Simulations of amperometric monitoring of exocytosis: moderate pH variations within the cell-electrode cleft with the buffer diffusion.

Amperometry with ultramicroelectrodes is nowadays a routine technique to investigate neurotransmitter secretion by vesicular exocytosis at the single-cell level. This electroanalytical tool allows one to understand many aspects of the vesicular release in terms of mechanisms. However, the electrochemical detection relies on the oxidation of released neurotransmitters that produce 2H+ and thus the possible acidification of the cell-electrode cleft. In a previous work, we considered a model involving the H+ diffusion or/and its reaction with buffer species. In this article, we report a more general model which takes into account the ability of buffer species to move and to be regenerated within the cell-electrode cleft. As a consequence, the pH within the cleft is still equal to its physiological value regardless of the electrochemical detection of the vesicular release for usual exocytotic cell frequencies. This confirms that amperometry at the single-cell level is a very robust technique for investigating vesicular exocytosis.

Cavitation Mean Expectation Time in a Stretched Lennard-Jones Fluid under Confinement.

We investigate the nucleation of cavitation bubbles in a confined Lennard-Jones fluid subjected to negative pressures in a cubic enclosure. We perform molecular dynamics (MD) simulations with tunable interatomic potentials that enable us to control the wettability of solid walls by the liquid, that is, its contact angle. For a given temperature and pressure, as the solid is taken more hydrophobic, we put in evidence, an increase in nucleation probability. A Voronoi tessellation method is used to accurately detect the bubble appearance and its nucleation rate as a function of the contact angle. We adapt classical nucleation theory (CNT) proposed for the heterogeneous case on a flat surface to our situation where bubbles may appear on flat walls, edges, or corners of the confined box. We finally calculate a theoretical mean expectation time in these three cases. The ratio of these calculated values over the homogeneous case is computed and compared successfully against MD simulations. Beyond the infinite liquid case, this work explores the heterogeneous nucleation of cavitation bubbles, not only in the flat surface case but for more complex confining geometries.

Capillary bridge technique to study superhydrophobic surfaces.

We present here the use of the capillary bridge technique to study the wetting properties (advancing and receding contact angles) of transparent, textured and superhydrophobic surfaces over large wetted area. Apparent contact angles on such surfaces are classically measured using a goniometer in combination with video camera side visualization and a drop shape analysis. Recent experiments of Schellenberger et al. [F. Schellenberger, N. Encinas, D. Vollmer and H. J. Butt, Phys. Rev. Lett., 2016, 116(9), 096101] show that this method can significantly underestimate the apparent advancing contact angle. We use for the first time the capillary bridge setup for such textured surfaces, leading to a large (up to several cm2) wetted area, instead of having a reduced contact zone as in the drop case (mm2 or less). (1) We show here how to use the method and its characteristics to explore the wetting properties of superhydrophobic surfaces. We have developed a new analysis method in order to obtain the value of the contact angle for any position of the substrate. (2) We compare with the classical drop side view method, showing that advancing contact angles are systematically higher. (3) We compare to a few existing models, concluding a good agreement for receding values but not for advancing angles, for which models must be refined.

Na(+)/H(+) antiporter (NHE1) and lactate/H(+) symporters (MCTs) in pH homeostasis and cancer metabolism.

The Na(+)/H(+)-exchanger NHE1 and the monocarboxylate transporters MCT1 and MCT4 are crucial for intracellular pH regulation, particularly under active metabolism. NHE1, a reversible antiporter, uses the energy provided by the Na(+) gradient to expel H(+) ions generated in the cytosol. The reversible H(+)/lactate(-) symporters MCT1 and 4 cotransport lactate and proton, leading to the net extrusion of lactic acid in glycolytic tumors. In the first two sections of this article we review important features and remaining questions on the structure, biochemical function and cellular roles of these transporters. We then use a fully-coupled mathematical model to simulate their relative contribution to pH regulation in response to lactate production, as it occurs in highly hypoxic and glycolytic tumor cells. This article is part of a Special Issue entitled: Mitochondrial Channels edited by Pierre Sonveaux, Pierre Maechler and Jean-Claude Martinou.

