ABSTRACT
Single solid-state nanopores find increasing use for electrical detection and/or manipulation of macromolecules. These applications exploit the changes in signals due to the geometry and electrical properties of the molecular species found within the nanopore. The sensitivity and resolution of such measurements are also influenced by the geometric and electrical properties of the nanopore. This paper continues the development of an analytical theory to predict the electrochemical impedance spectra of nanopores by including the influence of the presence of an unfolded protein using the variable topology finite Warburg impedance model previously published by the authors. The local excluded volume of, and charges present on, the segment of protein sampled by the nanopore are shown to influence the shape and peak frequency of the electrochemical impedance spectrum. An analytical theory is used to relate the capacitive response of the electrical double layer at the surface of the protein to both the charge density at the protein surface and the more commonly measured zeta potential. Illustrative examples show how the theory predicts that the varying sequential regions of surface charge density and excluded volume dictated by the protein primary structure may allow for an impedance-based approach to identifying unfolded proteins.
Subject(s)
Dielectric Spectroscopy/methods , Models, Theoretical , Nanopores , Protein Unfolding , Proteins/chemistry , Surface PropertiesABSTRACT
We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and ß-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and ß-hairpin configurations of model peptides, varying Morse potential parameters, the hydrophobicities of residue side chains, and pH, which determines the charges of residue side chains. We construct a model triblock polypeptide mimicking the sequence of residues α-synuclein at two different pHs. The conformations of this model polypeptide depend on pH similarly to the behavior observed experimentally. The suggested approach to accounting for hydrogen bond formation within the general DPD framework may make the DPD method a competitive alternative to CGMD for modeling equilibrium and dynamic properties of proteins and polypeptides, especially during their transport in confined environments.
ABSTRACT
Solid-state nanopores and nanocapillaries find increasing use in a variety of applications including DNA sequencing, synthetic nanopores, next-generation membranes for water purification, and other nanofluidic structures. This paper develops the use of electrochemical impedance spectroscopy to determine the geometry of nanocapillaries. A network equivalent circuit element is derived to include the effects of the capacitive double layer inside the nanocapillaries as well as the influence of varying nanocapillary radius. This variable topology function is similar to the finite Warburg impedance in certain limits. Analytical expressions for several different nanocapillary shapes are derived. The functions are evaluated to determine how the impedance signals will change with different nanocapillary aspect ratios and different degrees of constriction or inflation at the capillary center. Next, the complex impedance spectrum of a nanocapillary array membrane is measured at varying concentrations of electrolyte to separate the effects of nanocapillary double layer capacitance from those of nanocapillary geometry. The variable topology equivalent circuit element model of the nanocapillary is used in an equivalent circuit model that included contributions from the membrane and the measurement apparatus. The resulting values are consistent with the manufacturer's specified tolerances of the nanocapillary geometry. It is demonstrated that electrochemical impedance spectroscopy can be used as a tool for in situ determination of the geometry of nanocapillaries.
Subject(s)
Dielectric Spectroscopy/methods , Nanopores/ultrastructure , Dimethylpolysiloxanes/chemistry , Electrolytes/chemistry , Models, TheoreticalABSTRACT
Most in vitro investigations of alpha-Synuclein (alphaSyn) aggregation and amyloidogenesis use agitation in the presence of air and/or Teflon to accelerate kinetics. The effect of the agitation is implicitly or explicitly attributed to mass transfer or fibril fragmentation. This paper evaluates these hypotheses by agitating alphaSyn under typical amyloidogenic conditions with controlled numbers of balls made of polytetrafluoroethylene (PTFE), polymethylmethacrylate (PMMA), and borosilicate glass with no headspace. Amyloid was assayed using thioflavin T fluorescence and atomic force microscopy. The observed kinetics were proportional to the PTFE surface area; the effects of PMMA and glass balls were negligible by comparison. No amyloid was observed to form in the absence of mixing balls. Agitation with only air also showed accelerated kinetics but different aggregate morphology. The results indicate that the mechanism active in agitation experiments is dominated by reactions at the hydrophobic-water interface. Of the mass transfer, fragmentation, and hydrophobic interface hypotheses, only the last is capable of explaining the data. Condition and sequence determinants of amyloidogenic propensity that have thus far been reported must be reinterpreted as being reflective of partitioning to hydrophobic-water interfaces. Comparable hydrophobic interfaces are not found in vivo.
