基于基因调控网络刻画细胞异质性的数学模型及算法研究

Cellular heterogeneity research studies the differences of DNA, RNA and proteins between cells at single cell level, and provides better understanding of the mechanisms driving cellular heterogeneity. The main objectives of this research are to distinguish different cell states, reveal different regulation rules within each state and reconstruct cell lineage trajectories. Clustering models based on similarities between gene expression data were frequently applied to separate different cell states. However, the performance was not good enough and they cannot fully reveal the regulatory mechanism of cellular heterogeneity. We think the similarity of cells in the same state is determined by the similarity of gene regulatory networks based on previous research. In this project, we would propose a cyclic clustering model where we can obtain the gene regulatory network and the clusters of cell states at the same time. Moreover, network extropy would be applied to quantify the differentiation potential of a cell and explore the cell fate decision mechanism. Furthermore, we could reconstruct the cell lineage trajectories by combining the network entropy and clustering result. In the end, application of the proposed model to single cell RNA-seq data of tumor cells would help reveal the regulatory scheme of tumor stem cell, which would provide perspective for personalized treatment.

细胞异质性（Cellular heterogeneity）研究主要在单细胞层面探索细胞在DNA、RNA以及蛋白质等方面的差异性，进而揭示细胞发育过程中异质性形成机制。该研究的主要目标有：区分细胞状态并揭示特征调控机制；重构细胞谱系发育轨迹。传统的细胞状态分类模型主要基于基因表达数据的相似性进行聚类，效果并不理想，对于揭示细胞异质性形成机制尚不完备。基于前期研究工作，申请者认为处于同一状态的细胞的相似性由基因调控网络调控机制的相似性所决定。本项目拟基于该假设展开细胞异质性研究，建立循环聚类模型，创建细胞基因调控网络，同时得到细胞状态的划分。在此基础上，拟用网络熵量化分化潜能，探索细胞命运决定机制。此外，结合网络熵和聚类结果对发育细胞建立排序模型，重构细胞谱系发育轨迹。最后拟将设计算法用于肿瘤细胞的scRNA测序数据以揭示肿瘤干细胞的特征调控机制，为个性化治疗方案提供理论基础。

细胞异质性研究主要在单细胞层面探索细胞在DNA、RNA以及蛋白质等方面的差异性，进而揭示细胞发育过程中异质性形成机制。本项目主要基于矩阵分析建立数学模型，基于基因调控网络探索了单细胞表达数据填充算法、聚类算法以及细胞异质性研究的理论分析。主要研究成果包括：1）建立了区分不同细胞类型的最优基因集合模型，发展了相应识别算法，完善了最优基因集合识别理论；2）基于drop-out事件对细胞异质性分析的影响，建立了基于最优低秩矩阵填充的层次聚类算法，基于方差分析发展了最优秩选择模型，在此基础上，结合经典类个数估计算法，确定目标细胞类型个数；3）考虑原始表达矩阵的数据恢复问题，分别建立了基于图非负矩阵分解与基于数据融合的矩阵三分解模型，引入蛋白质相互作用网络等信息刻画单细胞数据的drop-out水平，探索缺失数据恢复对下游分析影响。最后，用理论和数值方法研究了所建立模型的有效性。综上，本项目发展了细胞异质性的建模思想以及相应的理论和数值研究方法，进而为肿瘤的个性化治疗方案、细胞谱系发育轨迹等研究提供理论参考。