Stochastic resonance as a possible mechanism of amplification of weak electric signals in living cells

The most important but still unresolved problem in bioelectromagnetics is the interaction of weak electromagnetic fields (EMFs) with living cells. Thermal and other types of noise pose restrictions in cell detection of weak signals. As a consequence, some extant experimental results that indicate low-intensity field effects cannot be accounted for, and this renders the results themselves questionable. One way out of this dead end is to search for possible mechanisms of signal amplification. In this paper, we discuss a general mechanism in which a weak signal is amplified by system noise itself. This mechanism was discovered several years ago in physics and is known, in its simplest form, as a stochastic resonance. It was shown that signal amplification may exceed a factor of 1000, which renders existing estimations of EMF thresholds highly speculative. The applicability of the stochastic resonance concept to cells is discussed particularly with respect to the possible role of the cell membrane in the amplification process. © 1994 Wiley-Liss, Inc.     

Signal transduction across alamethicin ion channels in the presence of noise.

We have studied voltage-dependent ion channels of alamethicin reconstituted into an artificial planar lipid bilayer membrane from the point of view of electric signal transduction. Signal transduction properties of these channels are highly sensitive to the external electric noise. Specifically, addition of bandwidth-restricted "white" noise of 10-20 mV (r.m.s.) to a small sine wave input signal increases the output signal by approximately 20-40 dB conserving, and even slightly increasing, the signal-to-noise ratio at the system output. We have developed a small-signal adiabatic theory of stochastic resonance for a threshold-free system of voltage-dependent ion channels. This theory describes our main experimental findings giving good qualitative understanding of the underlying mechanism. It predicts the right value of the output signal-to-noise ratio and provides a reliable estimate for the noise intensity corresponding to its maximum. Our results suggest that the alamethicin channel in a lipid bilayer is a good model system for studies of mechanisms of primary electrical signal processing in biology showing an important feature of signal transduction improvement by a fluctuating environment.     

ESTIMATION OF THE PHYSIOLOGICAL PARAMETERS OF A MEMBRANE CHANNEL EXPOSED TO ELECTROMAGNETIC FIELDS USING THE GPOF APPROACH

A method is proposed for the estimation of kinetic parameters of ionic channels in the cell membrane. The method is based on the generalized pencil-of-function approach, which exploits transient current signals from single channels to derive the frequency of the system poles. The proposed approach is validated for the well-known potassium channel by comparing the estimated values with the theoretical values given by Hodgkin and Huxley. The approach is superior to previous spectral approaches, both for its accuracy and for its robustness. It is especially useful for parameter estimation when the channel is exposed to electromagnetic fields. Results are given for exposure to 200-Hz and 915-MHz signals, to demonstrate the effect of fields on the kinetic parameters of the channel.     

Issues in electromagnetic field-biointeractions

Low level electromagnetic fields have been found to produce a variety of biological effects, though the mechanism of such interaction is still not completely understood. Cell membrane of the brain is a critical structure perceiving the action of microwaves, which has received greater attention in the recent past. The interactions of EMF with the living cells are considered as stochastic resonance, cooperative effects, non-equilibrium thermodynamic process and non-linear interactions. The living cells derive the energy from noise and pumps it into the modes of excitation at the driving frequency of an electromagnetic wave which give sufficient amplification of the signal and increase the signal to noise ratio. The non-linear mechanism plays their main role in the process of transmembrane coupling of the signal to the cytoplasm. The criteria for safe exposure limits of electromagnetic field to humans is also discussed.     

Frequency sensitivity in Hodgkin–Huxley systems

 The frequency sensitivity of weak periodic signal detection has been studied via numerical simulations for both a single neuron and a neuronal network. The dependence of the critical amplitude of the signal upon its frequency and a resonance between the intrinsic oscillations of a neuron and the signal could account for the frequency sensitivity. In the presence of both a subthreshold periodic signal and noise, the signal-to-noise ratio (SNR) of the output of either a single neuron or a neuronal network present the typical characteristics of stochastic resonance. In particular, there exists a frequency-sensitive range of 30–100 Hz, and for signals with frequencies within this range the SNRs have large values. This implies that the system under consideration (a single neuron or a neuronal network) is more sensitive to the detection of periodic signals, and the frequency sensitivity may be of a functional significance to signal processing. Received: 26 October 1999 / Accepted in revised form: 25 July 2000     

