基于高维、大噪声、小样本数据的复杂疾病恶性突变信号的挖掘与利用

In our previous work, on the basis of low dimensional data with large sample and small noise, we had some results about detecting the early-warning signal of sudden deterioration during the progression of complex diseases. This project is the continuation and promotion of our previous work. We will carry out research on the critical transition of complex diseases, when the disease-related biomolecule data are high-dimensional, small samples and perturbed by big noise. In a mathematical way, we will first develop the data mining method, including the denoising algorithm and optimal integration of biological high-throughput data in time series. Next, in order to illustrate the progression of diseases, based on the bio-molecular data and theory of system biology, we will infer and construct the set of dynamical regulatory networks. By analyzing the topological and bio-functional difference among these networks, it is possible to establish the mathematical disease model, based on which we will study the bifurcation behavior, and look for bifurcation point and the leading parameters, such that we can theoretically and numerically distinguish the important modules carrying the early-warning signal. At last, the theoretical and numerical results would be validated through real biological experiments for some specific diseases. By summarizing the approach of detecting the early-warning signal of the sudden deterioration of diseases, we provide the theoretical and algorithmic way in mathematics to achieve the early diagnosis of complex diseases.

在前期工作中，针对疾病生物分子数据是大样本、小噪声、低维度等情形，我们在复杂疾病恶性突变信号的挖掘方面，获得了一些结果。本项目是前期工作的继续和提升，针对具有恶性突变现象的复杂疾病，拟对疾病生物分子数据是小样本、大噪声、高维等情形开展研究。首先，将基于带大噪声和小样本的高维生物数据，改进数据除噪降噪的数学方法，优化整合高通量时序列分子数据；其次，根据优化整合后的数据和系统生物学理论，在分子层次上构建能表征疾病发展的动态调控网络集合，通过分析网络结构的差异性和生物功能的变化，建立相应的数学模型，探测数学模型的动态分支行为，确定分支参数和分支点，从理论和数值分析两方面寻找动态调控网络中携带预警信号的重要功能模块；最后，针对某些具体疾病，把理论结果、数值结果与实验结果进行比较，反复验证，去伪存真，筛选出有效的挖掘疾病突变信号的方法，为复杂疾病的预警提供定量的数学理论与计算方法。

在本项目的支持下，项目组针对具有恶性突变现象的复杂疾病，基于具有“小样本、大噪声、高维”等数据特征的生物分子数据开展研究，获得了理论和计算方法两方面的成果。首先，根据系统生物学理论，建立了相应的数学模型，研究了动力系统模型中的分岔现象，给出了解的显示表达，探测了数学模型的动态分岔行为，确定了分岔参数和分岔点，从理论和数值分析两方面寻找了动态调控网络中携带预警信号的重要功能模块；其次，优化了数据空间的重构方式，构建了具有对称结构的自动储备池神经网络计算框架，并进而开发出基于短时间序列的未来信息多步预测方法；第三，发展了推断表征疾病发展的动态调控网络集合的方法，基于待测单样本数据条件，通过分析网络结构的差异性和生物功能的变化，发展了基于生物分子调控网络的网络熵计算方法、基于样本分布信息的系统状态迁移确定方法等一系列计算方法，从而对复杂生物在某些条件下的临界状态进行预警；最后，针对败血症、乳腺癌和新冠肺炎等具体疾病，把理论和计算方法应用于解决实际的疾病预警的问题，为临床早诊、早治提供了计算手段与量化参考。