Surrogate Data Methods Based on a Shuffling of the Trials for Synchrony Detection: The Centering Issue.

We investigate several distribution-free dependence detection procedures, all based on a shuffling of the trials, from a statistical point of view. The mathematical justification of such procedures lies in the bootstrap principle and its approximation properties. In particular, we show that such a shuffling has mainly to be done on centered quantities-that is, quantities with zero mean under independence-to construct correct p-values, meaning that the corresponding tests control their false positive (FP) rate. Thanks to this study, we introduce a method, named permutation UE, which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count. Each involved single test of this procedure achieves the prescribed level, so that the corresponding multiple testing procedure controls the false discovery rate (FDR), and this with as few assumptions as possible on the underneath distribution, except independence and identical distribution across trials. The mathematical meaning of this assumption is discussed, and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross-trials stationarity. Some simulations show, moreover, that permutation UE outperforms the trial-shuffling of Pipa and Grün ( 2003 ) and the MTGAUE method of Tuleau-Malot et al. ( 2014 ) in terms of single levels and FDR, for a comparable amount of false negatives. Application to real data is also provided.

Biological fractionation of lithium isotopes by cellular Na+/H+ exchangers unravels fundamental transport mechanisms.

Lithium (Li) has a wide range of uses in science, medicine, and industry, but its isotopy is underexplored, except in nuclear science and in geoscience. 6Li and 7Li isotopic ratio exhibits the second largest variation on earth's surface and constitutes a widely used tool for reconstructing past oceans and climates. As large variations have been measured in mammalian organs, plants or marine species, and as 6Li elicits stronger effects than natural Li (∼95% 7Li), a central issue is the identification and quantification of biological influence of Li isotopes distribution. We show that membrane ion channels and Na+-Li+/H+ exchangers (NHEs) fractionate Li isotopes. This systematic 6Li enrichment is driven by membrane potential for channels, and by intracellular pH for NHEs, where it displays cooperativity, a hallmark of dimeric transport. Evidencing that transport proteins discriminate between isotopes differing by one neutron opens new avenues for transport mechanisms, Li physiology, and paleoenvironments.

How Does Our Knowledge on the Na+/H+ Exchanger NHE1 Obtained by Biochemical and Molecular Analyses Keep up With Its Recent Structure Determination?

Na+/H+ exchangers are membrane transporters conserved in all living systems and therefore are assumed to be amongst the most ancestral molecular devices that equipped the first protocells. Following the cloning and sequencing of its gene, the mammalian NHE1, that regulates pH and volume in all cells, has been thoroughly scrutinized by molecular and biochemical analyses. Those gave a series of crucial clues concerning its topology, dimeric organization, pharmacological profile, regulation, and the role of key amino acids. Recently thanks to cryogenic Electron Microscopy (Cryo-EM) the long-awaited molecular structures have been revealed. With this information in mind we will challenge the robustness of the earlier conclusions and highlight how the new information enriches our understanding of this key cellular player. At the mechanistic level, we will pinpoint how the NHE1 3D structures reveal that the previously identified amino acids and regions are organized to coordinate transported cations, and shape the allosteric transition that makes NHE1 able to sense intracellular pH and be regulated by signaling pathways.

Intracellular pH Control by Membrane Transport in Mammalian Cells. Insights Into the Selective Advantages of Functional Redundancy.

Intracellular pH is a vital parameter that is maintained close to neutrality in all mammalian cells and tissues and acidic in most intracellular compartments. After presenting the main techniques used for intracellular an vesicular pH measurements we will briefly recall the main molecular mechanisms that affect and regulate intracellular pH. Following this we will discuss the large functional redundancy found in the transporters of H+ or acid-base equivalents. For this purpose, we will use mathematical modeling to simulate cellular response to persistent and/or transient acidification, in the presence of different transporters, single or in combination. We will also test the presence or absence of intracellular buffering. This latter section will highlight how modeling can yield fundamental insight into deep biological questions such as the utility of functional redundancy in natural selection.

