Endogenous Electric Fields Research Articles

Microfluidic measurement of cell motility in response to applied non-homogeneous DC electric fields

Abstract. Endogenous electric fields (EFs) play an important role in many biological processes. In order to gain an insight into these biological phenomena, externally applied electric fields are used to study cellular responses. In this work, we report the construction and fabrication of a direct current (DC)-electrically stimulated microfluidic biochip and its validation with murine photoreceptor-derived 661 W cells. The presented device has the particularity of offering a non-homogeneous EF environment that best resembles the endogenous electric fields in vitro. The fabrication process is relatively easy, namely by photolithography and soft lithography techniques and, furthermore, it enables live-cell imaging under an inverted microscope. First experimental results reveal cathodal directional cell migration upon applied DC EFs. In summary, the microfluidic biochip has proven biocompatibility and suitability for cellular electrotaxis experiments in non-homogeneous DC electric fields.

Understanding the response of pulsed electric field on osteoblast functions in three-dimensional mesh structures

The endogenous electric field plays a determining role in impacting biological functions including communication with the physiological system, brain, and bone regeneration by influencing cellular functions. From this perspective, the objective of the study described here is to elucidate the effect of external electric field under dynamic conditions, in providing a guiding cue to osteoblasts in terms of cell-cell interactions and synthesis of prominent adhesion and cytoskeleton proteins. This was accomplished using pulsed direct current electric field of strength 0.1-1 V/cm. The electric field provided guided cue to the cells to migrate toward cathode. Membrane blebbing or necrosis was nearly absent in the vicinity of cathode at 0.1 and 0.5 V/cm electric field strength. Moreover, a higher cell proliferation as well as higher expression of vinculin and densely packed actin stress fibers was observed. At anode, the cells though healthy but expression of actin and vinculin was less. We underscore for the first time that the biological functionality can be favorably modulated on 3D printed scaffolds in the presence of electric field and under dynamic conditions with consequent positive effect on cell proliferation, growth, and expression level of prominent proteins.

The efficacy of electrical stimulation in experimentally induced cutaneous wounds in animals.

Complicated cutaneous wounds and their subsequent management can be a clinical challenge in veterinary medicine. There is still an unmet need for an ideal wound healing therapy that is able to stimulate efficiency and quality of repair. Skin wounds generate large and persistent endogenous electric currents and fields termed the "current of injury". The current of injury is involved in numerous processes of wound healing. These observations have led to the hypothesis that applied electrical stimulation (ES) may promote wound healing by imitating the natural electrical current that occurs in cutaneous wounds. This review details the use, effect and mechanism of ES in different preclinical experimental cutaneous wound models and discusses the potential of how ES could be translated into veterinary practice. Studies have found a variable effect of ES on wound healing. Some have been positive with faster rates of wound re-epithelialization, increased wound collagen formation and angiogenesis noted. Other studies have shown no effect or detrimental results. The effects of ES are highly influenced by the ES modality, polarity and parameters. Electrical stimulation has the potential to play a significant role in enhancing cutaneous wound healing in veterinary practice. Clinical studies are necessary to corroborate the findings from experimental studies which have shown promise including the use of alternating pulsed and direct current and the use of bio-electric dressings. The ideal ES device would need to be safe, easy to use, portable, noninvasive and aid wound healing by having a beneficial effect on all wound healing stages.

Lamellipodia and Membrane Blebs Drive Efficient Electrotactic Migration of Rat Walker Carcinosarcoma Cells WC 256.

