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.

Understanding associative polymer self-assembly with shrinking gate fluorescence correlation spectroscopy

The self-assembly of polymers is integral to their role in liquid formulations. In this study, we combine a dye whose lifetime is sensitive to the nanoviscosity of its local environment with shrinking gate fluorescence correlation spectroscopy (sgFCS) to study the self-assembly of a model telechelic polymer, hydrophobically modified ethoxylated urethane (HEUR). Fluorescence lifetime measurements show a monotonic increase in average lifetime with increasing HEUR concentration driven by a small fraction of dye (<1%) with long lifetimes strongly bound to HEUR. Despite this small fraction, sgFCS isolates the diffusional dynamics of the bound fraction with no a priori assumptions as to the distribution of lifetimes. Sensitivity is greatly enhanced compared to standard FCS, revealing micellar aggregates forming between 0.2 and 1 wt% followed by formation of a percolated network. This sgFCS approach, which we apply for the first time to polymers in this work, is readily extendable to any dye that changes lifetime on binding.

Diffusiophoresis in Polymer and Nanoparticle Gradients

Diffusiophoresis is the movement of the colloidal particles in response to a concentration gradient and can be observed for both electrolyte (e.g., salt) and nonelectrolyte (e.g., glucose) solutes. Here, we investigated the diffusiophoretic behavior of polystyrene (PS-carboxylate surface) microparticles in nonadsorbing charged and uncharged solute gradients [sodium polystyrenesulfonate (NaPSS), polyethylene glycol (PEG), and nanoscale colloidal silica (SiO2)] using a dead-end channel setup. We compared the diffusiophoretic motion in these gradient types with each other and to the case of using a monovalent salt gradient. In each of the nonadsorbing gradient systems (NaPSS, PEG, and SiO2 nanoparticles), the PS particles migrated toward the lower solute concentration. The exclusion distance values (from the initial position) of particles were recorded within the dead-end channel, and it was found that an increase in solute concentration increases exclusion from the main channel. In the polyelectrolyte case, the motion of PS microparticles was reduced by the addition of a background salt due to reduced electrostatic interaction, whereas it remained constant when using the neutral polymer. Particle diffusiophoresis in gradients of polyelectrolytes (charged macromolecules) is quite similar to the behavior when using a PEG gradient (uncharged macromolecule) in the presence of a background electrolyte. Moreover, we observed PS microparticles under different concentrations and molecular weights of PEG gradients. By combining the simulations, we estimated the exclusion length, which was previously proposed to be the order of the polymer radius. Furthermore, the movement of PS microparticles was analyzed in the gradient of silica nanoparticles. The exclusion distance was higher in silica nanoparticle gradients compared to similar-size PEG gradients because silica nanoparticles are charged. The diffusiophoretic transport of the PS microparticles could be simulated by considering the interaction between the PS microparticles and silica nanoparticles.

Preclustering Gelatin for Faster-Forming Injectable Hydrogels: A Strategy for Fabricating 3D Hydrogel Scaffolds with Improved Cell Dispersion

Gelatin-based injectable hydrogels capable of encapsulating cells are pivotal in tissue engineering because they can conform to any geometry and exhibit physical properties similar to those of living tissues. However, the slow gelation process observed in these cell-encapsulating hydrogels often causes an uneven dispersion of cells. This study proposes an approach for achieving fast gelation of unmodified gelatin under physiological conditions through gelatin preclustering. By using tetrafunctional succinimidyl-terminated poly(ethylene glycol) as a clustering agent, the gelation process is successfully expedited fivefold without requiring chemical modifications, effectively addressing the associated challenges of uneven cell distribution.

Size Sensitivity of Metabolite Diffusion in Macromolecular Crowds

Metabolites play crucial roles in cellular processes, yet their diffusion in the densely packed interiors of cells remains poorly understood, compounded by conflicting reports in existing studies. Here, we employ pulsed-gradient stimulated-echo NMR and Brownian/Stokesian dynamics simulations to elucidate the behavior of nano- and subnanometer-sized tracers in crowded environments. Using Ficoll as a crowder, we observe a linear decrease in tracer diffusivity with increasing occupied volume fraction, persisting─somewhat surprisingly─up to volume fractions of 30-40%. While simulations suggest a linear correlation between diffusivity slowdown and particle size, experimental findings hint at a more intricate relationship, possibly influenced by Ficoll's porosity. Simulations and numerical calculations of tracer diffusivity in the E. coli cytoplasm show a nonlinear yet monotonic diffusion slowdown with particle size. We discuss our results in the context of nanoviscosity and discrepancies with existing studies.