Subject(s)
Amyloid/biosynthesis , alpha-Synuclein/metabolism , Amino Acid Sequence , In Vitro Techniques , Microscopy, Atomic Force , Polymers/metabolismABSTRACT
This paper systematically investigates the effects of solution viscosity, applied voltage and DNA chain length on the distribution of DNA translocation times through 8 ± 2 nm diameter silicon nitride nanopores. Linear dsDNA translocation events were selected based on the magnitude of current blockage and accumulated into scatter plots of current blockage and event duration (translocation time). The translocation time distribution was fitted to the solution of a Smoluchowski-type equation for 1D biased diffusion to a sink. The DNA drifting speed under bias and diffusion constant were extracted from the fits as functions of solution viscosity, applied voltage and DNA chain length. Combined with the Einstein-Smoluchowski relation, this model allowed evaluation of the viscous drag force on DNA molecules. This model also allowed estimation of the uncertainty in determining the DNA chain length due to the influence of friction on the spread of translocation times in a nanopore measurement. The data analysis suggests that the simple 1D biased diffusion model fits the experimental data well for a wide range of conditions. Some deviations from predicted behavior were observed and show where additional phenomena are likely to contribute to the distribution of DNA translocation times.
Subject(s)
DNA/chemistry , Models, Chemical , Computer Simulation , Diffusion , Models, Statistical , Motion , Porosity , Statistical DistributionsABSTRACT
We combine atomic-force-microscopy particle-size-distribution measurements with earlier measurements on 1-anilino-8-naphthalene sulfonate, thioflavin T, and dynamic light scattering to develop a quantitative kinetic model for the aggregation of beta-lactoglobulin into amyloid. We directly compare our simulations to the population distributions provided by dynamic light scattering and atomic force microscopy. We combine species in the simulation according to structural type for comparison with fluorescence fingerprint results. The kinetic model of amyloidogenesis leads to an aggregation free-energy landscape. We define the roles of and propose a classification scheme for different oligomeric species based on their location in the aggregation free-energy landscape. We relate the different types of oligomers to the amyloid cascade hypothesis and the toxic oligomer hypothesis for amyloid-related diseases. We discuss existing kinetic mechanisms in terms of the different types of oligomers. We provide a possible resolution to the toxic oligomer-amyloid coincidence.
Subject(s)
Amyloid/chemistry , Amyloid/ultrastructure , Anilino Naphthalenesulfonates/chemistry , Animals , Cattle , Computer Simulation , Kinetics , Lactoglobulins/chemistry , Light , Microscopy, Atomic Force , Models, Chemical , Protein Structure, Quaternary , Reproducibility of Results , Scattering, Radiation , Thermodynamics , Time FactorsABSTRACT
We use single silicon nitride nanopores to study folded, partially folded, and unfolded single proteins by measuring their excluded volumes. The DNA-calibrated translocation signals of beta-lactoglobulin and histidine-containing phosphocarrier protein match quantitatively with that predicted by a simple sum of the partial volumes of the amino acids in the polypeptide segment inside the pore when translocation stalls due to the primary charge sequence. Our analysis suggests that the majority of the protein molecules were linear or looped during translocation and that the electrical forces present under physiologically relevant potentials can unfold proteins. Our results show that the nanopore translocation signals are sensitive enough to distinguish the folding state of a protein and distinguish between proteins based on the excluded volume of a local segment of the polypeptide chain that transiently stalls in the nanopore due to the primary sequence of charges.
