细胞粘弹性的分数阶微积分模型比整数阶模型更稳健地量化药物反应和成熟
Fractional calculus modeling of cell viscoelasticity quantifies drug response and maturation more robustly than integer order models
摘要：
最近发现，细胞的粘弹性是反映细胞复杂的生物学状态、功能和功能障碍的固有标志。虽然从许多细胞类型的粘弹性数据中提取模型参数已经成功地使用整数阶机械和幂律粘弹性模型，但仍有一些细胞类型和条件的拟合优度落后。因此，分数阶粘弹性模型已被提出作为更一般和更好地适合于这样的建模。在这项工作中，我们测试这种建议的一般性使用已公布的数据拟合整数阶模型。我们发现，细胞粘弹性数据可以拟合分数阶粘弹性模型在更多的情况下比整数阶。对于巨噬细胞，其是在免疫系统中起作用的白细胞之一，分数阶Kelvin-Voigt模型最好地捕获了药理学干预和细胞的成熟。巨噬细胞的稳态粘度在使用药物细胞松弛素D解聚F-肌动蛋白后降低，并且在使用Blebbistatin分解肌球蛋白II后也降低。当用细菌衍生的化学引诱物处理巨噬细胞时，稳态粘度降低。有趣的是，稳态粘度和弹性模量随着细胞变得成熟和接近衰老而逐渐改变。总之，这些结果表明，分数粘弹性建模比整数阶建模更稳健，能够进一步量化细胞功能和功能障碍，具有潜在的诊断和治疗应用，特别是在癌症和免疫系统功能障碍的情况下。
英文摘要：
It has recently been discovered that the viscoelastic properties of cells are inherent markers reflecting the complex biological states, functions and malfunctions of the cells. Although the extraction of model parameters from the viscoelasticity data of many cell types has been done successfully using integer order mechanical and power-law viscoelastic models, there are some cell types and conditions where the goodness of fits falls behind. Thus, fractional order viscoelastic models have been proposed as more general and better suited for such modeling. In this work, we test such proposed generality using published data already fitted by integer order models. We find that cell viscoelasticity data can be fitted using fractional order viscoelastic models in more situations than integer order. For macrophages, which are among the white blood cells that function in the immune system, the fractional order Kelvin-Voigt model best captures pharmacological interventions and maturation of the cells. The steady state viscosity of macrophages decreases following depolymerization of F-actin using the drug cytochalasin D, and also decreases following myosin II breakdown using Blebbistatin. When macrophages are treated with a bacterium-derived chemoattractant, the steady state viscosity decreases. Interestingly, both the steady state viscosity and elastic modulus are progressively altered as the cells become mature and approach senescence. Taken together, these results show that fractional viscoelastic modeling, more robustly than integer order modeling, enables the further quantification of cell function and malfunction, with potential diagnostic and therapeutic applications especially in cases of cancer and immune system dysfunctions.
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