Photobleaching pathways in single-molecule FRET experiments

To acquire accurate structural and dynamical information on complex biomolecular machines using single-molecule fluorescence resonance energy transfer (sm-FRET), a large flux of donor and acceptor photons is needed. To achieve such fluxes, one may use higher laser excitation intensity; however, this induces increased rates of photobleaching. Anti-oxidant additives have been extensively used for reducing acceptor's photobleaching. Here we focus on deciphering the initial step along the photobleaching pathway. Utilizing an array of recently developed single-molecule and ensemble spectroscopies and doubly labeled Acyl-CoA binding protein and double-stranded DNA as model systems, we study these photobleaching pathways, which place fundamental limitations on sm-FRET experiments. We find that: (i) acceptor photobleaching scales with FRET efficiency, (ii) acceptor photobleaching is enhanced under picosecond-pulsed (vs continuous-wave) excitation, and (iii) acceptor photobleaching scales with the intensity of only the short wavelength (donor) excitation laser. We infer from these findings that the main pathway for acceptor's photobleaching is through absorption of a short wavelength photon from the acceptor's first excited singlet state and that donor's photobleaching is usually not a concern. We conclude by suggesting the use of short pulses for donor excitation, among other possible remedies, for reducing acceptor's photobleaching in sm-FRET measurements.     

Computational spectroscopy of ubiquitin: comparison between theory and experiments

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution.     

Quantitative evaluation of cross correlation between two finite-length time series with applications to single-molecule FRET

The statistical properties of the cross correlation between two time series has been studied. An analytical expression for the cross correlation function's variance has been derived. On the basis of these results, a statistically robust method has been proposed to detect the existence and determine the direction of cross correlation between two time series. The proposed method has been characterized by computer simulations. Applications to single-molecule fluorescence spectroscopy are discussed. The results may also find immediate applications in fluorescence correlation spectroscopy (FCS) and its variants.     

Direct characterization of protein oligomers and their quaternary structures by single-molecule FRET

Using a single-molecule method, we directly distinguish among oligomers from monomers to tetramers and determine their quaternary structures. Using this method, we found that RecR forms a stable dimer and its oligomeric form is modulated by its own concentration and the interaction with RecO.     

Membrane distillation: theory and experiments

A theoretical approach is presented that describes membrane distillation processes due to the simultaneous action (in a proactive or in a counteractive way) of temperature and concentration differences through porous hydrophobic membranes. The model developed emphasizes the importance of the boundary layers, shows the existence of a coupling term between the two thermodynamic forces acting on the system, and permits the definition and characterization of the so-called steady states. In order to check the model, two membranes have been studied in different experimental conditions. The influence of some relevant parameters, such as solution concentration, stirring rate, mean temperature and temperature difference has been considered and the theoretical predictions of the model have been applied to the obtained results. The accordance may be considered good.     

Homogeneous nucleation of n-nonane and n-propanol mixtures: a comparison of classical nucleation theory and experiments

The homogeneous nucleation rates for n-nonane-n-propanol vapor mixtures have been calculated as a function of vapor-phase activities at 230 K using the classical nucleation theory (CNT) with both rigorous and approximate kinetic prefactors and compared to previously reported experimental data. The predicted nucleation rates resemble qualitatively the experimental results for low n-nonane gas phase activity. On the high nonane activity side the theoretical nucleation rates are about three orders of magnitude lower than the experimental data when using the CNT with the approximate kinetics. The accurate kinetics improves the situation by reducing the difference between theory and experiments to two orders of magnitude. Besides the nucleation rate comparison and the experimental and predicted onset activities, the critical cluster composition is presented. The total number of molecules is approximated by CNT with reasonable accuracy. Overall, the classical nucleation theory with rigorous kinetic prefactor seems to perform better. The thermodynamic parameters needed to calculate the nucleation rates are revised extensively. Up-to-date estimates of liquid phase activities using universal functional activity coefficient Dortmund method are presented together with the experimental values of surface tensions obtained in the present study.     

