Examining noise sources at the single-molecule level: 1/f noise of an open maltoporin channel

Probing electrophysiological activity of amphiphilic Dynorphin A in planar neutral membranes reveals both ion channel-like activity and neuropeptide translocation

Dynorphin A (DynA) is an endogenous neuropeptide that besides acting as a ligand of the κ-opioid receptor, presents some non-opioid pathophysiological properties associated to its ability to induce cell permeability similarly to cell-penetrating peptides (CPPs). Here, we use electrophysiology experiments to show that amphiphilic DynA generates aqueous pores in neutral membranes similar to those reported previously in charged membranes, but we also find other events thermodynamically incompatible with voltage-driven ion channel activity (i.e. non-zero currents with no applied voltage in symmetric salt conditions, reversal potentials that exceed the theoretical limit for a given salt concentration gradient). By comparison with current traces generated by other amphiphilic molecule known to spontaneously cross membranes, we hypothesize that DynA could directly translocate across neutral bilayers, a feature never observed in charged membranes following the same electrophysiological protocol. Our findings suggest that DynA interaction with the cellular membrane is modulated by the lipid charge distribution, enabling either passive ionic transport via membrane remodeling and pore formation or by peptide direct internalization independent of cellular transduction pathways.

Disentangling 1/f noise from confined ion dynamics

Ion transport through biological and solid-state nanochannels is known to be a highly noisy process. The power spectrum of current fluctuations is empirically known to scale like the inverse of frequency, following the long-standing yet poorly understood Hooge's law. Here, we report measurements of current fluctuations across nanometer-scale two-dimensional channels with different surface properties. The structure of fluctuations is found to depend on the channel's material. While in pristine channels current fluctuations scale like 1/f1+a with a = 0-0.5, the noise power spectrum of activated graphite channels displays different regimes depending on frequency. Based on these observations, we develop a theoretical formalism directly linking ion dynamics and current fluctuations. We predict that the noise power spectrum takes the form 1/f × Schannel(f), where 1/f fluctuations emerge in fluidic reservoirs on both sides of the channel and Schannel describes fluctuations inside it. Deviations to Hooge's law thus allow direct access to the ion transport dynamics of the channel - explaining the entire phenomenology observed in experiments on 2D nanochannels. Our results demonstrate how current fluctuations can be used to characterize nanoscale ion dynamics.

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

Observing finite regions of a bigger system is a common aim, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received little attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as 1/f3/2, where f is the frequency. This signature of fractional noise shows the universality of 1/f3/2 scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.

Chloroquine-analogues block anthrax protective antigen channels in steady-state and kinetic studies

The tripartite anthrax toxin from Bacillus anthracis represents the prototype of A-B type of toxins, where the effector A (an enzymatic subunit) is transported with the help of a binding component B into a target cell. Anthrax toxin consists of three different molecules, two effectors, lethal factor (LF) and edema factor (EF) and the binding component also known as protective antigen (PA). PA forms heptamers or octamers following binding to host cell's receptors and mediates the translocation of the effectors into the cytosol via the endosomal pathway. The cation-selective PA₆₃-channel is able to reconstitute in lipid membranes and can be blocked by chloroquine and other heterocyclic compounds. This suggests that the PA₆₃-channel contains a binding site for quinolines. In this study, we investigated the structure-function relationship of different quinolines for the block of the PA₆₃-channel. The affinity of the different chloroquine analogues to the PA₆₃-channel as provided by the equilibrium dissociation constant was measured using titrations. Some quinolines had a much higher affinity to the PA₆₃-channel than chloroquine itself. We also performed ligand-induced current noise measurements using fast Fourier transformation to get insight in the kinetics of the binding of some quinolines to the PA₆₃-channel. The on-rate constants of ligand binding were around 10⁸M^-1·s^-1 at 150mM KCl and were only little dependent on the individual quinoline. The off-rates varied between 4s^-1 and 160s^-1 and depended much more on the structure of the molecules than the on-rate constants. The possible use of the 4-aminoquinolines as a therapy is discussed.

Biphasic concentration patterns in ionic transport under nanoconfinement revealed in steady-state and time-dependent properties

Ion permeation across nanoscopic structures differs considerably from microfluidics because of strong steric constraints, transformed solvent properties, and charge-regulation effects revealed mostly in diluted solutions. However, little is known about nanofluidics in moderately concentrated solutions, which are critically important for industrial applications and living systems. Here, we show that nanoconfinement triggers general biphasic concentration patterns in a myriad of ion transport properties by using two contrasting systems: a biological ion channel and a much larger synthetic nanopore. Our findings show a low-concentration regime ruled by classical Debye screening and another one where ion-ion correlations and enhanced ion-surface interactions contribute differently to each electrophysiological property. Thus, different quantities (e.g., conductance vs noise) measured under the same conditions may appear contradictory because they belong to different concentration regimes. In addition, non-linear effects that are barely visible in bulk conductivity only in extremely concentrated solutions become apparent in nanochannels around physiological conditions.

