Fluctuation spectroscopy: determination of chemical reaction kinetics from the frequency spectrum of fluctuations

Ultrafast formation of ANFs with kinetic advantage and new insight into the mechanism

Aramid nanofibers (ANFs) have important applications in many fields, including electrical insulation and battery separators. However, a few limitations seriously restrict the application of ANFs currently, such as low preparation efficiency and the unclear preparation mechanism. To overcome these limitations, the present work proposes a new view-point from the perspective of reaction kinetics. The preparation efficiency was proven to essentially rely on the effective c(OH^-). With a simple pre-treatment, a kinetic advantage was created and the preparation time of ANFs was reduced from multiple hours to 10 minutes, which was a considerable step towards practical applications. Moreover, the resultant ANF membranes still exhibited excellent properties in terms of mechanical strength (tensile strength > 160 MPa), thermal stability, light transmittance, and electrical insulation (above 90 kV mm^-1). This work not only presents an ultrafast method to produce ANFs but also provides new insights into the mechanism that will benefit the subsequent development of ANF-based materials.

Trajectory and Cycle-Based Thermodynamics and Kinetics of Molecular Machines: The Importance of Microscopic Reversibility

A molecular machine is a nanoscale device that provides a mechanism for coupling energy from two (or more) processes that in the absence of the machine would be independent of one another. Examples include walking of a protein in one direction along a polymeric track (process 1, driving "force" X₁ = - F⃗· l⃗) and hydrolyzing ATP (process 2, driving "force" X₂ = Δμ_ATP); or synthesis of ATP (process 1, X₁ = -Δμ_ATP) and transport of protons from the periplasm to the cytoplasm across a membrane (process 2, X₂ = Δμ_H⁺); or rotation of a flagellum (process 1, X₁ = -torque) and transport of protons across a membrane (process 2, X₂ = Δμ_H⁺). In some ways, the function of a molecular machine is similar to that of a macroscopic machine such as a car that couples combustion of gasoline to translational motion. However, the low Reynolds number regime in which molecular machines operate is very different from that relevant for macroscopic machines. Inertia is negligible in comparison to viscous drag, and omnipresent thermal noise causes the machine to undergo continual transition among many states even at thermodynamic equilibrium. Cyclic trajectories among the states of the machine that result in a change in the environment can be broken into two classes: those in which process 1 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the environment; and those in which process 2 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the evironment. These two types of trajectories, [Formula: see text] and [Formula: see text], overlap, i.e., there are some trajectories in which both process 1 and process 2 occur, and for which the work exchanged is [Formula: see text]. The four subclasses of overlap trajectories [(+1,+2), (+1,-2), (-1,+2), (-1,-2)] are the coupled processes. The net probabilities for process 1 and process 2 are designated π₊₂ - π_-2 and π₊₁ - π_-1, respectively. The probabilities [Formula: see text] for any single trajectory [Formula: see text] and [Formula: see text] for its microscopic reverse [Formula: see text] are related by microscopic reversibility (MR), [Formula: see text], an equality that holds arbitrarily far from thermodynamic equilibrium, i.e., irrespective of the magnitudes of X₁ and X₂, and where [Formula: see text]. Using this formalism, we arrive at a remarkably simple and general expression for the rates of the processes, [Formula: see text], i = 1, 2, where the angle brackets indicate an average over the ensemble of all microscopic reverse trajectories. Stochastic description of coupling is doubtless less familiar than typical mechanical depictions of chemical coupling in terms of ATP induced violent kicks, judo throws, force generation and power-strokes. While the mechanical description of molecular machines is comforting in its familiarity, conclusions based on such a phenomenological perspective are often wrong. Specifically, a "power-stroke" model (i.e., a model based on energy driven "promotion" of a molecular machine to a high energy state followed by directional relaxation to a lower energy state) that has been the focus of mechanistic discussions of biomolecular machines for over a half century is, for catalysis driven molecular machines, incorrect. Instead, the key principle by which catalysis driven motors work is kinetic gating by a mechanism known as an information ratchet. Amazingly, this same principle is that by which catalytic molecular systems undergo adaptation to new steady states while facilitating an exergonic chemical reaction.