Two-photon excited-state dynamics of mEGFP-linker-mScarlet-I crowding biosensor in controlled environments

Macromolecular crowding affects many cellular processes such as diffusion, biochemical reaction kinetics, protein-protein interactions, and protein folding. Mapping the heterogeneous, dynamic crowding in living cells or tissues requires genetically encoded, site-specific, crowding sensors that are compatible with quantitative, noninvasive fluorescence micro-spectroscopy. Here, we carried out time-resolved 2P-fluorescence measurements of a new mEGFP-linker-mScarlet-I macromolecular crowding construct (GE2.3) to characterize its environmental sensitivity in biomimetic crowded solutions (Ficoll-70, 0-300 g L-1) via Förster resonance energy transfer (FRET) analysis. The 2P-fluorescence lifetime of the donor (mEGFP) was measured under magic-angle polarization, in the presence (intact) and absence (enzymatically cleaved) of the acceptor (mScarlet-I), as a function of the Ficoll-70 concentration. The FRET efficiency was used to quantify the sensitivity of GE2.3 to macromolecular crowding and to determine the environmental dependence of the mEGFP-mScarlet-I distance. We also carried out time-resolved 2P-fluorescence depolarization anisotropy to examine both macromolecular crowding and linker flexibility effects on GE2.3 rotational dynamics within the context of the Stokes-Einstein model as compared with theoretical predictions based on its molecular weight. These time-resolved 2P-fluorescence depolarization measurements and conformational population analyses of GE2.3 were also used to estimate the free energy gain upon the structural collapse in crowded environment. Our results further the development of a rational engineering design for bioenvironmental sensors without the interference of cellular autofluorescence. Additionally, these results in well-defined environments will inform our future in vivo studies of genetically encoded GE2.3 towards the mapping of the crowded intracellular environment under different physiological conditions.

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers

The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation dendrimers and linear chains in solution follow universal scaling laws independent of their topology. Analysis of the shape functions and internal density of dendrimers shows that they are more spherical than linear chains and have a dense core. At intermediate times, dendrimers become subdiffusive, with an exponent higher than that previously reported for nanoparticles in semidilute polymer solutions. The long-time diffusivity of dendrimers does not follow theoretical predictions for nanoparticles. We propose a new scaling law for the long-time diffusion coefficients of dendrimers which accounts for the fact that, unlike nanoparticles, dendrimers shrink with an increase in background solution concentration. Analysis of the properties of a special case of a higher functionality dendrimer shows a transition from polymer-like to nanoparticle-like behaviour.

Local and Large-Scale Conformational Dynamics in Unfolded Proteins and IDPs. I. Effect of Solvent Viscosity and Macromolecular Crowding

Protein/solvent interactions largely influence protein dynamics, particularly motions in unfolded and intrinsically disordered proteins (IDPs). Here, we apply triplet-triplet energy transfer (TTET) to investigate the coupling of internal protein motions to solvent motions by determining the effect of solvent viscosity (η) and macromolecular crowding on the rate constants of loop formation (kc) in several unfolded polypeptide chains including IDPs. The results show that the viscosity dependence of loop formation depends on amino acid sequence, loop length, and co-solute size. Below a critical size (rc), co-solutes exert a maximum effect, indicating that under these conditions microviscosity experienced by chain motions matches macroviscosity of the solvent. rc depends on chain stiffness and reflects the length scale of the chain motions, i.e., it is related to the persistence length. Above rc, the effect of solvent viscosity decreases with increasing co-solute size. For co-solutes typically used to mimic cellular environments, a scaling of kc ∝ η-0.1 is observed, suggesting that dynamics in unfolded proteins are only marginally modulated in cells. The effect of solvent viscosity on kc in the small co-solute limit (below rc) increases with increasing chain length and chain flexibility. Formation of long and very flexible loops exhibits a kc ∝ η-1 viscosity dependence, indicating full solvent coupling. Shorter and less flexible loops show weaker solvent coupling with values as low as kc ∝ η-0.75 ± 0.02. Coupling of formation of short loops to solvent motions is very little affected by amino acid sequence, but solvent coupling of long-range loop formation is decreased by side chain sterics.

Aqueous Two-Phase Systems within Selectively Permeable Vesicles

An aqueous two-phase system (ATPS) encapsulated within a vesicle organizes the vesicle core as two coexisting phases that partition encapsulated solutes. Here, we use microfluidic technologies to produce vesicles that efficiently encapsulate mixtures of macromolecules, providing a versatile platform to determine the phase behavior of ATPSs. Moreover, we use compartmentalized vesicles to investigate how membrane permeability affects the dynamics of the encapsulated ATPS. Designing a membrane selectively permeable to one of the components of the ATPS, we show that out-of-equilibrium phase separations formed by a rapid outflow of water can be spontaneously reversed by a slower outflow of the permeating component across the vesicle membrane. This dynamics may be exploited advantageously by cells to separate and connect metabolic and signaling routes within their nucleoplasm or cytoplasm depending on external conditions.

Single-Particle Tracking in Poly(Ethylene Glycol) Diacrylate: Probe Size Effect on the Diffusion Behaviors of Nanoparticles in Unentangled Polymer Solutions

A thorough understanding of the relevant factors governing the transport of nanoparticles in poly(ethylene glycol) diacrylate (PEGDA) is crucial for many applications utilizing this polymer. Here, single-particle tracking (SPT) was used to systematically investigate the role of the probe size (3-200 nm) on the diffusion behaviors of individual fluorescent nanoparticles in semidilute and unentangled PEGDA solutions. The quantitative assessment of the SPT data via the recorded single-particle trajectories and diffusion coefficients (D) not only showed that the observed probe dynamics in PEGDA were temporally and spatially heterogeneous, but more importantly that the measured D were observed to be significantly reduced (vs in solvent) and strongly size-dependent. We explained these results based on a modified multiscale model for particle diffusion, built upon well-established hydrodynamics and obstruction theories. We furthermore showed that the presence of steric interactions and probe confinement effects in highly crowded, unentangled PEGDA microstructures can lead to deviations in the single-particle displacements from the expected Gaussian behavior, as revealed by the van Hove displacement distributions and the associated non-Gaussian parameters. This study has demonstrated the power of SPT methods in offering an advanced characterization of the transport characteristics in complex polymer structures, overcoming challenges posed by traditional characterization techniques.