Weak Point of SARS-CoV-2: Human and Viral Ion Channels under External Physical Fields

The ionic E-nanochannel (viroporin) is the weak point of SARS-CoV-2, the virus responsible for the (still threatening) COVID-19 since it is vital to the virus's budding and propagation. Therefore, targeting it to disable its functions ought to incapacitate, or at least weaken, the virus. The ionic currents inside this channel could be affected and disturbed by direct physical attack via the actions of external fields. The paper presents the first step towards the application of such methods in the fight against the current pandemic, numerical simulations of external fields' impact on ionic currents through viral channels. These simulations-based on the actual, detailed physical nanostructure of ionic channels, measured experimentally and reported in the literature-show that external physical fields can diminish the channel's currents and that the lower the channel's selectivity, the stronger the effect. Simulations suggest that SARS-CoV-2 E-viroporin is almost non-selective, which means that the whole virus ought to be highly vulnerable to the actions of external physical fields, much more vulnerable than the much more selective human cell ionic channels. If corroborated by experiment, this observation may result in an innovative method of dealing with the recent pandemic caused by SARS-CoV-2 and other similar viruses.

The P. aeruginosa effector Tse5 forms membrane pores disrupting the membrane potential of intoxicated bacteria

The type VI secretion system (T6SS) of Pseudomonas aeruginosa injects effector proteins into neighbouring competitors and host cells, providing a fitness advantage that allows this opportunistic nosocomial pathogen to persist and prevail during the onset of infections. However, despite the high clinical relevance of P. aeruginosa, the identity and mode of action of most P. aeruginosa T6SS-dependent effectors remain to be discovered. Here, we report the molecular mechanism of Tse5-CT, the toxic auto-proteolytic product of the P. aeruginosa T6SS exported effector Tse5. Our results demonstrate that Tse5-CT is a pore-forming toxin that can transport ions across the membrane, causing membrane depolarisation and bacterial death. The membrane potential regulates a wide range of essential cellular functions; therefore, membrane depolarisation is an efficient strategy to compete with other microorganisms in polymicrobial environments.

Measurement of the low-frequency charge noise of bacteria

Bacteria meticulously regulate their intracellular ion concentrations and create ionic concentration gradients across the bacterial membrane. These ionic concentration gradients provide free energy for many cellular processes and are maintained by transmembrane transport. Given the physical dimensions of a bacterium and the stochasticity in transmembrane transport, intracellular ion concentrations and hence the charge state of a bacterium are bound to fluctuate. Here we investigate the charge noise of hundreds of nonmotile bacteria by combining electrical measurement techniques from condensed matter physics with microfluidics. In our experiments, bacteria in a microchannel generate charge density fluctuations in the embedding electrolyte due to random influx and efflux of ions. Detected as electrical resistance noise, these charge density fluctuations display a power spectral density proportional to 1/f^{2} for frequencies 0.05Hz≤f≤1Hz. Fits to a simple noise model suggest that the steady-state charge of a bacterium fluctuates by ±1.30×10^{6}e(e≈1.60×10^{-19}C), indicating that bacterial ion homeostasis is highly dynamic and dominated by strong charge noise. The rms charge noise can then be used to estimate the fluctuations in the membrane potential; however, the estimates are unreliable due to our limited understanding of the intracellular concentration gradients.

Current noise of a protein-selective biological nanopore

1/f current noise is ubiquitous in protein pores, porins, and channels. We have previously shown that a protein-selective biological nanopore with an external protein receptor can function as a 1/f noise generator when a high-affinity protein ligand is reversibly captured by the receptor. Here, we demonstrate that the binding affinity and concentration of the ligand are key determinants for the nature of current noise. For example, 1/f was absent when a protein ligand was reversibly captured at a much lower concentration than its equilibrium dissociation constant against the receptor. Furthermore, we also analyzed the composite current noise that resulted from mixtures of low-affinity and high-affinity ligands against the same receptor. This study highlights the significance of protein recognition events in the current noise fluctuations across biological membranes.

Dynorphin A induces membrane permeabilization by formation of proteolipidic pores. Insights from electrophysiology and computational simulations

Dynorphins are endogenous neuropeptides that function as ligands for the κ-opioid receptor. In addition to opioid activity, dynorphins can induce several pathological effects such as neurological dysfunctions and cell death. Previous studies have suggested that Dynorphin A (DynA) mediates some pathogenic actions through formation of transient pores in lipid domains of the plasma membrane. Here, we use planar bilayer electrophysiology to show that DynA induces pore formation in negatively charged membranes. We find a large variability in pore conformations showing equilibrium conductance fluctuations, what disregards electroporation as the dominant mechanism of pore formation. Ion selectivity measurements showing cationic selectivity indicate that positive protein charges of DynA are stabilized by phosphatidyl serine negative charges in the formation of combined structures. We complement our study with computational simulations that assess the stability of diverse peptide arrangements in the hydrophobic core of the bilayer. We show that DynA is capable of assembling in charged membranes to form water-filled pores that conduct ions.

Nonequilibrium, weak-field-induced cyclotron motion: A mechanism for magnetobiology

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a (classically) zero equilibrium response. Second, the friction in the cellular environment is large, preventing a weak field to alter nonequilibrium processes such as a free diffusion of charges. Here we study a class of nonequilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. Such nonequilibrium states are generated by a white noise acting on the ion additionally to the nonlocal (memory-containing) friction and noise generated by an equilibrium thermal bath. The intensity of this white noise can be weak, i.e., much smaller than the thermal noise intensity.

