Intramolecular dynamics of linear macromolecules by fluorescence correlation spectroscopy

Improved Modeling of Thioamide FRET Quenching by Including Conformational Restriction and Coulomb Coupling

Thioamide-containing amino acids have been shown to quench a wide range of fluorophores through distinct mechanisms. Here, we quantitatively analyze the mechanism through which the thioamide functional group quenches the fluorescence of p-cyanophenylalanine (Cnf), tyrosine (Tyr), and tryptophan (Trp). By comparing PyRosetta simulations to published experiments performed on polyproline ruler peptides, we corroborate previous findings that both Cnf and Tyr quenching occurs via Förster resonance energy transfer (FRET), while Trp quenching occurs through an alternate mechanism such as Dexter transfer. Additionally, optimization of the peptide sampling scheme and comparison of thioamides attached to the peptide backbone and side chain revealed that the significant conformational restriction associated with the thioamide moiety results in a high sensitivity of the apparent FRET efficiency to underlying conformational differences. Moreover, by computing FRET efficiencies from structural models using a variety of approaches, we find that quantitative accuracy in the role of Coulomb coupling is required to explain contributions to the observed quenching efficiency from individual structures on a detailed level. Last, we demonstrate that these additional considerations improve our ability to predict thioamide quenching efficiencies observed during binding of thioamide-labeled peptides to fluorophore-labeled variants of calmodulin.

Extensions of the worm-like-chain model to tethered active filaments under tension

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often, these filaments perform mechanical functions and interact with their networked environment through cross-links or have other similar constraints placed on them. Here, we examine the mechanical properties-under tension-of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces-thermal Brownian forces and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean square deflections, which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers that interact by local momentum-conserving stochastic MPCs. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t^-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L^-1/2. Good agreement is found between the analytical and simulation results.

Tethered Semiflexible Polymer under Large Amplitude Oscillatory Shear

The properties of a semiflexible polymer with fixed ends exposed to oscillatory shear flow are investigated by simulations. The two-dimensionally confined polymer is modeled as a linear bead-spring chain, and the interaction with the fluid is described by the Brownian multiparticle collision dynamics approach. For small shear rates, the tethering of the ends leads to a more-or-less linear oscillatory response. However, at high shear rates, we found a strongly nonlinear reaction, with a polymer (partially) wrapped around the fixation points. This leads to an overall shrinkage of the polymer. Dynamically, the location probability of the polymer center-of-mass position is largest on a spatial curve resembling a limaçon, although with an inhomogeneous distribution. We found shear-induced modifications of the normal-mode correlation functions, with a frequency doubling at high shear rates. Interestingly, an even-odd asymmetry for the Cartesian components of the correlation functions appears, with rather similar spectra for odd x- and even y-modes and vice versa. Overall, our simulations yielded an intriguing nonlinear behavior of tethered semiflexible polymers under oscillatory shear flow.

Anomalous Diffusion in Inverted Variable-Lengthscale Fluorescence Correlation Spectroscopy

Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.

Internal dynamics of semiflexible polymers with active noise

The intramolecular dynamics of flexible and semiflexible polymers in response to active noise is studied theoretically. The active noise may either originate from interactions of a passive polymer with a bath of active Brownian particles or the polymer itself is comprised of active Brownian particles. We describe the polymer by the continuous Gaussian semiflexible-polymer model, taking into account the finite polymer extensibility. Our analytical calculations predict a strong dependence of the polymer dynamics on the activity. In particular, active semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics at weak activity to that of flexible polymers at strong activity. The end-to-end vector correlation function decays exponentially for times longer than the longest polymer relaxation time. Thereby, the polymer relaxation determines the decay of the correlation function for long and flexible polymers. For shorter and stiffer polymers, the relaxation behavior of individual active Brownian particles dominates the decay above a certain activity. The diffusive dynamics of a polymer is substantially enhanced by the activity. Three regimes can be identified in the mean square displacement for sufficiently strong activities: an activity-induced ballistic regime at short times, followed by a Rouse-type polymer-specific regime for any polymer stiffness, and free diffusion at long times, again determined by the activity.