Potential-dependent restructuring and chemical noise at Au-Ag-Au atomic scale junctions

The effect of electrochemical potential on the behavior of electrochemically deposited Au-Ag-Au bimetallic atomic scale junctions (ASJs) is addressed here. A common strategy for ASJ production begins with overgrown nanojunctions and uses electromigration to back-thin the junction. Here, these steps are carried out with the entire junction under electrochemical potential control, and the relationship between junction stability and applied potential is characterized. The control of electrochemical potential provides a reliable method of regulating the size of nanojunctions. In general, more anodic potentials decrease junction stability and increase the rate at which conductance decays. Conductance behavior under these labile conditions is principally determined by Ag oxidation potential, electrochemical potential-induced surface stress, and the nature of the adsorbate. Junctions fabricated at more cathodic potentials experience only slight changes in conductance, likely due to surface atom diffusion and stress-induced structural rearrangement. Electrochemical potential also plays a significant role in determining adsorption-desorption kinetics of surface pyridine at steady state at Au-Ag-Au ASJs, as revealed through fluctuation spectroscopy. Average cutoff frequencies increase at more anodic potentials, as does the width of the cutoff frequency distribution measured over 80 independent runs. Three reversible reactions--pyridine adsorption, Ag atom desorption, and Ag-pyridine complex dissolution--can occur on the surface, and the combination of the three can explain the observed results.

Frequency domain detection of biomolecules using silicon nanowire biosensors

We demonstrate a new protein detection methodology based upon frequency domain electrical measurement using silicon nanowire field-effect transistor (SiNW FET) biosensors. The power spectral density of voltage from a current-biased SiNW FET shows 1/f-dependence in frequency domain for measurements of antibody functionalized SiNW devices in buffer solution or in the presence of protein not specific to the antibody receptor. In the presence of protein (antigen) recognized specifically by the antibody-functionalized SiNW FET, the frequency spectrum exhibits a Lorentzian shape with a characteristic frequency of several kilohertz. Frequency and conventional time domain measurements carried out with the same device as a function of antigen concentration show more than 10-fold increase in detection sensitivity in the frequency domain data. These concentration-dependent results together with studies of antibody receptor density effect further address possible origins of the Lorentzian frequency spectrum. Our results show that frequency domain measurements can be used as a complementary approach to conventional time domain measurements for ultrasensitive electrical detection of proteins and other biomolecules using nanoscale FETs.

Relaxation and fluctuations of the number of particles in a membrane channel at arbitrary particle-channel interaction

We analyze the relaxation of the particle number fluctuations in a membrane channel at arbitrary particle-channel interaction and derive general expressions for the relaxation time and low-frequency limit of the power spectral density. These expressions simplify significantly when the channel is symmetric. For a square-well potential of mean force that occupies the entire channel, we verify the accuracy of the analytical predictions by Brownian dynamics simulations. For such a channel we show that as the depth of the well increases, the familiar scaling of the relaxation time with the channel length squared is transformed into a linear dependence on the length.

Fluctuations as a source of information in fluorescence microscopy

Fluctuations in fluorescence spectroscopy and microscopy have traditionally been regarded as noise—they lower the resolution and contrast and do not permit high acquisition rates. However, fluctuations can also be used to gain additional information about a system. This fact has been exploited in single-point microscopic techniques, such as fluorescence correlation spectroscopy and analysis of single molecule trajectories, and also in the imaging field, e.g. in spatio-temporal image correlation spectroscopy. Here, we discuss how fluctuations are used to obtain more quantitative information from the data than that given by average values, while minimizing the effects of noise due to stochastic photon detection.

GFP-tagged regulatory light chain monitors single myosin lever-arm orientation in a muscle fiber

