Harmonic response of cellular membrane pumps to low frequency electric fields

Electrical stimulation for cartilage tissue engineering - A critical review from an engineer's perspective

Cartilage has a limited intrinsic healing capacity. Hence, cartilage degradation and lesions pose a huge clinical challenge, particularly in an ageing society. Osteoarthritis impacts a significant number of the population and requires the development of repair and tissue engineering methods for hyaline articular cartilage. In this context, electrical stimulation has been investigated for more than 50 years already. Yet, no well-established clinical therapy to treat osteoarthritis by means of electrical stimulation exists. We argue that one reason is the lack of replicability of electrical stimulation devices from a technical perspective together with lacking hypotheses of the biophysical mechanism. Hence, first, the electrical stimulation studies reported in the context of cartilage tissue engineering with a special focus on technical details are summarized. Then, an experimental and numerical approach is discussed to make the electrical stimulation experiments replicable. Finally, biophysical hypotheses have been reviewed on the interaction of electric fields and cells that are relevant for cartilage tissue engineering. With that, the aim is to inspire future research to enable clinical electrical stimulation therapies to fight osteoarthritis.

Controlling dynamics in extended molecular frameworks

Molecular machines are essential dynamic components for fuel production, cargo delivery, information storage and processing in living systems. Scientists have demonstrated that they can design and synthesize artificial molecular machines that operate efficiently in isolation - for example, at high dilution in solution - fuelled by chemicals, electricity or light. To organize the spatial arrangement and motion of these machines within close proximity to one another in solid frameworks, such that useful macroscopic work can be performed, remains a challenge in both chemical and materials science. In this Review, we summarize the progress that has been made during the past decade in organizing dynamic molecular entities in such solid frameworks. Emerging applications of these dynamic smart materials in the contexts of molecular recognition, optoelectronics, drug delivery, photodynamic therapy and water desalination are highlighted. Finally, we review recent work on a new non-equilibrium adsorption phenomenon for which we have coined the term mechanisorption. The ability to use external energy to drive directional processes in mechanized extended frameworks augurs well for the future development of artificial molecular factories.

Generation of nonlinearity in the electrical response of yeast suspensions

The mechanism through which nonlinearity is generated in the response waveform of the electric current obtained by applying alternating current voltage to yeast suspension has not yet been elucidated. In this paper, we showed that the response waveform depends on the applied voltage and frequency. The results showed that distortion (nonlinearity) in the waveform increases as the applied voltage increases and/or the frequency decreases. We suggest a model for the generation of nonlinearity based on the influx of potassium ions into the cell via potassium ion channels and transporters in the membrane due to the applied voltage. Furthermore, we validated this model by simulating an electrical circuit.

Nonlinear dielectric spectroscopy as an indirect probe of metabolic activity in thylakoid membrane

Nonlinear dielectric spectroscopy (NDS) is a non-invasive probe of cellular metabolic activity with potential application in the development of whole-cell biosensors. However, the mechanism of NDS interaction with metabolic membrane proteins is poorly understood, partly due to the inherent complexity of single cell organisms. Here we use the light-activated electron transport chain of spinach thylakoid membrane as a model system to study how NDS interacts with metabolic activity. We find protein modification, as opposed to membrane pump activity, to be the dominant source of NDS signal change in this system. Potential mechanisms for such protein modifications include reactive oxygen species generation and light-activated phosphorylation.

Cellular apoptosis by nanosecond, high-intensity electric pulses: model evaluation of the pulsing threshold and extrinsic pathway

A simple, bistable rate-equation based model is used to predict trends of cellular apoptosis following electric pulsing. The caspase-8 extrinsic pathway with inherent delays in its activation, cytochrome c release, and an internal feedback mechanism between caspase-3 and cleavage of Bid are incorporated. Results obtained were roughly in keeping with the experimental cell-survival data and include an electrical pulse-number threshold followed by a near-exponential fall-off. The extrinsic caspase-8 mechanism is predicted to be more sensitive than the mitochondrial intrinsic pathway for electric pulse induced cell apoptosis. Also, delays of about an hour are predicted for detectable molecular concentration increases following electrical pulsing. Finally, our results suggest that multi-needle electrode systems with adjustable field orientations would likely enhance apoptosis in the context of pulsed voltage-induced inactivation of tumor cells.