Measurement of Mesoscale Conformational Dynamics of Freely Diffusing Molecules with Tracking FCS

Few techniques are suited to probe the structure and dynamics of molecular complexes at the mesoscale level (∼100-1000 nm). We have developed a single-molecule technique that uses tracking fluorescence correlation spectroscopy (tFCS) to probe the conformation and dynamics of mesoscale molecular assemblies. tFCS measures the distance fluctuations between two fluorescently labeled sites within an untethered, freely diffusing biomolecule. To achieve subdiffraction spatial resolution, we developed a feedback scheme that allows us to maintain the molecule at an optimal position within the laser intensity gradient for fluorescence correlation spectroscopy. We characterized tFCS spatial sensitivity by measuring the Brownian end-to-end dynamics of DNA molecules as short as 1000 bp. We demonstrate that tFCS detects changes in the compaction of reconstituted nucleosome arrays and can assay transient protein-mediated interactions between distant sites in an individual DNA molecule. Our measurements highlight the applicability of tFCS to a wide variety of biochemical processes involving mesoscale conformational dynamics.

Conformational Properties of Active Semiflexible Polymers

The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surrounding active (Brownian) particles or from the inherent motion of the polymer itself, which may be composed of active Brownian particles. In the latter case, the respective monomers are independently propelled in directions changing diffusively. For the description of the polymer, we adopt the continuous Gaussian semiflexible polymer model. Specifically, the finite polymer extensibility is taken into account, which turns out to be essential for the polymer conformations. Our analytical calculations predict a strong dependence of the relaxation times on the activity. In particular, semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics to the flexible polymer dynamics with increasing activity. This leads to a significant activity-induced polymer shrinkage over a large range of self-propulsion velocities. For large activities, the polymers swell and their extension becomes comparable to the contour length. The scaling properties of the mean square end-to-end distance with respect to the polymer length and monomer activity are discussed.

Mean squared displacement from fluorescence correlation spectroscopy

Under certain conditions, the mean squared displacement (MSD) can be retrieved from fluorescence correlation spectroscopy (FCS) measurements. However, in the general case this procedure is not valid, and the apparent MSD obtained from FCS data may substantially differ from the true one. In this work we discuss under which conditions this procedure can be applied. Furthermore, we use computer simulations to obtain the MSD and the apparent MSD for the diffusion of a single polymer chain under various approximations. Based on the simulation results we discuss the reliability of the apparent MSD obtained from FCS, showing that it systematically deviates from the true MSD. We also propose a general procedure to verify the reliability of the apparent MSD by measurements at various focal spot sizes.

Accurate Diffusion Coefficients of Organosoluble Reference Dyes in Organic Media Measured by Dual-Focus Fluorescence Correlation Spectroscopy

Dual-focus fluorescence correlation spectroscopy (2fFCS) is a versatile method to determine accurate diffusion coefficients of fluorescent species in an absolute, reference-free manner. Whereas (either classical or dual-focus) FCS has been employed primarily in the life sciences and thus in aqueous environments, it is increasingly being used in materials chemistry, as well. These measurements are often performed in nonaqueous media such as organic solvents. However, the diffusion coefficients of reference dyes in organic solvents are not readily available. For this reason we determined the translational diffusion coefficients of several commercially available organosoluble fluorescent dyes by means of 2fFCS. The selected dyes and organic solvents span the visible spectrum and a broad range of refractive indices, respectively. The diffusion coefficients can be used as absolute reference values for the calibration of experimental FCS setups, allowing quantitative measurements to be performed. We show that reliable information about the hydrodynamic dimensions of the fluorescent species (including noncommercial compounds) within organic media can be extracted from the 2fFCS data.