Prediction of local pH variations during amperometric monitoring of vesicular exocytotic events at chromaffin cells.

Electrochemical monitoring of the exocytosis process is generally performed through amperometric oxidation of the electroactive messengers released by single living cells. Herein, we consider the vesicular release of catecholamines by chromaffin cells. Each exocytotic event is thus detected as a current spike whose morphology (intensity, duration, area, etc.) features the efficiency of the secretion process. However, the electrochemical oxidation of catechols produces quinone derivatives and protons. As a consequence, unless specific mechanisms may be adopted by a cell to regulate the pH near its membrane, the local pH between the cell membrane and the electrode necessarily drops within the electrode-cell cleft. Though this consequence of amperometric detection is generally ignored, it has been investigated in this work through simulation of the local pH drop created during the amperometric recording of a sequence of exocytotic events. This was performed based on frequencies and magnitudes of release detected at chromaffin cells. The corresponding acidification was shown to severely depend on the microelectrode radius. For usual 10 µm diameter carbon fiber electrodes, pH values below six were predicted to be reached within the electrode-cell cleft after monitoring a few current spikes.

Invariance of exocytotic events detected by amperometry as a function of the carbon fiber microelectrode diameter.

Etched carbon fiber microelectrodes of different radii have been used for amperometric measurements of single exocytotic events occurring at adrenal chromaffin cells. Frequency, kinetic, and quantitative information on exocytosis provided by amperometric spikes were analyzed as a function of the surface area of the microelectrodes. Interestingly, the percentage of spikes with foot (as well as their own characteristics), a category revealing the existence of sufficient long-lasting fusion pores, was found to be constant whatever the microelectrode diameter was, whereas the probability of overlapping spikes decreased with the electrode size. This confirmed that the prespike foot could not feature accidental superimposition of separated events occurring at different places. Moreover, the features of amperometric spikes investigated here (charge, intensity and kinetics) were found constant for all microelectrode diameters. This demonstrated that the electrochemical measurement does not introduce significant bias onto the kinetics and thermodynamics of release during individual exocytotic events. All in all, this work evidences that information on exocytosis amperometrically recorded with the usual 7 microm diameter carbon fiber electrodes is biologically relevant, although the frequent overlap between spikes requires a censorship of the data during the analytical treatment.

Ex vivo activities of beta-lapachone and alpha-lapachone on macrophages: a quantitative pharmacological analysis based on amperometric monitoring of oxidative bursts by single cells.

ARTIFICIAL SYNAPSES FOR FEMTOMOLAR DETECTION: Amperometry at platinized carbon fibre electrodes has been used to unravel the complexity of beta-lapachone's effects on cellular oxidative stress. Alpha-lapachone, the pharmacologically inactive para-quinone isomer, did not display such characteristics, but over longer incubation periods both quinones induced apoptosis. The observed effects were interpreted in terms of two mechanisms involving opposite reactivities of quinones in living cells. Beta-lapachone (1) has been widely used for its pharmacological activity, particularly against cancer. However, its mechanism of action at the cellular level remains unclear, although a common major hypothesis involves its prooxidant properties. Electrochemical measurements with microelectrodes were taken in order to quantitatively investigate the activity of 1 at different concentrations and several incubation times, on the oxidative bursts released by single macrophages. The exact natures of the electroactive reactive oxygen species (ROS) and reactive nitrogen species (RNS) released by macrophages under the effect of 1 were characterized, and their fluxes were measured quantitatively. This allowed the reconstruction of the primary O2*- and NO production by the cells. In the first hour, at 10 microM, the decrease in the oxidative burst involved mainly RNS, while the amount of H(2)O(2) was found to be higher than in controls. After a longer incubation time-that is, 4 h-at 1 microM, the total amount of ROS and RNS had increased, with significant enhancements of H(2)O(2) and NO. In contrast, alpha-lapachone, the pharmacologically inactive para-quinone isomer, was unable to increase the production of RONS by macrophages significantly. Over much longer incubation periods (about one day), however, each quinone induced cell death by apoptosis. All these effects were interpreted by consideration of two different mechanisms involving opposite reactivities of quinones in living cells.