Cell-Size Space Regulates the Behavior of Confined Polymers: From Nano- and Micromaterials Science to Biology

Polymer micromaterials in a liquid or gel phase covered with a surfactant membrane are widely used materials in pharmaceuticals, cosmetics, and foods. In particular, cell-sized micromaterials of biopolymer solutions covered with a lipid membrane have been studied as artificial cells to understand cells from a physicochemical perspective. The characteristics and phase transitions of polymers confined to a microscopic space often differ from those in bulk systems. The effect that causes this difference is referred to as the cell-size space effect (CSE), but the specific physicochemical factors remain unclear. This study introduces the analysis of CSE on molecular diffusion, nanostructure transition, and phase separation and presents their main factors, i.e., short- and long-range interactions with the membrane surface and small volume (finite element nature). This serves as a guide for determining the dominant factors of CSE. Furthermore, we also introduce other factors of CSE such as spatial closure and the relationships among space size, the characteristic length of periodicity, the structure size, and many others produced by biomolecular assemblies through the analysis of protein reaction-diffusion systems and biochemical reactions.

Partitioning of ribonucleoprotein complexes from the cellular actin cortex

The cell cortex plays a crucial role in cell mechanics, signaling, and development. However, little is known about the influence of the cortical meshwork on the spatial distribution of cytoplasmic biomolecules. Here, we describe a fluorescence microscopy method with the capacity to infer the intracellular distribution of labeled biomolecules with subresolution accuracy. Unexpectedly, we find that RNA binding proteins are partially excluded from the cytoplasmic volume adjacent to the plasma membrane that corresponds to the actin cortex. Complementary diffusion measurements of RNA-protein complexes suggest that a rudimentary model based on excluded volume interactions can explain this partitioning effect. Our results suggest the actin cortex meshwork may play a role in regulating the biomolecular content of the volume immediately adjacent to the plasma membrane.

Alignment of Colloidal Rods in Crowded Environments

Understanding the hydrodynamic alignment of colloidal rods in polymer solutions is pivotal for manufacturing structurally ordered materials. How polymer crowding influences the flow-induced alignment of suspended colloidal rods remains unclear when rods and polymers share similar length scales. We tackle this problem by analyzing the alignment of colloidal rods suspended in crowded polymer solutions and comparing that to the case where crowding is provided by additional colloidal rods in a pure solvent. We find that the polymer dynamics govern the onset of shear-induced alignment of colloidal rods suspended in polymer solutions, and the control parameter for the alignment of rods is the Weissenberg number, quantifying the elastic response of the polymer to an imposed flow. Moreover, we show that the increasing colloidal alignment with the shear rate follows a universal trend that is independent of the surrounding crowding environment. Our results indicate that colloidal rod alignment in polymer solutions can be predicted on the basis of the critical shear rate at which polymer coils are deformed by the flow, aiding the synthesis and design of anisotropic materials.

Through Diffusion Measurements of Molecules to a Numerical Model for Protein Crystallization in Viscous Polyethylene Glycol Solution

Protein crystallography has become a popular method for biochemists, but obtaining high-quality protein crystals for precise structural analysis and larger ones for neutron analysis requires further technical progress. Many studies have noted the importance of solvent viscosity for the probability of crystal nucleation and for mass transportation; therefore, in this paper, we have reported on experimental results and simulation studies regarding the use of viscous polyethylene glycol (PEG) solvents for protein crystals. We investigated the diffusion rates of proteins, peptides, and small molecules in viscous PEG solvents using fluorescence correlation spectroscopy. In high-molecular-weight PEG solutions (molecular weights: 10,000 and 20,000), solute diffusion showed deviations, with a faster diffusion than that estimated by the Stokes–Einstein equation. We showed that the extent of the deviation depends on the difference between the molecular sizes of the solute and PEG solvent, and succeeded in creating equations to predict diffusion coefficients in viscous PEG solutions. Using these equations, we have developed a new numerical model of 1D diffusion processes of proteins and precipitants in a counter-diffusion chamber during crystallization processes. Examples of the application of anomalous diffusion in counter-diffusion crystallization are shown by the growth of lysozyme crystals.

