Regression models for the prediction of the influence of magnesium ions on primary endothelial cell (HUVEC) proliferation and migration

Abstract

Angiogenesis is one of the first stages in fracture healing and bone repair. Therefore, numerous studies evaluating the effect of Mg as a promising degradable, metallic biomaterial on the proliferation and function of endothelial cells have been performed. However, these studies lack methodological homogeneity and therefore differ in fundamental conclusions. Here, Mg-concentration-, donor- and cell age- dependent relations to primary human umbilical cord vein endothelial cells (HUVEC) proliferation and migration were investigated systematically. The generated data were utilized to develop regression models in order to assess and predict the cell response on Mg exposition in a concentration range of 2-20 mM Mg in cell culture medium extract. A concentration of > 2 mM already induced a detrimental effect in the sensitive primary HUVECs. Molecular data quantifying angiogenesis markers supported this finding. An increased migration capacity has been observed at a concentration of 10 mM Mg. We compared linear regression, random forests, support vector machines, neural networks and large language models for the prediction of HUVEC proliferation for a number of scenarios. Using these machine learning methods, we were able to predict the proliferation of HUVECs for missing Mg concentrations and for missing passages with mean absolute errors below 10 % and as low as 8.5 %, respectively. Due to strong differences between the cell behaviour of different donors, information for missing donors can be predicted with mean absolute errors of 15.7 % only. Support vector machines with linear kernel performed best on the tested data, but large language models also showed promising results.

Keywords: Cell proliferation; HUVEC; Large Language Model; Regression models.

Graphical abstract

Fig. 1

Proliferation of HUVEC in % of control for passages 4, 5, 6 and 7 and donor 1 (black), donor 2 (light grey) and donor pool (dark grey) at different Mg concentrations. The red dashed line indicates 75 %.

Fig. 2

Example of microscopic images of the scratch test for HUVECs (donor 1, passage 7) subjected to different Mg concentrations. The area outlined in green is the cell-free area based on which the wound closure is computed.

Fig. 3

Wound area closure in % over 9 h to display HUVEC migration for passages 4, 5, 6 and 7 and donor 1, donor 2 and donor pool at different Mg concentrations.

Fig. 4

Mean absolute error (MAE) for test data for cases (I)-(v), with case (iv) divided per predicted passage. The results are given as mean ± standard deviation for all regression models tested: support vector regression (SVR – with linear or rbf kernel), random forest regression (RFR), linear regression (LR), neural networks (ANN) and the large language models GPT-4o and o4-mini. additionally, we introduce two simple baseline methods: label averaging, which predicts each missing label as the average of the corresponding labels in the training data; and data averaging, which uses only the available data from the current sample to predict missing values by averaging the preceding and succeeding concentrations or passages.

Fig. 5

Experimental data (black) and prediction from the best linear kernel SVR (dark gray) and LLM GPT-4o (light gray) for the passages tested in case (iv) of the regression of HUVEC proliferation. The red dashed line indicates 75 %.