Hydrodynamic correlations and diffusion coefficient of star polymers in solution

The center-of-mass dynamics of star polymers in dilute solution is analyzed by hybrid mesoscale simulations. The fluid is modeled by the multiparticle collision dynamics approach, a particle-based hydrodynamic simulation technique, which is combined with molecular dynamics simulations for the polymers. Star polymers of various functionalities are considered. We determine the center-of-mass velocity correlation functions, the corresponding mean square displacements, and diffusion coefficients. The velocity correlation functions exhibit a functionality-dependent and structure-specific intermediate time regime, with a slow decay. It is followed by the long-time tail t(-3/2), which is solely determined by the fluid. Infinite-system-size diffusion coefficients are determined from the velocity correlation function by a combination of simulation and analytical results, as well as from the center-of-mass mean square displacement for various systems sizes and extrapolation. In terms of the hydrodynamic radius, the star polymer hydrodynamic diffusion coefficient exhibits the same universal system-size dependence as a spherical colloid. The functionality dependence of the ratio of hydrodynamic radii and the radii of gyration agrees well with experimental predictions.

Effect of hydrodynamic correlations on the dynamics of polymers in dilute solution

We analyze the effect of time-dependent hydrodynamic interactions on the dynamics of flexible polymers in dilute solution. In analytical calculations, the fluctuating hydrodynamics approach is adopted to describe the fluid, and a Gaussian model to represented the polymer. Simulations are performed exploiting the multiparticle collision dynamics approach, a mesoscale hydrodynamic simulation technique, to explicitly describe the fluid. Polymer center-of-mass velocity correlation functions are calculated for various polymer lengths. Similarly, segment mean square displacements are discussed and polymer diffusion coefficients are determined. Particular attention is paid to the influence of sound propagation on the various properties. The simulations reveal a strong effect of hydrodynamic interactions. Specifically, the time dependence of the center-of-mass velocity correlation functions is determined by polymer properties over a length-dependent time window, but are asymptotically solely governed by fluid correlations, with a long-time tail decaying as t(-3/2). The correlation functions are heavily influenced by sound modes for short polymers, an effect which gradually disappears with increasing polymer length. We find excellent agreement between analytical and simulation results. This allows us to provide a theory-based asymptotic value for the polymer diffusion coefficient in the limit of large system sizes, which is based on a single finite-system-size simulation.

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size

The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.

Dynamics of a semiflexible polymer or polymer ring in shear flow

Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency f(c) in a linear shear flow of strength γ scales as a power law Wi(2/3) in the Weissenberg number Wi = γτ, where τ is a characteristic time of the polymer's relaxational dynamics. For a flexible polymer these theoretical results are well confirmed by a large body of experimental single molecule studies. However, for the intermediate semiflexible regime, especially relevant for cytoskeletal filaments like F-actin and microtubules, the situation is less clear. While recent experiments on single F-actin filaments are still interpreted within the classical Wi(2/3) scaling law, theoretical results indicated deviations from it. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l(p). We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f(c) τ* = Wi(3/4)f(c)(x) with Wi = γτ* and the scaling variable x = (l(p)/L)(Wi)(-1/3); here τ* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.

Methods for modeling cytoskeletal and DNA filaments

This review summarizes the models that researchers use to represent the conformations and dynamics of cytoskeletal and DNA filaments. It focuses on models that address individual filaments in continuous space. Conformation models include the freely jointed, Gaussian, angle-biased chain (ABC), and wormlike chain (WLC) models, of which the first three bend at discrete joints and the last bends continuously. Predictions from the WLC model generally agree well with experiment. Dynamics models include the Rouse, Zimm, stiff rod, dynamic WLC, and reptation models, of which the first four apply to isolated filaments and the last to entangled filaments. Experiments show that the dynamic WLC and reptation models are most accurate. They also show that biological filaments typically experience strong hydrodynamic coupling and/or constrained motion. Computer simulation methods that address filament dynamics typically compute filament segment velocities from local forces using the Langevin equation and then integrate these velocities with explicit or implicit methods; the former are more versatile and the latter are more efficient. Much remains to be discovered in biological filament modeling. In particular, filament dynamics in living cells are not well understood, and current computational methods are too slow and not sufficiently versatile. Although primarily a review, this paper also presents new statistical calculations for the ABC and WLC models. Additionally, it corrects several discrepancies in the literature about bending and torsional persistence length definitions, and their relations to flexural and torsional rigidities.