The endogenous electric field (EF) may provide an important signal for directional cell migration during wound healing, embryonic development and cancer metastasis but the mechanism of cell electrotaxis is poorly understood. Additionally, there is no research addressing the question on the difference in electrotactic motility of cells representing various strategies of cell movement—specifically blebbing vs. lamellipodial migration. In the current study we constructed a unique experimental model which allowed for the investigation of electrotactic movement of cells of the same origin but representing different modes of cell migration: weakly adherent, spontaneously blebbing (BC) and lamellipodia forming (LC) WC256 cells. We report that both BC and LC sublines show robust cathodal migration in a physiological EF (1–3 V/cm). The directionality of cell movement was completely reversible upon reversing the field polarity. However, the full reversal of cell direction after the change of EF polarity was much faster in the case of BC (10 minutes) than LC cells (30 minutes). We also investigated the distinct requirements for Rac, Cdc42 and Rho pathways and intracellular Ca2+ in electrotaxis of WC256 sublines forming different types of cell protrusions. It was found that Rac1 is required for directional movement of LC to a much greater extent than for BC, but Cdc42 and RhoA are more crucial for BC than for LC cells. The inhibition of ROCK did not affect electrotaxis of LC in contrast to BC cells. The results also showed that intracellular Ca2+ is essential only for the electrotactic reaction of BC cells. Moreover, inhibition of MLCK and myosin II did not affect the electrotaxis of LC in contrast to BC cells. In conclusion, our results revealed that both lamellipodia and membrane blebs can efficiently drive electrotactic migration of WC 256 carcinosarcoma cells, however directional migration is mediated by different signalling pathways.

Neuronal coupling by endogenous electric fields: cable theory and applications to coincidence detector neurons in the auditory brain stem.

The ongoing activity of neurons generates a spatially and time-varying field of extracellular voltage (Ve). This Ve field reflects population-level neural activity, but does it modulate neural dynamics and the function of neural circuits? We provide a cable theory framework to study how a bundle of model neurons generates Ve and how this Ve feeds back and influences membrane potential (Vm). We find that these "ephaptic interactions" are small but not negligible. The model neural population can generate Ve with millivolt-scale amplitude, and this Ve perturbs the Vm of "nearby" cables and effectively increases their electrotonic length. After using passive cable theory to systematically study ephaptic coupling, we explore a test case: the medial superior olive (MSO) in the auditory brain stem. The MSO is a possible locus of ephaptic interactions: sounds evoke large (millivolt scale)Vein vivo in this nucleus. The Ve response is thought to be generated by MSO neurons that perform a known neuronal computation with submillisecond temporal precision (coincidence detection to encode sound source location). Using a biophysically based model of MSO neurons, we find millivolt-scale ephaptic interactions consistent with the passive cable theory results. These subtle membrane potential perturbations induce changes in spike initiation threshold, spike time synchrony, and time difference sensitivity. These results suggest that ephaptic coupling may influence MSO function.

Electric field-mediated growth of osteoblasts - the significant impact of dynamic flow of medium.

The endogenous electric field plays an important role in accomplishing various functions including communication with the brain and with different parts of the physiological system, wound healing, and cellular functions. Furthermore, the endogenous electric field can be modified using the external electric field to induce changes in cell functionality. Given that the cells grow in contact with the dynamic flow of blood and nutrients, the objective of the study is to elucidate the effect of media flow (dynamic conditions) on osteoblast functions at a pulsed DC (direct current) electric field of strength of 0.5-1 V cm(-1) and compared with the static conditions (no flow of media and in the presence of an electric field). The electric field provided a guiding cue to cells to move towards the cathode. An interesting aspect of the electric field was the migration of cells towards the cathode with the axis parallel to the direction of the electric field such that the lamellipodia was aligned. Furthermore, there was an absence of membrane blebbing or necrosis at the cathode. However, cell growth and expression of proteins (actin and vinculin) were higher than the anode. In contrast, at the anode, while the cells were healthy, the cell growth was less such that the expression of vinculin was relatively low together with less densely packed actin stress fibers. It is underscored that the biological functionality is favorably altered in the presence of an electrical field under dynamic conditions with a consequent effect on cell proliferation, growth, and expression level of prominent proteins, actin and vinculin.

Can Neural Activity Propagate by Endogenous Electrical Field?

