Collective behavior of brain tumor cells: The role of hypoxia

Evgeniy Khain, Mark Katakowski, Scott Hopkins, Alexandra Szalad, Xuguang Zheng, Feng Jiang, and Michael Chopp

Phys. Rev. E 83, 031920 – Published 29 March 2011

Abstract

We consider emergent collective behavior of a multicellular biological system. Specifically, we investigate the role of hypoxia (lack of oxygen) in migration of brain tumor cells. We performed two series of cell migration experiments. In the first set of experiments, cell migration away from a tumor spheroid was investigated. The second set of experiments was performed in a typical wound-healing geometry: Cells were placed on a substrate, a scratch was made, and cell migration into the gap was investigated. Experiments show a surprising result: Cells under normal and hypoxic conditions have migrated the same distance in the “spheroid” experiment, while in the “scratch” experiment cells under normal conditions migrated much faster than under hypoxic conditions. To explain this paradox, we formulate a discrete stochastic model for cell dynamics. The theoretical model explains our experimental observations and suggests that hypoxia decreases both the motility of cells and the strength of cell-cell adhesion. The theoretical predictions were further verified in independent experiments.

Received 2 July 2010

DOI:https://doi.org/10.1103/PhysRevE.83.031920

Authors & Affiliations

Evgeniy Khain¹, Mark Katakowski², Scott Hopkins¹, Alexandra Szalad², Xuguang Zheng², Feng Jiang², and Michael Chopp^1,2

¹Department of Physics, Oakland University, Rochester, Michigan 48309, USA
²Department of Neurology, Henry Ford Hospital, Detroit, Michigan 48202, USA

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Vol. 83, Iss. 3 — March 2011

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Images

Figure 1
U87 glioma cell proliferation on a substrate: cell number as a function of time. Symbols show experimental results for cell proliferation under normoxic (circles) and hypoxic (squares) conditions. A theoretical fit given by Eq. (1) for the two expressions for $α (u)$ : $α_{1} (u)$ , $β = 1.73$ , solid lines and $α_{2} (u)$ , $ν = 6$ , dashed lines. The parameters are $u_{0} = 0.14$ , $α = 1 / 29$ hour $^{- 1}$ (upper solid line) and $α = 1 / 53$ hour $^{- 1}$ (lower solid line); $u_{0} = 0.14$ , $α = 1 / 29$ hour $^{- 1}$ (upper dashed line) and $α = 1 / 50$ hour $^{- 1}$ (lower dashed line).Reuse & Permissions
Figure 2
U87 glioma cell migration away from a tumor spheroid. The upper panel shows the invasive radius as a function of time for both normoxic (dashed line, squares) and hypoxic (dotted line, circles) cells; the results are averaged over $4$ sets of experiments. The lower panel shows a snapshot of the system kept under hypoxic conditions (view from above) $60$ hours after beginning of the experiment; the outer circle shows the borders of invasive region; the invasive radius here is approximately $1200$ $μ$ m.Reuse & Permissions
Figure 3
U87 glioma cell migration on a substrate: closing the scratch. Initially cells were uniformly placed on a plastic substrate, and a $2$ -mm-wide scratch was made (upper panel). The lower panel shows a snapshot of the system $24$ hours after the beginning of the experiment, under normoxic conditions. We measured the distance that cells had migrated in $24$ hours for both normoxic and hypoxic cells. Averaging over many experimental runs and over the lateral coordinate shows that normoxic cells have migrated $1.02 \pm 0.21$ mm, and hypoxic cells have migrated $0.73 \pm 0.14$ mm.Reuse & Permissions
Figure 4
Constant distance curves $r (t_{diff}, q) = r_{\exp}$ obtained from numerical simulations of the discrete stochastic model. The distance that the cells have migrated depends on two parameters: the diffusion time $t_{diff}$ and the adhesion parameter $q$ . Shown are four constant distance curves $r = r_{\exp}$ , which correspond to spheroid (dotted lines) and scratch (solid lines) experiments for normoxic (upper panel) and hypoxic (lower panel) cells. The region of probable intersection between the two curves in each panel (shown by circles) determines the cell parameters: $t_{diff}$ and $q$ . Comparing the two regions, one can see that $t_{diff}^{norm} < t_{diff}^{hyp}$ and $q_{norm} > q_{hyp}$ . The experimental parameters are $r_{\exp} = 1.30$ mm for spheroid experiments for both normoxic and hypoxic cells (Fig. 2); for the scratch experiment (Fig. 3) $r_{\exp} = 1.02$ mm and $r_{\exp} = 0.73$ mm for normoxic and hypoxic cells, respectively.Reuse & Permissions

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