Subject(s)
Bacteria/chemistry , Bacterial Proteins/chemistry , Lactoglobulins/chemistry , Nanostructures/chemistry , Phosphoenolpyruvate Sugar Phosphotransferase System/chemistry , Silicon Compounds/chemistry , Amino Acid Sequence , Animals , Cattle , DNA/chemistry , Hydrogen-Ion Concentration , Molecular Sequence Data , Protein Folding , Urea/chemistryABSTRACT
Time-correlated single photon counting allows luminescence lifetime information to be determined on a single molecule level. This paper develops a formalism to allow information theory analysis of the ability of luminescence lifetime measurements to resolve states in a single molecule. It analyzes the information content of the photon stream and the fraction of that information that is relevant to the state determination problem. Experimental losses of information due to instrument response, digitization, and different types of background are calculated and a procedure to determine the optimal value of experimental parameters is demonstrated. This paper shows how to use the information theoretical formalism to evaluate the number of photons required to distinguish dyes that differ only by lifetime. It extends this idea to include distinguishing molecular states that differ in the electron transfer quenching or resonant energy transfer and shows how the differences between the lifetime of signal and background can help distinguish the dye position in an excitation beam.
Subject(s)
Algorithms , Coloring Agents/chemistry , Computer Simulation , Fluorescence Resonance Energy Transfer/methods , Models, Chemical , Photons , Electrons , Energy Transfer , Luminescence , Thermodynamics , Time FactorsABSTRACT
We use time-dependent fluorescence Stokes shift (TDFSS) information to study the fluctuation rates of the lipocalin, beta-lactoglobulin A in the vicinity of an encapsulated coumarin 153 molecule. The system has three unique dielectric environments in which the fluorophore binds. We develop a method to decompose the static and dynamic contributions to the spectral heterogeneity. This method is applied to temperature-dependent steady-state fluorescence spectra providing us with site-specific information about thermodynamic transitions in beta-lactoglobulin. We confirm previously reported transitions and discuss the presence of an unreported transition of the central calyx at 18 degrees C. Our method also resolves the contributions to the TDFSS from the coumarin 153 centrally located in the calyx of beta-lactoglobulin despite overlapping signals from solvent exposed dyes. Our experiments show dynamics ranging from 3-12,00 ps. The analysis shows a decrease in the encapsulated dye's heterogeneity during the relaxation, which is taken as evidence of the breakdown of linear response.
Subject(s)
Coumarins/chemistry , Lactoglobulins/chemistry , Animals , Cattle , Fluorescence , Protein ConformationABSTRACT
We have investigated the aggregation and amyloid fibril formation of bovine beta-lactoglobulin variant A, with a focus on the early stages of aggregation. We used noncovalent labeling with thioflavin T and 1-anilino-8-naphthalenesulfonate to follow the conformational changes occurring in beta-lactoglobulin during aggregation using time resolved luminescence. 1-Anilino-8-naphthalenesulfonate monitored the involvement of the hydrophobic core/calyx of beta-lactoglobulin in the aggregation process. Thioflavin T luminescence monitored the formation of amyloid. The luminescence lifetime distributions of both probes showed changes that could be attributed to conformational changes occurring during and following aggregation. To correlate the luminescence measurements with the degree of aggregation and the morphology of the aggregates, we also measured dynamic light scattering and atomic force microscopy images. We evaluated the relative stability of the intermediates with an assay that is sensitive to aggregation reversibility. Our results suggest that initial aggregation during the first 5 days occurred with partial disruption of the characteristic calyx in beta-lactoglobulin. As the globular aggregates grew from days 5 to 16, the calyx was completely disrupted and the globular aggregates became more stable. After this second phase of aggregation, conversion into a fibrillar form occurred, marking the growth phase, and still more changes in the luminescence signals were observed. Based on these observations, we propose a three-step process by which monomer is converted first into weakly associated aggregates, which rearrange into stable aggregates, which eventually convert into protofibrils that elongate in the growth phase.