Allosteric model of an ion pump

We present a simple model of a free-energy transducer made of allosterically coupled two ratchet subsystems. Each of the subsystems transports particles from one particle reservoir to another. The coupling of the subsystems imposes correlated transitions of the potential profiles of the two subsystems. As a result, a downhill flux in one subsystem with higher chemical-potential difference drives an uphill flux in the other subsystem with lower chemical-potential difference. The direction of the driven flux inverts depending on the direction of the driving flux. The ratio between the fluxes conveyed by the two subsystems is variable and nonstoichiometric. By selecting appropriate parameters, the maximum ratio of the driven flux to driving flux and maximum free-energy transducing efficiency reaches some 90 and 40%, respectively. At a stalled state, the driven flux vanishes while the driving flux remains finite. The allosteric model enables explicit analysis of the timing between binding-unbinding of particles and transitions of potential profile. The behavior of the model is similar to but different from that of the alternate access model, which is a biochemical model for active transport proteins. Our model works also as a regulatory system. We suggest that the correlated transitions of the subsystems (subunits or domains) through allosteric interaction are the origin of the diverse functions of the protein machineries.

Design and evaluation of a fast Fourier transform-based nonlinear dielectric spectrometer

Nonlinear dielectric spectroscopy of micro-organism is carried out by applying a moderate electrical field to an aqueous sample through two metal electrodes. Several ad hoc nonlinear spectrometers were proposed in the literature. However, these designs barely compensated the nonlinear distortion derived from the electrode-electrolyte interfaces (EEI). Moreover, the contribution of the suspension is masked by the effect of the nonlinearity introduced by the electrode contacts. Conversely, the nonlinear capability of a commercial tetrapolar analyzer has not been fully investigated. In this paper a new nonlinear tetrapolar spectrometer is proposed based on a commercial linear apparatus and ad hoc control and signal processing software. The system was evaluated with discrete electronic phantoms and showed that it can measure nonlinear properties of aqueous suspension independently of the presence of EEI (ANOVA test, p>0.001). It was also tested with real aqueous samples. The harmonics observed in the current that circulates through the sample reveals useful information about the transfer function of the sample. The total harmonic distortion was computed for linear mediums. Values lower than -60 dB suggest that the system has enough capability to perform nonlinear microbiological analysis. Design specifications, sources of interference, and equipment's limitations are discussed.

Non-linear dielectric spectroscopy of microbiological suspensions

BACKGROUND

Non-linear dielectric spectroscopy (NLDS) of microorganism was characterized by the generation of harmonics in the polarization current when a microorganism suspension was exposed to a sinusoidal electric field. The biological nonlinear response initially described was not well verified by other authors and the results were susceptible to ambiguous interpretation. In this paper NLDS was performed to yeast suspension in tripolar and tetrapolar configuration with a recently developed analyzer.

METHODS

Tripolar analysis was carried out by applying sinusoidal voltages up to 1 V at the electrode interface. Tetrapolar analysis was carried on with sinusoidal field strengths from 0.1 V cm(-1) to 70 V cm(-1). Both analyses were performed within a frequency range from 1 Hz through 100 Hz. The harmonic amplitudes were Fourier-analyzed and expressed in dB. The third harmonic, as reported previously, was investigated. Statistical analysis (ANOVA) was used to test the effect of inhibitor an activator of the plasma membrane enzyme in the measured response.

RESULTS

No significant non-linearities were observed in tetrapolar analysis, and no observable changes occurred when inhibitor and activator were added to the suspension. Statistical analysis confirmed these results.When a pure sinus voltage was applied to an electrode-yeast suspension interface, variations higher than 25 dB for the 3rd harmonic were observed. Variation higher than 20 dB in the 3rd harmonics has also been found when adding an inhibitor or activator of the membrane-bounded enzymes. These variations did not occur when the suspension was boiled.

DISCUSSION

The lack of result in tetrapolar cells suggest that there is no, if any, harmonic generation in microbiological bulk suspension. The non-linear response observed was originated in the electrode-electrolyte interface. The frequency and voltage windows observed in previous tetrapolar analysis were repeated in the tripolar measurements, but maximum were not observed at the same values.