New gluconamide-type cationic surfactants: Interactions with DNA and lipid membranes

New linear cationic surfactants - 2-(alkyldimethylammonio)ethylgluconamide bromides, denoted as CnGAB, n=10, 12, 14 and 16 - were synthesized from natural resources and characterized with respect to their potential as gene-delivery agents in gene therapy applications. Interactions with plasmid DNA and with model membranes were studied both experimentally and theoretically. The compounds with n=12, 14 and 16 show exponentially increasing ability to fully condense DNA. C16GAB condenses DNA at 1:1 surfactant to nucleotide molar ratio. Furthermore, CnGABs interact with model membrane, slightly lowering the temperature of the main phase transition Tm of the DPPC bilayer. C10GAB is found to interact only at the membrane surface. C16GAB reduces Tm less than C12GAB and C14GAB, and forms domains in the bilayer at the surfactant/DPPC molar ratio of 0.1 and higher. The results suggest that C16GAB can be a promising candidate for building gene-delivery carrier systems.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Wanted: a positive control for anomalous subdiffusion

Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion. Anomalous subdiffusion measurements would be strengthened by an experimental standard, particularly one able to cross-calibrate the different types of measurements. Criteria for a calibration standard are proposed. First, diffusion must be anomalous over the length and timescales of the different measurements. The length-scale is fundamental; the time scale can be adjusted through the viscosity of the medium. Second, the standard must be theoretically well understood, with a known anomalous subdiffusion exponent, ideally readily tunable. Third, the standard must be simple, reproducible, and independently characterizable (by, for example, electron microscopy for nanostructures). Candidate experimental standards are evaluated, including obstructed lipid bilayers; aqueous systems obstructed by nanopillars; a continuum percolation system in which a prescribed fraction of randomly chosen obstacles in a regular array is ablated; single-file diffusion in pores; transient anomalous subdiffusion due to binding of particles in arrays such as transcription factors in randomized DNA arrays; and computer-generated physical trajectories.

Probing GFP-actin diffusion in living cells using fluorescence correlation spectroscopy

The cytoskeleton of eukaryotic cells is continuously remodeled by polymerization and depolymerization of actin. Consequently, the relative content of polymerized filamentous actin (F-actin) and monomeric globular actin (G-actin) is subject to temporal and spatial fluctuations. Since fluorescence correlation spectroscopy (FCS) can measure the diffusion of fluorescently labeled actin it seems likely that FCS allows us to determine the dynamics and hence indirectly the structural properties of the cytoskeleton components with high spatial resolution. To this end we investigate the FCS signal of GFP-actin in living Dictyostelium discoideum cells and explore the inherent spatial and temporal signatures of the actin cytoskeleton. Using the free green fluorescent protein (GFP) as a reference, we find that actin diffusion inside cells is dominated by G-actin and slower than diffusion in diluted cell extract. The FCS signal in the dense cortical F-actin network near the cell membrane is probed using the cytoskeleton protein LIM and is found to be slower than cytosolic G-actin diffusion. Furthermore, we show that polymerization of the cytoskeleton induced by Jasplakinolide leads to a substantial decrease of G-actin diffusion. Pronounced fluctuations in the distribution of the FCS correlation curves can be induced by latrunculin, which is known to induce actin waves. Our work suggests that the FCS signal of GFP-actin in combination with scanning or spatial correlation techniques yield valuable information about the local dynamics and concomitant cytoskeletal properties.

A fluorescence correlation spectroscopy study of macromolecular tracer diffusion in polymer solutions

We discuss the manner in which the dynamics of tracer polystyrene chains varies with the concentration of matrix polystyrene chains dissolved in toluene. Using fluorescence correlation spectroscopy and theory, it is shown that the cooperative diffusion coefficient of the matrix polystyrene chains can be measured by fluorescence correlation spectroscopy in the semidilute entangled concentration regime. In addition the self-diffusion coefficient of the tracer polystyrene chains can be detected for arbitrary concentrations. The measured cooperative diffusion coefficient is independent of the molecular weight of the tracer polystyrene chains because it is a characteristic feature of the transient entanglement network.

