Perrin Equation Research Articles

Development of a novel fluorimetric sensor based on polypyrrole doped with 4-(methylsulfonyl)-2-nitrobenzoic acid (MSNBA) for sensitive detection of copper (Cu2+)

In this study, we successfully electrochemically synthesized a polypyrrole film doped with 4-methylsulfonyl-2-nitrobenzoic acid (MSNBA) within an aqueous medium containing 0.01 M MSNBA, 0.003 M NaOH, and 0.01 M pyrrole. Our investigation encompassed a thorough exploration of both electrochemical and spectroscopic properties, confirming the effective incorporation of MSNBA as a dopant within the electroactive PPy chain. The morphological characterization of the film was undertaken using scanning electron microscopy (SEM). The optical properties, particularly UV–visible absorption, and fluorescence spectroscopy, were scrutinized in a dilute DMF solution. The UV–visible absorption spectra revealed a broad absorption band centered around 292 nm, attributed to the π→π* 1B - 1La/1Lb transitions of the oligo-benzenes in the film. In parallel, fluorescence spectra exhibited remarkable consistency between the solid state and solution, featuring an excitation peak at 345 nm (346 nm in solution) and an emission peak around 401 nm (403 nm in solution). Exploring the impact of copper (II) ions on absorption and fluorescence spectra unveiled a notable quenching effect along two distinct linearity domains. Various mathematical treatments, including the Stern-Volmer equation (R1 = 0.98, Ksv1 = 5.104 and R2 = 0.99, Ksv2 = 1.54.106), the Perrin equation, and the polynomial equation, were applied to elucidate the nature of this fluorescence quenching. Our findings indicated that the fluorescence extinction, as a function of Cu2+ ion concentration, aligns well with the polynomial equation, signifying a combination of dynamic and static quenching (Io/I = 1.08(±0.04) + 1.46(±0.44)105[Q]- 1.15(±0.75)1010 [Q]2). Moreover, we explored the potential application of this method for the determination of Cu2+. Calibration graphs demonstrated excellent linearity between fluorescence intensity and Cu2+ concentration in the range of 0–5.4 μM. Notably, the detection limit of 1.2 μM surpassed the LOD for Cu2+ (20 μM) in drinking water set by the EPA, suggesting the viability of this approach for sensitive detection in environmental monitoring.

Fluorescence superquenching of SYBR Green I in crowded DNA by gold nanoparticles

Gold nanoparticles (GNPs) are known to efficiently quench fluorescence with high constants (107-1011 M−1). Quenching efficiency is determined by GNPs parameters, the properties of dye complex with biomolecular substrate may also affect this efficiency. In the present work quenching of SYBR Green I fluorescence by 2.5 nm GNPs was investigated in an isotropic DNA solution and on cholesteric (DNA CLCD) and hexagonal (DNA HLCD) liquid crystalline dispersion templates obtained with polymer and salt-induced condensation. Superquenching of SYBR Green I fluorescence was observed in all investigated models. The quenching efficiency increased as the DNA molecules were spatially ordered: the greatest quenching was observed for DNA HLCD where DNA molecules are packed most densely. In the condensed DNA systems, unlike DNA solution, the mechanism of quenching was not only the formation of a nonfluorescent complex, but also energy transfer between dye molecules and GNPs. The Stern-Volmer and Perrin models were insufficient for description of quenching processes. The Perrin equation was in an agreement with experiment only for DNA in solution. The model of microphase separation most adequately described the SYBR Green I fluorescence quenching by GNPs in DNA solution as well as in the molecularly organized DNA CLCD and DNA HLCD.

Polarization study of carbon nanodots photoluminescence

The properties of luminescence centers in carbon nanodots synthesized in the pores of mesoporous silica are studied. The effects of annealing the nanodots in the reducing/oxidizing atmosphere on the nanodot luminescence are investigated. Analysis of the effects together with low-temperature luminescent spectroscopy of the nanodots indicates a significant contribution of oxygen atoms to the formation of luminescence centers in the carbon nanodots studied. The temperature dependence of the degree of the photoinduced linear polarization of the emission of colloidal solutions of carbon nanodots was investigated. Increasing temperature is found to result in the depolarization of nanodot emission. The thermal effect on the polarization degree is well described by the Levshin–Perrin equation, which proves the rotational mechanism of the nanodot emission depolarization. By comparing the experimental data and the theory, the size of the rotating elementary emitters was estimated. The size obtained (∼0.9 nm) is appreciably less than the diameter of carbon nanodots under study (∼3 nm), which indicates that the atomic groups responsible for the luminescence of carbon nanodots are nonrigidly connected with their cores and can rotate almost independently of them.