Synergistic effects in mixtures of oppositely charged surfactants as calculated from the Poisson-Boltzmann theory: a comparison between theoretical predictions and experiments

Critical micelle concentrations in mixtures of an anionic surfactant and a cationic amphiphilic drug have been investigated using a model-independent procedure to quantify observed synergistic effects. Experimental results were compared with a theory based on the Poisson-Boltzmann mean field approximation of a charged interface with a diffuse layer of counterions. Explicit expressions for the activity coefficients from which the critical micelle concentration can be calculated and quantitatively predicted have been derived and excellent agreement between experimental data and theory was obtained. As a result, we demonstrate that it is possible to rationalize and predict the magnitude of synergism in mixtures of oppositely charged surfactants in the presence of added salt.     

Thermodynamic driving force for diffusion: comparison between theory and simulation

In previous work, lattice density functional theory equations have been recast into differential form to determine a property whose gradient is universally proportional to the diffusive flux. For color counter diffusion, this property appears as the impingement rate onto vacancies and molecules of a species whose density gradient can be influenced by diffusion. Therefore, the impingement rate of a diffusing molecule depends on the mobility of its surroundings. In order to determine the validity of this finding, molecular dynamics simulations of color counter diffusion were performed in which the mobility of the solvent was varied to determine if the flux of the diffusing species responded to the change when all other factors, such as density gradient, available volume, and temperature are held constant.     

Colloidal crystals from surface-tension-assisted self-assembly: a novel matrix for single-molecule experiments

In this work, we develop a new method of creating colloidal crystals with cavities for the entrapment and long-term observation of single biomolecules. Colloidal crystals are first fabricated using surface-tension-assisted self-assembly. Surface tension helps to reduce the interparticle distance between dispensed colloids. Subsequently, the colloids are used as a matrix in which single fluorescently tagged molecules can be tracked using fluorescence microscopy. This method has a high efficiency of self-assembly for small volumes (4 microL) of colloidal suspensions (polystyrene colloids with diameters of 1000, 500, 200, and 100 nm) at low concentration (1% w/w). The spatial hindrance effect on the diffusion of molecules and their entrapment is discussed on the basis of fluorescence correlation spectroscopy results from the diffusion of molecules with different hydrodynamic radii in the cavities of colloidal crystals formed from micrometer- to nanometer-sized polystyrene spheres. Single horseradish peroxidase molecules turning over fluorescent products are tracked over a few seconds. This shows that colloidal crystals can be used to test the function of single molecules of enzymes and protein under controlled spatial confinement.     

Unfolded protein and peptide dynamics investigated with single-molecule FRET and correlation spectroscopy from picoseconds to seconds

Single-molecule fluorescence spectroscopy and correlation methods are finding increasing applications in the investigation of biomolecular dynamics, especially together with F?rster resonance energy transfer (FRET). Here, we use the combination of start-stop experiments and classical fluorescence correlation spectroscopy (FCS) to obtain complete intensity auto- and cross-correlation functions from picoseconds to seconds for investigating the dynamics of unfolded proteins and peptides. In combination with distance information from single-molecule transfer efficiency histograms, we can analyze the data in terms of a diffusive process on a potential of mean force to obtain intramolecular diffusion coefficients. This allows us to extend our previous analysis of the time scales of chain dynamics into the low nanosecond range for peptides and into the microsecond range for a small cold shock protein (Csp). Dynamics in short unstructured peptides can be detected down to a time scale of about 10 ns, placing a lower limit on the time scales accessible with correlation methods and currently used dye pairs. We find no evidence for microsecond fluctuations in unfolded Csp, suggesting that its global chain dynamics occur predominantly in the tens of nanosecond range. We further investigate the position dependence of these dynamics by placing donor and acceptor dyes at different positions within the chain and find a decrease in the intramolecular diffusion coefficient by a factor of 3 upon moving one of the dyes toward the center of the polypeptide. Obtaining dynamic information on a wide range of time scales from single-molecule photon statistics will be of increasing importance for the study of unfolded proteins and for biomolecules in general.     

Injection molded nanofluidic chips: fabrication method and functional tests using single-molecule DNA experiments

We demonstrate that fabrication of well-defined nanofluidic systems can be greatly simplified by injection molding of thermoplastic polymers. Chips featuring nanochannel arrays, microchannels and integrated interconnects are produced in a single processing step by injection molding. The resulting open channel structures are subsequently sealed by facile plasma-enhanced thermal bonding of a polymer film. This fast, inexpensive and industry-compatible method thus provides a single-use all-polymer platform for nanofluidic lab-on-a-chip applications. Its applicability for nanofluidics is demonstrated by DNA stretching experiments performed on individual double-stranded DNA molecules confined in the injection molded nanochannels. The obtained results are consistent with measurements performed in costly state-of-the-art silica nanochannels, for both straight and tapered channel geometries.     

