Boundedness of solutions of a non-local reaction–diffusion model for adhesion in cell aggregation and cancer invasion
Boundedness of solutions of a non-local reaction–diffusion model for adhesion in cell aggregation and cancer invasion
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细胞聚集和癌症侵袭中粘附的非局部反应扩散模型解的有界性
DOI：
10.1017/s0956792508007742
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发表时间：
2009
影响因子：
1.9
通讯作者：
K. Painter
中科院分区：
文献类型：
--
作者：
J. Sherratt;S. A. Gourley;N. Armstrong;K. Painter
细胞之间及其环境之间的粘连是许多生物过程的重要调节因素，但事实证明，很难将其纳入连续统数学模型。本文进一步发展了Armstrong等人提出的新的建模方法。(细胞-细胞黏附模型的连续体方法，J.Theor。比奥尔。243：98-113,2006)。本文所研究的模型使用了细胞行为的积分-偏微分方程式，其中积分表示细胞对其局部环境的感知。这使得能够有效地表示细胞-细胞黏附以及随机细胞运动和细胞增殖。作者使用这种建模方法来研究细胞-细胞黏附在细胞聚集过程中产生空间模式的能力。该模型还被扩展以给出一种新的肿瘤生长表示，其解反映了细胞-细胞和细胞-基质黏附在调节肿瘤侵袭中的平衡。这些模型中的非局域项意味着没有标准的理论可以推导出生物现实主义所需的有界性：具体地说，细胞密度的解必须介于零和与紧密细胞堆积对应的正密度之间。在这里，作者得到了一些条件，每个条件对于所需的有界性是充分的，并且他们数值地证明了对于某些不满足这些条件的参数集，胞元密度增加到上界以上。最后，作者概述了他们认为未来在这类模型的有界性方面所面临的主要数学挑战。
Adhesion of cells to one another and their environment is an important regulator of many biological processes but has proved difficult to incorporate into continuum mathematical models. This paper develops further the new modelling approach proposed by Armstrong et al. (A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243: 98–113, 2006). The models studied in the present paper use an integro-partial differential equation for cell behaviour, in which the integral represents the sensing by cells of their local environment. This enables an effective representation of cell–cell adhesion, as well as random cell movement, and cell proliferation. The authors use this modelling approach to investigate the ability of cell–cell adhesion to generate spatial patterns during cell aggregation. The model is also extended to give a new representation of cancer growth, whose solutions reflect the balance between cell–cell and cell–matrix adhesion in regulating cancer invasion. The non-local term in these models means that there is no standard theory from which one can deduce the boundedness required for biological realism: specifically, solutions for cell density must lie between zero and a positive density corresponding to close cell packing. Here the authors derive a number of conditions, each of which is sufficient for the required boundedness, and they demonstrate numerically that cell density increases above the upper bound for some parameter sets not satisfying these conditions. Finally the authors outline what they regard as the main mathematical challenges for future work on boundedness in models of this type.
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影响因子：
2
作者：
Armstrong, Nicola J.;Painter, Kevin J.;Sherratt, Jonathan A.
通讯作者：
Sherratt, Jonathan A.
影响因子：
11.2
作者：
Frieboes, HB;Zheng, X;Cristini, V
通讯作者：
Cristini, V
DOI：
--
发表时间：
2004
期刊：
--
影响因子：
--
作者：
J. Dallon;H. Othmer
通讯作者：
J. Dallon;H. Othmer
影响因子：
2.7
作者：
Foty, RA;Steinberg, MS
通讯作者：
Steinberg, MS
DOI：
10.1073/pnas.97.19.10448
发表时间：
2000-09-12
影响因子：
11.1
作者：
Palsson, E;Othmer, HG
通讯作者：
Othmer, HG