It is widely accepted that synaptic transmissions and gap junctions are the major governing mechanisms for signal traveling in the neural system. Yet, a group of neural waves, either physiological or pathological, share the same speed of ∼0.1 m/s without synaptic transmission or gap junctions, and this speed is not consistent with axonal conduction or ionic diffusion. The only explanation left is an electrical field effect. We tested the hypothesis that endogenous electric fields are sufficient to explain the propagation with in silico and in vitro experiments. Simulation results show that field effects alone can indeed mediate propagation across layers of neurons with speeds of 0.12 ± 0.09 m/s with pathological kinetics, and 0.11 ± 0.03 m/s with physiologic kinetics, both generating weak field amplitudes of ∼2-6 mV/mm. Further, the model predicted that propagation speed values are inversely proportional to the cell-to-cell distances, but do not significantly change with extracellular resistivity, membrane capacitance, or membrane resistance. In vitro recordings in mice hippocampi produced similar speeds (0.10 ± 0.03 m/s) and field amplitudes (2.5-5 mV/mm), and by applying a blocking field, the propagation speed was greatly reduced. Finally, osmolarity experiments confirmed the model's prediction that cell-to-cell distance inversely affects propagation speed. Together, these results show that despite their weak amplitude, electric fields can be solely responsible for spike propagation at ∼0.1 m/s. This phenomenon could be important to explain the slow propagation of epileptic activity and other normal propagations at similar speeds.

Elucidating the Role of Injury-Induced Electric Fields (EFs) in Regulating the Astrocytic Response to Injury in the Mammalian Central Nervous System.

Injury to the vertebrate central nervous system (CNS) induces astrocytes to change their morphology, to increase their rate of proliferation, and to display directional migration to the injury site, all to facilitate repair. These astrocytic responses to injury occur in a clear temporal sequence and, by their intensity and duration, can have both beneficial and detrimental effects on the repair of damaged CNS tissue. Studies on highly regenerative tissues in non-mammalian vertebrates have demonstrated that the intensity of direct-current extracellular electric fields (EFs) at the injury site, which are 50–100 fold greater than in uninjured tissue, represent a potent signal to drive tissue repair. In contrast, a 10-fold EF increase has been measured in many injured mammalian tissues where limited regeneration occurs. As the astrocytic response to CNS injury is crucial to the reparative outcome, we exposed purified rat cortical astrocytes to EF intensities associated with intact and injured mammalian tissues, as well as to those EF intensities measured in regenerating non-mammalian vertebrate tissues, to determine whether EFs may contribute to the astrocytic injury response. Astrocytes exposed to EF intensities associated with uninjured tissue showed little change in their cellular behavior. However, astrocytes exposed to EF intensities associated with injured tissue showed a dramatic increase in migration and proliferation. At EF intensities associated with regenerating non-mammalian vertebrate tissues, these cellular responses were even more robust and included morphological changes consistent with a regenerative phenotype. These findings suggest that endogenous EFs may be a crucial signal for regulating the astrocytic response to injury and that their manipulation may be a novel target for facilitating CNS repair.

Calcium Ion Flow Permeates Cells through SOCs to Promote Cathode-Directed Galvanotaxis.

Sensing and responding to endogenous electrical fields are important abilities for cells engaged in processes such as embryogenesis, regeneration and wound healing. Many types of cultured cells have been induced to migrate directionally within electrical fields in vitro using a process known as galvanotaxis. The underlying mechanism by which cells sense electrical fields is unknown. In this study, we assembled a polydimethylsiloxane (PDMS) galvanotaxis system and found that mouse fibroblasts and human prostate cancer PC3 cells migrated to the cathode. By comparing the effects of a pulsed direct current, a constant direct current and an anion-exchange membrane on the directed migration of mouse fibroblasts, we found that these cells responded to the ionic flow in the electrical fields. Taken together, the observed effects of the calcium content of the medium, the function of the store-operated calcium channels (SOCs) and the intracellular calcium content on galvanotaxis indicated that calcium ionic flow from the anode to the cathode within the culture medium permeated the cells through SOCs at the drift velocity, promoting migration toward the cathode. The RTK-PI3K pathway was involved in this process, but the ROCK and MAPK pathways were not. PC3 cells and mouse fibroblasts utilized the same mechanism of galvanotaxis. Together, these results indicated that the signaling pathway responsible for cathode-directed cellular galvanotaxis involved calcium ionic flow from the anode to the cathode within the culture medium, which permeated the cells through SOCs, causing cytoskeletal reorganization via PI3K signaling.