The initiation of shear band formation in deformed metallic glasses from soft localized domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u²⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u²⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

Hydrophobic Gating and 1/f Noise of the Anthrax Toxin Channel

"Pink" or 1/f noise is a natural phenomenon omnipresent in physics, economics, astrophysics, biology, and even music and languages. In electrophysiology, the stochastic activity of a number of biological ion channels and artificial nanopores could be characterized by current noise with a 1/f power spectral density. In the anthrax toxin channel (PA₆₃), it appears as fast voltage-independent current interruptions between conducting and nonconducting states. This behavior hampers potential development of PA₆₃ as an ion-channel biosensor. On the bright side, the PA₆₃ flickering represents a mesmerizing phenomenon to investigate. Notably, similar 1/f fluctuations are observed in the channel-forming components of clostridial binary C2 and iota toxins, which share functional and structural similarities with the anthrax toxin channel. Similar to PA₆₃, they are evolved to translocate the enzymatic components of the toxins into the cytosol. Here, using high-resolution single-channel lipid bilayer experiments and all-atom molecular dynamic simulations, we suggest that the 1/f noise in PA₆₃ occurs as a result of "hydrophobic gating" at the ϕ-clamp region, the phenomenon earlier observed in several water-filled channels "fastened" inside by the hydrophobic belts. The ϕ-clamp is a narrow "hydrophobic ring" in the PA₆₃ lumen formed by seven or eight phenylalanine residues at position 427, conserved in the C2 and iota toxin channels, which catalyzes protein translocation. Notably, the 1/f noise remains undetected in the F427A PA₆₃ mutant. This finding can elucidate the functional purpose of 1/f noise and its possible role in the transport of the enzymatic components of binary toxins.

Intrinsic fractional noise in nanopores: The effect of reservoirs

Fluctuations affect nanoporous transport in complex and intricate ways, making optimization of the signal-to-noise ratio in artificial designs challenging. Here, we focus on the simplest nanopore system, where non-interacting particles diffuse through a pore separating reservoirs. We find that the concentration difference between both sides (akin to the osmotic pressure drop) exhibits fractional noise in time t with mean square average that grows as t^1/2. This originates from the diffusive exchange of particles from one region to another. We fully rationalize this effect, with particle simulations and analytic solutions. We further infer the parameters (pore radius and pore thickness) that control this exotic behavior. As a consequence, we show that the number of particles within the pore also exhibits fractional noise. Such fractional noise is responsible for noise spectral density scaling as 1/f^3/2 with frequency f, and we quantify its amplitude. Our theoretical approach is applicable to more complex nanoporous systems (for example, with adsorption within the pore) and drastically simplifies both particle simulations and analytic calculus.

Specific adsorption of trivalent cations in biological nanopores determines conductance dynamics and reverses ionic selectivity

Adsorption processes are central to ionic transport in industrial and biological membrane systems. Multivalent cations modulate the conductive properties of nanofluidic devices through interactions with charged surfaces that depend principally on the ion charge number. Considering that ion channels are specialized valves that demand a sharp specificity in ion discrimination, we investigate the adsorption dynamics of trace amounts of different salts of trivalent cations in biological nanopores. We consider here OmpF from Escherichia coli, an archetypical protein nanopore, to probe the specificity of biological nanopores to multivalent cations. We systematically compare the effect of three trivalent electrolytes on OmpF current-voltage relationships and characterize the degree of rectification induced by each ion. We also analyze the open channel current noise to determine the existence of equilibrium/non-equilibrium mechanisms of ion adsorption and evaluate the extent of charge inversion through selectivity measurements. We show that the interaction of trivalent electrolytes with biological nanopores occurs via ion-specific adsorption yielding differential modulation of ion conduction and selectivity inversion. We also demonstrate the existence of non-equilibrium fluctuations likely related to ion-dependent trapping-detrapping processes. Our study provides fundamental information relevant to different biological and electrochemical systems where transport phenomena involve ion adsorption in charged surfaces under nanoscale confinement.

Assessment of 1/f noise associated with nanopores fabricated through chemically tuned controlled dielectric breakdown

Recently, we developed a fabrication method-chemically-tuned controlled dielectric breakdown (CT-CDB)-that produces nanopores (through thin silicon nitride membranes) surpassing legacy drawbacks associated with solid-state nanopores (SSNs). However, the noise characteristics of CT-CDB nanopores are largely unexplored. In this work, we investigated the 1/f noise of CT-CDB nanopores of varying solution pH, electrolyte type, electrolyte concentration, applied voltage, and pore diameter. Our findings indicate that the bulk Hooge parameter (α_b ) is about an order of magnitude greater than SSNs fabricated by transmission electron microscopy (TEM) while the surface Hooge parameter (α_s ) is ∼3 order magnitude greater. Theα_s of CT-CDB nanopores was ∼5 orders of magnitude greater than theirα_b , which suggests that the surface contribution plays a dominant role in 1/f noise. Experiments with DNA exhibited increasing capture rates with pH up to pH ∼8 followed by a drop at pH ∼9 perhaps due to the onset of electroosmotic force acting against the electrophoretic force. The1/f noise was also measured for several electrolytes and LiCl was found to outperform NaCl, KCl, RbCl, and CsCl. The 1/f noise was found to increase with the increasing electrolyte concentration and pore diameter. Taken together, the findings of this work suggest the pH approximate 7-8 range to be optimal for DNA sensing with CT-CDB nanopores.