Linear viscoelasticity of a single semiflexible polymer with internal friction

The linear viscoelastic behaviors of single semiflexible chains with internal friction are studied based on the wormlike-chain model. It is shown that the frequency dependence of the complex compliance in the high frequency limit is the same as that of the Voigt model. This asymptotic behavior appears also for the Rouse model with internal friction. We derive the characteristic times for both the high frequency limit and the low frequency limit and compare the results with those obtained by Khatri et al.

Intramolecular fluorescence correlation spectroscopy in a feedback tracking microscope

We derive the statistics of the signals generated by shape fluctuations of large molecules studied by feedback tracking microscopy. We account for the influence of intramolecular dynamics on the response of the tracking system and derive a general expression for the fluorescence autocorrelation function that applies when those dynamics are linear. We show that in comparison to traditional fluorescence correlation spectroscopy, tracking provides enhanced sensitivity to translational diffusion, molecular size, heterogeneity, and long-timescale decays. We demonstrate our approach using a three-dimensional tracking microscope to study genomic lambda-phage DNA molecules with various fluorescence label configurations.

Precise characterization of the conformation fluctuations of freely diffusing DNA: beyond Rouse and Zimm

We studied the dynamics of single freely diffusing fluorescence-labeled double-stranded lambda-phage DNA molecules using dual-color 3-dimensional feedback tracking microscopy and intramolecular fluorescence correlation spectroscopy. Our technique is independently sensitive to the molecule's diffusion coefficient D and radius of gyration R(g) and is concentration insensitive, providing greater precision for characterizing the molecule's intramolecular motion than other methods. We measured D = 0.80 +/- 0.05 microm(2)/s and R(g) approximately 420 nm, consistent with the Kirkwood-Riseman prediction for a flexible polymer with strong hydrodynamic interactions (HI), but we find the statistics of intramolecular motion inconsistent with the Zimm model for such a polymer. We address a dispute in the experimental literature, finding that previous measurements on double-stranded DNA likely lacked the sensitivity to distinguish between the Zimm model and the HI-free Rouse model. Finally, we observe fluorescence fluctuations with a correlation time of over 2 s that cannot be explained by either model and propose that they may be signatures of excluded volume interactions.

Lipopolythiourea/DNA interaction: a biophysical study

Lipopolythioureas (LPT) are original non cationic systems representing an alternative to cationic lipids. Their high transfection efficiency prompted us to investigate further their biophysical properties, and in particular how thiourea lipids interact with DNA. The interaction of lipopolythiourea with DNA was investigated by fluorescence correlation microscopy (FCS). Influence of the lipid length and nature of the thiourea head on the thiourea/DNA interaction were studied. FCS revealed a strong interaction between lipopolythiourea and DNA, occurring at 1 equivalent of a thiourea lipid by a DNA phosphate group, and leading to a condensed plasmid state. From previous in vitro experiments, we could conclude that the lipid leading to the more condensed state of DNA was also the more efficient to transfect cells.

Diffusion in polymer solutions studied by fluorescence correlation spectroscopy

We employed fluorescence correlation spectroscopy (FCS) to study the diffusion of molecular and macromolecular tracers in polystyrene solutions over a broad range of concentrations (c) and molecular weights (M(w,m)) of the matrix polymer. Molecular tracer diffusion scales only with the matrix concentration and superimposes on a single, nonpolymer specific, curve. On the contrary, the diffusion of macromolecular tracers in solutions of matrix polymers with M(w,m) sufficiently larger than the tracer molecular weight scales with c/c(p)*, where c(p)* is the tracer overlap concentration. We further demonstrate that FCS can address local and global dynamics simultaneously.