Weak electric fields serve as guidance cues that direct retinal ganglion cell axons in vitro

Growing axons are directed by an extracellular electric field in a process known as galvanotropism. The electric field is a predominant guidance cue directing retinal ganglion cell (RGC) axons to the future optic disc during embryonic development. Specifically, the axons of newborn RGCs grow along the extracellular voltage gradient that exists endogenously in the embryonic retina (Yamashita, 2013 [8]). To investigate the molecular mechanisms underlying galvanotropic behaviour, the quantification of the electric effect on axon orientation must be examined. In the present study, a culture system was built to apply a constant, uniform direct current (DC) electric field by supplying an electrical current to the culture medium, and this system also continuously recorded the voltage difference between the two points in the medium. A negative feedback circuit was designed to regulate the supplied current to maintain the voltage difference at the desired value. A chick embryo retinal strip was placed between the two points and cultured for 24h in an electric field in the opposite direction to the endogenous field, and growing axons were fluorescently labelled for live cell imaging (calcein-AM). The strength of the exogenous field varied from 0.0005mV/mm to 10.0mV/mm. The results showed that RGC axons grew in the reverse direction towards the cathode at voltage gradients of ≥0.0005mV/mm, and straightforward extensions were found in fields of ≥0.2–0.5mV/mm, which were far weaker than the endogenous voltage gradient (15mV/mm). These findings suggest that the endogenous electric field is sufficient to guide RGC axons in vivo.

Une thérapie innovante des ulcères de jambe : l’électrostimulation

Chronic wounds can take a long time to heal despite appropriate therapy based upon aetiology and use of suitable dressings. The success of electrostimulation is based upon the existence within the skin of the endogenous currents involved in the wound healing process. Where skin continuity is broken by a wound, these electrical potentials are short-circuited, resulting in leakage of electrical current. Woundel(®) therapy is the only such treatment currently available in France and is based on the use of continuous pulsed current that generates an electrical field near the endogenous electrical fields. It utilises a console to deliver the electrical impulses, a dressing electrode and a dispersion electrode. The electrode dressing is left on the wound for 3 days, and venous compression bandaging may be applied to the leg, taking care to leave the connector free. Negative polarity stimulates migration of fibroblasts, resulting in elimination of fibrin. Positive polarity causes keratinocyte migration, which in turn leads to epidermisation. Electrostimulation is of recognised utility in the healing of chronic wounds: it has been assigned a high-level recommendation in the European and American guidelines for the treatment of venous ulcers and bedsores with proof level of A. Further, the analgesic effect of electrostimulation has been demonstrated in several studies. Electrostimulation is already well developed in France among wound specialists, but prospective studies are planned so that it may be used at patients' homes.

Developmental changes in spontaneous electrocortical activity and network organization from early to late childhood

We investigated the development of spontaneous (resting state) cerebral electric fields and their network organization from early to late childhood in a large community sample of children. Critically, we examined electrocortical maturation across one-year windows rather than creating aggregate averages that can miss subtle maturational trends. We implemented several novel methodological approaches including a more fine grained examination of spectral features across multiple electrodes, the use of phase-lagged functional connectivity to control for the confounding effects of volume conduction and applying topological network analyses to weighted cortical adjacency matrices. Overall, there were major decreases in absolute EEG spectral density (particularly in the slow wave range) across cortical lobes as a function of age. Moreover, the peak of the alpha frequency increased with chronological age and there was a redistribution of relative spectral density toward the higher frequency ranges, consistent with much of the previous literature. There were age differences in long range functional brain connectivity, particularly in the alpha frequency band, culminating in the most dense and spatially variable networks in the oldest children. We discovered age-related reductions in characteristic path lengths, modularity and homogeneity of alpha-band cortical networks from early to late childhood. In summary, there is evidence of large scale reorganization in endogenous brain electric fields from early to late childhood, suggesting reduced signal amplitudes in the presence of more functionally integrated and band limited coordination of neuronal activity across the cerebral cortex.