Subject(s)
Amyloid/metabolism , Lactoglobulins/chemistry , Lactoglobulins/metabolism , Amyloid/chemistry , Amyloid/ultrastructure , Anilino Naphthalenesulfonates/metabolism , Animals , Benzothiazoles , Binding Sites , Cattle , Fluorescence , Hydrophobic and Hydrophilic Interactions , Lactoglobulins/ultrastructure , Light , Microscopy, Atomic Force , Protein Structure, Quaternary , Protein Structure, Secondary , Scattering, Radiation , Thiazoles/metabolismABSTRACT
We introduce a new approach to global data fitting based on a regularization condition that invokes continuity in the global data coordinate. Stabilization of the data fitting procedure comes from probabilistic constraint of the global solution to physically reasonable behavior rather than to specific models of the system behavior. This method is applicable to the fitting of many types of spectroscopic data including dynamic light scattering, time-correlated single-photon counting (TCSPC), and circular dichroism. We compare our method to traditional approaches to fitting an inverse Laplace transform by examining the evolution of multiple lifetime components in synthetic TCSPC data. The global regularizer recovers features in the data that are not apparent from traditional fitting. We show how our approach allows one to start from an essentially model-free fit and progress to a specific model by moving from probabilistic to deterministic constraints in both Laplace transformed and nontransformed coordinates.
Subject(s)
Algorithms , Luminescent Measurements/methods , Models, Statistical , Photons , Computer Simulation , Entropy , Models, Biological , Spectrum Analysis , Time FactorsABSTRACT
Glucose/galactose binding protein (GGBP) functions in two different larger systems of proteins used by enteric bacteria for molecular recognition and signaling. Here we report on the thermodynamics of conformational equilibrium distributions of GGBP. Three fluorescence components appear at zero glucose concentration and systematically transition to three components at high glucose concentration. Fluorescence anisotropy correlations, fluorescent lifetimes, thermodynamics, computational structure minimization, and literature work were used to assign the three components as open, closed, and twisted conformations of the protein. The existence of three states at all glucose concentrations indicates that the protein continuously fluctuates about its conformational state space via thermally driven state transitions; glucose biases the populations by reorganizing the free energy profile. These results and their implications are discussed in terms of the two types of specific and nonspecific interactions GGBP has with cytoplasmic membrane proteins.
Subject(s)
Bacterial Proteins/chemistry , Bacterial Proteins/metabolism , Enterobacteriaceae/metabolism , Monosaccharide Transport Proteins/chemistry , Monosaccharide Transport Proteins/metabolism , Biophysical Phenomena , Biophysics , Fluorescence Polarization , Galactose/metabolism , Glucose/metabolism , Ligands , Membrane Proteins/metabolism , Models, Molecular , Protein Binding , Protein Conformation , ThermodynamicsABSTRACT
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.
ABSTRACT
The interpretation of single-molecule measurements is greatly complicated by the presence of multiple fluorescent labels. However, many molecular systems of interest consist of multiple interacting components. We investigate this issue using multiply labeled dextran polymers that we intentionally photobleach to the background on a single-molecule basis. Hidden Markov models allow for unsupervised analysis of the data to determine the number of fluorescent subunits involved in the fluorescence intermittency of the 6-carboxy-tetramethylrhodamine labels by counting the discrete steps in fluorescence intensity. The Bayes information criterion allows us to distinguish between hidden Markov models that differ by the number of states, that is, the number of fluorescent molecules. We determine information-theoretical limits and show via Monte Carlo simulations that the hidden Markov model analysis approaches these theoretical limits. This technique has resolving power of one fluorescing unit up to as many as 30 fluorescent dyes with the appropriate choice of dye and adequate detection capability. We discuss the general utility of this method for determining aggregation-state distributions as could appear in many biologically important systems and its adaptability to general photometric experiments.