Diffusion in Model Networks as Studied by NMR and Fluorescence Correlation Spectroscopy

We have studied the diffusion of small solvent molecules (octane) and larger hydrophobic dye probes in octane-swollen poly(dimethyl siloxane) linear-chain solutions and end-linked model networks, using pulsed-gradient nuclear magnetic resonance (NMR) and fluorescence correlation spectroscopy (FCS), respectively, focusing on diffusion in the bulk polymer up to the equilibrium degree of swelling of the networks, that is, 4.8 at most. The combination of these results allows for new conclusions on the feasibility of different theories describing probe diffusion in concentrated polymer systems. While octane diffusion shows no cross-link dependence, the larger dyes are increasingly restricted by fixed chemical meshes. The simple Fujita free-volume theory proved most feasible to describe probe diffusion in linear long-chain solutions with realistic parameters, while better fits were obtained assuming a stretched exponential dependence on concentration. Importantly, we have analyzed the cross-link specific effect on probe diffusion independently of any specific model by comparing the best-fit interpolation of the solution data with the diffusion in the networks. The most reasonable description is obtained by assuming that the cross-link effect is additive in the effective friction coefficient of the probes. The concentration dependences as well as the data compared at the equilibrium degrees of swelling indicate that swelling heterogeneities and diffusant shape have a substantial influence on small-molecule diffusion in networks.

End-monomer Dynamics in Semiflexible Polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) 〈r(2)(t)〉 ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling 〈r(2)(t)〉 ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log〈r(2)(t)〉/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

Dynamic structure factor of a stiff polymer in a glassy solution

We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power law and logarithmic long-time tails in the dynamic structure factor.

Fluorescence correlation spectroscopy of finite-sized particles

A theory is presented to study fluorescence correlation spectroscopy for particles with size comparable to the beam waist of the observation volume. Analytical correlation curves are derived for some experimentally interesting particle geometries. It is found that the finiteness of the particle generally decreases the value of the correlation amplitude and increases the correlation time compared to a point particle model. Furthermore, not only the size but also the distribution of fluorophores affects the shape of the correlation function. This is experimentally demonstrated with surface and internally labeled fluorescent spheres. In addition, experiments are performed on fluorescent spheres of different radii to validate the model by comparing the results to theoretical predictions.

Equilibrium dynamics of spermine-induced plasmid DNA condensation revealed by fluorescence lifetime correlation spectroscopy

The spermine-induced DNA condensation is a first-order phase transition. Here, we apply a novel technique fluorescence lifetime correlation spectroscopy to analyze this transition in a greater detail. We show that the method allows for the observation of the condensed and uncondensed molecules simultaneously based solely on different fluorescence lifetimes of the intercalating fluorophore PicoGreen in the folded und unfolded domains of DNA. The auto- and cross-correlation functions reveal that a small fraction of the DNA molecules is involved in the dynamic intramolecular equilibrium. Careful inspection of the cross-correlation curves suggests that folding occurs gradually within milliseconds.

Monomer dynamics in single- and double-stranded DNA coils

In our paper (Tothova et al., Czech. J. Phys. 55, 221 (2005)), the first observation of the kinetics of individual polymer monomers using the fluorescence correlation technique (R. Shusterman et al., Phys. Rev. Lett. 92, 048303 (2004)) has been interpreted within the bead-spring theory. Optimizing the joint Rouse-Zimm model to the experimental data, the phenomenological parameters for the statistical-mechanical description of the universal behavior of double- and single-stranded DNA and the dominant types of their dynamics have been determined. Recently, these data have been corrected (R. Shusterman et al., Phys. Rev. Lett. 98, 029901 (2007)). In the present work, the fits of the theory to the new data are given. The main conclusions of our preceding paper remain unchanged but some of the polymer parameters have changed. The new data allow a significantly better agreement with the theory than the previous ones. Our calculations confirm that dsDNA follows mainly the classical Zimm-type kinetics rather than the Rouse one as it was proposed by Shusterman et al. Single-stranded DNA also behaves predominantly as the Zimm polymer. To support these conclusions, we analyze the draining effects on the monomer dynamics and the applicability of simple "universal" laws, according to which the monomer mean square displacement scales with the time as t 1/2 and t 2/3 for the Rouse and Zimm polymers, respectively.