Effects of electric fields on human mesenchymal stem cell behaviour and morphology using a novel multichannel device

The intrinsic piezoelectric nature of collagenous-rich tissues, such as bone and cartilage, can result in the production of small, endogenous electric fields (EFs) during applied mechanical stresses. In vivo, these EFs may influence cell migration, a vital component of wound healing. As a result, the application of small external EFs to bone fractures and cutaneous wounds is actively practiced clinically. Due to the significant regenerative potential of stem cells in bone and cartilage healing, and their potential role in the observed improved healing in vivo post applied EFs, using a novel medium throughput device, we investigated the impacts of physiological and aphysiological EFs on human bone marrow-derived mesenchymal stem cells (hBM-MSCs) for up to 15 hours. The applied EFs had significant impacts on hBM-MSC morphology and migration; cells displayed varying degrees of conversion to a highly elongated phenotype dependent on the EF strength, consistent perpendicular alignment to the EF vector, and definitive cathodal migration in response to EF strengths ≥0.5 V cm(-1), with the fastest migration speeds observed at between 1.7 and 3 V cm(-1). We observed variability in hBM-MSC donor-to-donor responses and overall tolerances to applied EFs. This study thus confirms hBM-MSCs are responsive to applied EFs, and their rate of migration towards the cathode is controllable depending on the EF strength, providing new insight into the physiology of hBM-MSCs and possibly a significant opportunity for the utilisation of EFs in directed scaffold colonisation in vitro for tissue engineering applications or in vivo post implantation.

The Galvanotactic Migration of Keratinocytes is Enhanced by Hypoxic Preconditioning.

The endogenous electric field (EF)-directed migration of keratinocytes (galvanotaxis) into wounds is an essential step in wound re-epithelialization. Hypoxia, which occurs immediately after injury, acts as an early stimulus to initiate the healing process; however, the mechanisms for this effect, remain elusive. We show here that the galvanotactic migration of keratinocytes was enhanced by hypoxia preconditioning as a result of the increased directionality rather than the increased motility of keratinocytes. This enhancement was both oxygen tension- and preconditioning time-dependent, with the maximum effects achieved using 2% O2 preconditioning for 6 hours. Hypoxic preconditioning (2% O2, 6 hours) decreased the threshold voltage of galvanotaxis to < 25 mV/mm, whereas this value was between 25 and 50 mV/mm in the normal culture control. In a scratch-wound monolayer assay in which the applied EF was in the default healing direction, hypoxic preconditioning accelerated healing by 1.38-fold compared with the control conditions. Scavenging of the induced ROS by N-acetylcysteine (NAC) abolished the enhanced galvanotaxis and the accelerated healing by hypoxic preconditioning. Our data demonstrate a novel and unsuspected role of hypoxia in supporting keratinocyte galvanotaxis. Enhancing the galvanotactic response of cells might therefore be a clinically attractive approach to induce improved wound healing.

Endogenous electric fields as guiding cue for cell migration.

This review covers two topics: (1) “membrane potential of low magnitude and related electric fields (bioelectricity)” and (2) “cell migration under the guiding cue of electric fields (EF).”Membrane potentials for this “bioelectricity” arise from the segregation of charges by special molecular machines (pumps, transporters, ion channels) situated within the plasma membrane of each cell type (including eukaryotic non-neural animal cells). The arising patterns of ion gradients direct many cell- and molecular biological processes such as embryogenesis, wound healing, regeneration. Furthermore, EF are important as guiding cues for cell migration and are often overriding chemical or topographic cues. In osteoblasts, for instance, the directional information of EF is captured by charged transporters on the cell membrane and transferred into signaling mechanisms that modulate the cytoskeleton and motor proteins. This results in a persistent directional migration along an EF guiding cue. As an outlook, we discuss questions concerning the fluctuation of EF and the frequencies and mapping of the “electric” interior of the cell. Another exciting topic for further research is the modeling of field concepts for such distant, non-chemical cellular interactions.