Temperature Quenching and Fluorescence Depolarization of Carbon Nanodots Obtained via Paraffin Pyrolysis

A temperature effect on fluorescence intensity and polarization of a colloidal system of carbon nanodots in glycerol under linearly polarized pumping conditions is studied. Nanodots are obtained via pyrolysis of paraffin in nanopores of a mesoporous silica. An increase in temperature leads to quenching of nanodots fluorescence, and activation energy of the quenching process is assessed. An experimental relationship between the linear fluorescence polarization and temperature is described by the Levshin–Perrin equation, which takes into account the rotational diffusion of luminescent particles (fluorophores) in a liquid matrix. The size of fluorophores is noticeably smaller than that of carbon nanodots according to the Levshin–Perrin model. A difference between the dimensions of the fluorophore and the nanodot indicates that the small atomic groups responsible for luminescence of the nanodot possess high segmental mobility.

Thermally Induced Depolarization of the Photoluminescence of Carbon Nanodots in a Colloidal Matrix

The effect of temperature on fluorescence polarization in a colloidal system of carbon nanodots in glycerol under linearly polarized excitation is investigated for the first time. It is found that the experimentally obtained temperature dependence of the degree of linear polarization of fluorescence can be described by the Levshin–Perrin equation, taking into account the rotational diffusion of luminescent particles (fluorophores) in the liquid matrix. The fluorophore size determined in the context of the Levshin–Perrin model is significantly smaller than the size of carbon nanodots. This discrepancy gives evidence that small atomic groups responsible for nanodot luminescence are characterized by high segmental mobility with a large amplitude of motion with respect to the nanodot core.

Температурное тушение и деполяризация флюоресценции углеродных наноточек полученных пиролизом парафина

AbstractA temperature effect on fluorescence intensity and polarization of a colloidal system of carbon nanodots in glycerol under linearly polarized pumping conditions is studied. Nanodots are obtained via pyrolysis of paraffin in nanopores of a mesoporous silica. An increase in temperature leads to quenching of nanodots fluorescence, and activation energy of the quenching process is assessed. An experimental relationship between the linear fluorescence polarization and temperature is described by the Levshin–Perrin equation, which takes into account the rotational diffusion of luminescent particles (fluorophores) in a liquid matrix. The size of fluorophores is noticeably smaller than that of carbon nanodots according to the Levshin–Perrin model. A difference between the dimensions of the fluorophore and the nanodot indicates that the small atomic groups responsible for luminescence of the nanodot possess high segmental mobility.

Fluorescence Quenching of Two Coumarin-3-carboxylic Acids by Trivalent Lanthanide Ions.

The effects of various trivalent lanthanide ions (acetates of Ce3+, Er3+, Eu3+, Nd3+) on the electronic absorption and fluorescence spectra of un-substituted coumarin-3-carboxylic acid (CCA) and 7-N,N-diethylamino-coumarin-3-carboxylic acid (DECCA) have been investigated in dimethylsulfoxide (DMSO) at room temperature. Depending on the lanthanide ion nature and concentration, significant spectral changes of absorption bands occurred for both coumarin derivatives. These spectral changes were attributed to the formation of ground-state complexes between the coumarin carboxylate derivatives and lanthanide ions. The fluorescence quenching of CCA and DECCA upon increasing the lanthanide ion concentration was studied. Different quantitative treatments, including the Stern-Volmer equation, the Perrin equation and a polynomial equation, were applied and compared in order to determine the nature of the quenching mechanisms for both coumarin derivatives. The results suggested the contribution of both dynamic and static quenching. Significant differences of CCA and DECCA fluorescence quenching efficiency were also observed, depending on the lanthanide ion. DECCA fluorescence lifetime measurements, performed in the absence and in the presence of Ln3+, confirmed a contribution of static quenching.

Energy versus charge transfer in π-conjugated polymer:fullerene blends

The article is focused on the detailed elucidation of fluorescence quenching by charge and/or energy transfer in π-conjugated polymers. The processes were studied in blends of MDMO-PPV, Tg-PPV, PCDTBT and PCBTDPP with fullerenes PC60BM and PC70BM in chlorobenzene. Fluorescence quenching was evaluated by the Perrin equation for static quenching and quenching sphere radiuses were calculated. These radiuses were found to be the same as the Förster critical distances for resonance energy transfer. It was concluded that energy transfer prevails over charge transfer under the conditions where the donor and acceptor are not in close contact.

