Inward rectifier K+-channel kinetics from analysis of the complex conductance of Aplysia neuronal membrane.

Conduction in inward rectifier, K+-channels in Aplysia neuron and Ba++ blockade of these channels were studied by rapid measurement of the membrane complex admittance in the frequency range 0.05 to 200 Hz during voltage clamps to membrane potentials in the range -90 to -40 mV. Complex ionic conductances of K+ and Cl- rectifiers were extracted from complex admittances of other membrane conduction processes and capacitance by vector subtraction of the membrane complex admittance during suppressed inward K+ current (near zero-mean current and in zero [K+]0) from complex admittances determined at other [K+]0 and membrane potentials. The contribution of the K+ rectifier to the admittance is distinguishable in the frequency domain above 1 Hz from the contribution of the Cl- rectifier, which is only apparent at frequencies less than 0.1 Hz. The voltage dependence (-90 to -40 mV) of the chord conductance (0.2 to 0.05 microS) and the relaxation time (4-8 ms) of K+ rectifier channels at [K+]0 = 40 mM were determined by curve fits of admittance data by a membrane admittance model based on the linearized Hodgkin-Huxley equations. The conductance of inward rectifier, K+ channels at a membrane potential of -80 mV had a square-root dependence on external K+ concentration, and the relaxation time increased from 2 to 7.5 ms for [K+]0 = 20 and 100 mM, respectively. The complex conductance of the inward K+ rectifier, affected by Ba++, was obtained by complex vector subtraction of the membrane admittance during blockage of inward rectifier, K+ channels (at -35 mV and [Ba++]0 = 5 mM) from admittances determined at -80 mV and at other Ba++ concentrations. The relaxation time of the blockade process decreased with increases in Ba++ concentration. An open-closed channel state model produces the inductive-like kinetic behavior in the complex conductance of inward rectifier, K+ channels and the addition of a blocked channel state accounts for the capacitive-like kinetic behavior of the Ba++ blockade process.     

The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes

The input impedance of muscle fibers of the crab was determined with microelectrodes over the frequency range 1 cps to 10 kc/sec. Care was taken to analyze, reduce, and correct for capacitive artifact. One dimensional cable theory was used to determine the properties of the equivalent circuit of the membrane admittance, and the errors introduced by the neglect of the three dimensional spread of current are discussed. In seven fibers the equivalent circuit of an element of the membrane admittance must contain a DC path and two capacitances, each in series with a resistance. In two fibers, the element of membrane admittance could be described by one capacitance in parallel with a resistance. In several fibers there was evidence for a third very large capacitance. The values of the elements of the equivalent circuit depend on which of several equivalent circuits is chosen. The circuit (with a minimum number of elements) that was considered most reasonably consistent with the anatomy of the fiber has two branches in parallel: one branch having a resistance R_e in series with a capacitance C_e; the other branch having a resistance R_b in series with a parallel combination of a resistance R_m and a capacitance C_m. The average circuit values (seven fibers) for this model, treating the fiber as a cylinder of sarcolemma without infoldings or tubular invaginations, are R_e = 21 ohm cm²; C_e = 47 µf/cm²; R_b = 10.2 ohm cm²; R_m = 173 ohm cm²; C_m = 9.0 µf/cm². The relation of this equivalent circuit and another with a nonminimum number of circuit elements to the fine structure of crab muscle is discussed. In the above equivalent circuit R_m and C_m are attributed to the sarcolemma; R_e and C_e, to the sarcotubular system; and R_b, to the amorphous material found around crab fibers. Estimates of actual surface area of the sarcolemma and sarcotubular system permit the average circuit values to be expressed in terms of unit membrane area. The values so expressed are consistent with the dielectric properties of predominantly lipid membranes.     

Analysis of spike electrogenesis of Eel electroplaques with phase plane and impedance measurements

Eel electroplaques provide experimental conditions in which registration of phase plane trajectories (dV/dt vs. V) and impedance measurements with an AC Wheatstone bridge, in conjunction with spike electrogenesis describe quantitatively the ionic processes of the electrogenesis. Thus, these data employing as they do measurements of transients, permit an independent test of the validity of the assumptions which underlie the Hodgkin-Huxley equivalent circuit: independent ionic channels with fixed ionic batteries and exhibiting time-variant conductance changes with different kinetics for the different channels. The analysis accords with earlier findings on voltage-clamped electroplaques and this agreement confirms the validity of the equivalent circuit despite the fact that the current-voltage characteristics of the axons and electroplaques differ profoundly. As for squid axons, the equivalent circuit of the electroplaques has four branches: a capacity and three ionic channels. One of the latter is an invariant leak channel (G_L) of high conductance. A K channel (G _K) is fully open at rest, but rapidly undergoes inactivation when the cell is depolarized by more than 40 mv. G_L and G _K have a common inside negative emf (E _K). A Na channel (G _Na) with an inside positive emf (E _Na) is closed at rest, but opens transiently upon depolarization.     