Electrokinetic filtration in clays: theory and experiments

The main aspects and results of some electrokinetic filtration tests are presented. Both theory and tests show the key role played by the electrochemical boundary phenomena, such as the electrode reactions, and by the mineralogy of the soil. The aforementioned results show the necessity to run long duration tests. Indeed the macroscopic properties of the soil can change widely during the tests, therefore affecting the expected results in terms of environmental remediation or consolidation but also in terms of energy consumption and efficiency.     

Optical properties of N-succinimidyl bithiophene and the effects of the binding to biomolecules: comparison between coupled-cluster and time-dependent density functional theory calculations and experiments

We report a joint theoretical-experimental study on the optical properties of 5-N-succinimidyl-2,2'-bithiophene (NS-2T), a prototype system for a new class of biomarkers. Time-dependent density functional theory (TD-DFT) and approximate coupled-cluster single and doubles (CC2) calculations are performed in the ground and excited states. Theoretical results are compared with absorption, photoluminescence (PL), time-resolved PL, and PL quantum efficiency measurements. The excited state of NS-2T has a larger dipole moment as compared to that of the ground state, explaining the experimental shift of the PL peak in solvents of different polarity, and a smaller intersystem crossing (ISC) rate as compared to that of isolated bithiophene (2T), explaining the increased PL quantum efficiency. We also studied two model systems to describe the effects of the covalent binding of NS-2T to biomolecules and proteins with the epsilon-NH(2) lysine groups. These model systems show optical properties closer to 2T, as the PL quantum efficiency is reduced due to the increased ISC rate. Theoretical calculations and experimental results show that covalent binding of NS-2T to a biomolecule will blue-shift the absorption but not the photoluminescence. CC2 and TD-DFT can very well describe the absorption and photoluminescence energies of all three systems, but the presence of several charge-transfer transitions in the TD-DFT spectrum of NS-2T required the use of a correlated method to validate the TD-DFT results.     

Springs and speeds in free energy reconstruction from irreversible single-molecule pulling experiments

The nonequilibrium work relation allows for the calculation of equilibrium free energy differences between states based on the exponential average of accumulated work from irreversible transitions. Here, we compare two distinct approaches of calculating free energy surfaces from unidirectional single-molecule pulling experiments: the stiff spring approximation and the Hummer-Szabo method. First, we perform steered molecular dynamics simulations to mechanically stretch the model peptide deca-alanine using harmonic potentials with different spring stiffnesses and at various constant pulling velocities. We then calculate free energy surfaces based on the two methods and their variants, including the first and second cumulant expansion of the exponentially weighted work and the Gaussian position approximation for the delta function in Hummer and Szabo's expression. We find that with large harmonic force constants, the second cumulant expansion performs well in conjunction with either the stiff spring approximation or the Hummer-Szabo method. When interpreting dynamic force spectroscopy (pullings at different speeds), the second cumulant expansion of the stiff spring approximation performs the best when pulling velocities are similar, but variants of the Hummer-Szabo perform the best when they are spread over a large spectrum. While these conclusion are not definitive for all systems, the insights should prove useful for scientists interpreting nonequilibrium pulling experiments.     

Drainage of the air-water-quartz film: experiments and theory

Experimental results of the kinetics of drainage of the trapped water film between an approaching air bubble and a quartz plate have been analysed using recent theoretical advances in formulating and solving the flow problem in deformable films. Excellent agreement is obtained between experimental data and a model that assumes the bubble-water interface is tangentially immobile in its hydrodynamic response. The coupling between hydrodynamic pressure, disjoining pressure and film deformation is critical in determining the dynamic behaviour of the drainage process. The Reynolds parallel film model that omits the effects of film deformation predicts results that are qualitatively incorrect.     