Biological Nanopores: Engineering on Demand

Nanopore-based sensing is a powerful technique for the detection of diverse organic and inorganic molecules, long-read sequencing of nucleic acids, and single-molecule analyses of enzymatic reactions. Selected from natural sources, protein-based nanopores enable rapid, label-free detection of analytes. Furthermore, these proteins are easy to produce, form pores with defined sizes, and can be easily manipulated with standard molecular biology techniques. The range of possible analytes can be extended by using externally added adapter molecules. Here, we provide an overview of current nanopore applications with a focus on engineering strategies and solutions.

Protein Ligand-Induced Amplification in the 1/f Noise of a Protein-Selective Nanopore

Previous studies of transmembrane protein channels have employed noise analysis to examine their statistical current fluctuations. In general, these explorations determined a substrate-induced amplification in the Gaussian white noise of these systems at a low-frequency regime. This outcome implies a lack of slowly appearing fluctuations in the number and local mobility of diffusing charges in the presence of channel substrates. Such parameters are among the key factors in generating a low-frequency 1/f noise. Here, we show that a protein-selective biological nanopore exhibits a substrate-induced amplification in the 1/f noise. The modular composition of this biological nanopore includes a hydrophilic transmembrane protein pore fused to a water-soluble binding protein on its extramembranous side. In addition, this protein nanopore shows an open substate populated by a high-frequency current noise because of the flickering of an engineered polypeptide adaptor at the tip of the pore. However, the physical association of the protein ligand with the binding domain reversibly switches the protein nanopore from a high-frequency noise substate into a quiet substate. In the absence of the protein ligand, our nanopore shows a low-frequency white noise. Remarkably, in the presence of the protein ligand, an amplified low-frequency 1/f noise was detected in a ligand concentration-dependent fashion. This finding suggests slowly occurring equilibrium fluctuations in the density and local mobility of charge carriers under these conditions. Furthermore, we report that the excess in 1/f noise is generated by reversible switches between the noisy ligand-released substate and the quiet ligand-captured substate. Finally, quantitative aspects of the low-frequency 1/f noise are in accord with theoretical predictions of the current noise analysis of protein channel-ligand interactions.

Single-molecule conformational dynamics of viroporin ion channels regulated by lipid-protein interactions

Classic swine fever is a highly contagious and often fatal viral disease that is caused by the classical swine fever virus (CSFV). Protein p7 of CFSV is a prototype of viroporin, a family of small, highly hydrophobic proteins postulated to modulate virus-host interactions during the processes of virus entry, replication and assembly. It has been shown that CSFV p7 displays substantial ion channel activity when incorporated into membrane systems, but a deep rationalization of the size and dynamics of the induced pores is yet to emerge. Here, we use high-resolution conductance measurements and current fluctuation analysis to demonstrate that CSFV p7 channels are ruled by equilibrium conformational dynamics involving protein-lipid interactions. Atomic force microscopy (AFM) confirms the existence of a variety of pore sizes and their tight regulation by solution pH. We conclude that p7 viroporin forms subnanometric channels involved in virus propagation, but also much larger pores (1-10 nm in diameter) with potentially significant roles in virus pathogenicity. Our findings provide new insights into the sources of noise in protein electrochemistry and demonstrate the existence of slow complex dynamics characteristic of crowded systems like biomembrane surfaces.

Low-frequency noise induced by cation exchange fluctuation on the wall of silicon nitride nanopore

Nanopore-based biosensors have attracted attention as highly sensitive microscopes for detecting single molecules in aqueous solutions. However, the ionic current noise through a nanopore degrades the measurement accuracy. In this study, the magnitude of the low-frequency noise in the ionic current through a silicon nitride nanopore was found to change depending on the metal ion species in the aqueous solution. The order of the low-frequency noise magnitudes of the alkali metal ionic current was consistent with the order of the adsorption affinities of the metal ions for the silanol surface of the nanopore (Li <Na <K < Rb <Cs). For the more adsorptive alkaline earth metal ions (Mg and Ca), the low-frequency noise magnitudes were as low as those for Li ions. This tendency, i.e., metal ions having a very high or low adsorption affinity causing a reduction in low-frequency noise, suggests that the low-frequency noise was induced by the exchange reactions between protons and metal ions occurring on the silanol surface. In addition, the low-frequency noise in the ionic current remained low even after replacing the CaCl₂ aqueous solution with a CsCl aqueous solution, indicating that Ca ions continued being adsorbed onto silanol groups even after removing the aqueous solution.

Comparing Current Noise in Biological and Solid-State Nanopores

Nanopores bear great potential as single-molecule tools for bioanalytical sensing and sequencing, due to their exceptional sensing capabilities, high-throughput, and low cost. The detection principle relies on detecting small differences in the ionic current as biomolecules traverse the nanopore. A major bottleneck for the further progress of this technology is the noise that is present in the ionic current recordings, because it limits the signal-to-noise ratio (SNR) and thereby the effective time resolution of the experiment. Here, we review the main types of noise at low and high frequencies and discuss the underlying physics. Moreover, we compare biological and solid-state nanopores in terms of the SNR, the important figure of merit, by measuring translocations of a short ssDNA through a selected set of nanopores under typical experimental conditions. We find that SiNx solid-state nanopores provide the highest SNR, due to the large currents at which they can be operated and the relatively low noise at high frequencies. However, the real game-changer for many applications is a controlled slowdown of the translocation speed, which for MspA was shown to increase the SNR > 160-fold. Finally, we discuss practical approaches for lowering the noise for optimal experimental performance and further development of the nanopore technology.