Plasmid DNA Undergoes Two Compaction Regimes under Macromolecular Crowding

The laser light scattering experiments were performed to explore the role of dextran (size (d): 2.6, 6.9, and 17.0 nm) in compacting the plasmids (pBS: 2.9 kbps; pCMV-Tag2B: 4.3 kbps; and pET28a: 5.3 kbps) in vitro in the volume fraction (ϕ) range 0.01 to 0.15 of the macromolecular crowder. Two compaction regimes were observed in terms of the radius of gyration (R_g) for plasmid-dextran combinations, wherein the plasmid diffusivity is governed by normal diffusion and subdiffusion, respectively. Generalized scaling, R_g ∼ ϕ^-1/(1+x), where x represents the conformational geometry of plasmids, is reported. The plasmid conformation depends on the crowder's size, with larger conformational changes observed in the presence of smaller crowders. The second virial coefficient (A₂) and translational diffusion coefficient (D_t) indicate that entropically driven depletion of crowders, excluded volume, and interplasmid repulsive interactions govern plasmids' conformational changes, validated herein from the scaling of D_t with molecular weight.

Continuous, autonomous subsurface cargo shuttling by nature-inspired meniscus-climbing systems

Water-walking insects can harness capillary forces by changing their body posture to climb or descend the meniscus between the surface of water and a solid object. Controlling surface tension in this manner is necessary for predation, escape and survival. Inspired by this behaviour, we demonstrate autonomous, aqueous-based synthetic systems that overcome the meniscus barrier and shuttle cargo subsurface to and from a landing site and a targeted drop-off site. We change the sign of the contact angle of a coacervate sac containing an aqueous phase or of a hydrogel droplet hanging from the surface by controlling the normal force acting on the sac or droplet. The cyclic buoyancy-induced cargo shuttling occurs continuously, as long as the supply of reactants diffusing to the sac or droplet from the surrounding aqueous phase is not exhausted. These findings may lead to potential applications in autonomously driven reaction or delivery systems and micro-/milli-robotics.

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, N_reb, 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 N_reb is defined as a ratio of the activation-limited rate constant k_a to the diffusion-limited rate constant, k_D. 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.

Effects of Macromolecular Crowding on Nanoparticle Diffusion: New Insights from Mössbauer Spectroscopy

In this work, we used Mössbauer spectroscopy as a new approach for experimental quantification of the self-diffusion coefficient (D_Mössbauer) and hydrodynamic (HD) size of iron-containing nanoparticles (NPs) in complex crowded solutions, mimicking cell cytoplasm. As a probe, we used 9 nm cobalt ferrite NPs (CFNs) dispersed in solutions of bovine serum albumin (BSA) with a volume fraction (φ_BSA) of 0-0.2. Our results show that the broadening of Mössbauer spectra is highly sensitive to the diffusion of CFNs, while when φ_BSA = 0.2, the CFN-normalized diffusivity is reduced by 86% compared to that of a protein-free solution. CFN colloids were also studied by dynamic light scattering (DLS). Comparison of the experimental data shows that DLS significantly underestimates the diffusion coefficient of CFNs and, consequently, overestimates the HD size of CFNs at φ_BSA > 0, which cannot be attributed to the formation of the BSA monolayer on the surface of CFNs.

Nanoparticle diffusion in polymer melts in the presence of weak nanoparticle-monomer attractive interactions: A mode-coupling theory study

Mode-coupling theory is developed and employed to compute the nanoparticle diffusion coefficient in polymer solutions. Theoretical results are compared with molecular dynamics simulation data for a similar model. The theory properly reproduces the simulated effects of the nanoparticle size, mass, and concentration on the nanoparticle diffusion coefficient. Within the mode-coupling theory framework, a microscopic interpretation of the nonmonotonic dependence of the diffusion coefficient on the nanoparticle concentration is given in terms of structural and dynamic effects. Both the size dependence and mass dependence of the diffusion coefficient indicate a pronounced breakdown of the Stokes-Einstein relation for the present model.

Fast nanoparticle rotational and translational diffusion in synovial fluid and hyaluronic acid solutions

Nanoparticles are under investigation as diagnostic and therapeutic agents for joint diseases, such as osteoarthritis. However, there is incomplete understanding of nanoparticle diffusion in synovial fluid, the fluid inside the joint, which consists of a mixture of the polyelectrolyte hyaluronic acid, proteins, and other components. Here, we show that rotational and translational diffusion of polymer-coated nanoparticles in quiescent synovial fluid and in hyaluronic acid solutions is well described by the Stokes-Einstein relationship, albeit with an effective medium viscosity that is much smaller than the macroscopic low shear viscosity of the fluid. This effective medium viscosity is well described by an equation for the viscosity of dilute polymer chains, where the additional viscous dissipation arises because of the presence of the polymer segments. These results shed light on the diffusive behavior of polymer-coated inorganic nanoparticles in complex and crowded biological environments, such as in the joint.

Quantitative evaluation of macromolecular crowding environment based on translational and rotational diffusion using polarization dependent fluorescence correlation spectroscopy

Macromolecular crowding (MMC) in cells is a hot topic in biology; therefore, well-characterized measurement standards for the evaluation of the nano-environment in MMC solutions are necessary. We propose to use polarization-dependent fluorescence correlation spectroscopy (Pol-FCS) for evaluation of macromolecular crowding in solutions. Pol-FCS can simultaneously measure the relaxation times of rotational and translational diffusion of fluorescent molecules at the same position, even in living cells with low damage. In this report, the differences in the nano-environment among solutions of small molecules, gels, and MMC solutions were evaluated by comparing their rotational and translational diffusion using Pol-FCS. Moreover, this method could distinguish the phase shift in the polyethylene glycol solution. Finally, we separately evaluated the nano-environment in the cytosol and nucleus of living cells in different cell lines and cell cycles. We expect this evaluation method to be useful in characterizing the nano-environment in MMC studies. In addition, the proposed method may be useful for other nano-environments such as liquid-liquid phase separation.

