Department of Mathematics, University of California, Riverside, CA, United States of America.
Department of Mathematics, Lafayette College, Easton, PA, United States of America.
J Theor Biol. 2023 Feb 21;559:111377. doi: 10.1016/j.jtbi.2022.111377. Epub 2022 Dec 5.
The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously. Each design is tested on data generated from the Lotka-Volterra model with noise added, to determine efficacy in an ideal sense. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model - i.e., its ability to fit data for initial ratios other than those to which it was calibrated - is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.
Lotka-Volterra 模型被广泛用于模拟两种生物之间的相互作用。在这里，我们生成了模拟两种肿瘤细胞系之间竞争、互利和拮抗相互作用的合成数据，然后使用 Lotka-Volterra 模型推断相互作用类型。Lotka-Volterra 模型的结构可识别性得到了确认，并针对三种实验设计评估了其实用可识别性：(a) 使用单个数据集，同时观察两种细胞系随时间的混合；(b) 顺序设计，其中使用每种细胞系单独培养的实验数据来估计增长率和承载能力，然后从涉及两种细胞系混合的实验中估计相互作用参数；(c) 平行实验设计，其中所有模型参数都拟合到两个混合物（包含两种细胞系，但初始比例不同）的数据中。每个设计都在添加噪声的 Lotka-Volterra 模型生成的数据上进行测试，以确定理想意义上的有效性。除了评估每个设计的实用可识别性外，我们还研究了模型的预测能力——即它拟合初始比例与校准比例不同的数据的能力——如何受到实验设计选择的影响。并行校准程序被发现是最优的，并进一步在基于空间分辨细胞自动机模型生成的虚拟数据上进行了测试，该模型考虑了氧气消耗，并允许两种细胞系之间相互作用的强度水平发生变化。我们使用这项研究来强调在使用空间平均 Lotka-Volterra 模型进行校准并与空间分辨细胞自动机模型生成的数据进行比较时，必须谨慎解释参数估计，因为在 CA 模型中对空间和资源的基线竞争可能导致用于生成 CA 数据的相互作用类型与推断的相互作用类型之间存在差异 LV 模型。
