Section Computational Science, University of Amsterdam, Amsterdam, The Netherlands.
Section Computational Science, University of Amsterdam, Amsterdam, The Netherlands; FOM Institute AMOLF, Amsterdam, The Netherlands.
PLoS Comput Biol. 2014 Jun 19;10(6):e1003687. doi: 10.1371/journal.pcbi.1003687. eCollection 2014 Jun.
Controlled synthesis of silicon is a major challenge in nanotechnology and material science. Diatoms, the unicellular algae, are an inspiring example of silica biosynthesis, producing complex and delicate nano-structures. This happens in several cell compartments, including cytoplasm and silica deposition vesicle (SDV). Considering the low concentration of silicic acid in oceans, cells have developed silicon transporter proteins (SIT). Moreover, cells change the level of active SITs during one cell cycle, likely as a response to the level of external nutrients and internal deposition rates. Despite this topic being of fundamental interest, the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood. One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales, and even when possible, data often contain large errors. Therefore, using computational techniques seems inevitable. We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment, cytoplasm, SDV and deposited silica. The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations. In order to find the free parameters of the model from sparse, noisy experimental data, an optimization technique (global and local search), together with enzyme related penalty terms, has been applied. We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells. Our model is robust, proven by sensitivity and perturbation analysis, and predicts dynamics of intracellular nutrients and enzymes in different compartments. The model produces different uptake regimes, previously recognized as surge, externally-controlled and internally-controlled uptakes. Finally, we imposed a flux of SITs to the model and compared it with previous classical kinetics. The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations.
硅的可控合成是纳米技术和材料科学的一大挑战。硅藻，单细胞藻类，是生物合成二氧化硅的一个鼓舞人心的例子，产生复杂而精细的纳米结构。这发生在几个细胞隔室中，包括细胞质和硅沉积囊泡（SDV）。考虑到海洋中硅酸的浓度较低，细胞已经开发出硅转运蛋白（SIT）。此外，细胞在一个细胞周期内改变活性 SIT 的水平，这可能是对外界营养物质水平和内部沉积速率的响应。尽管这个话题具有基础性的兴趣，但营养物质的细胞内动力学和细胞调节策略仍然知之甚少。一个原因是在如此小的尺度上测量和操纵这些机制存在困难，即使可能，数据通常也包含较大的误差。因此，使用计算技术似乎是不可避免的。我们已经在四个隔室中构建了硅藻 Thalassiosira pseudonana 中硅动力学的数学模型：外部环境、细胞质、SDV 和沉积的二氧化硅。该模型基于质量守恒和米氏-门捷列夫动力学作为质量传输方程。为了从稀疏、嘈杂的实验数据中找到模型的自由参数，已经应用了一种优化技术（全局和局部搜索），以及与酶相关的惩罚项。我们将群体水平的数据与个体细胞水平的数量联系起来，包括非同步细胞早期分裂的影响。我们的模型是稳健的，通过灵敏度和扰动分析得到证明，并预测了不同隔室中细胞内营养物质和酶的动力学。该模型产生了不同的摄取模式，之前被认为是脉冲、外部控制和内部控制的摄取。最后，我们将 SIT 的通量施加到模型中，并将其与之前的经典动力学进行了比较。所引入的模型可以通过切换质量传输方程系统来推广，以分析不同的生物矿化生物和测试不同的化学途径。