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.

Disentangling Nano- and Macroscopic Viscosities of Aqueous Polymer Solutions Using a Fluorescent Molecular Rotor

The macroscopic viscosity of polymer solutions in general differs strongly from the viscosity at the nanometer scale, and the relation between the two can be complicated. To investigate this relation, we use a fluorescent molecular rotor that probes the local viscosity of its molecular environment. For a range of chain lengths and concentrations, the dependence of the fluorescence on the macroscopic viscosity is well described by the classical Förster-Hoffmann (FH) equation, but the value of the FH exponent depends on the polymer chain length. We show that all data can be collapsed onto a master curve by plotting the fluorescence versus polymer concentration, which we explain in terms of the characteristic mesh size of the polymer solution. Using known scaling laws for polymers then allows us to quantitatively explain the relation between the FH exponent and the polymer chain length, allowing us to link the nano- to the macroviscosity.

Yield stress "in a flash": investigation of nonlinearity and yielding in soft materials with an optofluidic microrheometer

Yield stress materials deform as elastic solids or flow as viscous liquids, depending on the applied stress, which also allows them to trap particles below a certain size or density threshold. To investigate the conditions for such a transition at the microscale, we use an optofluidic microrheometer, based on the scattering of an infrared beam onto a microbead, which reaches forces in the nN scale. We perform creep experiments on a model soft material composed of swollen microgels, determining the limits of linear response and yield stress values, and observe quantitative agreement with bulk measurements. However, the motion of the microbead, both below and above yielding, reflects distinctive microscale features of the surrounding material, whose plastic rearrangements were investigated by us using small, passive tracers.

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.

Exploring Single-Nanoparticle Dynamics at High Temperature by Optical Tweezers

The experimental determination of the velocity of a colloidal nanoparticle (v_NP) has recently became a hot topic. The thermal dependence of v_NP is still left to be explored although it is a valuable source of information allowing, for instance, the discernment between ballistic and diffusive regimes. Optical tweezers (OTs) constitute a tool especially useful for the experimental determination of v_NP although they have only been capable of determining it at room temperature. In this work, we demonstrate that it is possible to determine the temperature dependence of the diffusive velocity of a single colloidal nanoparticle by analyzing the temperature dependence of optical forces. The comparison between experimental results and theoretical predictions allowed us to discover the impact that the anomalous temperature dependence of water properties has on the dynamics of colloidal nanoparticles in this temperature range.

Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology

In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length L_h between 200 nm and 650 nm, and cobalt ferrite spheres with diameter d_h between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration R_g or the correlation length ξ of the polymer solution.

Nanoscale Viscosity of Cytoplasm Is Conserved in Human Cell Lines

Metabolic reactions in living cells are limited by diffusion of reagents in the cytoplasm. Any attempt to quantify the kinetics of biochemical reactions in the cytosol should be preceded by careful measurements of the physical properties of the cellular interior. The cytoplasm is a complex, crowded fluid characterized by effective viscosity dependent on its structure at a nanoscopic length scale. In this work, we present and validate the model describing the cytoplasmic nanoviscosity, based on measurements in seven human cell lines, for nanoprobes ranging in diameters from 1 to 150 nm. Irrespective of cell line origin (epithelial-mesenchymal, cancerous-noncancerous, male-female, young-adult), we obtained a similar dependence of the viscosity on the size of the nanoprobes, with characteristic length-scales of 20 ± 11 nm (hydrodynamic radii of major crowders in the cytoplasm) and 4.6 ± 0.7 nm (radii of intercrowder gaps). Moreover, we revealed that the cytoplasm behaves as a liquid for length scales smaller than 100 nm and as a physical gel for larger length scales.

Local Confinement Controls Diffusive Nanoparticle Dynamics in Semidilute Polyelectrolyte Solutions

We investigate the mobility of polystyrene particles ranging from 100 to 790 nm in diameter in dilute and semidilute sodium polystyrene sulfonate (NaPSS) solutions using fluorescence microscopy. We tune the polymer conformations by varying the ionic strength of the solution. The nanoparticle mean-squared displacements evolve linearly with time at all time scales, indicating Fickian diffusive dynamics. In solutions of high ionic strength, chains adopt a random walk conformation and particle dynamics couple to the bulk zero-shear rate viscosity, according to the Stokes-Einstein picture. In solutions of low ionic strength, however, particle dynamics nonmonotonically deviate from bulk predictions as polymer concentration increases and are not accurately predicted by the available models. These nonmonotonic dynamics directly correlate with the non-Gaussianity in distributions of particle displacements, suggesting the emergence of a local confining length scale as polyelectrolyte concentration increases.