Protein and DNA reactions stimulated by electromagnetic fields

The stimulation of protein and DNA by electromagnetic fields (EMF) has been problematic because the fields do not appear to have sufficient energy to directly affect such large molecules. Studies with electric and magnetic fields in the extremely low-frequency range have shown that weak fields can cause charge movement. It has also been known for some time that redistribution of charges in large molecules can trigger conformational changes that are driven by large hydration energies. This review considers examples of direct effects of electric and magnetic fields on charge transfer, and structural changes driven by such changes. Conformational changes that arise from alterations in charge distribution play a key role in membrane transport proteins, including ion channels, and probably account for DNA stimulation to initiate protein synthesis. It appears likely that weak EMF can control and amplify biological processes through their effects on charge distribution.     

Magnetic Entropy as a Proposed Gating Mechanism for Magnetogenetic Ion Channels

Magnetically sensitive ion channels would allow researchers to better study how specific brain cells affect behavior in freely moving animals; however, recent reports of “magnetogenetic” ion channels based on biogenic ferritin nanoparticles have been questioned because known biophysical mechanisms cannot explain experimental observations. Here, we reproduce a weak magnetically mediated calcium response in HEK cells expressing a previously published TRPV4-ferritin fusion protein. We find that this magnetic sensitivity is attenuated when we reduce the temperature sensitivity of the channel but not when we reduce the mechanical sensitivity of the channel, suggesting that the magnetic sensitivity of this channel is thermally mediated. As a potential mechanism for this thermally mediated magnetic response, we propose that changes in the magnetic entropy of the ferritin particle can generate heat via the magnetocaloric effect and consequently gate the associated temperature-sensitive ion channel. Unlike other forms of magnetic heating, the magnetocaloric mechanism can cool magnetic particles during demagnetization. To test this prediction, we constructed a magnetogenetic channel based on the cold-sensitive TRPM8 channel. Our observation of a magnetic response in cold-gated channels is consistent with the magnetocaloric hypothesis. Together, these new data and our proposed mechanism of action provide additional resources for understanding how ion channels could be activated by low-frequency magnetic fields.     

NONLINEAR PROCESSES OF INTRACELLULAR CALCIUM SIGNALING AS A TARGET FOR THE INFLUENCE OF EXTREMELY LOW-FREQUENCY FIELDS

Theoretical analysis of peculiarities of reception of weak extremely low-frequency periodic signals by calcium-dependent intracellular regulatory systems was performed on the reduced “minimal” model for calcium oscillations suggested by Goldbeter et al. (Proc. Natl. Acad. Sci. USA 87, 1461–1465, 1990). The model considered the following calcium-dependent processes: the rise in intracellular free calcium concentration ([Ca²⁺]_i) due to calcium ionophore A23187 action on a cell, activation of the Ca²⁺ entry through calcium channels in the plasma membrane by the initial rise in [Ca²⁺]_i, and the Ca²⁺ release from intracellular stores by the calcium-induced calcium release mechanism. Calcium channels of plasma membrane were chosen as a target for the modulating signal and an additive noise influence in the model. An increase in [Ca²⁺]_i under the influence of the modulating signal was demonstrated to depend not only on the amplitude and frequency of this signal, but also on the phase of the signal with respect to a momentary chemical stimulation of the cell. Such an effect was found only at high strengths of chemical stimulation and with a particular sequence of delivery of the chemical and electromagnetic stimuli. An increase in noise intensity led to magnification of the mean level of [Ca²⁺]_i in a narrow frequency range by the mechanism of stochastic resonance. Under the influence of a modulating periodic signal, the gradual increase in strength of chemical stimulation induced a system transition from regular to chaotic behavior, and then to induced periodic oscillations. A boundary of the transition from chaotic to periodic oscillations corresponded to a “threshold” of sensitivity of calcium-dependent intracellular signaling systems on [Ca²⁺]_i to the influence of the modulating signal. Results of the theoretical analysis led us to conclude that the narrow-band response of a system to an external electromagnetic signal is determined purely by nonlinear properties of the system.     

