Rotational and translational diffusion of biomolecules in complex liquids and HeLa cells.

Diffusive motion accompanies many physical and biological processes. The Stokes-Sutherland-Einstein relation for the translational diffusion coefficient, DT, agrees with experiments done in simple fluids but fails for complex fluids. Moreover, the interdependence between DT and rotational diffusion coefficient, DR, also deviates in complex fluids from the classical relation of DT/DR = 4r2/3 known in simple fluids. Makuch et al. Soft Matter, 2020, 16, 114-124 presented a generalization of the classical translational and rotational diffusion theory for complex fluids. In this work, we empirically verify this model based on simultaneous translational and rotational diffusion measurements. We use fluorescently stained cowpea chlorotic mottle virus (CCMV) particles as monodisperse probes and aqueous polyethylene glycol (PEG) solutions as a model complex fluid. The theory and experimental data obtained from fluorescence correlation spectroscopy (FCS) measurements agreed. Finally, we used the same model and analyzed the diffusion of Yo-Pro-1 stained large ribosomal subunits (LSU) in the cytoplasm and nucleus of living HeLa cells.

Trimethylguanosine cap-fluorescent molecular rotor (TMG-FMR) conjugates are potent, specific snurportin1 ligands enabling visualization in living cells.

The trimethylguanosine (TMG) cap is a motif present inter alia at the 5' end of small nuclear RNAs, which are involved in RNA splicing. The TMG cap plays a crucial role in RNA processing and stability as it protects the RNA molecule from degradation by exonucleases and facilitates its export from the nucleus. Additionally, the TMG cap plays a role in the recognition of snRNA by snurportin, a protein that facilitates nuclear import. TMG cap analogs are used in biochemical experiments as molecular tools to substitute the natural TMG cap. To expand the range of available TMG-based tools, here we conjugated the TMG cap to Fluorescent Molecular Rotors (FMRs) to open the possibility of detecting protein-ligand interactions in vitro and, potentially, in vivo, particularly visualizing interactions with snurportin. Consequently, we report the synthesis of 34 differently modified TMG cap-FMR conjugates and their evaluation as molecular probes for snurportin. As FMRs we selected three GFP-like chromophores (derived from green fluorescent protein) and one julolidine derivative. The evaluation of binding affinities for snurportin showed unexpectedly a strong stabilizing effect for TMGpppG-derived dinucleotides containing the FMR at the 2'-O-position of guanosine. These newly discovered compounds are potent snurportin ligands with nanomolar KD (dissociation constant) values, which are two orders of magnitude lower than that of natural TMGpppG. The effect is diminished by ∼50-fold for the corresponding 3'-regioisomers. To deepen the understanding of the structure-activity relationship, we synthesized and tested FMR conjugates lacking the TMG cap moiety. These studies, supported by molecular docking, suggested that the enhanced affinity arises from additional hydrophobic contacts provided by the FMR moiety. The strongest snurportin ligand, which also gave the greatest fluorescence enhancement (Fm/F0) when saturated with the protein, were tested in living cells to detect interactions and visualize complexes by fluorescence lifetime monitoring. This approach has potential applications in the study of RNA processing and RNA-protein interactions.

Influence of molecular rebinding on the reaction rate of complex formation.

We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, Nreb, is proportional to the target's size and inversely proportional to the diffusion coefficient D and simulation time-step Δt. We found the proportionality constant close to π-1/2. We confirmed that Nreb is defined as a ratio of the activation-limited rate constant ka to the diffusion-limited rate constant, kD. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/Δt)1/2. Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δt time-scale. We show that for the photodissociation of a proton, the Δt is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δt is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.

Two Intercalation Mechanisms of Oxazole Yellow Dimer (YOYO-1) into DNA.

The oxazole yellow dye, YOYO-1 (a symmetric homodimer), is a commonly used molecule for staining DNA. We applied the brightness analysis to study the intercalation of YOYO-1 into the DNA. We distinguished two binding modes of the dye to dsDNA: mono-intercalation and bis-intercalation. Bis-intercalation consists of two consecutive mono-intercalation steps, characterised by two distinct equilibrium constants (with the average number of base pair per binding site equals 3.5): K1=3.36±0.43×107M-1 and K2=1.90±0.61×105M-1, respectively. Mono-intercalation dominates at high concentrations of YOYO-1. Bis-intercalation occurs at low concentrations.

