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Dose Response. 2010; 8(4): 518–526.
Published online 2010 July 26. doi:  10.2203/dose-response.10-009.Fosslien
PMCID: PMC2990067

Hormetic Electric Field Theory of Pattern Formation

Egil Fosslien, Professor of Pathology (emeritus)


The hormetic morphogen theory of curvature (Fosslien 2009) proposes that hormetic morphogen concentration gradients modulate the synthesis of adenosine triphosphate (ATP) by cells along the gradients (field cells) and thus regulate their proliferation and induce curvature such as vascular wall curvature; however, it is unclear whether such morphogen gradients can also determine the histological pattern of the walls. Here, I propose that the ATP gradients modulate export of H+ by vacuolar H+-ATPase (V-ATPase) located on the surface of field cells and generate extracellular ion concentration gradients, ion currents and electrical fields along the paths of morphogen gradients. In vitro, electrical fields can induce directional migration and elongation of vascular cells and align the cells with their long axis perpendicular to electrical field vectors (Bai et al. 2004). I suggest that likewise, in vivo vascular transmural electrical fields induced by hormetic morphogen concentration gradients can modulate cell shape i.e. cell elongation and cell curvature, and determine cell orientation. Moreover, I suggest that the electrical fields can modulate bidirectional cell migration and cell sorting via dynamic hormetic galvanotaxis analogous to in vitro isoelectric focusing in proton gradients, thus, hormetic morphogen gradients can determine the curvature of vessel walls and their histological patterns.

Keywords: Theoretical biology, hormesis, morphogens, gradients, ion flux, electrical fields, pattern formation


I have proposed (Fosslien 2002) that in vivo concentration gradients of transforming growth factor-beta (TGF-β) can induce tissue curvature by down- and up-regulating proliferation of cells (field cells) along their gradients at high and low concentrations respectively. I have theorized and discussed evidence that indicates that TGF-β can modulate mammalian cell mitochondrial ATP synthesis in a concentration-dependent manner, down- and up-regulating the synthesis of ATP at high and low morphogen concentrations respectively; and I suggested to use the term hormetic morphogen for morphogens such as TGF-β in mammals and IAA in plants that induce hormetic energetic and proliferative responses in their field cells (Fosslien 2008, 2009).

When concentration gradients of a hormetic morphogen such as TGF-β modulate the synthesis of adenosine triphosphate (ATP) of mitochondria of field cells, the ATP levels of each field cell along the morphogen gradients will differ depending upon the concentration of hormetic morphogen to which the individual field cell is exposed. This causes the formation of gradients in the amplitude of field cell synthesis of ATP and corresponding gradients of field cell proliferation along the hormetic morphogen gradients. This differential growth along hormetic morphogen gradients causes the tissue to curve (Fosslien 2009).

Whether and if so how, hormetic morphogen concentration gradients can also determine the histological pattern of curved tissues such as the histology of vascular walls is unclear. In view of the fact that electrical field gradients have been shown to play significant causal roles during developmental pattern formation, I have developed a theory that outlines how hormetic morphogens can induce electrical fields along their concentration gradients. I propose logical, evidence-based but not exclusive mechanisms for generation of electrical fields by hormetic morphogen gradients and theorize that the electrical fields help organize and coordinate pattern formation with curvature formation, and that the electrical fields provide feedback that modulates and stabilizes the effects of hormetic morphogen gradients.


Cellular ATP can drive export of ions such as H+ by vacuolar H+-ATPase (V-ATPase) located in the membranes of the cells. The theory proposes that hormetic morphogen-induced amplitude modulation of field cell ATP synthesis modulates ion export by field cells into the extracellular space.

