Rasolonjanahary Manan'Iarivo, Vasiev Bakhtier
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
J Theor Biol. 2016 Sep 7;404:109-119. doi: 10.1016/j.jtbi.2016.05.035. Epub 2016 May 31.
Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns.
多细胞生物的发育通常与单个细胞对称为形态发生素的化学物质浓度的反应相关。形态发生素的浓度场构成了生物模式形成的基础，并确保其特性，包括与生物体大小成比例的能力。虽然形态发生素梯度形成的潜在机制已得到较好的理解，但对其比例缩放的相关过程却知之甚少。在这里，我们对连续系统中形成的化学模式的比例缩放进行了形式分析。我们引入一个表示系统对其大小变化敏感性的量，并使用它来分析在几个不同系统中形成的模式的比例缩放特性。特别是，我们考虑在扩散 - 衰减系统中形成的形态发生素梯度的比例缩放特性如何依赖于边界条件，以及如何通过系统中形态发生素的被动调制或主动运输来改善比例缩放。我们还分析了由两个相反梯度引起的形态发生信号的比例缩放，并考虑了激活剂 - 抑制剂系统中形成的模式的比例缩放特性。我们最后得出了一些允许形态发生模式进行比例缩放的可能机制。