Single yeast cell vacuolar milieu viscosity assessment by fluorescence polarization microscopy with computer image analysis

This study was undertaken to evaluate the apparent viscosity within the vacuoles of single Saccharomyces cerevisiae cells by steady-state fluorescence anisotropy measurements of quinacrine, using wide-field fluorescence polarization microscopy combined with computer image analysis. Quinacrine was shown to be rather specifically accumulated within the vacuoles of the cells. This accumulation was effectively reversed by ATP depletion of the cells, with no detectable binding of the dye within the vacuoles. Quinacrine fluorescence anisotropy in the sucrose solutions of various viscosities obeyed the Perrin equation. The fluorescence anisotropy of quinacrine was measured in the vacuoles of 39 cells. From cell to cell, this parameter changed in the range 0.032-0.086. Using the Perrin plot as a calibration curve, apparent viscosity values of the vacuolar milieu were calculated for each cell. The population of the cells studied was heterogeneous with regard to vacuolar viscosity, which was in the range 3.5 ± 0.4-14.06 ± 0.64 cP. There was a characteristic distribution of the frequencies of cells with apparent viscosities within certain limits, and cells with viscosity values in the range 5-6 cP were the most frequent. No relationship was found between the sizes of the vacuoles and their apparent viscosities.

Calcium-induced Folding of Intrinsically Disordered Repeat-in-Toxin (RTX) Motifs via Changes of Protein Charges and Oligomerization States

Ligand-induced disorder-to-order transition plays a key role in the biological functions of many proteins that contain intrinsically disordered regions. This trait is exhibited by so-called RTX (repeat-in-toxin) motifs found in many virulence factors secreted by numerous gram-negative pathogenic bacteria: RTX proteins are natively disordered in the absence of calcium but fold upon calcium binding. The adenylate cyclase toxin (CyaA) produced by Bordetella pertussis, the causative agent of whooping cough, contains ∼40 RTX motifs organized in five successive blocks separated by non-RTX flanking regions. This RTX domain mediates toxin binding to its eukaryotic cell receptor. We previously showed that the last block of the RTX domain, block V, which is critical for CyaA toxicity, exhibits the hallmarks of intrinsically disordered proteins in the absence of calcium. Moreover, the C-terminal flanking region of CyaA block V is required for its calcium-induced folding. Here, we describe a comprehensive analysis of the hydrodynamic and electrophoretic properties of several block V RTX polypeptides that differ in the presence and/or length of the flanking regions. Our results indicate that the length of the C-terminal flanking region not only controls the calcium-induced folding but also the calcium-induced multimerization of the RTX polypeptides. Moreover, we showed that calcium binding is accompanied by a strong reduction of the net charge of the RTX polypeptides. These data indicate that the disorder-to-order transition in RTX proteins is controlled by a calcium-induced change of the polypeptide charges and stabilized by multimerization.

Fluorescence Anisotropy of Molecular Rotors

We present polarization-resolved fluorescence measurements of fluorescent molecular rotors 9-(2-carboxy-2-cyanovinyl)julolidine (CCVJ), 9-(2,2-dicyanovinyl)julolidine (DCVJ), and a meso-substituted boron dipyrromethene (BODIPY-C(12)). The photophysical properties of these molecules are highly dependent on the viscosity of the surrounding solvent. The relationship between their quantum yields and the viscosity of the surrounding medium is given by an equation first described and presented by Förster and Hoffmann and can be used to determine the microviscosity of the environment around a fluorophore. Herein we evaluate the applicability of molecular rotors as probes of apparent viscosity on a microscopic scale based on their viscosity dependent fluorescence depolarization. We develop a theoretical framework, combining the Förster-Hoffmann equation with the Perrin equation and compare the dynamic ranges and usable working regimes for these dyes in terms of utilising fluorescence anisotropy as a measure of viscosity. We present polarization-resolved fluorescence spectra and steady-state fluorescence anisotropy imaging data for measurements of intracellular viscosity. We find that the dynamic range for fluorescence anisotropy for CCVJ and DCVJ is significantly lower than that of BODIPY-C(12) in the viscosity range 0.6<η<600 cP. Moreover, using steady-state anisotropy measurements to probe microviscosity in the low (<3 cP) viscosity regime, the molecular rotors can offer a better dynamic range in anisotropy compared with a rigid dye as a probe of microviscosity, and a higher total working dynamic range in terms of viscosity.

