Jin Wang, Shah Esha T, Penington Catherine J, McCue Scott W, Maini Philip K, Simpson Matthew J
School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, Australia.
Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK.
Bull Math Biol. 2017 May;79(5):1028-1050. doi: 10.1007/s11538-017-0267-4. Epub 2017 Mar 23.
Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell monolayer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch assays. These models typically include a logistic source term to describe carrying capacity-limited proliferation; however, the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the time evolution of the cell density away from the location of the scratch reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. Our findings suggest that the logistic growth model is valid for the entire duration of the proliferation assay. On the other hand, guided by data, we suggest that there are two phases of proliferation in a scratch assay; at short time, we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. These two phases are observed across a large number of experiments performed at different initial cell densities. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.
划痕实验用于研究细胞单层被划伤后，一群细胞如何重新定殖二维基质上的空白区域。这些实验被用于许多应用中，包括癌症和慢性伤口治疗的药物设计。为了深入了解驱动划痕实验的机制，连续反应扩散模型的解已根据划痕实验数据进行了校准。这些模型通常包括一个逻辑源项来描述承载能力限制下的增殖；然而，使用逻辑源项的选择往往未经检验其有效性就做出了。在这里，我们研究了PC-3前列腺癌细胞在划痕实验中的增殖情况。将划痕实验的所有实验结果与细胞单层未划伤的增殖实验的等效结果进行了比较。对远离划痕位置的细胞密度随时间演变的目视检查揭示了一系列S形曲线，这些曲线可能会被天真地校准为逻辑增长模型的解。然而，对人均增长率作为密度函数的仔细分析揭示了划痕实验和增殖实验中细胞增殖之间的几个关键差异。我们的研究结果表明，逻辑增长模型在增殖实验的整个持续时间内都是有效的。另一方面，在数据的指导下，我们认为划痕实验中有两个增殖阶段；在短时间内，我们有一个干扰阶段，此时增殖不是逻辑增长的，随后是一个生长阶段，此时增殖似乎是逻辑增长的。在不同初始细胞密度下进行的大量实验中都观察到了这两个阶段。总体而言，我们的研究表明，简单地将连续模型的解校准到划痕实验可能会产生误导性的参数估计，并且通过区分干扰阶段和生长阶段可以解决这个问题。对其他划痕实验重复我们的过程将有助于深入了解干扰阶段和生长阶段在不同细胞系以及在不同基质上进行的划痕实验中的作用。