Reconstructing the functional connectivity of multiple spike trains using Hawkes models.

BACKGROUND: Statistical models that predict neuron spike occurrence from the earlier spiking activity of the whole recorded network are promising tools to reconstruct functional connectivity graphs. Some of the previously used methods are in the general statistical framework of the multivariate Hawkes processes. However, they usually require a huge amount of data, some prior knowledge about the recorded network, and/or may produce an increasing number of spikes along time during simulation. NEW METHOD: Here, we present a method, based on least-square estimators and LASSO penalty criteria, for a particular class of Hawkes processes that can be used for simulation. RESULTS: Testing our method on small networks modeled with Leaky Integrate and Fire demonstrated that it efficiently detects both excitatory and inhibitory connections. The few errors that occasionally occur with complex networks including common inputs, weak and chained connections, can be discarded based on objective criteria. COMPARISON WITH EXISTING METHODS: With respect to other existing methods, the present one allows to reconstruct functional connectivity of small networks without prior knowledge of their properties or architecture, using an experimentally realistic amount of data. CONCLUSIONS: The present method is robust, stable, and can be used on a personal computer as a routine procedure to infer connectivity graphs and generate simulation models from simultaneous spike train recordings.

Bubble dynamics inside an outgassing hydrogel confined in a Hele-Shaw cell.

We report an experimental study of bubble dynamics in a non-Newtonian fluid subjected to a pressure decrease. The fluid is a hydrogel, composed of water and a synthetic clay, prepared and sandwiched between two glass plates in a Hele-Shaw geometry. The rheological properties of the material can be tuned by the clay concentration. As the imposed pressure decreases, the gas initially dissolved in the hydrogel triggers bubble formation. Different stages of the process are observed: bubble nucleation, growth, interaction, and creation of domains by bubble contact or coalescence. Initially bubble behave independently. They are trapped and advected by the mean deformation of the hydrogel, and the bubble growth is mainly driven by the diffusion of the dissolved gas through the hydrogel and its outgassing at the reactive-advected hydrogel-bubble interface. In this regime, the rheology of the fluid does not play a significant role on the bubble growth. A model is proposed and gives a simple scaling that relates the bubble growth rate and the imposed pressure. Carbon dioxide is shown to be the gas at play, and the hydrogel is degassing at the millimeter scale as a water solution does at a smaller scale. Later, bubbles are not independent anymore. The growth rate decreases, and the morphology becomes more anisotropic as bubbles interact because they are separated by a distance smaller than the individual stress field extension. Our measurements show that the interaction distance scales with the bubbles' size.

Capturing intracellular pH dynamics by coupling its molecular mechanisms within a fully tractable mathematical model.

We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems.

A dynamical model for the Utricularia trap.

We propose a model that captures the dynamics of a carnivorous plant, Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surroundings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap.

Nitric oxide release during evoked neuronal activity in cerebellum slices: detection with platinized carbon-fiber microelectrodes.

Nitric oxide is an important biological messenger that particularly induces the relaxation of smooth muscle cells surrounding vessels, and, hence, controls the flow of blood. This mechanism is essential for brain function, and its fine control, termed functional hyperemia, is supposed to be realized by certain neurons that may release bursts of NO*. The aim of the present study is to examine the advantages of platinized carbon-fiber microelectrodes (5-7 microm tip diameter) for the direct and in situ electrochemical detection of NO* released by neurons into ex vivo cerebellum slices. After establishing the different analytical properties of the platinized carbon-fiber microelectrodes in vitro on NO* solutions at 50 nM to 1 mM concentration, they were characterized using DEA-NONOate solutions that chemically decompose into NO*, and therefore mimic the measurement of transient variations of NO* concentration in biological samples. This validated the present approach, so that direct, in situ ex vivo measurements of nitric oxide released by neurons in a rat cerebellar slice are presented and discussed.