A model for conductance changes in the squid giant axon. II. Channel kinetics

The kinetics of the sodium and potassium channels in voltage clamped squid giant axon following a relaxation of the membrane subunits are examined and compared with the Hodgkin-Huxley equations. Mechanisms are suggested for the turn-off of the sodium conductance and a set of kinetic states are proposed for the potassium channel which are consistent with the experimental observations. Determination of the rate constants for relaxation of the surface subunits which triggers the subsequent changes within the independent channels provide information on the equilibrium constant and free energy for this process. The free energy is observed to approach zero as the depolarizing voltage of the clamp approaches $\text{E}{}_{\mathrm{<mtext>Na</mtext>}}$, the voltage for zero sodium current in voltage clamped axons. Analysis of the final rate constants in the kinetic sequence for potassium indicates a symmetry of the channel when it is in its steady-state configuration during clamp in the absence of external gradients.     

Electrogenic transport of sodium ions in cytoplasmic and extracellular ion access channels of Na+,K+-ATPase probed by admittance measurement technique

Electrogenic movements of sodium ions in cytoplasmic and extracellular access channel of the Na⁺,K⁺-ATPase have been studied by the admittance measurement technique which allows the detection of small changes of the membrane capacitance and conductance induced by phosphorylation of the ion pump. The measurements were carried out on a model system consisting of a bilayer lipid membrane, to which membrane fragments with ion pumps were adsorbed that contain the ion pumps in high density. Small changes of the membrane capacitance and conductance were induced by a fast release of ATP from caged ATP. The effect was measured at various frequencies and in solutions with different Na⁺ concentrations. The experimentally observed frequency dependences were explained using a theoretical model assuming that Na⁺ movement through the cytoplasmic access channel occurs in one step and through the extracellular access channel, in two steps. The phosphorylation of the protein by ATP leads to a block of the cytoplasmic access channel and an opening the extracellular access channel. The disappearance of electrogenic Na⁺ movements on the cytoplasmic side produces a negative change of capacitance and conductance, while the emergence of extracellular Na⁺ movements generates a positive change. Fitting the experimental dependences of capacitance and conductance by theoretical curves allowed the determination equilibrium and kinetic parameters of sodium transport in the access channels. The text was submitted by the authors in English.     

K+ Block Is the Mechanism of Functional Asymmetry in Bacterial Nav Channels

Crystal structures of several bacterial Na_v channels have been recently published and molecular dynamics simulations of ion permeation through these channels are consistent with many electrophysiological properties of eukaryotic channels. Bacterial Na_v channels have been characterized as functionally asymmetric, and the mechanism of this asymmetry has not been clearly understood. To address this question, we combined non-equilibrium simulation data with two-dimensional equilibrium unperturbed landscapes generated by umbrella sampling and Weighted Histogram Analysis Methods for multiple ions traversing the selectivity filter of bacterial Na_vAb channel. This approach provided new insight into the mechanism of selective ion permeation in bacterial Na_v channels. The non-equilibrium simulations indicate that two or three extracellular K⁺ ions can block the entrance to the selectivity filter of Na_vAb in the presence of applied forces in the inward direction, but not in the outward direction. The block state occurs in an unstable local minimum of the equilibrium unperturbed free-energy landscape of two K⁺ ions that can be ‘locked’ in place by modest applied forces. In contrast to K⁺, three Na⁺ ions move favorably through the selectivity filter together as a unit in a loose “knock-on” mechanism of permeation in both inward and outward directions, and there is no similar local minimum in the two-dimensional free-energy landscape of two Na⁺ ions for a block state. The useful work predicted by the non-equilibrium simulations that is required to break the K⁺ block is equivalent to large applied potentials experimentally measured for two bacterial Na_v channels to induce inward currents of K⁺ ions. These results illustrate how inclusion of non-equilibrium factors in the simulations can provide detailed information about mechanisms of ion selectivity that is missing from mechanisms derived from either crystal structures or equilibrium unperturbed free-energy landscapes.     