Anti-cross-correlation between the adjacent open and closed durations of Markovian channels

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of N independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as M out of N subunits in the open state with N>M>0. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

Probing Thermotropic Phase Behavior of Dipalmitoylphosphatidylcholine Bilayers from Electrical and Topographic Data in a Horizontal Black Lipid Membrane Model

Here, a homemade device allowed preparing horizontal lipid bilayer membranes (hBLMs) for recording electrical and topographical data simultaneously and in real-time, under temperature (T)-controlled conditions along a cooling process of dipalmitoylphosphatidylcholine (DPPC) bilayers. Electrical parameters (ionic current intensity, I, and transmembrane resistance, R = ΔV/I) plotted against T exhibited discontinuities at the main transition (T_Pβ'→Lα) and pretransition (T_Lβ→Pβ') temperatures of DPPC. The T-dependent sensitivity to ΔV-induced electrostriction was revealed by capacitance measurements. The patterns of I fluctuation described long-range correlations reflected by 1/f-type noise in the ripple phase (P_β') and Brownian-type fluctuations in the liquid-crystalline (L_α) phase at voltage intensities lower than a voltage threshold (ΔV_th = ±160 mV), indicating that autocorrelations arise from an underlying structural connectivity that takes place within ordered phases. At |V| ≥ V_th, the fluctuation dynamics exhibited a 1/f behavior over the whole temperature range analyzed, suggesting that upon a certain intensity of external electrical perturbation, the membrane system evolves toward a voltage-induced percolated-pore state. At T > T_Pβ'→Lα, differential interference contrast micrographs showed droplet-like structures, probably containing solvent traces of the lipid solution, which were reverted upon cooling. However, droplets did not interfere with the thermotropic equilibrium of the bilayer phase. This suggested that the temperature-induced changes in the electrical properties of the bilayer, as well as in the complexity of the fluctuation patterns (emergency of long- and short-range correlations), were strongly associated with the characteristic thermotropic behavior of DPPC, without significant deviations induced by the presence of residual n-decane in the bilayer. Our hBLM model membrane proved useful for correlating thermotropic phase changes with electro-biophysical and topographical information.

Adsorption Kinetics in Open Nanopores as a Source of Low-Frequency Noise

Ionic current measurements through solid-state nanopores consistently show a power spectral density that scales as 1/f ^α at low frequency f, with an exponent α ∼ 0.5-1.5, but strikingly, the physical origin of this behavior remains elusive. Here, we perform simulations of particles reversibly adsorbing at the surface of a nanopore and show that the fluctuations in the number of adsorbed particles exhibit low-frequency pink noise. We furthermore propose theoretical modeling for the time-dependent adsorption of particles on the nanopore surface for various geometries, which predicts a frequency spectrum in very good agreement with the simulation results. Altogether, our results highlight that the low-frequency noise takes its origin in the reversible adsorption of ions at the pore surface combined with the long-lasting excursions of the ions in the reservoirs. The scaling regime of the power spectrum extends down to a cutoff frequency which is far smaller than simple diffusion estimates. Using realistic values for the pore dimensions and the adsorption-desorption kinetics, this predicts the observation of pink noise for frequencies down to the hertz for a typical solid-state nanopore, in good agreement with experiments.

Single measurement detection of individual cell ionic oscillations using an n-type semiconductor - electrolyte interface

Pollen tubes are used as models in studies on the type of tip-growth in plants. They are an example of polarised and rapid growth because pollen tubes are able to quickly invade the flower pistil in order to accomplish fertilisation. How different ionic fluxes are perceived, processed or generated in the pollen tube is still not satisfactorily understood. In order to measure the H⁺, K⁺, Ca²⁺ and Cl⁻ fluxes of a single pollen tube, we developed an Electrical Lab on a Photovoltaic-Chip (ELoPvC) on which the evolving cell was immersed in an electrolyte of a germination medium. Pollen from Hyacinthus orientalis L. was investigated ex vivo. We observed that the growing cell changed the (redox) potential in the medium in a periodic manner. This subtle measurement was feasible due to the effects that were taking place at the semiconductor-liquid interface. The experiment confirmed the existence of the ionic oscillations that accompany the periodic extension of pollen tubes, thereby providing – in a single run – the complete discrete frequency spectrum and phase relationships of the ion gradients and fluxes, while all of the metabolic and enzymatic functions of the cell life cycle were preserved. Furthermore, the global 1/f^α characteristic of the power spectral density, which corresponds to the membrane channel noise, was found.

Current fluctuations across a nano-pore

The frequency-dependent spectrum of current fluctuations through nano-scale channels is studied using analytical and computational techniques. Using a stochastic Nernst-Planck description and neglecting the interactions between the ions inside the channel, an expression is derived for the current fluctuations, assuming that the geometry of the channel can be incorporated through the lower limits for various wave-vector modes. Since the resulting expression turns out to be quite complex, a number of further approximations are discussed such that relatively simple expressions can be used for practical purposes. The analytical results are validated using Langevin dynamics simulations.

Sensing Magnetic Fields with Magnetosensitive Ion Channels

[-15]Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k B T in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved.

Measuring a frequency spectrum for single-molecule interactions with a confined nanopore

The time-domain nanopore signal is preciously converted into energy–frequency–time spectra with high frequency resolution and high time resolution using the Hilbert–Huang transform for revealing the detail behaviours of single-molecule weak interactions.

