probability, we assumed that the copy number follows Poisson distrib