Two emerging topics regarding long-range physical signaling in neurosystems: Membrane nanotubes and electromagnetic fields.

In this review paper, an overview is given of two emerging research topics that address the importance of long-range physical signaling in living biosystems. The first topic concerns the biophysical principles and the physiological significance of long-range cell-to-cell signaling through electrical signals facilitated by membrane nanotubes (MNTs) (also called "tunneling nanotubes"), namely long membrane extensions that connect cells, discovered about 10 years ago. This review paper looks at experimental results that showed electrical signals being propagated through MNTs, and that MNT-mediated electrical coupling between brain cells involves activation of low-voltage-gated calcium channels. The significance of electrical cell-to-cell coupling through MNT for neuronal communication is discussed. The second topic deals with endogenous electromagnetic fields generated by nerve cells. The review concludes that these fields are not just an "epiphenomenon" but play a fundamental role in neuronal processes. For example, electromagnetic fields from brain cells feed back to their generating cells and to other cells (ephaptic coupling) and, for example, modulate the spiking timing of them. It is also discussed that cell membranes of neurons have specific resonance properties which possibly determine the impact of endogenous electric field fluctuations with respect to field strength and frequency. In addition, it is reviewed how traveling and standing waves of the endogenous electromagnetic field produced by neuronal and non-neuronal cells may play an integral part in global neuronal network dynamics. Finally, an outlook is given on which research questions should be addressed in the future regarding these two topics.

ARP2/3 complex is required for directional migration of neural stem cell-derived oligodendrocyte precursors in electric fields.

IntroductionThe loss of oligodendrocytes in a lesion of the central nervous system causes demyelination and therefore impairs axon function and survival. Transplantation of neural stem cell-derived oligodendrocyte precursor cells (NSC-OPCs) results in increased oligodendrocyte formation and enhanced remyelination. The directional migration of grafted cells to the target can promote the establishment of functional reconnection and myelination in the process of neural regeneration. Endogenous electric fields (EFs) that were detected in the development of the central nervous system can regulate cell migration.MethodsNSCs were isolated from the brains of ARPC2+/+ and ARPC2−/− mouse embryo and differentiated into OPCs. After differentiation, the cultured oligospheres were stimulated with EFs (50, 100, or 200 mV/mm). The migration of OPCs from oligospheres was recorded using time-lapse microscopy. The cell migration directedness and speed were analyzed and quantified.ResultsIn this study, we found that NSC-OPCs migrated toward the cathode pole in EFs. The directedness and displacement of cathodal migration increased significantly when the EF strength increased from 50 to 200 mV/mm. However, the EF did not significantly change the cell migration speed. We also showed that the migration speed of ARPC2−/− OPCs, deficient in the actin-related proteins 2 and 3 (ARP2/3) complex, was significantly lower than that of wild type of OPCs. ARPC2−/− OPCs migrated randomly in EFs.ConclusionsThe migration direction of NSC-OPCs can be controlled by EFs. The function of the ARP complex is required for the cathodal migration of NSC-OPCs in EFs. EF-guided cell migration is an effective model to understanding the intracellular signaling pathway in the regulation of cell migration directness and motility.Electronic supplementary materialThe online version of this article (doi:10.1186/s13287-015-0042-0) contains supplementary material, which is available to authorized users.