Phosphorylation of rat brain purified mitochondrial Voltage-Dependent Anion Channel by c-Jun N-terminal kinase-3 modifies open-channel noise

The drift kinetic energy of ionic flow through single ion channels cause vibrations of the pore walls which are observed as open-state current fluctuations (open-channel noise) during single-channel recordings. Vibration of the pore wall leads to transitions among different conformational sub-states of the channel protein in the open-state. Open-channel noise analysis can provide important information about the different conformational sub-state transitions and how biochemical modifications of ion channels would affect their transport properties. It has been shown that c-Jun N-terminal kinase-3 (JNK3) becomes activated by phosphorylation in various neurodegenerative diseases and phosphorylates outer mitochondrion associated proteins leading to neuronal apoptosis. In our earlier work, JNK3 has been reported to phosphorylate purified rat brain mitochondrial voltage-dependent anion channel (VDAC) in vitro and modify its conductance and opening probability. In this article we have compared the open-state noise profile of the native and the JNK3 phosphorylated VDAC using Power Spectral Density vs frequency plots. Power spectral density analysis of open-state noise indicated power law with average slope value α ≈1 for native VDAC at both positive and negative voltage whereas average α value < 0.5 for JNK3 phosphorylated VDAC at both positive and negative voltage. It is proposed that 1/f¹ power law in native VDAC open-state noise arises due to coupling of ionic transport and conformational sub-states transitions in open-state and this coupling is perturbed as a result of channel phosphorylation.

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f)∼A/f^{2}, i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).

The Power Spectrum of Ionic Nanopore Currents: The Role of Ion Correlations

We calculate the power spectrum of electric-field-driven ion transport through nanometer-scale membrane pores using both linearized mean-field theory and Langevin dynamics simulations. Remarkably, the linearized mean-field theory predicts a plateau in the power spectral density at low frequency ω, which is confirmed by the simulations at low ion concentration. At high ion concentration, however, the power spectral density follows a power law that is reminiscent of the 1/ω(α) dependence found experimentally at low frequency. On the basis of simulations with and without ion-ion interactions, we attribute the low-frequency power-law dependence to ion-ion correlations. We show that neither a static surface charge density, nor an increased pore length, nor an increased ion valency have a significant effect on the shape of the power spectral density at low frequency.

Fullerenol C60(OH)24 increases ion permeability of lipid membranes in a pH-dependent manner

Fullerenols are water-soluble analogs of fullerene exhibiting both antioxidant and prooxidant activities in vitro and in vivo. Here we report, for the first time, that fullerenol C60(OH)24 can induce ion permeability of a planar lipid bilayer membrane via the formation of ion pores or conductive defects with a preference for cations over anions. The fullerenol-mediated electrical current displayed non-linear concentration dependence and was reversibly enhanced by alkalinization. Calcium and magnesium ions decreased the fullerenol-induced potassium ion permeability. Voltage dependence of the current was sensitive to membrane composition, with the conductance being well pronounced in fully saturated diphytanoylphosphatidylcholine. Fullerenol did not induce carboxyfluorescein leakage from liposomes, suggesting a small size of fullerenol-induced pores. In contrast to ion permeability, the binding of C60(OH)24 to liposomes increased at acidic pH, as measured by fluorescence quenching of pyrene-labeled lipid. In line with this, the photodynamic action of fullerenol on the peptide gramicidin A also increased at low pH. It is hypothesized that aggregates of fullerenol may stabilize transient conductive lipid defects or pores formed under a variety of stress conditions.

Accurate Langevin approaches to simulate Markovian channel dynamics

The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

Tailored Polymeric Membranes for Mycobacterium Smegmatis Porin A (MspA) Based Biosensors

Nanopores based on protein channels inserted into lipid membranes have paved the way towards a wide-range of inexpensive biosensors, especially for DNA sequencing. A key obstacle in using these biological ion channels as nanodevices is the poor stability of lipid bilayer membranes. Amphiphilic block copolymer membranes have emerged as a robust alternative to lipid membranes. While previous efforts have shown feasibility, we demonstrate for the first time the effect of polymer composition on MspA protein functionality. We show that membrane-protein interaction depends on the hydrophobic-hydrophilic ratio (f-ratio) of the block copolymer. These effects are particularly pronounced in asymmetric protein pores like MspA compared to the cylindrical α-Hemolysin pore. A key effect of membrane-protein interaction is the increased 1/fα noise. After first showing increases in 1/fα behaviour arise from increased substate activity, the noise power spectral density S(f) was used as a qualitative tool for understanding protein-membrane interactions in polymer membranes. Polymer compositions with f-ratios close to lipid membranes caused noise behaviour not observed in lipid membranes. However, by modifying the f-ratio using a modular synthetic approach, we were able to design a block copolymer exhibiting noise properties similar to a lipid membrane, albeit with better stability. Thus, by careful optimization, block copolymer membranes can emerge as a robust alternative for protein-pore based nano-biosensors.

Excess white noise to probe transport mechanisms in a membrane channel

Current fluctuation analysis has been successfully used over the years to investigate the physical properties of different systems. Here, we perform single-channel time-resolved current experiments in a protein channel to evaluate the different transport mechanisms governing the channel function. Using different salts of monovalent and divalent cations in a wide range of concentrations and applied potentials, we analyze current fluctuations focusing on the voltage dependence of the additional white noise that appears in the low-frequency range of the spectra. We demonstrate that the channel displays two characteristic transport regimes: at low salt concentrations (10 mM to 1 M) ion permeation is controlled by the protein fixed charges that induce accumulation or exclusion of ions to preserve local electroneutrality. At high salt concentrations (>1M) adsorption processes associated to the binding of cations to the channel charges regulate the transport properties.