Cellular target of weak magnetic fields: ionic conduction along actin filaments of microvilli

The interaction of weakelectromagnetic fields (EMF) with living cells is a most important butstill unresolved biophysical problem. For this interaction, thermal andother types of noise appear to cause severe restrictions in the actionof weak signals on relevant components of the cell. A recentlypresented general concept of regulation of ion and substrate pathwaysthrough microvilli provides a possible theoretical basis for thecomprehension of physiological effects of even extremely low magneticfields. The actin-based core of microfilaments in microvilli isproposed to represent a cellular interaction site for magnetic fields.Both the central role of F-actin in Ca²⁺ signaling and itspolyelectrolyte nature eliciting specific ion conduction propertiesrender the microvillar actin filament bundle an ideal interaction sitefor magnetic and electric fields. Ion channels at the tip of microvilliare connected with the cytoplasm by a bundle of microfilaments forminga diffusion barrier system. Because of its polyelectrolyte nature, themicrofilament core of microvilli allows Ca²⁺ entry into thecytoplasm via nonlinear cable-like cation conduction through arrays ofcondensed ion clouds. The interaction of ion clouds with periodicallyapplied EMFs and field-induced cation pumping through the cascade ofpotential barriers on the F-actin polyelectrolyte followswell-known physical principles of ion-magnetic field (MF) interactionand signal discrimination as described by the stochastic resonance andBrownian motor hypotheses. The proposed interaction mechanismis in accord with our present knowledge about Ca²⁺signaling as the biological main target of MFs and the postulated extreme sensitivity for coherent excitation by very low field energieswithin specific amplitude and frequency windows. Microvillar F-actinbundles shielded by a lipid membrane appear to function like electronicintegration devices for signal-to-noise enhancement; the influence ofcoherent signals on cation transduction is amplified, whereas that ofrandom noise is reduced.

     

Generic UMTS test signal for RF bioelectromagnetic studies

This report outlines the characteristics of universal mobile telecommunications system (UMTS) signals and discusses the signal parameters with respect to their possible biological relevance in order to define a generic UMTS test signal (GUS) for experiments aiming at the investigation of biological effects of weak electromagnetic fields. The GUS includes features of a real UMTS signal and especially the characteristics of UMTS, which differ from those of already applied second generation mobile communication systems (GSM 900, DCS1800, PCS1900, IS-95). It has been specified on the basis of the recommendations of a working group of the German Forschungsgemeinschaft Funk (FGF) with a focus on the mechanisms of UMTS which are responsible for slow term signal contributions, i.e., low frequency variations of the radio frequency (RF) envelope, since the hypothetical possibility of biological relevance of weak electromagnetic fields is often attributed to time variations of the RF envelope with frequencies close to those of natural processes. In this respect, it is also shown that the mandatory power control loop in UMTS gives rise to very strong 1.5 kHz variations on the air interface. Based upon the concept of the GUS, a UMTS test signal generator (GUS6960S) is described.     

A ratiometric imaging method for mapping ion flux densities

A heterogeneous distribution of ion channels on the cell surface is a prerequisite for several cellular functions. Thus, there has been considerable interest in methods allowing the mapping of ion channel distributions. Here we report on a novel ratiometric imaging technique appropriate to measure spatially resolved ion flux signals by using ion sensitive dyes. However, given that certain relevant cell properties like the surface to volume ratio may exhibit significant spatial heterogeneities, the local influx signal cannot be interpreted as a measure of the local open channel concentration or flux density. To overcome this problem, we suggest an internal normalization procedure, which, in analogy to, but clearly distinct from, well-established ratioing techniques, eliminates effects which would otherwise obscure the desired result. Ratioing is performed on flux signals from a given cell, triggered by two different, subsequent stimuli. If the two stimuli address different ion channels, the flux density distribution caused by two channel types can be determined relative to each other. In cases where one of the stimuli triggers a spatially homogeneous flux signal, ratioing yields an ion flux density map for a given channel type. Thus distribution patterns of ion channels active during a given stimulus may be derived.     

Calmodulin contributes to gating control in olfactory calcium-activated chloride channels

In sensory neurons of the peripheral nervous system, receptor potentials can be amplified by depolarizing Cl currents. In mammalian olfactory sensory neurons (OSNs), this anion-based signal amplification results from the sequential activation of two distinct types of transduction channels: cAMP-gated Ca channels and Ca-activated Cl channels. The Cl current increases the initial receptor current about 10-fold and leads to the excitation of the neuron. Here we examine the activation mechanism of the Ca-dependent Cl channel. We focus on calmodulin, which is known to mediate Ca effects on various ion channels. We show that the cell line Odora, which is derived from OSN precursor cells in the rat olfactory epithelium, expresses Ca-activated Cl channels. Single-channel conductance, ion selectivity, voltage dependence, sensitivity to niflumic acid, and Ca sensitivity match between Odora channels and OSN channels. Transfection of Odora cells with CaM mutants reduces the Ca sensitivity of the Cl channels. This result points to the participation of calmodulin in the gating process of Ca-ativated Cl channels, and helps to understand how signal amplification works in the olfactory sensory cilia. Calmodulin was previously shown to mediate feedback inhibition of cAMP-synthesis and of the cAMP-gated Ca channels in OSNs. Our results suggest that calmodulin may also be instrumental in the generation of the excitatory Cl current. It appears to play a pivotal role in the peripheral signal processing of olfactory sensory information. Moreover, recent results from other peripheral neurons, as well as from smooth muscle cells, indicate that the calmodulin-controlled, anion-based signal amplification operates in various cell types where it converts Ca signals into membrane depolarization.     