Nanoparticle diffusion in polymer melts: Molecular dynamics simulations and mode-coupling theory

Nanoparticle diffusion in polymer melts is studied by the combination of Molecular Dynamics (MD) simulations and Mode-Coupling Theory (MCT). In accord with earlier experimental, simulation, and theoretical studies, we find that the Stokes-Einstein (SE) hydrodynamic relation D_n ∼ 1/R_n holds when the nanoparticle radius R_n is greater than the polymer gyration radius R_g, while in the opposite regime, the measured nanoparticle diffusion coefficient D_n exceeds the SE value by as much as an order of magnitude. The MCT values of D_n are found to be consistently higher than the MD simulation values. The observed discrepancy is attributed to the approximations involved in constructing the microscopic friction as well as to the approximate forms for dynamic structure factors used in MCT. In a thorough test of underlying MCT assumptions and approximations, various structural and dynamical quantities required as input for MCT are obtained directly from MD simulations. We present the improved MCT approach, which involves splitting of the microscopic time-dependent friction into two terms: binary (originating from short-time dynamics) and collective (due to long-time dynamics). Using MD data as input in MCT, we demonstrate that the total friction is largely dominated by its binary short-time term, which, if neglected, leads to severe overestimation of D_n. As a result, the revised version of MCT, in agreement with the present MD data, predicts 1/R_n ² scaling of the probe diffusion coefficient in a non-hydrodynamic regime when R_n < R_g. If the total friction is dominated by the collective long-time component, one would observe 1/R_n ³ scaling of D_n in accordance with previous studies.

Depletion interactions modulate the binding between disordered proteins in crowded environments

The molecular environment in a biological cell is much more crowded than the conditions commonly used in biochemical and biophysical experiments in vitro. It is therefore important to understand how the conformations and interactions of biological macromolecules are affected by such crowding. Addressing these questions quantitatively, however, has been challenging owing to a lack of sufficiently detailed experimental information and theoretical concepts suitable for describing crowding, especially when polymeric crowding agents and biomolecules are involved. Here, we use the combination of extensive single-molecule experiments with established and recent theoretical concepts to investigate the interaction between two intrinsically disordered proteins. We observe pronounced effects of crowding on their interactions and provide a quantitative framework for rationalizing these effects.

Intrinsically disordered proteins (IDPs) abound in cellular regulation. Their interactions are often transitory and highly sensitive to salt concentration and posttranslational modifications. However, little is known about the effect of macromolecular crowding on the interactions of IDPs with their cellular targets. Here, we investigate the influence of crowding on the interaction between two IDPs that fold upon binding, with polyethylene glycol as a crowding agent. Single-molecule spectroscopy allows us to quantify the effects of crowding on a comprehensive set of observables simultaneously: the equilibrium stability of the complex, the association and dissociation kinetics, and the microviscosity, which governs translational diffusion. We show that a quantitative and coherent explanation of all observables is possible within the framework of depletion interactions if the polymeric nature of IDPs and crowders is incorporated based on recent theoretical developments. The resulting integrated framework can also rationalize important functional consequences, for example, that the interaction between the two IDPs is less enhanced by crowding than expected for folded proteins of the same size.

TiO2 superstructures with oriented nanospaces: a strategy for efficient and selective photocatalysis

Highly ordered superstructures of semiconductor nanocrystals contain abundant nanometer-scale pores between the crystals; however, there have been difficulties in controlling the size and orientation of these nanospaces without the use of a template or a capping reagent. This constraint has affected their development and applications in potential fields including catalysis and optoelectronics adversely. In this study, we synthesized a rod-shaped TiO2 mesocrystal (TMC) having a length of a few hundreds of micrometers and comprising regularly ordered anatase TiO2 nanocrystals that form oriented nanospaces by exposed {001} facets. Finite-difference time-domain (FDTD) calculations of electric fields and in situ fluorescence imaging with a polarization sensitive dye on a single mesocrystal were performed to reveal anisotropic adsorption and excitation of the dyes. Furthermore, the photodegradation of the dyes was found to be more facilitated in nanospaces formed by the specific facets, as compared with the dyes randomly adsorbed on the outer surfaces. Consequently, the selectivity of photocatalytic reactions based on the molecular size and redox was enhanced by introducing the concept of oriented nanospace.

3D-MiXD: 3D-printed X-ray-compatible microfluidic devices for rapid, low-consumption serial synchrotron crystallography data collection in flow

Serial crystallography has enabled the study of complex biological questions through the determination of biomolecular structures at room temperature using low X-ray doses. Furthermore, it has enabled the study of protein dynamics by the capture of atomically resolved and time-resolved molecular movies. However, the study of many biologically relevant targets is still severely hindered by high sample consumption and lengthy data-collection times. By combining serial synchrotron crystallography (SSX) with 3D printing, a new experimental platform has been created that tackles these challenges. An affordable 3D-printed, X-ray-compatible microfluidic device (3D-MiXD) is reported that allows data to be collected from protein microcrystals in a 3D flow with very high hit and indexing rates, while keeping the sample consumption low. The miniaturized 3D-MiXD can be rapidly installed into virtually any synchrotron beamline with only minimal adjustments. This efficient collection scheme in combination with its mixing geometry paves the way for recording molecular movies at synchrotrons by mixing-triggered millisecond time-resolved SSX.