As an example, in the vasculature, as transmural hormetic morphogen gradients induce transmural ATP gradients that cause gradients of field cell proliferation and thus mural curvature, the hormetic morphogen gradients also cause formation of transmural ATP-driven gradients and thereby gradients of ion export by the mural cells. The extracellular ion gradients cause ion flux along the morphogen gradients, which induces electrical fields along the paths of the morphogen gradient. The electrical fields modulate cell shape, i.e. cell elongation and individual cell curvature, and determine cell orientation. Moreover, the theory proposes that the electrical fields can modulate bidirectional cell migration and cell sorting via dynamic hormetic galvanotaxis/electrotaxis analogous to in vitro isoelectric focusing in proton gradients and provide feedback to adjust field cell responses to hormetic morphogens.

In summary (Fig. 1), the theory predicts that in the vasculature, there is parallel processing of radial gradients of hormetic morphogens, ATP gradients, ion gradients, and radial electrical fields that determine the mural curvature and the mural histology, e.g. the shape and location of the mural cells and other histological structures such as vascular elastic laminas. Evidence in support of the theory is discussed below.

Evidence-based and theoretical illustration of tissue curvature formation and tissue patterning induced by radial gradients of hormetic morphogen: Morphogen concentration-dependent amplitude modulation of adenosine triphosphate (ATP) synthesis in cells ...


Transforming growth factor β (TGF-β) can regulate mammalian cell proliferation, migration, differentiation, and extracellular matrix synthesis by endothelial cells (ECs) and by smooth smuscle cell (SMCs) (Bertolino et al. 2005). In vitro, TGF-β stimulates and inhibits cell proliferation at low and high concentrations respectively (Battegay et al. 1990; Qiu 1995; Fosslien et al. 1997; McAnulty et al. 1997) and in plants the hormone auxin (indolacetic acid, IAA) stimulates and inhibits Avena coleoptile elongation at low and high concentrations respectively (Foster et al. 1952); (Pennazio 2002). These dose-responses are characteristic of hormesis (Calabrese and Baldwin 2001a, b); (Mattson 2007); (Calabrese 2008); (Calabrese and Blain 2009).

Hormetic morphogen, ATP, and curvature

Indoleacetic acid induces hormetic growth elongation of Avena segments, inhibiting and stimulating growth at high and low concentrations respectively (Bonner 1933). The biphasic effects of IAA are consistent with signaling via two-point binding of IAA (Foster et al. 1952), which suggests that IAA like TGF-β may signal via inhibitory and stimulatory pathways. Furthermore, hormetic amplitude modulation of ATP regulation of the adenine nucleotide transporter (ANT) by TGF-β in mammalian cells in principle resembles hormetic modulation of ATP synthesis in plant by IAA via IAA-induced modulation of ADP phosphorylation by mitochondrial ATPase (Fosslien 2008, 2009). Curvature formation in plants in principle resembles curvature formation induced by TGF-β in mammals: IAA unilaterally applied to one side of cut bean internode sections curved the sections toward the application side, indicating that the curvature was induced by IAA migration causing lateral IAA concentration gradients, from high IAA concentrations on the application side to low concentrations on the opposite side. The curvature was proportional to the log concentration of the applied IAA (Bialek et al. 1983]), which suggests that a gradient of exponentially declining IAA concentration could induce a linear growth gradient along its path.

Electrical fields

Electrical fields can orient cell division and regulate cell division rates in vitro and in vivo (Zhao et al. 1999); (Song et al. 2002). The fields can promote or inhibit curvature formation induced by differential growth and induce bi-directional migration, i.e. they can induce biphasic, hormetic responses, and thus, in this paper, I use the term hormetic electrical field.

Several investigators have described opposite biological effects of electrical fields. For example, in vitro, formation of curvature by differential growth in the Avena coleoptile (Navez and Robinson 1932) can be inhibited by electrical shunting (Schrank 1950). On the other hand, electrical fields can induce differential growth and curvature. (Rajnicek et al. 1994) showed that bacteria curve towards the cathode when exposed to an electric field; the curvature was caused by faster growth on the anode side compared to the growth on the side facing the cathode.