Allosteric Gating of a Large Conductance Ca-activated K+ Channel

Large-conductance Ca-activated potassium channels (BK channels) are uniquely sensitive to both membrane potential and intracellular Ca²⁺. Recent work has demonstrated that in the gating of these channels there are voltage-sensitive steps that are separate from Ca²⁺ binding steps. Based on this result and the macroscopic steady state and kinetic properties of the cloned BK channel mslo, we have recently proposed a general kinetic scheme to describe the interaction between voltage and Ca²⁺ in the gating of the mslo channel (Cui, J., D.H. Cox, and R.W. Aldrich. 1997. J. Gen. Physiol. In press.). This scheme supposes that the channel exists in two main conformations, closed and open. The conformational change between closed and open is voltage dependent. Ca²⁺ binds to both the closed and open conformations, but on average binds more tightly to the open conformation and thereby promotes channel opening. Here we describe the basic properties of models of this form and test their ability to mimic mslo macroscopic steady state and kinetic behavior. The simplest form of this scheme corresponds to a voltage-dependent version of the Monod-Wyman-Changeux (MWC) model of allosteric proteins. The success of voltage-dependent MWC models in describing many aspects of mslo gating suggests that these channels may share a common molecular mechanism with other allosteric proteins whose behaviors have been modeled using the MWC formalism. We also demonstrate how this scheme can arise as a simplification of a more complex scheme that is based on the premise that the channel is a homotetramer with a single Ca²⁺ binding site and a single voltage sensor in each subunit. Aspects of the mslo data not well fitted by the simplified scheme will likely be better accounted for by this more general scheme. The kinetic schemes discussed in this paper may be useful in interpreting the effects of BK channel modifications or mutations.     

A mechanism stabilizing a long-lived charge-separated state of photosynthetic reaction centers frozen under intense illumination

It is experimentally shown that slow chilling of photosynthetic reaction centers from purple bacteria Rhodobacter sphaeroides to <230 K under intense illumination leads to appearance of long-lived chargeseparated states (P⁺Q _A ^? ). This longevity implies that the recombination is blocked or the charge-separated state is stabilized. The longevity effect is caused by structural relaxation of reaction centers to a new equilibrium state that diminishes the free energy difference of recombination. The possible mechanism of such relaxation involves orientation of the polar water molecules in the semiquinone local electrostatic field. Detailed analysis of the longevity effect has been carried out, and its outcome supports the idea that many electron transfer reactions in biological systems are non-equilibrium.     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.     

Inward and outward currents of native and cloned K(ATP) channels (Kir6.2/SUR1) share single-channel kinetic properties

BackgroundThe ATP-sensitive K⁺ (K(ATP)) channel is found in a variety of tissues extending from the heart and vascular smooth muscles to the endocrine pancreas and brain. Common to all K(ATP) channels is the pore-forming subunit Kir6.x, a member of the family of small inwardly rectifying K⁺ channels, and the regulatory subunit sulfonylurea receptor (SURx). In insulin secreting β-cells in the endocrine part of the pancreas, where the channel is best studied, the K(ATP) channel consists of Kir6.2 and SUR1. Under physiological conditions, the K(ATP) channel current flow is outward at membrane potentials more positive than the K⁺ equilibrium potential around ?80 mV. However, K(ATP) channel kinetics have been extensively investigated for inward currents and the single-channel kinetic model is based on this type of recording, whereas only a limited amount of work has focused on outward current kinetics.MethodsWe have estimated the kinetic properties of both native and cloned K(ATP) channels under varying ionic gradients and membrane potentials using the patch-clamp technique.ResultsAnalyses of outward currents in K(ATP) and cloned Kir6.2ΔC26 channels, alone or co-expressed with SUR1, show openings that are not grouped in bursts as seen for inward currents. Burst duration for inward current corresponds well to open time for outward current.ConclusionsOutward K(ATP) channel currents are not grouped in bursts regardless of membrane potential, and channel open time for outward currents corresponds to burst duration for inward currents.     