Myosin is the molecular motor in muscle-binding actin and executing a power stroke by rotating its lever arm through an angle of approximately 70 degrees to translate actin against resistive force. A green fluorescent protein (GFP)-tagged human cardiac myosin regulatory light chain (HCRLC) was constructed to study in situ lever arm orientation one molecule at a time by polarized fluorescence emitted from the GFP probe. The recombinant protein physically and functionally replaced the native RLC on myosin lever arms in the thick filaments of permeabilized skeletal muscle fibers. Detecting single molecules in fibers where myosin concentration reaches 300 microM is accomplished using total internal reflection fluorescence microscopy. With total internal reflection fluorescence, evanescent field excitation, supercritical angle fluorescence detection, and CCD detector pixel size limits detection volume to just a few attoliters. Data analysis manages both the perturbing effect of the TIR interface on probe emission and the effect of high numerical aperture collection of light. The natural myosin concentration gradient in a muscle fiber allows observation of fluorescence polarization from C-term GFP-tagged HCRLC exchanged myosin from regions in the thick filament containing low and high myosin concentrations. In rigor, cross-bridges at low concentration at the end of the thick filament maintain GFP dipole moments at two distinct polar angles relative to the fiber symmetry axis. The lower angle, where the dipole is nearly parallel to fiber axis, is more highly populated than the alternative, larger angle. Cross-bridges at higher concentration in the center of the thick filament are oriented in a homogeneous band at approximately 45 degrees to the fiber axis. The data suggests molecular crowding impacts myosin conformation, implying mutual interactions between cross-bridges alter how the muscle generates force. The GFP-tagged RLC is a novel probe to assess single-lever-arm orientation characteristics in situ.

Modulation of proton-induced current fluctuations in the human nicotinic acetylcholine receptor channel

The nicotinic acetylcholine receptor (nAChR) is a ligand-gated ion channel that switches upon activation from a closed state to a full conducting state. We found that the mutation delta S268K, located at 12' position of the second transmembrane domain of the delta subunit of the human nAChR generates a long-lived intermediate conducting state, from which openings to a wild-type like conductance level occur on a submillisecond time scale. Aiming to understand the interplay between structural changes near the 12' position and channel gating, we investigated the influence of various parameters: different ligands (acetylcholine, choline and epibatidine), ligand concentrations, transmembrane voltages and both fetal and adult nAChRs. Since sojourns in the high conductance state are not fully resolved in time, spectral noise analysis was used as a complement to dwell time analysis to determine the gating rate constants. Open channel current fluctuations are described by a two-state Markov model. The characteristic time of the process is markedly influenced by the ligand and the receptor type, whereas the frequency of openings to the high conductance state increases with membrane hyperpolarization. Conductance changes are discussed with regard to reversible transfer reaction of single protons at the lysine 12' side chain.

In situ fluorescent protein imaging with metal film-enhanced total internal reflection microscopy

Fluorescence detection of single molecules provides a means to investigate protein dynamics minus ambiguities introduced by ensemble averages of unsynchronized protein movement or of protein movement mimicking a local symmetry. For proteins in a biological assembly, taking advantage of the single molecule approach could require single protein isolation from within a high protein concentration milieu. Myosin cross-bridges in a muscle fiber are proteins attaining concentrations of approximately 120 muM, implying single myosin detection volume for this biological assembly is approximately 1 attoL (10(-18) L) provided that just 2% of the cross-bridges are fluorescently labeled. With total internal reflection microscopy (TIRM) an exponentially decaying electromagnetic field established on the surface of a glass-substrate/aqueous-sample interface defines a subdiffraction limit penetration depth into the sample that, when combined with confocal microscopy, permits image formation from approximately 3 attoL volumes. Demonstrated here is a variation of TIRM incorporating a nanometer scale metal film into the substrate/glass interface. Comparison of TIRM images from rhodamine-labeled cross-bridges in muscle fibers contacting simultaneously the bare glass and metal-coated interface show the metal film noticeably reduces both background fluorescence and the depth into the sample from which fluorescence is detected. High contrast metal film-enhanced TIRM images allow secondary label visualization in the muscle fibers, facilitating elucidation of Z-disk structure. Reduction of both background fluorescence and detection depth will enhance TIRM's usefulness for single molecule isolation within biological assemblies.

Functional subconformations in protein folding: evidence from single-channel experiments

We study fluctuations in ion conductance and enzymatic rates of the sugar-specific channel-forming membrane protein, Maltoporin, at the single-molecule level. Specifically, we analyze time-persistent deviations in the transport parameters of individual channels from the multichannel averages and discuss our findings in the context of static disorder in protein folding. We show that the disorder responsible for variations in ion conductance does not affect sugar binding, suggesting that Maltoporin can exist in a wide set of fully functional, yet distinctly different, subconformations.