Quantitative Analysis of Membrane Surface and Small Confinement Effects on Molecular Diffusion

Molecular behaviors in small liquid droplets (picoliter scale), such as phase transitions and chemical reactions, are essential for the industrial application of small droplets and their use as artificial cells. However, the droplets often differ from those in bulk solutions (milliliter scale). Since the droplet size is much larger than the molecular size, the so-called size effect that draws these differences has attracted attention as a target to be solved. Although the small volume and the membrane surface surrounding the droplet are thought to be the origin of the size effect, there were little attempts to separate and quantify them. To solve the problem, we develop a series of systems for the evaluation. Using these systems, we have evaluated the size effect of concentrated polymer solutions on molecular diffusion by dividing it into small volume and membrane surface contributions. Our results demonstrate that the size effect on the molecular diffusion originates from the long-range interaction with the surface enhanced with decreasing volume. The quantitative size effect revealed by the systems provides novel insights in the biophysical understanding of molecular behaviors in cells and to the regulation and design of micrometer-sized materials.

Size effects on rotational particle diffusion in complex fluids as probed by Magnetic Particle Nanorheology

Rheological approaches based on micro- or nanoscopic probe objects are of interest due to the low volume requirement, the option of spatially resolved probing, and the minimal-invasive nature often connected to such probes. For the study of microstructured systems or biological environments, such methods show potential for investigating the local, size-dependent diffusivity and particle-matrix interactions. For the latter, the relative length scale of the used probes compared to the size of the structural units of the matrix becomes relevant. In this study, a rotational-dynamic approach based on Magnetic Particle Nanorheology (MPN) is used to extract size- and frequency-dependent nanorheological properties by using an otherwise well-established polymer model system. We use magnetically blocked CoFe2O4 nanoparticles as tracers and systematically vary their hydrodynamic size by coating them with a silica shell. On the polymer side, we employ aqueous solutions of poly(ethylene glycol) (PEG) by varying molar mass M and volume fraction φ. The complex Brownian relaxation behavior of the tracer particles in solutions of systematically varied composition is investigated by means of AC susceptometry (ACS), and the results provide access to frequency dependent rheological properties. The size-dependent particle diffusivity is evaluated based on theoretical descriptions and macroscopic measurements. The results allow the classification of the investigated compositions into three regimes, taking into account the probe particle size and the length scales of the polymer solution. While a fuzzy cross-over is indicated between the well-known macroscopic behavior and structurally dominated spectra, where the hydrodynamic radius is equal to the radius of gyration of the polymer (rh ∼ Rg), the frequency-related scaling behavior is dominated by the correlation length ξ respectively by the tube diameter a in entangled solutions for rh < Rg.

Confinement-Free Wide-Field Ratiometric Tracking of Single Fluorescent Molecules

Single-molecule fluorescence has been highly instrumental in elucidating interactions and dynamics of biological molecules in the past two decades. Single-molecule fluorescence experiments usually rely on one of two detection geometries, either confocal point-detection or wide-field area detection, typically in a total internal reflection fluorescence (TIRF) format. However, each of these techniques suffers from fundamental drawbacks that limit their application. In this work, we present a new technique, solution wide-field imaging (SWiFi) of diffusing molecules, as an alternative to the existing methods. SWiFi is a simple extension to existing objective-type TIRF microscopes that allows wide-field observations of fast-diffusing molecules down to single fluorophores without the need of tethering the molecules to the surface. We demonstrate that SWiFi enables high-throughput ratiometric measurements with several thousands of individual data points per minute on double-stranded DNA standard (dsDNA) samples containing Förster resonance energy transfer pairs. We further display the capabilities of SWiFi by reporting on mobility and ratiometric characterization of fluorescent nanodiamonds, DNA Holliday junctions, and protein-DNA interactions. The ability of SWiFi for high-throughput, ratiometric measurements of fast-diffusing species renders it a valuable tool for the single-molecule research community by bridging between confocal and TIRF detection geometries in a simple and efficient way.

Diffusion of nanoparticles within a semidilute polyelectrolyte solution

We studied the diffusion of charged gold nanoparticles within a semidilute solution of weakly charged polyelectrolyte, polyacrylic acid (PAA) of high molecular weight (M_w = 10⁶ g mol^-1) by using fluorescence correlation spectroscopy (FCS). Nanoparticle size (d) was varied between 5 nm to 40 nm and PAA volume fraction (φ) in water ranged from about 8φ* to 33φ*, where φ* is the overlap volume fraction. The reduced diffusion coefficient - defined as -D/D_o, where D is the diffusion coefficient in PAA solution and D_o is that in neat water - has a weak dependence on the particle size. D follows a power law of the form ∼φ^-0.5, which can be explained by a mean-field hydrodynamic theory in porous medium. Additional, rheology measurements showed a zero shear rate viscosity and shear thinning, which are typical of high molecular weight polyelectrolytes.