Can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels?

Ion channels are protein molecules, which can assume distinct open and closed conformational states, a phenomenon termed ion channel kinetics. The transitions from one state to another depend on the potential energy barrier that separates those two states. Therefore, it is rational to suppose that electromagnetic waves could interact with this barrier and induce changes in the rate transitions of this kinetic process. Our aim is to answer the question: can electromagnetic radiations induce changes in the kinetics of voltage-dependent ion channels? We simulated the effects of the low and high frequency electromagnetic waves on the sodium and potassium channels of the giant axon of Loligo. The key parameter measured was the fractional open time (fv), because it reflects the voltage dependence of the kinetics of channels. The electromagnetic radiations induced the following changes in the kinetics of the potassium and sodium channels: i/ low frequency waves kept the potassium channel 50% of the time open independent on the mean voltage applied through the membrane; ii/ a gradual inhibition of the inactivation on the sodium channel, when the amplitudes of the low frequency waves were increased; iii/ high frequency waves on the potassium channel, decreased both Vo (voltage in which the channel stays 50% open) and the steepness of fv (d fv/dV) as the amplitudes of the waves increased, and iv/ high frequency and low amplitude radiations on the sodium channel decreased the maximum value of fv (in relation to control), while high amplitudes increased this value. In conclusion, high and low frequency electromagnetic radiations were able to change the kinetics of the potassium and sodium channels in a squid giant axon model.     

Optimal noise filtering in the chemotactic response of Escherichia coli

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.     

Influence of Electromagnetic Signal of Antibiotics Excited by Low-Frequency Pulsed Electromagnetic Fields on Growth of Escherichia coli

Energy medicine (EM) provides a new medical choice for patients, and its advantages are the noninvasive detection and nondrug treatment. An electromagnetic signal, a kind of EM, induced from antibiotic coupling with weak, extremely low-frequency pulsed electromagnetic fields (PEMFs) is utilized for investigating the growth speed of Escherichia coli (E. coli). PEMFs are produced by solenoidal coils for coupling the electromagnetic signal of antibiotics (penicillin). The growth retardation rate (GRR) of E. coli is used to investigate the efficacy of the electromagnetic signal of antibiotics. The E. coli is cultivated in the exposure of PEMFs coupling with the electromagnetic signal of antibiotics. The maximum GRR of PEMFs with and without the electromagnetic signal of antibiotics on the growth of E. coli cells in the logarithmic is 17.4 and 9.08 %, respectively. The electromagnetic signal of antibiotics is successfully coupled by the electromagnetic signal coupling instrument to affect the growth of E. coli. In addition, the retardation effect on E. coli growth can be improved of by changing the carrier frequency of PEMFs coupling with the electromagnetic signal of antibiotics. GRR caused by the electromagnetic signal of antibiotics can be fixed by a different carrier frequency in a different phase of E. coli growth.     

Glycoproteins bound to ion channels mediate detection of electric fields: a proposed mechanism and supporting evidence

The mechanism by which animals detect weak electric and magnetic fields has not yet been elucidated. We propose that transduction of an electric field (E) occurs at the apical membrane of a specialized cell as a consequence of an interaction between the field and glycoproteins bound to the gates of ion channels. According to the model, a glycoprotein mass (M) could control the gates of ion channels, where M > 1.4 x 10(-18)/E, resulting in a signal of sufficient strength to overcome thermal noise. Using the electroreceptor organ of Kryptopterus as a mathematical and experimental model, we showed that at the frequency of maximum sensitivity (10 Hz), fields as low as 2 microV/m could be detected, and that the observation could be explained if a glycoprotein mass of 0.7 x 10(-12) kg (a sphere 11 microm in diameter) were bound to channel gates. Antibodies against apical membrane structures in Kryptopterus blocked field transduction, which was consistent with the proposal that it occurred at the membrane surface. Although the target of the field was hypothesized to be an ion channel, the proposed mechanism can easily be extended to include other kinds of membrane proteins.     