In chicken embryos, Hotary and Robinson (1990) detected steep voltage gradients of as much as 33mV/mm. As the investigators noted, this exceeds the minimum field strength for in vitro directional migration of embryonic cells, and such field strength could very likely provide guidance for neural crest cell migration during normal development. In Xenopus embryos, they measured transmural electrical fields of up to 21mV during neural tube morphogenesis, the lumen being negative with respect to the surrounding tissue (Hotary and Robinson 1991).

Most significantly, disrupting endogenous currents in Xenopus embryos causes developmental abnormalities as shown by Hotary and Robinson (1994) who altered endogenous electrical fields by passing counteracting electrical currents through implanted miniaturized glass capillaries containing conductive gels. The alteration of the endogenous electrical fields led to multiple abnormalities such as aberrant morphogenesis of heads and eyes, and failure of neural tube closure.

ATP and ion flux

A number of investigators have demonstrated that extracellular ion flux is important for normal morphogenesis and pattern formation. Some of the studies have focused on errors of left-right asymmetry of internal organs, a rare developmental anomaly, occurring only in 1 of 10,000 human births; however, the asymmetry is highly conserved among vertebrates (Hackett 2002). In animal models, the right-left asymmetry of organs is associated with extracellular ion flux abnormalities.

For example, in sea urchin development, ion flow mechanisms involving protons, sodium ions and calcium ions have all been implicated in the control of left-right asymmetry (Hibino et al. 2006). The animal models have revealed that mechanisms that preserve left-right asymmetry involve common ion pumps, foremost H+-ATPase and H+K+-ATPase.

Vacuolar H+-ATPase (V-ATPase) is an ATP-driven proton pump in plasma membranes of animal phyla (Nelson and Harvey 1999) that has been implicated in right-left and anterior-posterior patterning and development of the pancreas. (Adams et al. 2006) reported that H+-ATPase is essential for development of left-right asymmetry in Xenopus, chick, and zebrafish; the investigators found that both physiological functions of the enzyme, cytoplasmic acidity regulation, and membrane voltage regulation, were required for proper left-right asymmetry development; inhibition of H+-ATPase using an ectopic H+ pump or a dominant negative subunit of the enzyme caused situs ambiguous. (Cruciat et al. 2010) reported that in the Xenopus, V-ATPase is essential for Wnt-induced {is Wnt hormetic?} anterior-posterior patterning of the central nervous system.

Hettiarachchi et al. (2004) found that chronic exposure of mice to sub-toxic doses of bafilomycin or concanamycin, products of the plant-pathogen Streptomyces that inhibit V-ATPase, reduced pancreatic islet size, and the mice suffered early onset of diabetes.

Pérez-Sayáns et al. (2009) pointed out that cancer tissue is acidic primarily due to proton extrusion into the extracellular space by V-ATPase, and proposed to employ V-ATPase inhibitors to overcome cancer chemoresistance. However, if ion flux controlled by V-ATPase is important for normal pattern formation and histogenesis, inhibition of V-ATPase could potentially lead to disruption of development and maintenance of normal tissue architecture. Even so, as particular hormetic morphogens may be expressed only in a temporal window during development and tissue maintenance and repair, therapeutic inhibition may not be deleterious except during those time periods.

Further evidence in support of important roles of ion flux during pattern formation is provided by experiments that disrupt the function of H+K+-ATPase pump. Shimeld and Levin (2006) used omeprazole, a specific inhibitor of the H+K+-ATPase, to disrupt left-right asymmetry in Ciona intestinalis (a sea squirt). Hibino et al. (2006) reported that omeprazole and other H+K+-ATPase blockers as well as the calcium ionophore A23187 disrupted normal left-right distribution of marker genes that are usually asymmetrically expressed during development.

Borgen and Shi (1995) injected amiloride and benzamil to block pumping of Na+ out of fused neural tubes of Axolotl embryos; the blockers reduced the normal 40–90mV transmural neural tube electrical voltage gradients, reversing neural tube development with regression of neural-tube related structures such as brain, notochord, and otic structures. Surprisingly, in some of the embryos, disruption of formation of neural tube-dependent structures failed to halt morphogenesis of external structures.