Diffusion and flow in complex liquids.

Thermal motion of particles and molecules in liquids underlies many chemical and biological processes. Liquids, especially in biology, are complex due to structure at multiple relevant length scales. While diffusion in homogeneous simple liquids is well understood through the Stokes-Einstein relation, this equation fails completely in describing diffusion in complex media. Modeling, understanding, engineering and controlling processes at the nanoscale, most importantly inside living cells, requires a theoretical framework for the description of viscous response to allow predictions of diffusion rates in complex fluids. Here we use a general framework with the viscosity η(k) described by a function of wave vector in reciprocal space. We introduce a formulation that allows one to relate the rotational and translational diffusion coefficients and determine the viscosity η(k) directly from experiments. We apply our theory to provide a database for rotational diffusion coefficients of proteins/protein complexes in the bacterium E. coli. We also provide a database for the diffusion coefficient of proteins sliding along major grooves of DNA in E. coli. These parameters allow predictions of rate constants for association of proteins. In addition to constituting a theoretical framework for description of diffusion of probes and viscosity in complex fluids, the formulation that we propose should decrease substantially the cost of numerical simulations of transport in complex media by replacing the simulation of individual crowding particles with a continuous medium characterized by a wave-length dependent viscosity η(k).

Quantitative influence of macromolecular crowding on gene regulation kinetics.

We introduce macromolecular crowding quantitatively into the model for kinetics of gene regulation in Escherichia coli. We analyse and compute the specific-site searching time for 180 known transcription factors (TFs) regulating 1300 operons. The time is between 160 s (e.g. for SoxS Mw = 12.91 kDa) and 1550 s (e.g. for PepA6 of Mw = 329.28 kDa). Diffusion coefficients for one-dimensional sliding are between for large proteins up to for small monomers or dimers. Three-dimensional diffusion coefficients in the cytoplasm are 2 orders of magnitude larger than 1D sliding coefficients, nevertheless the sliding enhances the binding rates of TF to specific sites by 1-2 orders of magnitude. The latter effect is due to ubiquitous non-specific binding. We compare the model to experimental data for LacI repressor and find that non-specific binding of the protein to DNA is activation- and not diffusion-limited. We show that the target location rate by LacI repressor is optimized with respect to microscopic rate constant for association to non-specific sites on DNA. We analyse the effect of oligomerization of TFs and DNA looping effects on searching kinetics. We show that optimal searching strategy depends on TF abundance.

Tracking structural transitions of bovine serum albumin in surfactant solutions by fluorescence correlation spectroscopy and fluorescence lifetime analysis.

The structural dynamics of proteins is crucial to their biological functions. A precise and convenient method to determine the structural changes of a protein is still urgently needed. Herein, we employ fluorescence correlation spectroscopy (FCS) to track the structural transition of bovine serum albumin (BSA) in low concentrated cationic (cetyltrimethylammonium chloride, CTAC), anionic (sodium dodecyl sulfate, SDS), and nonionic (pentaethylene glycol monododecyl ether, C12E5 and octaethylene glycol monododecyl ether, C12E8) surfactant solutions. BSA is labelled with the fluorescence dye called ATTO-488 (ATTO-BSA) to obtain steady fluorescence signals for measurements. We find that the diffusion coefficient of BSA decreases abruptly with the surfactant concentration in ionic surfactant solutions at concentrations below the critical micelle concentration (CMC), while it is constant in nonionic surfactant solutions. According to the Stokes-Sutherland-Einstein equation, the hydrodynamic radius of BSA in ionic surfactant solutions amounts to ∼6.5 nm, which is 1.7 times larger than in pure water or in nonionic surfactant solutions (3.9 nm). The interaction between BSA and ionic surfactant monomers is believed to cause the structural transition of BSA. We confirm this proposal by observing a sudden shift of the fluorescence lifetime of ATTO-BSA, from 2.3 ns to ∼3.0 ns, in ionic surfactant solutions at the concentration below CMC. No change in the fluorescence lifetime is detected in nonionic surfactant solutions. Moreover, by using FCS we are also able to identify whether the structural change of protein results from its self-aggregation or unfolding.

Living Cell as a Self-Synchronized Chemical Reactor.