Time-Dependent Molecular Memory in Single Voltage-Gated Sodium Channel

Excitability in neurons is associated with firing of action potentials and requires the opening of voltage-gated sodium channels with membrane depolarization. Sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, can have profound implications on the biophysical properties of voltage-gated ion channels. Therefore, we sought to characterize the effect of sustained membrane depolarization on single voltage-gated Na⁺ channels. Single-channel activity was recorded in the cell-attached patch-clamp mode from the rNa_v1.2α channels expressed in CHO cells. Classical statistical analysis revealed complex nonlinear changes in channel dwell times and unitary conductance of single Na⁺ channels as a function of conditioning membrane depolarization. Signal processing tools like weighted wavelet Z (WWZ) and discrete Fourier transform analyses attributed a “pseudo-oscillatory” nature to the observed nonlinear variation in the kinetic parameters. Modeling studies using the hidden Markov model (HMM) illustrated significant changes in kinetic states and underlying state transition rate constants upon conditioning depolarization. Our results suggest that sustained membrane depolarization induces novel nonlinear properties in voltage-gated Na⁺ channels. Prolonged membrane depolarization also induced a “molecular memory” phenomenon, characterized by clusters of dwell time events and strong autocorrelation in the dwell time series similar to that reported recently for single enzyme molecules. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Voltage-gated Na⁺ channel with the observed time-dependent nonlinear properties and the molecular memory phenomenon may determine the functional state of the channel and, in turn, the excitability of a neuron.     

Subconductance Gating and Voltage Sensitivity of Sarcoplasmic Reticulum K+ Channels: A Modeling Approach

Sarcoplasmic reticulum (SR) K⁺ channels are voltage-regulated channels that are thought to be actively gating when the membrane potential across the SR is close to zero as is expected physiologically. A characteristic of SR K⁺ channels is that they gate to subconductance open states but the relevance of the subconductance events and their contribution to the overall current flowing through the channels at physiological membrane potentials is not known. We have investigated the relationship between subconductance and full conductance openings and developed kinetic models to describe the voltage sensitivity of channel gating. Because there may be two subtypes of SR K⁺ channels (TRIC-A and TRIC-B) present in most tissues, to conduct our study on a homogeneous population of SR K⁺ channels, we incorporated SR vesicles derived from Tric-a knockout mice into artificial membranes to examine the remaining SR K⁺ channel (TRIC-B) function. The channels displayed very low open probability (Po) at negative potentials (≤0 mV) and opened predominantly to subconductance open states. Positive holding potentials primarily increased the frequency of subconductance state openings and thereby increased the number of subsequent transitions into the full open state, although a slowing of transitions back to the sublevels was also important. We investigated whether the subconductance gating could arise as an artifact of incomplete resolution of rapid transitions between full open and closed states; however, we were not able to produce a model that could fit the data as well as one that included multiple distinct current amplitudes. Our results suggest that the apparent subconductance openings will provide most of the K⁺ flux when the SR membrane potential is close to zero. The relative contribution played by openings to the full open state would increase if negative charge developed within the SR thus increasing the capacity of the channel to compensate for ionic imbalances.     

Na(+) transport, and the E(1)P-E(2)P conformational transition of the Na(+)/K(+)-ATPase

We have used admittance analysis together with the black lipid membrane technique to analyze electrogenic reactions within the Na(+) branch of the reaction cycle of the Na(+)/K(+)-ATPase. ATP release by flash photolysis of caged ATP induced changes in the admittance of the compound membrane system that are associated with partial reactions of the Na(+)/K(+)-ATPase. Frequency spectra and the Na(+) dependence of the capacitive signal are consistent with an electrogenic or electroneutral E(1)P <--> E(2)P conformational transition which is rate limiting for a faster electrogenic Na(+) dissociation reaction. We determine the relaxation rate of the rate-limiting reaction and the equilibrium constants for both reactions at pH 6.2-8.5. The relaxation rate has a maximum value at pH 7.4 (approximately 320 s(-1)), which drops to acidic (approximately 190 s(-1)) and basic (approximately 110 s(-1)) pH. The E(1)P <--> E(2)P equilibrium is approximately at a midpoint position at pH 6.2 (equilibrium constant approximately 0.8) but moves more to the E(1)P side at basic pH 8.5 (equilibrium constant approximately 0.4). The Na(+) affinity at the extracellular binding site decreases from approximately 900 mM at pH 6.2 to approximately 200 mM at pH 8.5. The results suggest that during Na(+) transport the free energy supplied by the hydrolysis of ATP is mainly used for the generation of a low-affinity extracellular Na(+) discharge site. Ionic strength and lyotropic anions both decrease the relaxation rate. However, while ionic strength does not change the position of the conformational equilibrium E(1)P <--> E(2)P, lyotropic anions shift it to E(1)P.     