Interaction of zwitterionic penicillins with the OmpF channel facilitates their translocation

To study translocation of beta-lactam antibiotics of different size and charge across the outer bacterial membrane, we combine an analysis of ion currents through single trimeric outer membrane protein F (OmpF) porins in planar lipid bilayers with molecular dynamics simulations. Because the size of penicillin molecules is close to the size of the narrowest part of the OmpF pore, penicillins occlude the pore during their translocation. Favorably interacting penicillins cause time-resolvable transient blockages of the small-ion current through the channel and thereby provide information about their dynamics within the pore. Analyzing these random fluctuations, we find that ampicillin and amoxicillin have a relatively high affinity for OmpF. In contrast, no or only a weak interaction is detected for carbenicillin, azlocillin, and piperacillin. Molecular dynamics simulations suggest a possible pathway of these drugs through the OmpF channel and rationalize our experimental findings. For zwitterionic ampicillin and amoxicillin, we identify a region of binding sites near the narrowest part of the channel pore. Interactions with these sites partially compensate for the entropic cost of drug confinement by the channel. Whereas azlocillin and piperacillin are clearly too big to pass through the channel constriction, dianionic carbenicillin does not find an efficient binding region in the constriction zone. Carbenicillin's favorable interactions are limited to the extracellular vestibule. These observations confirm our earlier suggestion that a set of high-affinity sites at the narrowest part of the OmpF channel improves a drug's ability to cross the membrane via the pore.

ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis

The "molecular Coulter counter" concept has been used to study transport of ATP molecules through the nanometer-scale aqueous pore of the voltage-dependent mitochondrial ion channel, VDAC. We examine the ATP-induced current fluctuations and the change in average current through a single fully open channel reconstituted into a planar lipid bilayer. At high salt concentration (1 M NaCl), the addition of ATP reduces both solution conductivity and channel conductance, but the effect on the channel is several times stronger and shows saturation behavior even at 50 mM ATP concentration. These results and simple steric considerations indicate pronounced attraction of ATP molecules to VDAC's aqueous pore and permit us to evaluate the effect of a single ATP molecule on channel conductance. ATP addition also generates an excess noise in the ionic current through the channel. Analysis of this excess noise shows that its spectrum is flat in the accessible frequency interval up to several kilohertz. ATP exchange between the pore and the bulk is fast enough not to display any dispersion at these frequencies. By relating the low-frequency spectral density of the noise to the equilibrium diffusion of ATP molecules in the aqueous pore, we calculate a diffusion coefficient D = (1.6-3.3)10(-11) m2/s. This is one order of magnitude smaller than the ATP diffusion coefficient in the bulk, but it agrees with recent results on ATP flux measurements in multichannel membranes using the luciferin/luciferase method.

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.

Counting polymers moving through a single ion channel

The change in conductance of a small electrolyte-filled capillary owing to the passage of sub-micrometre-sized particles has long been used for particle counting and sizing. A commercial device for such measurements, the Coulter counter, is able to detect particles of sizes down to several tenths of a micrometre. Nuclepore technology (in which pores are etched particle tracks) has extended the lower limit of size detection to 60-nm particles by using a capillary of diameter 0.45 micron (ref. 4). Here we show that natural channel-forming peptides incorporated into a bilayer lipid membrane can be used to detect the passage of single molecules with gyration radii as small as 5-15 A. From our experiments with alamethicin pores we infer both the average number and the diffusion coefficients of poly(ethylene glycol) molecules in the pore. Our approach provides a means of observing the statistics and mechanics of flexible polymers moving within the confines of precisely defined single-molecule structures.

Frequency spectrum of enthalpy fluctuations associated with macromolecular transitions

A multifrequency calorimeter has been designed to measure the amplitude and time regime of the enthalpic fluctuations associated with structural or conformational transitions in biological macromolecular systems. The heat capacity function at constant pressure is directly proportional to the magnitude of the enthalpic fluctuations in a system. Biological macromolecules undergo thermally induced transitions of different kinds. Within the transition region, these systems exhibit relatively large enthalpy fluctuations that give rise to the characteristic peaks observed by conventional differential scanning calorimetry. The multifrequency calorimeter developed in this laboratory has been designed to measure the frequency spectrum of the enthalpy fluctuations, thus allowing us to estimate thermodynamic parameters as well as relaxation times. This information is obtained from the attenuation in the amplitude or phase-angle shift of the response of the system to a periodic temperature oscillation. This instrument has been used to study the gel-liquid crystalline transition of phosphatidylcholine bilayers. The frequency-temperature response surface for large dimyristoyl phosphatidylcholine vesicles has been measured in the frequency range 0.04-1 Hz. The data are consistent with two enthalpic relaxation processes with time constants on the order of 3.8 s and 80 ms at the midpoint of the main gel-liquid crystalline transition.

