Diffusion and Viscosity in a Crowded Environment: from Nano- to Macroscale

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.

Activity-induced diffusion recovery in crowded colloidal suspensions

We show that the forces generated by active enzyme molecules are strong enough to influence the dynamics of their surroundings under artificial crowded environments. We measured the behavior of polymer microparticles in a quasi-two-dimensional system under aqueous environment, at various area fraction values of particles. In the presence of enzymatic activity, not only was the diffusion of the suspended particles enhanced at shorter time-scales, but the system also showed a transition from subdiffusive to diffusive dynamics at longer time-scale limits. Similar observations were also recorded with enzyme-functionalized microparticles. Brownian dynamics simulations have been performed to support the experimental observations.

Cy3-Based Nanoviscosity Determination of Mucus: Effect of Mucus Collection Methods and Antibiotics Treatment

The integrity of the protective mucus layer as a primary defense against pathogen invasion and microbial leakage into the intestinal epithelium can be compromised by the effects of antibiotics on the commensal microbiome. Changes in mucus integrity directly affect the solvent viscosity in the immediate vicinity of the mucin network, that is, the nanoviscosity, which in turn affects both biochemical reactions and selective transport. To assess mucus nanoviscosity, a reliable readout via the viscosity-dependent fluorescence lifetime of the molecular rotor dye cyanine 3 is established and nanoviscosities from porcine and murine ex vivo mucus are determined. To account for different mucin concentrations due to the removal of digestive residues during mucus collection, the power law dependence of mucin concentration on viscosity is used. The impact of antibiotics combinations (meropenem/vancomycin, gentamycin/ampicillin) on ex vivo intestinal mucus nanoviscosity is presented. The significant increase in viscosity of murine intestinal mucus after treatment suggests an effect of antibiotics on the microbiota that affects mucus integrity. This method will be a useful tool to assess how drugs, directly or indirectly, affect mucus integrity. Additionally, the method can be utilized to analyze the role of mucus nanoviscosity in health and disease, as well as in drug development.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Single-Molecule Tracking of Reagent Diffusion during Chemical Reactions

Recent experiments have shown that the diffusion of reagent molecules is inconsistent with what the Stokes-Einstein equation predicts during a chemical reaction. Here, we used single-molecule tracking to observe the diffusion of reactive reagent molecules during click and Diels-Alder (DA) reactions. We found that the diffusion coefficient of the reagents remained unchanged within the experimental uncertainty upon the DA reaction. Yet, diffusion of reagent molecules is faster than predicted during the click reaction when the reagent concentration and catalyst concentration exceed a threshold. A stepwise analysis suggested that the fast diffusion scenario is due to the reaction but not the involvement of the tracer with the reaction itself. The present results provide experimental evidence on the faster-than-expected reagent diffusion during a CuAAC reaction in specific conditions and propose new insights into understanding this unexpected behavior.

Spongy all-in-liquid materials by in-situ formation of emulsions at oil-water interfaces

Printing a structured network of functionalized droplets in a liquid medium enables engineering collectives of living cells for functional purposes and promises enormous applications in processes ranging from energy storage to tissue engineering. Current approaches are limited to drop-by-drop printing or face limitations in reproducing the sophisticated internal features of a structured material and its interactions with the surrounding media. Here, we report a simple approach for creating stable liquid filaments of silica nanoparticle dispersions and use them as inks to print all-in-liquid materials that consist of a network of droplets. Silica nanoparticles stabilize liquid filaments at Weber numbers two orders of magnitude smaller than previously reported in liquid-liquid systems by rapidly producing a concentrated emulsion zone at the oil-water interface. We experimentally demonstrate the printed aqueous phase is emulsified in-situ; consequently, a 3D structure is achieved with flexible walls consisting of layered emulsions. The tube-like printed features have a spongy texture resembling miniaturized versions of “tube sponges” found in the oceans. A scaling analysis based on the interplay between hydrodynamics and emulsification kinetics reveals that filaments are formed when emulsions are generated and remain at the interface during the printing period. Stabilized filaments are utilized for printing liquid-based fluidic channels.

All-in-liquid printing promises applications from energy storage to drug delivery and tissue engineering. Here, authors present the in-situ generation of layered emulsion in a fraction of a second at the oil-water interface forming 3D tube-like structures in a liquid medium.

Nanoswimmers Based on Capped Janus Nanospheres

Nanoswimmers are synthetic nanoscale objects that convert the available surrounding free energy to a directed motion. For example, bacteria with various flagella types serve as textbook examples of the minuscule swimmers found in nature. Along these lines, a plethora of artificial hybrid and non-hybrid nanoswimmers have been introduced, and they could find many uses, e.g., for targeted drug delivery systems (TDDSs) and controlled drug treatments. Here, we discuss a certain class of nanoparticles, i.e., functional, capped Janus nanospheres that can be employed as nanoswimmers, their subclasses and properties, as well as their various implementations. A brief outlook is given on different fabrication and synthesis methods, as well as on the diverse compositions used to prepare nanoswimmers, with a focus on the particle types and materials suitable for biomedical applications. Several recent studies have shown remarkable success in achieving temporally and spatially controlled drug delivery in vitro using Janus-particle-based TDDSs. We believe that this review will serve as a concise introductory synopsis for the interested readers. Therefore, we hope that it will deepen the general understanding of nanoparticle behavior in biological matrices.