Electrophysiology investigation of Trichogin GA IV activity in planar lipid membranes reveals ion channels of well-defined size

Trichogin GA IV, an antimicrobial peptaibol, exerts its function by augmenting membrane permeability, but the molecular aspects of its pore-forming mechanism are still debated. Several lines of evidence indicate a 'barrel-stave' channel structure, similar to that of alamethicin, but the length of a trichogin helix is too short to span a normal bilayer. Herein, we present electrophysiology measurements in planar bilayers, showing that trichogin does form channels of a well-defined size (R=4.2⋅10(9)  Ω; corresponding at least to a trimeric aggregate) that span the membrane and allow ion diffusion, but do not exhibit voltage-dependent rectification, unlike those of alamethicin.

Origin of 1/f noise in hydration dynamics on lipid membrane surfaces

Water molecules on lipid membrane surfaces are known to contribute to membrane stability by connecting lipid molecules and acting as a water bridge. Although water structures and diffusivities near the membrane surfaces have been extensively studied, hydration dynamics on the surfaces has remained an open question. Here we investigate residence time statistics of water molecules on the surface of lipid membranes using all-atom molecular dynamics simulations. We show that hydration dynamics on the lipid membranes exhibits 1/f noise. Constructing a dichotomous process for the hydration dynamics, we find that residence times in each state follow a power-law with exponential cutoff and that the process can be regarded as a correlated renewal process where interoccurrence times are correlated. The results imply that the origin of the 1/f noise in hydration dynamics on the membrane surfaces is a combination of a power-law distribution with cutoff of interoccurrence times of switching events and a long-term correlation between the interoccurrence times. These results suggest that the 1/f noise attributed to the correlated renewal process may contribute to the stability of the hydration layers and lipid membranes.

Effect of confinement on DNA, solvent and counterion dynamics in a model biological nanopore

The application of recent advances in nanopore technology to high-throughput DNA sequencing requires a more detailed understanding of solvent, ion and DNA interactions occurring within these pores. Here we present a combination of atomistic and coarse-grained modeling studies of the dynamics of short single-stranded DNA (ssDNA) homopolymers within the alpha-hemolysin pore, for the two single-stranded homopolymers poly(dA)40 and poly(dC)40. Analysis of atomistic simulations along with the per-residue decomposition of protein-DNA interactions in these simulations gives new insight into the very complex issues that have yet to be fully addressed with detailed MD simulations. We discuss a modification of the solvent properties and ion distribution around DNA within nanopore confinement and put it into the general framework of counterion condensation theory. There is a reasonable agreement in computed properties from our all-atom simulations and the resulting predictions from analytical theories with experimental data, and our equilibrium results here support the conclusions from our previous non-equilibrium Brownian dynamics studies with a recently developed BROMOC protocol that cations are the primary charge carriers through alpha-hemolysin nanopores under an applied voltage in the presence of ssDNA. Clustering analysis led to an identification of distinct conformational states of captured polymer and depth of the current blockade. Therefore, our data suggest that confined polymer may act as a flickering gate, thus contributing to excess noise phenomena. We also discuss the extent of water structuring due to nanopore confinement and the relationship between the conformational dynamics of a captured polymer and the distribution of blocked current.

1/ f noise from the laws of thermodynamics for finite-size fluctuations

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals and to show non-Gaussian fluctuations characteristic of nanoscale systems.

1/ f Fluctuations of amino acids regulate water transportation in aquaporin 1

Aquaporins (AQPs), which transport water molecules across cell membranes, are involved in many physiological processes. Recently, it is reported that the water-water interactions within the channel are broken at the aromatic/arginine selectivity filter (ar/R region), which prevents proton transportation [U. K. Eriksson et al., Science 340, 1346 (2013)]. However, the effects of the conformational fluctuations of amino acids on water transportation remain unclear. Using all-atom molecular dynamics simulations, we analyze water transportation and fluctuations of amino acids within AQP1. The amino acids exhibit 1/f fluctuations, indicating possession of long-term memory. Moreover, we find that water molecules crossing the ar/R region obey a non-Poisson process. To investigate the effect of 1/f fluctuations on water transportation, we perform restrained molecular dynamics simulations of AQP1 and simple Langevin stochastic simulations. As a result, we confirm that 1/f fluctuations of amino acids contribute to water transportation in AQP1. These findings appreciably enhance our understanding of AQPs and suggest possibilities for developing biomimetic nanopores.