Regulation of exocytosis in chromaffin cells by trans-insertion of lysophosphatidylcholine and arachidonic acid into the outer leaflet of the cell membrane.

Vesicular exocytosis is an important complex process in the communication between cells in organisms. It controls the release of chemical and biochemical messengers stored in an emitting cell. In this report, exocytosis is studied amperometrically (at carbon fiber ultramicroelectrodes) at adrenal chromaffin cells, which release catecholamines after appropriate stimulation, while testing the effects due to trans-insertion of two exogenous compounds (lysophosphatidylcholine (LPC) and arachidonic acid (AA)) on the kinetics of exocytotic events. Amperometric analyses showed that, under the present conditions (short incubation times and micromolar LPC or AA solutions), LPC favors catecholamine release (rate, event frequency, charge released) while AA disfavors the exocytotic processes. The observed kinetic features are rationalized quantitatively by considering a stalk model, for the fusion pore formation, and the physical constraints applied to the cell membrane by the presence of small fractions of LPC and AA diluted in its external leaflet (trans-insertion). We also observed that the detected amount of neurotransmitters in the presence of LPC was larger than under control conditions, while the opposite trend is observed with AA.

Correlation between vesicle quantal size and fusion pore release in chromaffin cell exocytosis.

A significant number of exocytosis events recorded with amperometry demonstrate a prespike feature termed a "foot" and this foot has been correlated with messengers released via a transitory fusion pore before full exocytosis. We have compared amperometric spikes with a foot with spikes without a foot at chromaffin cells and found that the probability of detecting a distinct foot event is correlated to the amount of catecholamine released. The mean charge of the spikes with a foot was found to be twice that of the spikes without a foot, and the frequency of spikes displaying a foot was zero for small spikes increasing to approximately 50% for large spikes. It is hypothesized that in chromaffin cells, where the dense core is believed to nearly fill the vesicle, the expanding core is a controlling factor in opening the fusion pore, that prefusion of two smaller vesicles leads to excess membrane, and that this slows pore expansion leading to an increased observation of events with a foot. Clearly, the physicochemical properties of vesicles are key factors in the control of the dynamics of release through the fusion pore and the high and variable frequency of this release makes it highly significant.

Molecular dynamics simulations of the lipid bilayer edge.

Phospholipid bilayers have been intensively studied by molecular dynamics (MD) simulation in recent years. The properties of bilayer edges are important in determining the structure and stability of pores formed in vesicles and biomembranes. In this work, we use molecular dynamics simulation to investigate the structure, dynamics, and line tension of the edges of bilayer ribbons composed of pure dimyristoylphosphatidylcholine (DMPC) or palmitoyl-oleoylphosphatidylethanolamine (POPE). As expected, we observe a significant reorganization of lipids at and near the edges. The treatment of electrostatic effects is shown to have a qualitative impact on the structure and stability of the edge, and significant differences are observed in the dynamics and structure of edges formed by DMPC and palmitoyl-oleoylphosphatidylethanolamine. From the pressure anisotropy in the simulation box, we calculate a line tension of approximately 10-30 pN for the DMPC edge, in qualitative agreement with experimental estimates for similar lipids.

Dynamics of full fusion during vesicular exocytotic events: release of adrenaline by chromaffin cells.

Vesicular exocytosis is important in the communication between cells in complex organisms. It controls the release of specific chemical or biochemical messengers stored in the emitting cell, which elicit a response upon detection by the target cells. Secretion of a messenger molecule (a neurotransmitter) was measured electrochemically, which allowed the quantification of cellular events and the validation of current physicochemical models. This model led us to formulate predictions about the occurrence and kinetics of vesicular exocytotic events based on the physicochemical meaning of its key parameters. These predictions were tested successfully through a series of experiments on chromaffin cells, involving changes of osmotic conditions, presence of trivalent ions and cholesterol-induced structuring of the cell plasmic membrane.