A theoretical framework to study the influence of electrical fields on mesenchymal stem cells

Abstract

2Mesenchymal stem cell dynamics involves cell proliferation and cell differentiation into cells 3 of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically 4 active implants influence these dynamics for the regeneration of the cells in damaged tissues. 5 How applied electric field influences processes of individual stem cells is a problem mostly 6 unaddressed. The mathematical approaches to study stem cell dynamics have focused on the 7 stem cell population as a whole, without resolving individual cells and intracellular processes. 8 In this paper, we present a theoretical framework to describe the dynamics of a population of 9 stem cells, taking into account the processes of the individual cells. We study the influence 10 of the applied electric field on the cellular processes. We test our mean-field theory with the 11 experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that 12 a simple model can quantitatively describe the experimentally observed time-course behavior of 13 the total number of cells and the total alkaline phosphate activity in a population of mesenchymal 14 stem cells. Our results show that the stem cell differentiation rate is dependent on the applied 15 electrical field, confirming published experimental findings. Moreover, our analysis supports the 16 cell density-dependent proliferation rate. Since the experimental results are averaged over many 17 cells, our theoretical framework presents a robust and sensitive method for determining the effect 18 of applied electric fields at the scale of the individual cell. These results indicate that the electric 19 field stimulation may be effective in promoting bone regeneration by accelerating osteogenic 20 differentiation. 21 Human mesenchymal stem cells (hMSCs) possess a unique capability of self-renewal and differentiation 23 into cells of various types of tissues, such as bone, cartilage, and adipose. Thus the hMSCs are the promising 24 cell types for regenerative medicine and tissue engineering. The gene expression levels of an hMSC are 25 known to be the decisive regulators of hMSCs differentiation. These gene expression levels might be 26 influenced by both cell internal cues [De-Leon and Davidson (2007); Ralston (2008)] and external cues Experimental studies [Mousavi and Hamdy Doweidar (2015)] have shown that the in vitro differentiation 29 of hMSC into cells of distinct functional types can be controlled by external factors. Therefore, stem cell 30 differentiation mediated by external factors is a compelling approach that has led to the development of 31 bio-implants, for clinical applications in regenerative medicine. 32The applied electric field (EF) is one of the proven external factors known to influence hMSCs dynamics 33 such as migration [Funk (2015); Banks et al. (2015); Ciombor and Aaron (1993); Schemitsch and Kuzyk 34 (2009)], elongation [Rajnicek et al. (2008); Tandon et al. (2009)], proliferation [Sun et al. (2009); Hartig 35 et al. (2000); Ki...