Thermal fluctuations power all processes inside living cells. Therefore, these processes are inherently random. However, myriad multistep chemical reactions act in concerto inside a cell, finally leading to this chemical reactor's self-replication. We speculate that an underlying mechanism in nature must exist that allows all of these reactions to synchronize at multiple time and length scales, overcoming in this way the random nature of any single process in a cell. This Perspective discusses what type of research is needed to understand this undiscovered synchronization law.

Biologistics--diffusion coefficients for complete proteome of Escherichia coli.

MOTIVATION: Biologistics provides data for quantitative analysis of transport (diffusion) processes and their spatio-temporal correlations in cells. Mobility of proteins is one of the few parameters necessary to describe reaction rates for gene regulation. Although understanding of diffusion-limited biochemical reactions in vivo requires mobility data for the largest possible number of proteins in their native forms, currently, there is no database that would contain the complete information about the diffusion coefficients (DCs) of proteins in a given cell type. RESULTS: We demonstrate a method for the determination of in vivo DCs for any molecule--regardless of its molecular weight, size and structure--in any type of cell. We exemplify the method with the database of in vivo DC for all proteins (4302 records) from the proteome of K12 strain of Escherichia coli, together with examples of DC of amino acids, sugars, RNA and DNA. The database follows from the scale-dependent viscosity reference curve (sdVRC). Construction of sdVRC for prokaryotic or eukaryotic cell requires ~20 in vivo measurements using techniques such as fluorescence correlation spectroscopy (FCS), fluorescence recovery after photobleaching (FRAP), nuclear magnetic resonance (NMR) or particle tracking. The shape of the sdVRC would be different for each organism, but the mathematical form of the curve remains the same. The presented method has a high predictive power, as the measurements of DCs of several inert, properly chosen probes in a single cell type allows to determine the DCs of thousands of proteins. Additionally, obtained mobility data allow quantitative study of biochemical interactions in vivo. CONTACT: rholyst@ichf.edu.pl. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics Online.

Activation energy for mobility of dyes and proteins in polymer solutions: from diffusion of single particles to macroscale flow.

We measure the activation energy Ea for the diffusion of molecular probes (dyes and proteins of radii from 0.52 to 6.9 nm) and for macroscopic flow in a model complex liquid-aqueous solutions of polyethylene glycol. We cover a broad range of polymer molecular weights, concentrations, and temperatures. Fluorescence correlation spectroscopy and rheometry experiments reveal a relationship between the excess of the activation energy in polymer solutions over the one in pure solvent ΔEa and simple parameters describing the structure of the system: probe radius, polymer hydrodynamic radius, and correlation length. ΔEa varies by more than an order of magnitude in the investigated systems (in the range of ca. 1-15 kJ/mol) and for probes significantly larger than the polymer hydrodynamic radius approaches the value measured for macroscopic flow. We develop an explicit formula describing the smooth transition of ΔEa from the diffusion of molecular probes to macroscopic flow. This formula is a reference for the quantitative analysis of specific interactions of moving nano-objects with their environment as well as active transport. For instance, the power developed by a molecular motor moving at constant velocity u is proportional to u2exp(Ea/RT).

Anomalous effect of flow rate on the electrochemical behavior at a liquid|liquid interface under microfluidic conditions.

We have investigated the oxidation of ferrocene at a flowing organic solvent|aqueous electrolyte|solid electrode junction in a microfluidic setup using cyclic voltammetry and fluorescent laser scanning confocal microscopy. At low flow rates the oxidation current decreases with increasing flow, contrary to the Levich equation, but at higher flow rates the current increases linearly with the cube root of the flow rate. This behavior is explained using a simple model postulating a smallest effective width of the three-phase junction, which after fitting to the data comes to be ca. 20 µm. The fluorescence microscopy reveals mixing of the two phases close to the PDMS cover, but the liquid|liquid junction is stable close to the glass support. This study shows the importance of the solid|liquid|liquid junctions for the behavior of multiphase systems under microfluidic conditions.

Comparative analysis of viscosity of complex liquids and cytoplasm of mammalian cells at the nanoscale.