Effect of syncytium structure of receptor systems on stochastic resonance induced by chaotic potential fluctuation.

To study a role of syncytium structure of sensory receptor systems in the detection of weak signals through stochastic resonance, we present a model of a receptor system with syncytium structure in which receptor cells are interconnected by gap junctions. The apical membrane of each cell includes two kinds of ion channels whose gating processes are described by the deterministic model. The membrane potential of each cell fluctuates chaotically or periodically, depending on the dynamical state of collective channel gating. The chaotic fluctuation of membrane potential acts as internal noise for the stochastic resonance. The detection ability of the system increases as the electric conductance between adjacent cells generated by the gap junction increases. This effect of gap junctions arises mainly from the fact that the synchronization of chaotic fluctuation of membrane potential between the receptor cells is strengthened as the density of gap junctions is increased.     

Possible involvement of the ampullary electroreceptor system in detection of frequency-modulated electrocommunication signals in Eigenmannia

Behavioral and electrophysiological experiments were conducted to examine whether frequency-modulated electrocommunication signals are detected by the ampullary electroreceptor system in Eigenmannia. First, frequency-modulated electric organ discharges were found to contain a low-frequency component that could be detected by the ampullary system. Second, fish were successfully trained to distinguish a frequency-modulated signal, which contained a low-frequency component as in natural signals, from an artificial signal in which the low-frequency component was eliminated but still modulated in frequency. Subsequently, the trained fish responded without reinforcement to a low-frequency sinusoidal signal which mimicked the low-frequency component in the frequency-modulated signal, suggesting that the fish used the ampullary system to detect frequency modulation. Finally, physiological recording from ampullary afferent fibers demonstrated that they respond to frequency-modulated signals as predicted from the signal's low-frequency component. Electrophysiological study also showed that detection of frequency modulation by the ampullary system is immune to the presence of other constant electric organ discharges. Accepted: 28 June 1998     

Hearing Sensitivity to Shifts of Rippled-Spectrum Sound Signals in Masking Noise

The goal of the study was to enlarge knowledge of discrimination of complex sound signals by the auditory system in masking noise. For that, influence of masking noise on detection of shift of rippled spectrum was studied in normal listeners. The signal was a shift of ripple phase within a 0.5-oct wide rippled spectrum centered at 2 kHz. The ripples were frequency-proportional (throughout the band, ripple spacing was a constant proportion of the ripple center frequency). Simultaneous masker was a 0.5-oct noise below-, on-, or above the signal band. Both the low-frequency (center frequency 1 kHz) and on-frequency (the same center frequency as for the signal) maskers increased the thresholds for detecting ripple phase shift. However, the threshold dependence on the masker level was different for these two maskers. For the on-frequency masker, the masking effect primarily depended on the masker/signal ratio: the threshold steeply increased at a ratio of 5 dB, and no shift was detectable at a ratio of 10 dB. For the low-frequency masker, the masking effect primarily depended on the masker level: the threshold increased at a masker level of 80 dB SPL, and no shift was detectable at a masker level of 90 dB (for a signal level of 50 dB) or 100 dB (for a signal level of 80 dB). The high-frequency masker had little effect. The data were successfully simulated using an excitation-pattern model. In this model, the effect of the on-frequency masker appeared to be primarily due to a decrease of ripple depth. The effect of the low-frequency masker appeared due to widening of the auditory filters at high sound levels.     

Superposition properties of independent ion channels

Membrane patches usually contain several ion channels of a given type. However, most of the stochastic modelling on which data analysis (in particular, estimation of kinetic constants) is currently based, relates to a single channel rather than to multiple channels. Attempts to circumvent this problem experimentally by recording under conditions where channel activity is low are restrictive and can introduce bias; moreover, possibly important information on how multichannel systems behave will be missed. We have extended existing theory to multichannel systems by applying results from point process theory to derive some distributional properties of the various types of sojourn time that occur when a given number of channels are open in a system containing a specified number of independent channels in equilibrium. Separate development of properties of a single channel and the superposition of several such independent channels simplifies the presentation of known results and extensions. To illustrate the general theory, particular attention is given to the types of sojourn time that occur in a two channel system; detailed expressions are presented for a selection of models, both Markov and non-Markov.