General two-species interacting Lotka-Volterra system: Population dynamics and wave propagation

A cell model about symmetric and asymmetric stem cell division

We construct a multi-stage cell lineage model including self-renewal, apoptosis, cell movement and the symmetrical/asymmetrical division of stem cells. The evolution of cell populations can be described by coupled reaction-diffusion partial differential equations, and the propagating wavefront speeds can be obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effect of symmetric/asymmetric division of stem cells on the population and propagating dynamics of cell lineage. It is found that stem cells' asymmetric cell division (ACD) can move the phase boundary of the homogenous solution of the system. The population of the cell lineage will be promoted in presence of ACD. The concentration of stem cells increases with ACD but that of differentiated daughter cells decreases with ACD. In addition, it is found that the propagating speed of the stem cells can be evaluated with ACD. When the daughter cells move fast to a new space, stem cells can catch them up through increasing ACD. Our results may suggest a mechanism of collective migration of cell lineage through cooperation between ACD of stem cells and fast diffusion of the daughter cells.

Regulatory feedback effects on tissue growth dynamics in a two-stage cell lineage model

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signaling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the nontrivial fixed point and the trivial fixed point, respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic timescales for these two growth modes are also derived. Remarkably, the trivial and nontrivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bistable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

Potential Osteoinductive Effects of Hydroxyapatite Nanoparticles on Mesenchymal Stem Cells by Endothelial Cell Interaction

Nano-hydroxyapatite (nano-HA) has attracted substantial attention in the field of regenerative medicine. Endothelial cell (EC)-mesenchymal stem cell (MSC) interactions are necessary for bone reconstruction, but the manner in which nano-HA interacts in this process remains unknown. Herein, we investigated the cytotoxicity and osteoinductive effects of HA nanoparticles (HANPs) on MSCs using an indirect co-culture model mediated by ECs and highlighted the underlying mechanisms. It was found that at a subcytotoxic dose, HANPs increased the viability and expression of osteoblast genes, as well as mineralized nodules and alkaline phosphatase production of MSCs. These phenomena relied on HIF-1α secreted by ECs, which triggered the ERK1/2 signaling cascade. In addition, a two-stage cell-lineage mathematical model was established to quantitatively analyze the impact of HIF-1α on the osteogenic differentiation of MSCs. It demonstrated that HIF-1α exerted a dose-dependent stimulatory effect on the osteogenic differentiation rate of MSCs up to 1500 pg/mL, which was in agreement with the above results. Our data implied that cooperative interactions between HANPs, ECs, and MSCs likely serve to stimulate bone regeneration. Furthermore, the two-stage cell-lineage model is helpful in vitro system for assessing the potential influence of effector molecules in bone tissue engineering.