The development of particokinetic models describing the delivery of insoluble or poorly soluble nanoparticles to cells in liquid cell culture systems has improved the basis for dose-response analysis, hazard ranking from high-throughput systems, and now allows for translation of exposures across in vitro and in vivo test systems. Complimentary particokinetic models that address processes controlling delivery of both particles and released ions to cells, and the influence of particle size changes from dissolution on particle delivery for cell-culture systems would help advance our understanding of the role of particles and ion dosimetry on cellular toxicology. We developed ISD3, an extension of our previously published model for insoluble particles, by deriving a specific formulation of the Population Balance Equation for soluble particles. ISD3 describes the time, concentration and particle size dependent dissolution of particles, their delivery to cells, and the delivery and uptake of ions to cells in in vitro liquid test systems. We applied the model to calculate the particle and ion dosimetry of nanosilver and silver ions in vitro after calibration of two empirical models, one for particle dissolution and one for ion uptake. Total media ion concentration, particle concentration and total cell-associated silver time-courses were well described by the model, across 2 concentrations of 20 and 110 nm particles. ISD3 was calibrated to dissolution data for 20 nm particles as a function of serum protein concentration, but successfully described the media and cell dosimetry time-course for both particles at all concentrations and time points. We also report the finding that protein content in media affects the initial rate of dissolution and the resulting near-steady state ion concentration in solution for the systems we have studied. By combining experiments and modeling, we were able to quantify the influence of proteins on silver particle solubility, determine the relative amounts of silver ions and particles in exposed cells, and demonstrate the influence of particle size changes resulting from dissolution on particle delivery to cells in culture. ISD3 is modular and can be adapted to new applications by replacing descriptions of dissolution, sedimentation and boundary conditions with those appropriate for particles other than silver.

中文翻译：

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ISD3：一种粒子动力学模型，用于预测颗粒沉降、扩散和溶解对体外系统细胞剂量测定的综合影响。

描述不溶性或难溶性纳米颗粒向液体细胞培养系统中的细胞的递送的粒子动力学模型的开发改进了剂量反应分析、高通量系统的危险等级的基础，并且现在允许在体外和体外的暴露转换体内测试系统。互补的粒子动力学模型解决了控制颗粒和释放离子向细胞输送的过程，以及溶解引起的粒径变化对细胞培养系统颗粒输送的影响，将有助于加深我们对颗粒和离子剂量测定在细胞毒理学中的作用的理解。我们通过推导可溶性颗粒群体平衡方程的特定公式，开发了 ISD3，它是我们之前发布的不溶性颗粒模型的扩展。ISD3 描述了体外液体测试系统中颗粒的时间、浓度和粒径依赖性溶解、颗粒向细胞的递送以及离子向细胞的递送和摄取。在校准两个经验模型（一个用于颗粒溶解，一个用于离子吸收）后，我们应用该模型计算体外纳米银和银离子的颗粒和离子剂量测定。该模型很好地描述了 20 和 110 nm 颗粒的 2 个浓度的总介质离子浓度、颗粒浓度和总细胞相关银时间过程。ISD3 被校准为 20 nm 颗粒的溶出数据，作为血清蛋白浓度的函数，但成功描述了两种颗粒在所有浓度和时间点的介质和细胞剂量测定时间过程。我们还报告了这样的发现：介质中的蛋白质含量影响我们所研究的系统的初始溶解速率以及溶液中所产生的接近稳态的离子浓度。通过结合实验和建模，我们能够量化蛋白质对银颗粒溶解度的影响，确定暴露细胞中银离子和颗粒的相对量，并证明溶解引起的颗粒尺寸变化对颗粒递送至细胞的影响。文化。ISD3 是模块化的，可以通过用适用于银以外的颗粒的描述替换溶解、沉降和边界条件的描述来适应新的应用。