Hartung Niklas, Benary Uwe, Wolf Jana, Kofahl Bente
University of Potsdam, Institute of Mathematics, Karl-Liebknecht-Str. 24, Potsdam, 14476, Germany.
Mathematical Modelling of Cellular Processes, Max Delbrueck Center for Molecular Medicine, Robert-Roessle-Str. 10, Berlin, 13125, Germany.
BMC Syst Biol. 2017 Oct 13;11(1):98. doi: 10.1186/s12918-017-0470-9.
Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/ β-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/ β-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells.
Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/ β-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength.
Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter- and intracellular processes, such as Dkk feedback, diffusion and Wnt/ β-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.
细胞能够通过分泌因子在组织内进行通讯并协调其功能。癌细胞的异常分泌可调节这种细胞间通讯,尤其是在肝脏等高度组织化的组织中。肝细胞是肝脏的主要细胞类型,分泌Dickkopf(Dkk),它以自分泌和旁分泌方式抑制Wnt/β-连环蛋白信号通路。因此,Dkk调节Wnt/β-连环蛋白靶基因的表达。我们提出了一个数学模型,该模型描述了在野生型条件下以及存在突变细胞时Dkk对肝脏基因表达的自分泌和旁分泌调节。
我们的空间模型描述了Dkk和Wnt在受体水平的竞争、细胞内Wnt/β-连环蛋白信号传导以及21个单个肝细胞的靶基因表达调控。自分泌和旁分泌调节是通过Dkk的反馈机制以及Dkk沿门-中央轴的扩散介导的。沿着该轴,APC浓度梯度被建模为在肝脏中实验检测到的那样。突变细胞的模拟表明,仅一个突变细胞就会增加总体Dkk浓度。突变细胞对周围野生型肝细胞基因表达的影响在幅度上有限,并且仅限于紧邻的肝细胞。为了探索潜在的分子机制,我们对模型参数进行了全面分析,如扩散系数、突变强度和反馈强度。
我们的模拟表明,在存在突变细胞的情况下Dkk浓度会升高。然而,这些升高的Dkk水平对野生型肝细胞的影响在空间和幅度上是有限的。细胞间和细胞内过程的结合,如Dkk反馈、扩散和Wnt/β-连环蛋白信号转导,使野生型肝细胞能够在很大程度上维持其基因表达。