CONCLUSION

Contrary to previous assertions, no repeatable dielectric non-linearity was exhibited in the bulk suspensions tested under the field and frequency condition reported with this recently designed analyzer. Indeed, interface related harmonics were observed and monitored during biochemical stimuli. The changes were coherent with the expected biological response.

Importance of intermediary transitions and waveform in the enzyme-electric field interaction

The current theory of enzymes and electric field interaction does not account for all the observed data since we could not observe non-linear behavior of cell suspensions as anticipated by other authors. In our case, we used a pure sinusoidal source, however the experiments that do account for responses used a sum of a central sinusoidal and its harmonics frequencies. As a result, we suggest that the enzyme and electric interaction are favored when the field has a non-strictly sinusoidal waveform, and this behavior is related to the true intermediate transitions of the enzyme during its catalytic cycle. Therefore, we developed an iterative model of the interaction process based on previous models and actual trends. The model well verified all the previous simulations and showed that, for a non-symmetrical enzyme, the energy can harvest its maximal for non sinusoidal fields.

Effects of oscillatory electric fields on internal membranes: an analytical model

We derive an analytical model of the potential differences induced across plasma and internal organelle membranes in suspended cells exposed to oscillatory electric fields. Multiple shells are modeled using iterative applications of the single-shell calculation with mobile charges. This work is motivated, in part, by recent results suggesting the ability to use alternating current (ac) fields to noninvasively monitor enzyme activity within internal membranes, particularly the mitochondrial electron transport chain. Previous work, on induced transmembrane voltages in cells subjected to ac fields, has mainly been limited to oscillatory potentials across the plasma membrane. Here we first develop a three-membrane model, consisting of a plasma membrane surrounding inner and outer membranes representing an internal organelle, such as a mitochondrion. Frequency-dependent transmembrane potentials are modeled for spherical, weakly conducting membrane shells enclosing a conductive cytoplasm surrounding an idealized internal organelle. We then use a two-shell model to simulate induced ac membrane potentials of a suspended isolated mitochondrion in which the outer membrane is usually much more permeable than the inner membrane.

Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.

Microscopic calculations of local lipid membrane permittivities and diffusion coefficients for application to electroporation analyses

Interaction of electric fields with biological systems has begun to receive considerable attention for applications that include field-assisted drug delivery, medical interventions, and genetic engineering. External fields induce the strongest effects at membranes with electroporation being a common feature. Membrane transport in this context of poration is often based on continuum approaches utilizing macroscopic parameters such as the permittivity, diffusion coefficients, and mobilities. In such modeling, field dependences, local inhomogeneities, and microscopic details are usually ignored. Here, a molecular dynamics (MD) scheme is used for a more rigorous and physically realistic evaluation of such parameters for potential application to electroporative transport model development. A suitable membrane structure containing a nanopore derived from MD analysis is used as the initial geometric configuration. Both static and frequency dependent diffusion coefficients have been evaluated. Permittivities are also calculated and shown to be dramatically non-uniform in the vicinity of membranes under high external fields. A positive feedback mechanism leading to enhanced membrane fields is discussed.

Harmonic generation by yeast cells in response to low-frequency electric fields

We report on harmonic generation by budding yeast cells (Saccharomyces cerevisiae, 10(8) cells/ml) in response to sinusoidal electric fields with amplitudes ranging from zero to 5 V/cm in the frequency range 10-300 Hz. The cell-generated harmonics are found to exhibit strong amplitude and frequency dependence. Sodium metavanadate, an inhibitor of the proton pump known as H+-ATPase, and glucose, a substrate of H+-ATPase, are found to increase harmonic production at low amplitudes while reducing it at large amplitudes. This P-type proton pump can be driven by an oscillatory transmembrane potential, and its nonlinear response is believed to be largely responsible for harmonic production at low frequencies in yeast cells. We find that the observed harmonics show dramatic changes with time and in their field and frequency dependence after perturbing the system by adding an inhibitor, substrate, or membrane depolarizer to the cell suspension.