DREISS: Using State-Space Models to Infer the Dynamics of Gene Expression Driven by External and Internal Regulatory Networks

Gene expression is controlled by the combinatorial effects of regulatory factors from different biological subsystems such as general transcription factors (TFs), cellular growth factors and microRNAs. A subsystem’s gene expression may be controlled by its internal regulatory factors, exclusively, or by external subsystems, or by both. It is thus useful to distinguish the degree to which a subsystem is regulated internally or externally–e.g., how non-conserved, species-specific TFs affect the expression of conserved, cross-species genes during evolution. We developed a computational method (DREISS, dreiss.gerteinlab.org) for analyzing the Dynamics of gene expression driven by Regulatory networks, both External and Internal based on State Space models. Given a subsystem, the “state” and “control” in the model refer to its own (internal) and another subsystem’s (external) gene expression levels. The state at a given time is determined by the state and control at a previous time. Because typical time-series data do not have enough samples to fully estimate the model’s parameters, DREISS uses dimensionality reduction, and identifies canonical temporal expression trajectories (e.g., degradation, growth and oscillation) representing the regulatory effects emanating from various subsystems. To demonstrate capabilities of DREISS, we study the regulatory effects of evolutionarily conserved vs. divergent TFs across distant species. In particular, we applied DREISS to the time-series gene expression datasets of C. elegans and D. melanogaster during their embryonic development. We analyzed the expression dynamics of the conserved, orthologous genes (orthologs), seeing the degree to which these can be accounted for by orthologous (internal) versus species-specific (external) TFs. We found that between two species, the orthologs have matched, internally driven expression patterns but very different externally driven ones. This is particularly true for genes with evolutionarily ancient functions (e.g. the ribosomal proteins), in contrast to those with more recently evolved functions (e.g., cell-cell communication). This suggests that despite striking morphological differences, some fundamental embryonic-developmental processes are still controlled by ancient regulatory systems.

基因表达受来自不同生物子系统的调控因子的组合效应调控，这些子系统包括通用转录因子（Transcription Factors, TFs）、细胞生长因子以及微小RNA（microRNAs）。某一子系统的基因表达可完全由其内部调控因子控制，亦可由外部子系统调控，或同时受二者共同调控。因此，区分一个子系统受内部或外部调控的程度具有重要意义——例如，在进化过程中，非保守的物种特异性转录因子如何影响保守的跨物种基因的表达。我们开发了一种名为DREISS（dreiss.gerteinlab.org）的计算方法，用于基于状态空间模型（State Space models）分析由内外调控网络驱动的基因表达动态。对于给定子系统，模型中的“状态”与“控制”变量分别对应该子系统自身（内部）以及另一子系统（外部）的基因表达水平。给定时刻的状态由前一时刻的状态与控制变量共同决定。由于典型的时序基因表达数据样本量不足，无法完全估计模型参数，DREISS采用降维方法，识别出代表源自各子系统调控效应的典型时序表达轨迹（如降解、生长与振荡模式）。为验证DREISS的性能，我们研究了不同远缘物种间进化保守与分化的转录因子的调控效应。具体而言，我们将DREISS应用于秀丽隐杆线虫（C. elegans）与黑腹果蝇（D. melanogaster）胚胎发育过程中的时序基因表达数据集。我们分析了保守的直系同源基因（orthologs）的表达动态，探究这些基因的表达在多大程度上可由直系同源（内部）与物种特异性（外部）转录因子解释。研究发现，在两个物种间，直系同源基因的内部驱动表达模式具有一致性，但外部驱动模式差异显著。对于具有进化古老功能的基因（如核糖体蛋白）而言，这一现象尤为明显，而新近进化功能的基因（如细胞间通讯相关基因）则与此相反。这表明，尽管二者存在显著的形态学差异，但某些基本胚胎发育过程仍由古老的调控系统所控制。