Viscosity of Plasma as a Key Factor in Assessment of Extracellular Vesicles by Light Scattering

Extracellular vesicles (EVs) isolated from biological samples are a promising material for use in medicine and technology. However, the assessment methods that would yield repeatable concentrations, sizes and compositions of the harvested material are missing. A plausible model for the description of EV isolates has not been developed. Furthermore, the identity and genesis of EVs are still obscure and the relevant parameters have not yet been identified. The purpose of this work is to better understand the mechanisms taking place during harvesting of EVs, in particular the role of viscosity of EV suspension. The EVs were harvested from blood plasma by repeated centrifugation and washing of samples. Their size and shape were assessed by using a combination of static and dynamic light scattering. The average shape parameter of the assessed particles was found to be ρ ~ 1 (0.94–1.1 in exosome standards and 0.7–1.2 in blood plasma and EV isolates), pertaining to spherical shells (spherical vesicles). This study has estimated the value of the viscosity coefficient of the medium in blood plasma to be 1.2 mPa/s. It can be concluded that light scattering could be a plausible method for the assessment of EVs upon considering that EVs are a dynamic material with a transient identity.

Self-diffusion of a highly concentrated monoclonal antibody by fluorescence correlation spectroscopy: insight into protein-protein interactions and self-association

The dynamic behavior of monoclonal antibodies (mAbs) at high concentration provides insight into protein microstructure and protein-protein interactions (PPI) that influence solution viscosity and protein stability. At high concentration, interpretation of the collective-diffusion coefficient Dc, as determined by dynamic light scattering (DLS), is highly challenging given the complex hydrodynamics and PPI at close spacings. In contrast, self-diffusion of a tracer particle by Brownian motion is simpler to understand. Herein, we develop fluorescence correlation spectroscopy (FCS) for the measurement of the long-time self-diffusion of mAb2 over a wide range of concentrations and viscosities in multiple co-solute formulations with varying PPI. The normalized self-diffusion coefficient D0/Ds (equal to the microscopic relative viscosity ηeff/η0) was found to be smaller than η/η0. Smaller ratios of the microscopic to macroscopic viscosity (ηeff/η) are attributed to a combination of weaker PPI and less self-association. The interaction parameters extracted from fits of D0/Ds with a length scale dependent viscosity model agree with previous measurements of PPI by SLS and SAXS. Trends in the degree of self-association, estimated from ηeff/η with a microviscosity model, are consistent with oligomer sizes measured by SLS. Finally, measurements of collective diffusion and osmotic compressibility were combined with FCS data to demonstrate that the changes in self-diffusion between formulations are due primarily to changes in the protein-protein friction in these systems, and not to protein-solvent friction. Thus, FCS is a robust and accessible technique for measuring mAb self-diffusion, and, by extension, microviscosity, PPI and self-association that govern mAb solution dynamics.

Quantifying the protein-protein association rate in polymer solutions: crowding-induced diffusion and energy modifications

A theoretical framework is developed to study protein-protein association in polymer solutions under diffusion-limited conditions. Starting from the basal association rate, two fundamental aspects concerning macromolecular crowding are particularly taken into account. One is the effect of microviscosity on protein diffusion. The length-scale dependent relations of translational and rotational diffusion coefficients are incorporated. Another is relevant to the crowding-induced effective interaction between the pair of proteins. The resultant energy modifications to the basal association rate are properly introduced, following an instructive classification with increasing crowder size: repulsive interaction dominant, repulsive and attractive interactions competitive, and attractive interaction prevailing. With specific energy modification terms, we are able to investigate the deviations of the association rate from the Stokes-Einstein (SE) behavior (i.e., the linear relationship with respect to the reciprocal of macroviscosity) in a quantitative manner. Our theory is applied to study the association of TEM1-β-lactamase (TEM) and the β-lactamase inhibitor protein (BLIP) in polyethylene glycol (PEG) solutions, with varying concentration and polymerization. We explicitly evaluate the relative association rate constant as a function of the solution macroviscosity. The theoretical results demonstrate very good agreement with the experimental data. Moreover, the complicated non-trivial deviations, either positive (slower than SE) or negative (faster than SE), are systematically rationalized. The precise role of energy modifications and the microviscosity effect on diffusion, in particular on rotational diffusion, are clearly unraveled.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

The extracellular fluid macromolecular composition differentially affects cell-substrate adhesion and cell morphology

Soluble macromolecules present in the tumour microenvironment (TME) alter the physical characteristics of the extracellular fluid and can affect cancer cell behaviour. A fundamental step in cancer progression is the formation of a new vascular network which may originate from both pre-existing normal endothelium and cancer-derived cells. To study the role of extracellular macromolecules in the TME affecting endothelial cells we exposed normal and cancer-derived endothelial cells to inert polymer solutions with different physicochemical characteristics. The cancer cell line SK-HEP-1, but not normal human umbilical vein endothelial cells, responded to high-macromolecular-content solutions by elongating and aligning with other cells, an effect that was molecular weight-dependent. Moreover, we found that neither bulk viscosity, osmotic pressure, nor the fractional volume occupancy of polymers alone account for the induction of these effects. Furthermore, these morphological changes were accompanied by an increased extracellular matrix deposition. Conversely, cell-substrate adhesion was enhanced by polymers increasing the bulk viscosity of the culture medium independently of polymer molecular weight. These results show that the complex macromolecular composition of the extracellular fluid strongly influences cancer-derived endothelial cell behaviour, which may be crucial to understanding the role of the TME in cancer progression.