Use of nonelectrolytes reveals the channel size and oligomeric constitution of the Borrelia burgdorferi P66 porin

In the Lyme disease spirochete Borrelia burgdorferi, the outer membrane protein P66 is capable of pore formation with an atypical high single-channel conductance of 11 nS in 1 M KCl, which suggested that it could have a larger diameter than 'normal' Gram-negative bacterial porins. We studied the diameter of the P66 channel by analyzing its single-channel conductance in black lipid bilayers in the presence of different nonelectrolytes with known hydrodynamic radii. We calculated the filling of the channel with these nonelectrolytes and the results suggested that nonelectrolytes (NEs) with hydrodynamic radii of 0.34 nm or smaller pass through the pore, whereas neutral molecules with greater radii only partially filled the channel or were not able to enter it at all. The diameter of the entrance of the P66 channel was determined to be ≤1.9 nm and the channel has a central constriction of about 0.8 nm. The size of the channel appeared to be symmetrical as judged from one-sidedness of addition of NEs. Furthermore, the P66-induced membrane conductance could be blocked by 80-90% by the addition of the nonelectrolytes PEG 400, PEG 600 and maltohexaose to the aqueous phase in the low millimolar range. The analysis of the power density spectra of ion current through P66 after blockage with these NEs revealed no chemical reaction responsible for channel block. Interestingly, the blockage of the single-channel conductance of P66 by these NEs occurred in about eight subconductance states, indicating that the P66 channel could be an oligomer of about eight individual channels. The organization of P66 as a possible octamer was confirmed by Blue Native PAGE and immunoblot analysis, which both demonstrated that P66 forms a complex with a mass of approximately 460 kDa. Two dimension SDS PAGE revealed that P66 is the only polypeptide in the complex.

Designed azolopyridinium salts block protective antigen pores in vitro and protect cells from anthrax toxin

Background

Several intracellular acting bacterial protein toxins of the AB-type, which are known to enter cells by endocytosis, are shown to produce channels. This holds true for protective antigen (PA), the binding component of the tripartite anthrax-toxin of Bacillus anthracis. Evidence has been presented that translocation of the enzymatic components of anthrax-toxin across the endosomal membrane of target cells and channel formation by the heptameric/octameric PA₆₃ binding/translocation component are related phenomena. Chloroquine and some 4-aminoquinolones, known as potent drugs against Plasmodium falciparium infection of humans, block efficiently the PA₆₃-channel in a dose dependent way.

Methodology/Principal Findings

Here we demonstrate that related positively charged heterocyclic azolopyridinium salts block the PA₆₃-channel in the µM range, when both, inhibitor and PA₆₃ are added to the same side of the membrane, the cis-side, which corresponds to the lumen of acidified endosomal vesicles of target cells. Noise-analysis allowed the study of the kinetics of the plug formation by the heterocycles. In vivo experiments using J774A.1 macrophages demonstrated that the inhibitors of PA₆₃-channel function also efficiently block intoxication of the cells by the combination lethal factor and PA₆₃ in the same concentration range as they block the channels in vitro.

Conclusions/Significance

These results strongly argue in favor of a transport of lethal factor through the PA₆₃-channel and suggest that the heterocycles used in this study could represent attractive candidates for development of novel therapeutic strategies against anthrax.

Self-assembled DNA nanopores that span lipid bilayers

DNA nanotechnology excels at rationally designing bottom-up structures that can functionally replicate naturally occurring proteins. Here we describe the design and generation of a stable DNA-based nanopore that structurally mimics the amphiphilic nature of protein pores and inserts into bilayers to support a steady transmembrane flow of ions. The pore carries an outer hydrophobic belt comprised of small chemical alkyl groups which mask the negatively charged oligonucleotide backbone. This modification overcomes the otherwise inherent energetic mismatch to the hydrophobic environment of the membrane. By merging the fields of nanopores and DNA nanotechnology, we expect that the small membrane-spanning DNA pore will help open up the design of entirely new molecular devices for a broad range of applications including sensing, electric circuits, catalysis, and research into nanofluidics and controlled transmembrane transport.

Interactions of high-affinity cationic blockers with the translocation pores of B. anthracis, C. botulinum, and C. perfringens binary toxins

Cationic β-cyclodextrin derivatives were recently introduced as highly effective, potentially universal blockers of three binary bacterial toxins: anthrax toxin of Bacillus anthracis, C2 toxin of Clostridium botulinum, and iota toxin of Clostridium perfringens. The binary toxins are made of two separate components: the enzymatic A component, which acts on certain intracellular targets, and the binding/translocation B component, which forms oligomeric channels in the target cell membrane. Here we studied the voltage and salt dependence of the rate constants of binding and dissociation reactions of two structurally different β-cyclodextrins (AmPrβCD and AMBnTβCD) in the PA(63), C2IIa, and Ib channels (B components of anthrax, C2, and iota toxins, respectively). With all three channels, the blocker carrying extra hydrophobic aromatic groups on the thio-alkyl linkers of positively charged amino groups, AMBnTβCD, demonstrated significantly stronger binding compared with AmPrβCD. This effect is seen as an increased residence time of the blocker in the channels, whereas the time between blockages characterizing the binding reaction on-rate stays practically unchanged. Surprisingly, the voltage sensitivity, expressed as a slope of the logarithm of the blocker residence time as a function of voltage, turned out to be practically the same for all six cases studied, suggesting structural similarities among the three channels. Also, the more-effective AMBnTβCD blocker shows weaker salt dependence of the binding and dissociation rate constants compared with AmPrβCD. By estimating the relative contributions of the applied transmembrane field, long-range Coulomb, and salt-concentration-independent, short-range forces, we found that the latter represent the leading interaction, which accounts for the high efficiency of blockage. In a search for the putative groups in the channel lumen that are responsible for the short-range forces, we performed measurements with the F427A mutant of PA(63), which lacks the functionally important phenylalanine clamp. We found that the on-rates of the blockage were virtually conserved, but the residence times and, correspondingly, the binding constants dropped by more than an order of magnitude, which also reduced the difference between the efficiencies of the two blockers.