Size and Shape of Protein Molecules at the Nanometer Level Determined by Sedimentation, Gel Filtration, and Electron Microscopy

An important part of characterizing any protein molecule is to determine its size and shape. Sedimentation and gel filtration are hydrodynamic techniques that can be used for this medium resolution structural analysis. This review collects a number of simple calculations that are useful for thinking about protein structure at the nanometer level. Readers are reminded that the Perrin equation is generally not a valid approach to determine the shape of proteins. Instead, a simple guideline is presented, based on the measured sedimentation coefficient and a calculated maximum S, to estimate if a protein is globular or elongated. It is recalled that a gel filtration column fractionates proteins on the basis of their Stokes radius, not molecular weight. The molecular weight can be determined by combining gradient sedimentation and gel filtration, techniques available in most biochemistry laboratories, as originally proposed by Siegel and Monte. Finally, rotary shadowing and negative stain electron microscopy are powerful techniques for resolving the size and shape of single protein molecules and complexes at the nanometer level. A combination of hydrodynamics and electron microscopy is especially powerful.

Volatile interface of biological oxidant and luminescent CdTequantum dots: implications in nanodiagnostics

In order to explore the feasibility of using quantum dots (QDs) as nanodiagnostic tools in cells under oxidative stress, the interaction of cysteine-functionalized CdTe QDs with peroxynitrite (PN), a powerful biological oxidant, was spectroscopically investigated. The photoluminescence (PL) of CdTe QDs was quenched to the extent of 85% at 86 microM concentration of peroxynitrite. In contrast, the loss of PL intensity was merely 7% for CdS QDs under identical conditions. The quenching pattern shows a positive deviation from Stern-Volmer equation, but obeys the Perrin equation for static quenching. The Perrin quenching constants increased with decreasing temperature. Size dependence was also prominently observed as quenching efficiency increased by 70% on moving from 4.0 nm sized CdTe QDs to 2.8 nm ones. Interestingly, the QDs exhibited a time-dependent auto-recovery of photoluminescence. At 25 and 15 degrees C, the recovery time was found to be 1.25 and 3.5 h, respectively, however, the extent of recovery remained nearly the same, about 22%. Peroxynitrite followed a first order decay kinetics with a half-life of 45.6 min, which got substantially reduced to 2.9 min in the presence of CdTe QDs. The over-all mechanism of the interaction has been explained as a two-pronged attack of peroxynitrite on (i) the cysteine-capping layer and (ii) the CdTe core, resulting in a reversible and irreversible loss of QD-photoluminescence.

Fluorescence anisotropy as a means to determine extracellular polysaccharide hydrolase activity in environmental samples

Current approaches to measure the activities of microbial extracellular enzymes in aquatic environments are hampered by slow throughput or by differences between the structure of simple substrate proxies and macromolecules. Here we show that measurements of fluorescence anisotropy can be used to determine the hydrolysis rate of two fluorescently labeled polysaccharides, laminarin and xylan, in environmental samples. A simple analysis shows that the anisotropy of these fluorescently labeled polysaccharides can be approximated using a modification of the Perrin equation.

Triplet Energy Transfer Insight in Coordination of Unsaturated Hydrocarbons by d0Bent Metallocenes (Zr, Hf)

For a class of pi-complexes as energy donors, with the use of highly emissive d(0) metallocenes Cp(2)MCl(2) where M = Zr and Hf, it is shown that radiationless triplet energy transfer to unsaturated hydrocarbons in a rigid nonpolar methylcyclohexane (MCH) matrix (where molecular diffusion is absent) obeys the Perrin equation, occurs at radii R(0), being close to the diameter of interacting molecules, and is well described by an electron-exchange resonant (Dexter) mechanism of interaction. Principle correlation between values of the critical radius and a number of C atoms in a linear alpha-olefin is for the first time reported, viz. R(0) (Angstrom) = -2.47 + 1.35n (obtained for systems [Cp(2)HfCl(2) + CnH(2)n + MCH] at 77 K). Pronounced blue shifts (up to 1000 cm(-1)) of low-temperature emission spectra of Cp(2)ZrCl(2) in MCH in the presence of dienes, possessing nonconjugated C=C bonds, are observed, thus suggesting inner-sphere diene coordination. In view of the experimental data, inner- and outer-sphere coordinative interaction between the components of catalytic systems for polymerization (d(0) metallocene precatalysts and alkenes and dienes) is rationalized.

Effect of the coordination sphere of d0 metallocene on triplet-triplet energy transfer

The triplet nature of rare long-lived states of d0 metallocenes formed upon ligand-to-metal energy transfer was confirmed by studies of triplet-triplet charge transfer in biscyclopentadienyl complexes Cp2MCl2 (M = Zr (1), Hf (2)). The interaction between precatalysts and substrates of catalytic polymerization systems, viz., complexes 1 and 2 and unsaturated hydrocarbons (alkenes and dienes), was studied in the region of concentrations close to catalytic values. For organometallic π-complexes, it has been shown for the first time that, in the case of the unsaturated hydrocarbons, the efficiency of energy transfer obeys the Perrin equation. The process occurs at distances R0 close to the diameter of the interacting molecules and is well described by the exchange-resonant mechanism of interaction. In the case of the cyclopentadiene-Cp2MCl2 (M = Zr, Hf) systems, R0 = 14.6 A. A linear relationship between the critical radius of the quenching sphere R0 and the number of carbon atoms in a linear α-olefin has been revealed for the first time and evidences the formation of a π-complex between the precatalyst and substrate molecules.