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

The dynamics of weakly bending polymers is analyzed on the basis of a Gaussian semiflexible chain model and the fluorescence correlation spectroscopy (FCS) correlation function is determined. Particular attention is paid to the influence of the rotational motion on the decay of the FCS correlation function. An analytical expression for the correlation function is derived, from which the averaged segmental mean square displacement can be determined independent of any specific model for the polymer dynamics. The theoretical analysis exhibits a strong dependence of the correlation function on the rotational motion for semiflexible polymers with typical lengths and persistence lengths of actin filaments or fd viruses. Hence, FCS allows for a measurement of the rotational motion of such semiflexible polymers. The theoretical results agree well with experimental measurements on actin filaments and confirm the importance of large relaxation times.

Fluorescence correlation spectroscopy analysis of segmental dynamics in actin filaments

We adapt fluorescence correlation spectroscopy (FCS) formalism to the studies of the dynamics of semiflexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean-square displacements of polymer segments. The obtained relations do not depend on any specific model of polymer dynamics. We use the derived expressions to measure the dynamics of actin filaments in two experimental situations: filaments labeled at distinct positions and homogeneously labeled filaments. Both approaches give consistent results and allow to measure the temporal dependence of the segmental mean-square displacement over almost five decades in time, from approximately 40 micros to approximately 2 s. These noninvasive measurements allow for a detailed quantitative comparison of the experimental data to the current theories of semiflexible polymer dynamics. Good quantitative agreement is found between the experimental results and theories explicitly accounting for the hydrodynamic interactions between polymer segments.

Direct observation of single molecule mobility in semidilute polymer solutions

We determine the mobility of dye-labeled polystyrene molecules in solution by fluorescence correlation spectroscopy (FCS) over a wide range of concentrations and molecular weights (ranging from 3.9 x 10{3} to 1550 x 10{3} g/mol ). In order to obtain absolute values of the diffusion coefficient, which can be compared to diffusion coefficients determined by other methods, the size of the focal volume has been determined by independent experiments and theoretical calculations. All data demonstrate that FCS is uniquely suited to explore polymer dynamics in solution. The mobility of the chains as expressed through the self-diffusion coefficient is significantly slowed down above the overlap concentration c{*}. The dependence of c{*} on molecular weight is well described by the power law c{*} proportional, variant M{w};{1-3nu} ( nu: Flory exponent). A comparison with the data taken from the literature demonstrates that the overlap concentration presents a robust concept that holds for a wide range of molecular weights.

Internal structure and dynamics of isolated Escherichia coli nucleoids assessed by fluorescence correlation spectroscopy

The morphology and dynamics of DNA in a bacterial nucleoid affects the kinetics of such major processes as DNA replication, gene expression. and chromosome segregation. In this work, we have applied fluorescence correlation spectroscopy to assess the structure and internal dynamics of isolated Escherichia coli nucleoids. We show that structural information can be extracted from the amplitude of fluorescence correlation spectroscopy correlation functions of randomly labeled nucleoids. Based on the developed formalism we estimate the characteristic size of nucleoid structural units for native, relaxed, and positively supercoiled nucleoids. The degree of supercoiling was varied using the intercalating agent chloroquine and evaluated from fluorescence microscopy images. The relaxation of superhelicity was accompanied by 15-fold decrease in the length of nucleoid units (from approximately 50 kbp to approximately 3 kbp).

Diffusion and segmental dynamics of double-stranded DNA

Diffusion and segmental dynamics of the double-stranded lambda-phage DNA polymer are quantitatively studied over the transition range from stiff to semiflexible chains. Spectroscopy of fluorescence fluctuations of single-end fluorescently labeled monodisperse DNA fragments unambiguously shows that double-stranded DNA in the length range of 10(2) - 2 x 10(4) base pairs behaves as a semiflexible polymer with segmental dynamics controlled by hydrodynamic interactions.

Dynamics of semiflexible polymers in a flow field

We present a method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments, we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.