Subject(s)
Chromogenic Compounds/chemistry , Markov Chains , Models, Biological , Monte Carlo Method , Photobleaching , Dextrans/chemistry , Fluorescent Dyes/chemistry , Models, Statistical , Rhodamines/chemistryABSTRACT
We use Shannon's definition of information to develop a theory to predict a photon-counting-based single-molecule experiment's ability to measure the desired property. We treat three phenomena that are commonly measured on single molecules: spectral fluctuations of a solvatochromic dye; assignment of the azimuthal dipole angle; determination of a distance by fluorescence resonant energy transfer using Förster's theory. We consider the effect of background and other "imperfections" on the measurement through the decrease in information.
Subject(s)
Models, Chemical , Research Design , Computer Simulation , Coumarins/chemistry , Molecular Structure , Photons , Spectrum AnalysisABSTRACT
The measurement of fluorescence from single protein molecules has become an important new tool in the study of dynamic processes, allowing for the direct visualization of the motions experienced by individual proteins and macromolecular complexes. The data from such single-molecule experiments are in the form of photon trajectories, consisting of arrival times and wavelength information on individual photons. The analysis of photon trajectories can be difficult, particularly if the motions are occurring at rates comparable to the photon arrival rate or in the presence of noise. In this paper, we introduce the use of hidden Markov models (HMMs) for the analysis of photon trajectory data that operate using the photon data directly, without the need for ensemble averaging of the data as implied by correlation function analysis. Using a simple kinetic model, we examine the relationship between the uncertainty in the estimates of the motional rate and the photon detection rate. Remarkably, we obtain relative uncertainties in the rate constants of as little as 3% even when the interconversion rate is equal to the photon detection rate, and the uncertainty increases to only 10% when the interconversion rate is 10 times the photon detection rate. This suggests that useful information can be obtained for much faster kinetic regimes than have typically been studied. We also examine the impact of background photons on the determination of the rate and demonstrate that the HMM-based approach is robust, displaying small uncertainties for background photon arrival rates approaching that of the signal. These results not only are relevant in establishing the theoretical limits on precision, but are also useful in the context of experimental design. Finally, to demonstrate how the methodology can be extended to more complex kinetic models and how it can allow one to make use of the full power of statistics for purposes of model evaluation and selection, we consider a four-state kinetic model for protein conformational transitions previously studied by Schenter et al. (J. Phys. Chem. A1999, 103, 10477). We show how an HMM can be used as an alternative to higher-order correlation function analysis for the detection of "conformational memory" and apparent non-Markovian dynamics arising from such temporally inhomogeneous kinetic schemes.
ABSTRACT
Gas phase 308 and 350-370 nm photolysis of bis(1,1,1,5,5,5-hexafluoro-2,4-pentanedionato)copper(II), Cu(hfac)(2), produces CuF as well as copper atoms and dimers. These metal-containing fragments, identified by luminescence spectroscopy, are studied under a variety of gas phase conditions ranging from 1 bar in a static chamber to 10(-4) mbar in a collision-free molecular beam. Copper atom and dimer luminescence is observed at the higher pressures, whereas at low pressures (total pressure no greater than the vapor pressure of the sample) exclusively CuF emission is observed. The a, A (omega = 0, 1, 2), B, and C excited states at 681.0, 567.6, and 505.1, and 491.7 nm are observed. The (3)Pi(0)(-) component of the A state is observed for the first time. The CuF luminescence obeys a quadratic power law with 308 nm excitation. The partitioning of excess energy into fragment degrees of freedom is determined from the intensities of the emission lines. The vibrational and rotational temperatures of the CuF fragment are in excess of 1700 K. Mechanisms of CuF formation, comparisons with the free ligand and with other volatile copper complexes, and the implications for laser-assisted chemical vapor deposition are discussed.