Simultaneous determination of glycols based on fluorescence anisotropy

Simultaneous determination of non-fluorescent glycols in mixtures without separation or chemical transformation steps is described. Two methods based in the measure of fluorescence anisotropy of a probe such as fluorescein dissolved in the analyte or analyte mixtures are described. In the first method, the anisotropy spectra of pure and mixtures of analytes are used to quantitative determination (if the fluorophor concentration is in a range where fluorescence intensity is proportional to concentration). In the second method, a calibration curve anisotropy–concentration based on the application of the Perrin equation is established. The methods presented here are capable of directly resolving binary mixtures of non-fluorescent glycols on the basis of differences on the fluorescence anisotropy of a fluorescence tracer. Best analytical performances were obtained by application of the method based on Perrin equation. This method is simple, rapid and allows the determination of mixtures of glycols with reasonable accuracy and precision. Detection limits are limited by the quantum yield and anisotropy values of the tracer in the solvents. Recovery values are related to the differences in anisotropy values of the tracer in the pure solvents. Mixtures of glycerine/ethylene glycol (GL/EG), ethylene glycol/1,2-propane diol (EG/1,2-PPD) and polyethylene glycol 400/1,2-propane diol (PEG 400/1,2-PPD) were analysed and recovery values are within 95–120% in the Perrin method. Relative standard deviation are in the range 1.3–2.9% and detection limits in the range 3.9–8.9%.

Microscopic dynamics of thin hard rods

We analyze the microscopic dynamics and transport properties of a gas of thin hard rods. Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalized Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean-square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualitative agreement for higher densities.

Affinity Assays Using Fluorescence Anisotropy with Capillary Electrophoresis Separation

A novel approach to detecting affinity interactions that combines fluorescence anisotropy with capillary electrophoresis (FACE) was developed. In the method, sample is injected into a capillary filled with buffer that contains a fluorescent probe that possesses low fluorescence anisotropy. If proteins or other large molecules in the sample bind the fluorescent probe, their migration through the capillary can be detected as a positive anisotropy shift. Thus, the method provides both separation and confirmation of binding to the probe. Calculations based on combining the Perrin equation and dissociation constant were used to predict the effect of conditions on aniostropy detection. These calculations predict that low probe concentrations yield the best sensitivity while higher concentrations increase the dynamic range for detection of binding partner. The assay was applied to detection of G proteins using BODIPY FL GTPgammaS as the fluorescent probe. Experimental measurements exhibited trends in anisotropy with varying probe and protein concentrations that were consistent with the calculations. The limit of detection for G(alphai1) was 3 nM when the electrophoresis buffer contained 250 nM BODIPY FL GTPgammaS. FACE affinity assay is envisioned as a method that can quantify selected binding partners and screen complex samples for compounds that possess affinity for a particular small molecule that is used as a probe.

Correlation of the Thermal Stability of Phospholipid‐Based Emulsions and the Microviscosity Measurements Using Fluorescence Polarization

The fluorescence polarization technique was used to measure the microviscosity of a series of phospholipid‐based emulsions. Fourteen different oil‐in‐water emulsions containing 20% medium chain length triglycerides, various concentrations and types of phospholipids, and 2.2% glycerin were prepared by microfluidization and pH‐adjusted to 4.0 or 7.4. Microviscosity was measured by determining the anisotropy of a fluorophore probe (1,6‐phenyl 1,3,5‐hexatriene) which was found to obey Perrin's equation as has been previously reported for liposomes and membrane bilayers. Moreover the method was validated by comparing viscosities of phospholipid–oil mixtures measured by rheometry and fluorescence polarization. The viscosities determined by fluorescence polarization were within 6% of the values obtained by classic rheometry. Emulsions were also subjected to thermal stress at 121°C. The droplet growth rate was estimated by measuring the time‐dependent mean droplet diameter using photon correlation spectroscopy. The logarithm of the droplet growth rate was found to be directly proportional to the interfacial rigidity (i.e., the inverse microviscosity) which suggested that coalescence rather than molecular diffusion is the primary mechanism of droplet growth under these conditions of thermal stress.