Aggregation kinetics of polymer colloids in reaction limited regime: experiments and simulations

The kinetics of reaction-limited cluster aggregation of fluorinated polymer colloids in a broad range of particle volume fractions has been investigated experimentally by measuring independently the Fuchs stability ratio W and the time evolution of both the average radius of gyration and the average hydrodynamic radius of the aggregates mass distribution. The W value is determined from the aggregation rate at the very initial stage of the aggregation, where the presence of triplets is negligible. The time evolutions of and are then simulated using the cluster mass distribution calculated from the population balance equations with various aggregation kernels proposed in the literature. It is found that, when the measured W value is used, the only kernels that can correctly simulate the experimental results are the product kernel and the one derived by Odriozola et al. (Europhys. Lett. 53 (2001) 797), with some proper tuning of the exponent in the kernel. For the particle volume fraction phi<1%, the obtained value for the exponent is 0.4 and independent of phi, while it tends to decrease for larger phi values, most likely indicating a significant effect of multi-body interactions on the aggregation kinetics.     

Eudragit as controlled release system for anti-inflammatory drugs: A comparison between DSC and dialysis experiments

A comparative study between the release of Ibuprofen (IBU) from Eudragit RS100^® (RS) and RL100^® (RL) nanosuspensions as well as the free drug to a biological model membrane, consisting of dimyristoylphosphatidylcholine (DMPC) multilamellar vesicles (MLV), was carried out by DSC technique. The aim was to assess the suitability of such calorimetric technique to determine the kinetics of drug release from a polymer system, compared with a classical release test by dialysis method. Nanosuspensions were prepared by a modification of the quasi-emulsion solvent diffusion technique (QESD), a particular approach to the general solvent-change method. This kind of system was planned for the ophthalmic release of non-steroidal anti-inflammatory drugs in ocular diseases associated with inflammatory processes (i.e. post-cataract surgery or uveitis). The drug release was monitored by differential scanning calorimetry (DSC), following the effects exerted by IBU on the thermotropic behaviour of DMPC multilamellar vesicles. IBU affects the main transition temperature (T_m) of phospholipid vesicles, causing a shift towards lower values, driven by the drug fraction entering the lipid bilayer. The obtained values have been used as a calibration curve. DSC was performed on suspensions of blank liposomes added to fixed amounts of unloaded and IBU-loaded Eudragit RS100^® and RL100^® nanosuspensions as well as to powdered free drug. The T_m shifts caused by the drug released from the polymer system or by the free drug, during incubation cycles at 37 °C, were compared to the calibration curve in order to obtain the fraction of drug released. The results were also compared with in vitro dialysis release experiments. The suitability of the two different techniques to follow the drug release as well as the differences between the RL and RS polymer systems was compared, confirming the efficacy of DSC for studying the release from polymer nanoparticulate systems. Explanation of the different rate of kinetic release could be due to void liposomes, which represent a better up-taking system than the aqueous solution phase in the dialysis experiments.     

Surface forces in polymer fluids: a comparison between simulations and density functional theory

A polymer density functional theory is evaluated in terms of its ability to predict interactions between large surfaces in a polymer fluid. Comparisons are made with results from simulations in an expanded isotension ensemble. The variation of the net surface-surface interaction with adsorption strength is examined. Cases where the monomers interact via a pure hard sphere potential are investigated, but we have also studied the effect of attractions between the monomers. In all cases, we obtain an almost quantitative agreement between the simulated results and the predictions from the polymer density functional theory.     

Elastic constants of uniaxial nematic liquid crystals: A comparison between theory and experiment

Using the unified molecular theory developed in our earlier paper (1992, Phys. Rev. A, 45, 974) we study in detail the influence of molecular interactions on the fundamental elastic properties of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. The expressions for the elastic moduli associated with 'splay', 'twist' and 'bend' modes of deformations are written in terms of order parameters characterizing the nature and amount of ordering in the phase and the structural parameters which involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. Numerical calculations are done for a model system, the molecules of which have prolate ellipsoid of revolution symmetry and interact via a pair potential having both repulsive and attractive parts. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution. The attractive potential is represented by the dispersion and electrostatic interactions. Results for the elastic constants are reported for a range of molecular length-width ratio, temperature, density and molecular parameters and are compared with the experimental values of p-azoxyanisole (PAA) and 4'-n-octyloxy-4-cyanobiphenyl (8OCB). It is found that the inclusion of electrostatic interactions reduces the values of the ratios K₂/K₁ and K₃/K₁. The absolute values of the elastic constants and their ratios are in good agreement with the experimental and computer simulation values. The temperature dependence of the elastic constants and their ratios is studied. It is observed that the twist elastic constant has a weak temperature dependence but a pronounced influence is observed on the bend moduli. We also observed a pronounced increase in the values of the twist and bend elastic constants on approaching the nematic-smectic A transition temperature.