We present a scaling formula for size-dependent viscosity coefficients for proteins, polymers, and fluorescent dyes diffusing in complex liquids. The formula was used to analyze the mobilities of probes of different sizes in HeLa and Swiss 3T3 mammalian cells. This analysis unveils in the cytoplasm two length scales: (i) the correlation length ξ (approximately 5 nm in HeLa and 7 nm in Swiss 3T3 cells) and (ii) the limiting length scale that marks the crossover between nano- and macroscale viscosity (approximately 86 nm in HeLa and 30 nm in Swiss 3T3 cells). During motion, probes smaller than ξ experienced matrix viscosity: η(matrix) ≈ 2.0 mPa·s for HeLa and 0.88 mPa·s for Swiss 3T3 cells. Probes much larger than the limiting length scale experienced macroscopic viscosity, η(macro) ≈ 4.4 × 10(-2) and 2.4 × 10(-2) Pa·s for HeLa and Swiss 3T3 cells, respectively. Our results are persistent for the lengths scales from 0.14 nm to a few hundred nanometers.

Macroscopic Viscosity of Polymer Solutions from the Nanoscale Analysis.

The effective viscosity in polymer solutions probed by diffusion of nanoparticles depends on their size. It is a well-defined function of the probe size, the radius of gyration, mesh size (correlation length), activation energy, and its parameters. As the nanoparticle's size exceeds the radius of gyration of polymer coils, the effective viscosity approaches its macroscopic limiting value. Here, we apply the equation for effective viscosity in the macroscopic limit to the following polymer solutions: hydroxypropyl cellulose (HPC) in water, polymethylmethacrylate (PMMA) in toluene, and polyacrylonitrile (PAN) in dimethyl sulfoxide (DMSO). We compare them with previous data for PEG/PEO in water and PDMS in ethyl acetate. We determine polymer parameters from the measurements of the macroscopic viscosity in a wide range of average polymer molecular weights (24-300 kg/mol), temperatures (283-303 K), and concentrations (0.005-1.000 g/cm3). In addition, the polydispersity of polymers is taken into account in the appropriate molecular weight averaging functions. We provide the model applicable for the study of nanoscale probe diffusion in polymer solutions and macroscopic characterization of different polymer materials via rheological measurements.

Quantifying Nanoscale Viscosity and Structures of Living Cells Nucleus from Mobility Measurements.

Understanding the mobility of nano-objects in the eukaryotic cell nucleus, at multiple length-scales, is essential for dissecting nuclear structure-function relationships both in space and in time. Here, we demonstrate, using single-molecule fluorescent correlation spectroscopies, that motion of inert probes (proteins, polymers, or nanoparticles) with diameters ranging from 2.6 to 150 nm is mostly unobstructed in a nucleus. Supported by the analysis of electron tomography images, these results advocate the ∼150 nm-wide interchromosomal channels filled with the aqueous diluted protein solution. The nucleus is percolated by these channels to allow various cargos to migrate freely at the nanoscale. We determined the volume of interchromosomal channels in the HeLa cell nucleus to 237 ± 61 fL, which constitutes 34% of the cell nucleus volume. The volume fraction of mobile proteins in channels equals 16% ± 4%, and the concentration is 1 mM.

Reverse vesicles from a salt-free catanionic surfactant system: a confocal fluorescence microscopy study.

We give a detailed confocal fluorescence microscopy study on reverse vesicles from a salt-free catanionic surfactant system. When tetradecyltrimethylammonium laurate (TTAL) and lauric acid (LA) are mixed in cyclohexane at the presence of a small amount of water, stable reverse vesicular phases form spontaneously. The reverse vesicular phases can be easily labeled with dyes of varying molecular size and hydrophobicity while the dyes are nearly insoluble in cyclohexane without reverse vesicles. This indicates the reverse vesicular phases can be good candidates to host guest molecules. With the help of a fluorescence microscope combined a confocal method, the features of these interesting reverse supramolecular self-assemblies were revealed for the first time. Because of the absence of electrostatic repulsions and hydration forces between adjacent vesicles, the reverse vesicles have a strong propensity to aggregate with each other and form three-dimensional clusters. The size distributions of both individual reverse vesicles and clusters are polydisperse. Huge multilamellar reverse vesicles with closely stacked thick walls (giant reverse onions) were observed. Besides the spherical reverse vesicles and onions, other supramolecular structures such as tubes have also been detected and structural evolutions between different structures were noticed. These interesting supramolecular self-assemblies form in a nonpolar organic solvent may serve as ideal micro- or nanoreaction centers for biological reactions and synthesis of inorganic nanomaterials.

Phase transition in salt-free catanionic surfactant mixtures induced by temperature.

