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A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge 'soakage' is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge 'soakage') have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell's equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.

Changes in expression and localization of proteins that regulate cell and tissue polarity are frequently observed in carcinoma. However, the mechanisms by which changes in cell polarity proteins regulate carcinoma progression are not well understood. Here, we report that loss of polarity protein expression in epithelial cells primes them for cooperation with oncogenes or changes in tissue microenvironment to promote invasive behavior. Activation of ErbB2 in cells lacking the polarity regulators Scribble, Dlg1 or AF-6, induced invasive properties. This cooperation required the ability of ErbB2 to regulate the Par6/aPKC polarity complex. Inhibition of the ErbB2-Par6 pathway was sufficient to block ErbB2-induced invasion suggesting that two polarity hits may be needed for ErbB2 to promote invasion. Interestingly, in the absence of ErbB2 activation, either a combined loss of two polarity proteins, or exposure of cells lacking one polarity protein to cytokines IL-6 or TNFα induced invasive behavior in epithelial cells. We observed the invasive behavior only when cells were plated on a stiff matrix (Matrigel/Collagen-1) and not when plated on a soft matrix (Matrigel alone). Cells lacking two polarity proteins upregulated expression of EGFR and activated Akt. Inhibition of Akt activity blocked the invasive behavior identifying a mechanism by which loss of polarity promotes invasion of epithelial cells. Thus, we demonstrate that loss of polarity proteins confers phenotypic plasticity to epithelial cells such that they display normal behavior under normal culture conditions but display aggressive behavior in response to activation of oncogenes or exposure to cytokines.