确定细胞尺度过程如何导致组织尺度模式是理解激素和形态发生原如何在生物组织内分布和控制发育过程的关键。在这篇文章中,我们使用多尺度渐近分析得出长细胞中激素转运的连续近似,以确定亚细胞区室和细胞生长和分裂如何影响组织尺度激素转运.把我们的研究重点放在植物组织上,我们首先提出了一个离散的多细胞ODE模型,跟踪每个细胞的细胞质中的激素浓度,亚细胞液泡,和周围的质外体,由单元格文件几何体中的单独隔室表示。我们允许细胞以依赖于空间和时间的速度生长,考虑细胞质和液泡扩张。多尺度渐近分析使我们能够系统地推导相应的连续模型,获得了有效的反应-对流-扩散方程,并揭示了有效扩散系数,有效平流速度,有效汇项取决于细胞尺度模型中的参数。连续体近似揭示了亚细胞区室,比如空泡,可以充当储存容器,显著改变了激素转运的有效特性,如有效扩散率和诱导有效速度。此外,我们展示了细胞生长和跨细胞长度的空间方差如何影响有效扩散率和诱导的有效速度,以及这些如何影响组织规模的激素分布。特别是,我们发现细胞生长自然诱导生长方向的有效速度,而跨细胞长度的空间差异由于额外隔室的存在而诱导有效速度,如质外体和液泡,以及跨单元格文件的隔室之间的相对大小的变化。揭示了激素在长度减少的细胞中的转运比长度增加的细胞更快。我们还研究了细胞分裂对运输动力学的影响,假设每个细胞一旦大小加倍就会分裂,发现增加连续细胞分裂之间的时间会降低生长速率,这增强了细胞分裂在减缓激素运输中的作用。由于最近的实验发现,我们讨论了赤霉酸(GA)转运的特殊应用,一种重要的生长激素,在拟南芥根内。该模型精确揭示了介导促进GA转运的膜蛋白如何影响有效的组织尺度转运。然而,结果足够普遍,与其他植物激素相关,或以类似方式在任何类型的细胞中运输的其他物质。
Determining how cell-scale processes lead to tissue-scale patterns is key to understanding how hormones and morphogens are distributed within biological tissues and control developmental processes. In this article, we use multiscale asymptotic analysis to derive a continuum approximation for hormone transport in a long file of cells to determine how subcellular compartments and cell growth and division affect tissue-scale hormone transport. Focusing our study on plant tissues, we begin by presenting a discrete multicellular ODE model tracking the hormone concentration in each cell\'s cytoplasm, subcellular vacuole, and surrounding apoplast, represented by separate compartments in the cell-file geometry. We allow the cells to grow at a rate that can depend both on space and time, accounting for both cytoplasmic and vacuolar expansion. Multiscale asymptotic analysis enables us to systematically derive the corresponding continuum model, obtaining an effective reaction-advection-diffusion equation and revealing how the effective diffusivity, effective advective velocity, and the effective sink term depend on the parameters in the cell-scale model. The continuum approximation reveals how subcellular compartments, such as vacuoles, can act as storage vessels, that significantly alter the effective properties of hormone transport, such as the effective diffusivity and the induced effective velocity. Furthermore, we show how cell growth and spatial variance across cell lengths affect the effective diffusivity and the induced effective velocity, and how these affect the tissue-scale hormone distribution. In particular, we find that cell growth naturally induces an effective velocity in the direction of growth, whereas spatial variance across cell lengths induces effective velocity due to the presence of an extra compartment, such as the apoplast and the vacuole, and variations in the relative sizes between the compartments across the file of cells. It is revealed that hormone transport is faster across cells of decreasing lengths than cells with increasing lengths. We also investigate the effect of cell division on transport dynamics, assuming that each cell divides as soon as it doubles in size, and find that increasing the time between successive cell divisions decreases the growth rate, which enhances the effect of cell division in slowing hormone transport. Motivated by recent experimental discoveries, we discuss particular applications for transport of gibberellic acid (GA), an important growth hormone, within the Arabidopsis root. The model reveals precisely how membrane proteins that mediate facilitated GA transport affect the effective tissue-scale transport. However, the results are general enough to be relevant to other plant hormones, or other substances that are transported in a similar way in any type of cells.