Biological cell-electrical field interaction: stochastic approach

Abstract

The present work demonstrates how a stochastic model can be implemented to obtain a realistic description of the interaction of a biological cell with an external electric field. In our model formulation, the stochasticity is adopted by introducing various levels of forcing intensities in model parameters. The presence of noise in nuclear membrane capacitance has the most significant effect on the current flow through a biological cell. A plausible explanation based on underlying physics and biological structure of the nuclear membrane is proposed to explain such results.

Keywords: Biological cell; E-field; Micro-organelles; Stochasticity.

Fig. 1

Schematic of the macroscopic view of the passage of electrical current through multiple cells, dispersed in extracellular matrix (ECM)

Fig. 2

The electrical analog circuit of a single cell, placed in an electric field

Fig. 3

Plot of i(t) against time for fixed , and different forcing intensities for σ₃ and σ₄, bσ₃ = 0.025, , cσ₃ = 0.015, , dσ₃ = 0.005, . For comparison, the deterministic values of i(t) are plotted in a

Fig. 4

Plot of i(t) before reaching the time constant values for four different numerical runs with forcing intensities , , σ₃ = 0.025,

Fig. 5

Plot of time constant for stochastic case at different forcing intensities on η (for different values of σ₄ as mentioned in the scale of horizontal axis). Numerical simulations are performed for the parametric values , , ζ₀ = 11.58, η₀ = 4728230 and fixed forcing intensities , and σ₃ = 0.025

Fig. 6

Plot of maximum values attained by i(t) at different forcing intensities σ₄, and all other parameter values are same as mentioned in the caption of Fig. 5

Fig. 7

Plot of minimum values attained by i(t) at different forcing intensities σ₄, these minimum values are obtained from the numerical simulations carried out for Fig. 6

Fig. 8

Plot of mean of i(t), obtained from 100 simulation runs of (8) and (12) for parametric values , , ζ₀ = 11.58, η₀ = 4,728,230 and fixed forcing intensities , , σ₃ = 0.015 and

Fig. 9

Plot of standard deviation of i(t), obtained from 100 simulation runs of (8) and (12) for parametric values as mentioned in the caption of Fig. 7