Mathematical Modeling of Calcium Waves Induced by Mechanical Stimulation in Keratinocytes

Abstract

Recent studies have shown that the behavior of calcium in the epidermis is closely related to the conditions of the skin, especially the differentiation of the epidermal keratinocytes and the permeability barrier function, and therefore a correct understanding of the calcium dynamics is important in explaining epidermal homeostasis. Here we report on experimental observations of in vitro calcium waves in keratinocytes induced by mechanical stimulation, and present a mathematical model that can describe the experimentally observed wave behavior that includes finite-range wave propagation and a ring-shaped pattern. A mechanism of the ring formation hypothesized by our model may be related to similar calcium propagation patterns observed during the wound healing process in the epidermis. We discuss a possible extension of our model that may serve as a tool for investigating the mechanisms of various skin diseases.

Sustained dynamics of a weakly excitable system with nonlocal interactions

“…Also note that the cells inside the wave front have the same activity. In 2D continuous systems this would be a disk-shaped wave pattern propagating within a finite distance, which has been observed in calcium dynamics of epidermis and also theoretically investigated [22]. …”

“…In epidermis, the propagation range of calcium waves in epidermal cells depends on stimulation intensity, and sustained local excitations are also observed when strong stimulation is given [22]. On the other hand, the nerve fibers do behave as usual excitable systems.…”

“…Therefore, in our model it would be both uninteresting and unrealistic to consider too large propagation ranges, while the cases of short propagation ranges might be responsible for sustained sensation observed in pathological epidermal systems [23], where the density of nerve fibers is not necessarily large but many branchings are found [24], which provide places for axon reflexes and thereby yield many nonlocal connections. Indeed, as a more realistic model of epidermal systems it is possible to construct a continuous version of the present model, incorporating a model of calcium propagation in the epidermis [22].…”

Model for calcium-mediated reduction of structural fluctuations in epidermis

“…A normal differentiation process is represented by α, and when calcium exists, differentiation is accelerated by a factor β [7]. Calcium dynamics obeys the diffusion equation with decay, which accounts for experimental observations that calcium waves in the epidermis propagate only within a finite range [5,[8][9][10]. The source of calcium ions, which is represented by the δ function, is considered to be located along the upper interface z = h(x,t), according to an experimental finding that sustained calcium excitation occurs around dead cells, which might account for the calcium localization layer beneath the SC [11].…”

“…Motivated by these observations, we have recently proposed a mathematical model of the epidermis, which has revealed that calcium dynamics can stabilize the structure of the SC [5,6]. This model was based on particle dynamics for cell movements and reactiondiffusion process for calcium dynamics, where individual cells are assigned the degree of differentiation as an inner variable, which is affected by calcium dynamics.…”