Molecular mechanism for depolarization-induced modulation of Kv channel closure

Voltage-dependent potassium (Kv) channels provide the repolarizing power that shapes the action potential duration and helps control the firing frequency of neurons. The K⁺ permeation through the channel pore is controlled by an intracellularly located bundle-crossing (BC) gate that communicates with the voltage-sensing domains (VSDs). During prolonged membrane depolarizations, most Kv channels display C-type inactivation that halts K⁺ conduction through constriction of the K⁺ selectivity filter. Besides triggering C-type inactivation, we show that in Shaker and Kv1.2 channels (expressed in Xenopus laevis oocytes), prolonged membrane depolarizations also slow down the kinetics of VSD deactivation and BC gate closure during the subsequent membrane repolarization. Measurements of deactivating gating currents (reporting VSD movement) and ionic currents (BC gate status) showed that the kinetics of both slowed down in two distinct phases with increasing duration of the depolarizing prepulse. The biphasic slowing in VSD deactivation and BC gate closure was strongly correlated in time and magnitude. Simultaneous recordings of ionic currents and fluorescence from a probe tracking VSD movement in Shaker directly demonstrated that both processes were synchronized. Whereas the first slowing originates from a stabilization imposed by BC gate opening, the subsequent slowing reflects the rearrangement of the VSD toward its relaxed state (relaxation). The VSD relaxation was observed in the Ciona intestinalis voltage-sensitive phosphatase and in its isolated VSD. Collectively, our results show that the VSD relaxation is not kinetically related to C-type inactivation and is an intrinsic property of the VSD. We propose VSD relaxation as a general mechanism for depolarization-induced slowing of BC gate closure that may enable Kv1.2 channels to modulate the firing frequency of neurons based on the depolarization history.     

Single voltage-dependent K+ and Cl- channels in cultured rat astrocytes

The kinetic reactions of a voltage-dependent K+ channel, which constituted about 14% of all the recorded K+ channels in the membrane of cultured rat astrocytes were studied in detail. A scheme of one open and three closed states is necessary to describe the kinetic reactions of this channel. The channel contributes little to the resting membrane potential. Its steady state open probability (Po) is 0.06 at -70 mV. When the cell is depolarized to O mV, Po approaches 1. This represents a 17-fold increase. Such channels could contribute to the potassium clearance by enhancing the effect of "spatial buffering." Additionally, single anion-selective channels with very high conductances were found in inside-out patches in approximately 15% of all recorded channels in the membrane of rat astrocytes. Channel openings are characterized by more than one conductance level; the main level showed a mean conductance of 400 pS. These channels are divided into two groups. Approximately 90% of the recorded chloride channels showed a strong voltage dependency of their current fluctuations. Within a relatively small potential range (+/- 15 mV) the channels have a high probability of being in the active state. After a voltage jump to varying testing potentials in the range of +/- 20 to +/- 50 mV the channels continued to be in the active state for some time and then closed to a shut state. If the testing potential persisted, the channels were not able to leave this shut state.(ABSTRACT TRUNCATED AT 250 WORDS)     

Open-State Occupancy Prevents Gating Charge Relaxation of N-type (CaV2.2) Calcium Channels

N-type and L-type channels have significant gating differences, and we wondered whether some of these differences are linked to the relationship between charge movement and channel opening. The time constants for N-channel closing (τ_Deact) and Off-gating charge movement (τQ_Off) were compared over a range of voltages. τQ_Off was significantly larger than τ_Deact at voltages < −10 mV, and the voltage dependence of the τQ_Off was less steep than that for τ_Deact, which suggests that gating charge relaxation does not limit channel closing. Roscovitine, a drug that slows N-channel closing by holding the channel in a high open-probability state, was found to slow both τQ_Off and τ_Deact, and thus the time courses of channel closing and gating charge relaxation were similar. Our gating current results were reproduced with the addition of a voltage-independent, closed-closed transition to our previously published two-open-state N-channel model. This work suggests that, like L-type channels, there is a voltage-independent transition along the N-channel activation/deactivation pathway, but this transition occurs between closed states instead of the closed-open states of the L-channel. Also unlike L-type channels, the gating charge appears to be locked into the activated position by the N-channel open state.     