Aggregate transitions in salt-free catanionic surfactant mixtures of tetradecyltrimethylammonium hydroxide (TTAOH)/fatty acid were investigated as a function of surfactant concentration and temperature. Lauric acid (LA), myristic acid (MA), and palmitic acid (PA) were chosen for the current study. The TTAOH/LA mixture exhibited rich phase behavior at room temperature. With increasing total surfactant concentration (c(T)), a bluish vesicular (L(alphav)) phase, an isotropic micellar (L(1)) phase, and a birefringent lamellar (L(alpha)) phase were observed. Between the L(alphav) phase and the L(1) phase, a narrow L(alpha)'/L(1) two-phase region was determined. With increasing temperature, a transition from the L(alpha) phase to the L(1) phase was induced at higher c(T) whereas at lower c(T) an opposite transition from the L(1) phase to the L(alphav) phase was noticed. Thus surprisingly, we observed bilayer-to-micelle and micelle-to-bilayer transitions in the same catanionic surfactant system, both induced by the temperature increase. Replacing LA by MA and PA caused a continuous increase in the average Krafft point of the mixture. The L(alphav)-phase region and phase-separated region become larger. Moreover, a single L(1)-phase region was absent within the investigated temperature range.

Analysis of Brightness of a Single Fluorophore for Quantitative Characterization of Biochemical Reactions.

Intrinsic molecular brightness (MB) is a number of emitted photons per second per molecule. When a substrate labeled by a fluorophore and a second unlabeled substrate form a complex in solution, the MB of the fluorophore changes. Here we use this change to determine the equilibrium constant (K) for the formation of the complex at pM concentrations. To illustrate this method, we used a reaction of DNA hybridization, where only one of the strands was fluorescently labeled. We determined K at the substrate concentrations from 80 pM to 30 nM. We validated this method against Förster resonance energy transfer (FRET). This method is much simpler than FRET as it requires only one fluorophore in the complex with a very small (a f̃ew percent) change in MB.

Transport of nanoprobes in multicellular spheroids.

The efficient delivery of drugs to cells depends on their diffusion through the extracellular matrix (ECM) of tissues. Here we present a study on the diffusion of nanoprobes of radius from 1 nm to over 100 nm in the ECM of spheroids of three cell types (HeLa, MCF-7 and fibroblasts). We quantified the nanoparticle transport in the spheroids' proliferating zone. We determined the size-dependent viscosity of the ECM. We revealed that nanoobjects up to 10 nm in radius exhibited unobstructed diffusion in the ECM, regardless of the spheroid type. The presented length-scale dependent viscosity profiles for spheroids pave the way for advanced modelling of drug administration through tissues.

Photoluminescent, Ferromagnetic, and Hydrophobic Sponges for Oil-Water Separation.

To find a facile way to produce a hydrophobic sponge that can effectively absorb oils is urgent to resolve the environmental pollution and ecological disaster caused by oil spillage. Here, alkylated carbon dots (C dots) were prepared from pyrolysis of a mixture of dodecylamine and citric acid followed by purification through silica gel column chromatography. Polyurethane sponge was modified by alkylated C dots by a simple dip-coating method, which endows the photoluminescent and hydrophobic sponge with good absorption capacities for various oils and nonpolar organic solvents with high recyclability. The water contact angle of the modified sponge can reach 138.8°. Interestingly, the sponge enables visual absorption under UV irradiation in the dark, which has not been achieved by other carbon-based adsorbents. The sponge was further made ferromagnetic by introducing alkylated Fe3O4 nanoparticles into its structure, which allowed controllable oil-water separation.

Self-Stabilized Giant Aggregates in Water from Room-Temperature Ionic Liquids with an Asymmetric Polar-Apolar-Polar Architecture.

We report the assembly of four imidazolium bromides, each of which bears a naphthyl on one side of the imidazolium cation and a branched alkyl chain on the other. This design creates a new type of amphiphilic ionic liquid with an apolar-polar-apolar structure and a low melting point (mp, <-20 °C), which has not been achieved by reported counterparts bearing linear alkyl chains. In solvent-free states, microphase segregation occurs where polar and apolar domains arrange bicontinuously as proved by molecular dynamics (MD) simulations. When dispersed in water, self-stabilized giant aggregates formed with ultrahigh colloidal stability (up to years). MD simulations provide clues of discrete bicontinuous phases within the giant aggregates. These newly discovered self-assemblies provide a heterogeneous reservoir that can accommodate guest molecules including the highly apolar fullerene C60, paving the way for a wide range of potential applications.