The latter observation appears to support a suggestion in my hormetic morphogen theory of curvature (Fosslien 2009) that genetically-driven morphogen gradient programs contain morphogenetic subroutines that, once initiated, can run independently of the main morphogenetic program. Furthermore, such compartmentalization would simplify transmission of gene-to-phenotype morphogenetic information transfer as it suggests that each morphogenetic subroutine may utilize similar principles of hormetic morphogenesis. However, whereas simultaneously running subroutines could use different hormetic morphogen/receptor signaling systems to prevent unwanted interference, temporally separated sequential subroutines could easily reuse hormetic morphogens/receptor systems employed during earlier stages of development. On the other hand, cross-talk and cooperation between different morphogen signaling gradients appears to be common during development.

Migration and alignment

In vitro, electrical fields can induce directional migration and elongation of vascular cells and align the cells with their long axis perpendicular to electrical field vectors (Bai et al. 2004). Sato et al. (2009) demonstrated that genes can control the direction of electrotaxis and field-strength-dependent direction of cell migration, i.e., the hormetic cell response to external direct current electrical fields. Their findings suggest that during pattern formation of the histology of vessel walls, cell differentiation induced by the hormetic morphogen determines the hormetic response of vascular mural cells to mural radial electrical gradient (also induced by the morphogen), thus the mural cells will automatically migrate to their proper coaxial mural locations along the electrical gradients.

Chemokinetic responses may exhibit dose-dependent hormesis (Calabrese 2001), and it seems very likely that mural cells migrate due to hormetic chemotaxis and bidirectional, hormetic electrotaxis. Besides, McCaig et al. (2009) noted that electrical and chemical gradients may interact to control cell behavior, and Jennings et al. (2008) reported that electrical fields can significantly alter transcription of genes of the TGF-β signaling pathways. This effect would alter the hormetic responses to hormetic morphogens, which indicates that hormetic morphogen-induced electrical fields may be involved in feedback regulation of hormetic morphogen signaling as well.


The hormetic electrical field theory of pattern formation proposes that hormetic morphogen concentration gradients can coordinate formation of curvature of tissues such as vascular walls and the development of their histological patterns. The theory outlines a mechanism for hormetic morphogen gradient-induced electrical fields along the morphogen gradients and predicts that the electrical fields help integrate tissue curvature and the mural histology i.e. the phenotype, location, shape and alignment of vascular mural cells and the location of mural histological structures such as vascular elastic laminas.

The theory proposes that the electrical fields are formed as follows: First, hormetic morphogen concentration-dependent amplitude modulation of ATP synthesis by mitochondria of cells along the morphogen gradients (field cells) generates gradients of ATP production along the hormetic morphogen gradients. Second, the amount of field cell ATP regulates field cell export of H+ by V-ATPase, which generates proton gradients along the morphogen gradients. Third, the proton gradients induce proton flux that generates electrical fields along the hormetic morphogen gradients. Fourth, the electrical field strength is determined by the differential concentration of hormetic morphogen along their gradients.

The electrical fields modulate cell shape, individual cell curvature, and cell orientation. Moreover, the theory proposes that the electrical fields can modulate bidirectional cell migration and cell sorting via dynamic hormetic galvanotaxis/electrotaxis analogous to in vitro isoelectric focusing in proton gradients and that the electrical fields provide feedback to adjust field cell responses to hormetic morphogens.

The theory predicts that therapeutic drugs that inhibit field cell surface ion pumps and significantly alter hormetic morphogen-induced extracellular ion gradients can have potential teratogenic effects and should therefore only be used with caution and with an understanding of important roles of electrical fields in tissue development, repair and maintenance. On the other hand, there may be circumstances, such as in cancer where the tissue acidity may be unnaturally high, when inhibition of V-ATPase may be beneficial.

Whereas the theory has been explained using V-ATPase and protons as the ion and vasculogenesis as specific examples, I believe that the theory may also apply to the formation, remodeling and repair of the histology of other types of curved structures in biology.


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