Equivalent Circuits as Related to Ionic Systems

The purpose of this paper is to clarify the relationship between certain “equivalent circuits” and the fundamental flux equations of Nernst and Planck. It is shown that as a direct algebraic consequence of these equations one may construct two types of equivalent circuits for a homogeneous (charged or uncharged) membrane. The one, which we term the “pure electrical equivalent circuit,” correctly predicts all of the electrical properties of the membrane for both steady and transient states. The other, which we call the “mixed equivalent circuit,” predicts the steady state I, Ψ characteristics of the membrane and the steady state ionic fluxes; it is not applicable to non-steady state properties or measurements. We emphasize that with regard to the portrayal of the physical basis of the properties of a homogeneous membrane, the mixed equivalent circuit can be misleading. This is particularly significant because this same circuit can also be used to depict a mosaic membrane, in which case the circuit gives a realistic pictorialization of the physical origin of the membrane properties. It is hoped that our analysis will be of aid to workers in electrophysiology who make use of equivalent circuit terminology in discussing the behavior of the plasma membrane.     

Simulation of chlorophyll fluorescence rise and decay kinetics,and P<Subscript>700</Subscript>-related absorbance changes by using a rule-based kinetic Monte-Carlo method

A model of primary photosynthetic reactions in the thylakoid membrane was developed and its validity was tested by simulating three types of experimental kinetic curves: (1) the light-induced chlorophyll a fluorescence rise (OJIP transients) reflecting the stepwise transition of the photosynthetic electron transport chain from the oxidized to the fully reduced state; (2) the dark relaxation of the flash-induced fluorescence yield attributed to the Q_A^? oxidation kinetics in PSII; and (3) the light-induced absorbance changes near 820 or 705 nm assigned to the redox transitions of P₇₀₀ in PSI. A model was implemented by using a rule-based kinetic Monte-Carlo method and verified by simulating experimental curves under different treatments including photosynthetic inhibitors, heat stress, anaerobic conditions, and very high light intensity.     

Association of Model Neurotransmitters with Lipid Bilayer Membranes

Aimed at reproducing the results of electrophysiological studies of synaptic signal transduction, conventional models of neurotransmission are based on the specific binding of neurotransmitters to ligand-gated receptor ion channels. However, the complex kinetic behavior observed in synaptic transmission cannot be reproduced in a standard kinetic model without the ad hoc postulation of additional conformational channel states. On the other hand, if one invokes unspecific neurotransmitter adsorption to the bilayer—a process not considered in the established models—the electrophysiological data can be rationalized with only the standard set of three conformational receptor states that also depend on this indirect coupling of neurotransmitters via their membrane interaction. Experimental verification has been difficult because binding affinities of neurotransmitters to the lipid bilayer are low. We quantify this interaction with surface plasmon resonance to measure equilibrium dissociation constants in neurotransmitter membrane association. Neutron reflection measurements on artificial membranes, so-called sparsely tethered bilayer lipid membranes, reveal the structural aspects of neurotransmitters’ association with zwitterionic and anionic bilayers. We thus establish that serotonin interacts nonspecifically with the membrane at physiologically relevant concentrations, whereas γ-aminobutyric acid does not. Surface plasmon resonance shows that serotonin adsorbs with millimolar affinity, and neutron reflectometry shows that it penetrates the membrane deeply, whereas γ-aminobutyric is excluded from the bilayer.     

Distance of the reduced Brusselator from equilibrium

The new concept of a nonequilibrium parameter P is applied to a reduced Brusselator, considered as a kinetic model for cellular processes. The reduction corresponds to omitting a monomolecular reaction. The deviation from equilibrium is due to a fixed nonequilibrium value of an extracellular concentration B, responsible for energizing and determining the steady-state value of the overall chemical affinity ?. The value of ? is insensitive to different steady states possible for a given set of rate constants. In contrast, the parameter P is state dependent. In particular, it may jump together with state variables. Two limiting cases of high ? are investigated, B→ 0 and B→ 1. In the first case P grows monotonically with ?. In the second case there is always a steady state solution with P→ 0. The physical interpretation of this effect of “equilibrium far from equilibrium” reveals the real predictive power of the parameter P. Relaxation regimes are investigated for a doubly reduced Brusselator. Both P and ? are in general time dependent and have jumps in their time derivatives. The canonical form of P is compared with the noncanonical one in the context of robustness of the new concept with respect to incomplete information about the system studied. These forms of P are different in relaxation to a nonequilibrium state and coincide in relaxation to an equilibrium state.