Cross-correlation laser scattering

Cross-correlation between two detectors was applied to analyze laser light-scattering fluctuations. Laser scattering from random concentration fluctuations is spatially coherent over small angular areas that are inversely proportional in size to the dimension of the scattering volume. By cross-correlating scattering intensity fluctuations in different angles, the correlation due to relaxation of concentration fluctuations is practically eliminated, and correlations reflecting changes in the scattering from the individual particles can be enhanced. Rotational diffusion of assymetric particles, conformational relaxation of random coils, and association-dissociation dynamics are determined here using the above approach.

Fluctuation x-ray scattering from biological particles in frozen solution by using synchrotron radiation

Determination of the structure of biological particles, randomly oriented in solution, from spatial correlation analysis of fluctuations in x-ray scattering has recently been proposed. The feasibility of scattering fluctuation measurements was evaluated by using an x-ray synchrotron radiation camera to obtain the spatial correlation for a solution of tobacco mosaic virus along a line. The experimental system, analysis of data, and requirements for the determination of structures in solution are discussed using this example.

Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy

The theoretical basis of a new technique for measuring equilibrium adsorption/desorption kinetics and surface diffusion of fluorescent-labeled solute molecules at solid surfaces has been developed. The technique combines total internal reflection fluorescence (TIR) with either fluorescence photobleaching recovery (FPR) or fluorescence correlation spectroscopy (FCS). A laser beam totally internally reflects at a solid/liquid interface; the shallow evanescent field in the liquid excites the fluorescence of surface adsorbed molecules. In TIR/FPR, adsorbed molecules are bleaching by a flash of the focused laser beam; subsequent fluorescence recovery is monitored as bleached molecules exchange with unbleached ones from the solution or surrounding nonilluminated regions of the surface. In TIR/FCS, spontaneous fluorescence fluctuations due to individual molecules entering and leaving a well-defined portion of the evanescent field are autocorrelated. Under appropriate experimental conditions, the rate constants and surface diffusion coefficient can be readily obtained from the TIR/FPR and TIR/FCS curves. In general, the shape of the theoretical TIR/FPR and TIR/FCS curves depends in a complex manner upon the bulk and surface diffusion coefficients, the size of the iluminated or observed region, and the adsorption/desorption/kinetic rate constants. The theory can be applied both to specific binding between immobilized receptors and soluble ligands, and to nonspecific adsorption processes. A discussion of experimental considerations and the application of this technique to the adsorption of serum proteins on quartz may be found in the accompanying paper (Burghardt and Axelrod. 1981. Biophys. J. 33:455).

Tension fluctuations in contracting myofibrils and their interpretation

A self-consistent cycling steady-state model of contracting muscle is postulated to relate the autocorrelation functions of force fluctuations to the kinetic constants governing the operation of the cross-bridges. The fluctuations in the concentration of various intermediates in the model are due to the probabilistic nature of the transitions between states. It is shown that the decay rate of the autocorrelation of fluctuations in force is dependent on, and only on, the two rate constants governing transitions between attached states, and hence that the experimental autocorrelation functions can be used to estimate these rate constants. The model relates the time behavior of fluctuations in the concentration of any pair of enzymatic intermediates through the cross-correlation functions of fluctuations, and thus suggests a way to establish experimentally whether coupling exists between enzymatic and mechanical events during muscle contraction.

A mechanism for 1/f noise in diffusing membrane channels

The diffusion polarization effect is shown to produce 1/f (omega-1) noise in the conductance of membranes containing diffusing ion channels. The magnitude and frequency range of the effect are calculated.

Determination of molecular weights by fluctuation spectroscopy: application to DNA

A method for determining molecular weights of macromolecules by measuring spontaneous concentration fluctuations is described. The method is absolute, rapid, and requires no shearing forces on the molecules. We have applied this technique to the determination of molecular weight of DNA molecules. The molecular weight values obtained for T2 phage DNA (1.14 X 10(8)) and replicating Escherichia coli DNA (3.9 X 10(9)) agree with previous results. By monitoring individual molecules, an estimate of the molecular weight of nuclei and individual chromosomal DNA molecules of Drosophila melanogaster was obtained.