Effect of electric fields on proliferation and migration of epidermal stem cells

Objective To investigate the effect of endogenous electric fields on proliferation and migration of epidermal stem cells (EpSCs) in vitro. Methods EpSCs in the first passage were cultured on simulated endogenous electric field. Galvanic stimulation set at an intensity of 0 mV/mm (GroupⅠ), 100 mV/mm (GroupⅡ) and 200 mV/mm(Group Ⅲ) was given twice a day for 3 days with each time continuing1 hour and resting 1 hour. Effect of bio-electric field on cell proliferation was measured by direct cell counting in fixed visual field. Repeated experiment but continued stimulation for 3 hours was performed. Live cell migration was monitored to determine the effect of bio-electric field on the process of cell migration. Results For the EpSCs cultured in endogenous bio-electric simulation platform for 24, 48 and 72 hours, cell proliferation rate was the highest in Group Ⅲ[(107.4±21.9)%, (270.2±71.4)%, (544.0±95.1)% ] (P<0. 01). And higher cell proliferation was observed in Group Ⅰ[(35.1±21.0)%, (138.6±31.0)%, (323.5±23.0)%] than in Group Ⅱ[(66.9±24.2)% , (192.1±36.2)%, (406.7±50.7)%] (P<0. 01). After continued galvanic stimulation for 3 hours, cells in Groups Ⅱ and Ⅲ oriented towards cathode, but cells in Group Ⅰ moved randomly. In measurements of track velocity (Vt), displacement velocity (Vd) and electric field migration rate (Vx), Group Ⅲ revealed increased values[(42.5±2.8), (32.3 ±1.8), (29.7±1.3)μm/h] as compared with GroupⅠ[(36.2±2.2), (23.6±2.9), (18.2±1.8)μm/h] and Group Ⅱ[(34.3±1.6), (23.8±1.2), (21.2±1.6)μm/h] (P<0.01). Conclusion In vitro experiments reveal that endogenous electric fields can promote the proliferation of EpSCs and induce oriented movements towards the cathode. Key words: Stem cells; Cell proliferation; Cell movement; In vitro

A Model of Electrostimulation Based on the Membrane Capacitance as Electromechanical Transducer for Pore Gating.

Electrostimulation has gained enormous importance in modern medicine, for example, in implantable pacemakers and defibrillators, pain stimulators, and cochlear implants. Most electrostimulation macromodels use the electrical current as the primary parameter to describe the conventional strength-duration relationship of the output of a generator. These models normally assume that the stimulation pulse charges up the passive cell membrane capacitance, and then the increased (less-negative) transmembrane potential activates voltage-gated sodium channels. However, this model has mechanistic and accuracy limitations. Our model assumes that the membrane capacitance is an electromechanical transducer and that the membrane is compressed by the endogenous electric field. The pressure is quadratically correlated with the transmembrane voltage. If the pressure is reduced by an exogenous field, the compression is released and, thus, opening the pores for Na(+) influx initiates excitation. The exogenous electric field must always be equal to or greater than the rheobase field strength (rheobase condition). This concept yields a final result that the voltage-pulse-content produced by the exogenous field between the two ends of a cell is a linear function of the pulse duration at threshold level. Thus, the model yields mathematical formulations that can describe and explain the characteristic features of electrostimulation. Our model of electrostimulation can describe and explain electrostimulation at cellular level. The model's predictions are consistent with published experimental studies. Practical applications in cardiology are discussed in the light of this model of electrostimulation.

The role of microtubules in electrotaxis of rat Walker carcinosarcoma WC256 cells.

The endogenous electric field may provide an important signal for directional cell migration during cancer metastasis but the mechanism of cell electrotaxis is poorly understood. It was postulated that microtubules play a central role in the polarization and directional migration of several types of cells. In this paper we investigated the role of microtubules in electrotaxis of rat Walker carcinosarcoma WC256 cells. We found that colchicine-stimulated disassembly of microtubules caused the formation of blebs instead of lamellipodia at the front of about 45% of cells. Most of the remaining cells contracted and became rounded or transformed into non-polar cells. Depolymerization of microtubules in both subpopulations of cells reduced the directionality of cell migration to about 50% of the control, but bleb- forming cells migrated much more efficiently than lamellipodia-forming cells. The analysis of microtubules architecture in the presence of an endogenous electric field showed that there is no relationship between the direction of migration and the polarization of microtubules. These results suggest that microtubules are not indispensable for electrotaxis of WC256 cells, however they may improve the directionality of cell migration.