A bioelectric model of carcinogenesis, including propagation of cell membrane depolarization and reversal therapies

Abstract

As the main theory of carcinogenesis, the Somatic Mutation Theory, increasingly presents difficulties to explain some experimental observations, different theories are being proposed. A major alternative approach is the Tissue Organization Field Theory, which explains cancer origin as a tissue regulation disease instead of having a mainly cellular origin. This work fits in the latter hypothesis, proposing the bioelectric field, in particular the cell membrane polarization state, and ionic exchange through ion channels and gap junctions, as an important mechanism of cell communication and tissue organization and regulation. Taking into account recent experimental results and proposed bioelectric models, a computational model of cancer initiation was developed, including the propagation of a cell depolarization wave in the tissue under consideration. Cell depolarization leads to a change in its state, with the activation and deactivation of several regulation pathways, increasing cell proliferation and motility, changing its epigenetic state to a more stem cell-like behavior without the requirement of genomic mutation. The intercellular communication via gap junctions leads, in certain circumstances, to a bioelectric state propagation to neighbor cells, in a chain-like reaction, till an electric discontinuity is reached. However, this is a reversible process, and it was shown experimentally that, by implementing a therapy targeted on cell ion exchange channels, it is possible to reverse the state and repolarize cells. This mechanism can be an important alternative way in cancer prevention, diagnosis and therapy, and new experiments are proposed to test the presented hypothesis.

Figure 1

(a) Single cell gap junction ionic conductivity as a function of the cell membrane electric potential, as given by Eq. (4), with the parameters used in this work ($V_{1/2}=0$ mV) and the ones used in ($V_{1/2}=-30$ mV). (b) Evolution in time of an isolated cell membrane electric potential for different initial membrane electric potential values. There are two stable points, at $\simeq -2$ mV and $\simeq -57$ mV, with the separation taking place at $\simeq -35$ mV

Figure 2

Tissue depolarization for randomly distributed depolarized cells on a polarized domain. Left: example of the two-dimensional domain polarization state after 10 seconds (yellow corresponds to depolarized cells and blue to polarized ones; the color bar shows the membrane electrical potential in mV). Figure S3 shows the spatial distribution of the depolarized cells at different time points, and Supplementary Movie 3 shows an animation of the system evolution in space and time. Right: evolution of the number of depolarized cells for different percentages of depolarized cells randomly initially distributed on the domain (25%, 27% and 30% of the total number of cells depolarized). The initial decrease on the number of depolarized cells (see Fig. S2 for the same plot in semi-logarithmic scale for a more detailed display of the first time steps) is due to a community effect, where depolarized cells with a high number of polarized neighbors will polarize fast. The bands show the standard deviation of the mean of $n=20$ simulation runs.

Figure 3

Tissue depolarization after the introduction of a patch of depolarized cells on a polarized tissue. Top row: evolution of the number of depolarized cells for different sizes of a square patch, introduced on the top left corner of the domain, with a width of 12, 24, and 36 cells (a), and on the domain center, with a width of 8, 16, and 24 cells (b). Bottom row: evolution of the number of depolarized cells for different sizes of a circular patch, with a radius of 12, 24, and 36 cells, centered on the top left corner of the domain (c), and placed on the domain center, with a radius of 4, 8 and 12 cells (d). The bands show the standard deviation of the mean of $n=20$ simulation runs.

Figure 4

Repolarization therapies. Evolution of the number of depolarized cells for therapies that increase the polarization ion channel conductivity ($G_{\text{pol}}^0$, left) or decrease the depolarization ion channel conductivity ($G_{\text{dep}}^0$, right). Initially all the cells were depolarized. The bands show the standard deviation of the mean of $n=20$ simulation runs.

Figure 5

Parameters sensitivity tests. Top row: evolution of the number of depolarized cells for different values of the cells polarization channel conductivity $G_{\text{pol}}^0$. Bottom row: evolution of the number of depolarized cells for different values of the standard deviation $\sigma$ of the cells’ bioelectric properties. The results are shown for 27% of depolarized cells randomly distributed on the domain at the start of the simulation (left column), and for an initial circular depolarization patch (with $R=8$ cells’ width) at the center of the domain (right column). There is a saturation at 10 k cells, the total number of cells in the domain. The bands show the standard deviation of the mean of $n=20$ simulation runs.

Figure 6

Effect of electrical isolating obstacles. Example of the two-dimensional domain polarization state after 10 seconds (left column, yellow corresponds to depolarized cells and blue to polarized ones) and the evolution of the number of depolarized cells (right column) for a domain with 4 isolating walls (top row, yellow horizontal bands) and with 8 isolating walls (bottom row). Initially all the cells were depolarized and an initial circular depolarized patch, with $R=8$ cells’ width, is placed on the center of the domain. The bands show the standard deviation of the mean of $n=20$ simulation runs.

Figure 7

Community effect. Evolution of the number of depolarized cells for different values of the gap junction conductivity parameter $G_{\text{max}}^0$. The depolarization starts from a random distribution of depolarized cells, 27% of the total (left), or from a circle of depolarized cells, with $R=8$ cells’ width, at the center of the two dimensional domain (right). The bands show the standard deviation of the mean of $n=50$ simulation runs.