NMR Provides Unique Insight into the Functional Dynamics and Interactions of Intrinsically Disordered Proteins

Intrinsically disordered proteins are ubiquitous throughout all known proteomes, playing essential roles in all aspects of cellular and extracellular biochemistry. To understand their function, it is necessary to determine their structural and dynamic behavior and to describe the physical chemistry of their interaction trajectories. Nuclear magnetic resonance is perfectly adapted to this task, providing ensemble averaged structural and dynamic parameters that report on each assigned resonance in the molecule, unveiling otherwise inaccessible insight into the reaction kinetics and thermodynamics that are essential for function. In this review, we describe recent applications of NMR-based approaches to understanding the conformational energy landscape, the nature and time scales of local and long-range dynamics and how they depend on the environment, even in the cell. Finally, we illustrate the ability of NMR to uncover the mechanistic basis of functional disordered molecular assemblies that are important for human health.

High rates of calcium-free diffusion in the cytosol of living cells

Calcium (Ca²⁺) is a universal second messenger that participates in the regulation of innumerous physiological processes. The way in which local elevations of the cytosolic Ca²⁺ concentration spread in space and time is key for the versatility of the signals. Ca²⁺ diffusion in the cytosol is hindered by its interaction with proteins that act as buffers. Depending on the concentrations and the kinetics of the interactions, there is a large range of values at which Ca²⁺ diffusion can proceed. Having reliable estimates of this range, particularly of its highest end, which corresponds to the ions free diffusion, is key to understand how the signals propagate. In this work, we present the first experimental results with which the Ca²⁺-free diffusion coefficient is directly quantified in the cytosol of living cells. By means of fluorescence correlation spectroscopy experiments performed in Xenopus laevis oocytes and in cells of Saccharomyces cerevisiae, we show that the ions can freely diffuse in the cytosol at a higher rate than previously thought.

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.

Fluid Viscoelasticity Triggers Fast Transitions of a Brownian Particle in a Double Well Optical Potential

Thermally activated transitions are ubiquitous in nature, occurring in complex environments which are typically conceived as ideal viscous fluids. We report the first direct observations of a Brownian bead transiting between the wells of a bistable optical potential in a viscoelastic fluid with a single long relaxation time. We precisely characterize both the potential and the fluid, thus enabling a neat comparison between our experimental results and a theoretical model based on the generalized Langevin equation. Our findings reveal a drastic amplification of the transition rates compared to those in a Newtonian fluid, stemming from the relaxation of the fluid during the particle crossing events.

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.

Membrane Surface Modulates Slow Diffusion in Small Crowded Droplets

Membranes are ubiquitous structures in cells. The effects of membranes on various functional molecules have been reported, but their behaviors under macromolecular crowding and cell-sized confinement have not fully been understood. In this study, we model an intracellular environment by crowding micrometer-sized droplets and investigate the effects of membrane properties on molecular diffusion. The molecular diffusion inside small droplets covered with a lipid layer of phosphatidylcholine (PC) becomes slower compared with that of the corresponding bulk solutions under a crowding condition of polysaccharide dextran but not of its monomer unit, glucose. The addition of a poly(ethylene glycol) conjugated lipid (PEGylated lipid) to the PC membrane significantly alters the degree of slow diffusion observed inside small droplets of concentrated dextran. Interestingly, the change is not monotonic against dextran concentration; that is, the PEGylated membrane increases and decreases the degree of slow diffusion with increasing dextran concentration. We explain the nonmonotonic alternation from the increase in effective dextran concentration and the hindered temporal adsorption of dextran to the membrane. Because diffusion alteration by adding PEGylated lipid is observed for condensed small droplets of linear polymer PEG and hydrophilic protein bovine serum albumin, the phenomenon is general for other polymer systems as well. Furthermore, our findings may facilitate the understanding of intracellular molecular behaviors based on membrane effects as well as the development of numerous applications using polymer droplets.

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy

The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant-matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant-matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.

Generalization of Langevin Dynamics from Spatio-Temporal Dressed Dynamics Perspective

Understanding multiscale dynamics characteristics has been the holy grail in a broad range of scientific disciplines from physics, chemistry, to biology, and beyond. The seminal Langevin equation successfully unravels remarkable details of Brownian motion dynamics involving stochastic collisions from the fluidic medium. However, extraordinary phenomena beyond the scope of Langevin dynamics were observed to exhibit a series of multiscale dynamic features in recent years. Here, an explicit spatio-temporal coupled kernel is developed to provide the microscopic account for delicate dynamic coupling between particle and medium in the dressed dynamics perspective. This methodology is applied to investigate an aqueous solvation shell model with an explicit spatial boundary to illustrate the significance of spatial and temporal coupling, leading to a general temporal profile of dressed dynamics over 12 orders of magnitude in time In particular, the time-resolved viscosity is formulated to address the remarkable enhancement of viscosity measured by the liquid cell electron microscopy. The understanding of dressed dynamics processes will be greatly enriched by further studies on the detailed dynamics that manifests the microscopic inhomogeneity of medium.

Unraveling Dynamic Transitions in Time-Resolved Biomolecular Motions by A Dressed Diffusion Model

Recent experimental data reveal the complexity of diffusion dynamics beyond the scope of classical Brownian dynamics. The particles exhibit diverse diffusive motions from the anomalous toward classical diffusion over a wide range of temporal scales. Here a dressed diffusion model is developed to account for non-Brownian phenomena. By coupling the particle dynamics with a local field, the dressed diffusion model generalizes the Langevin equation through coupled damping kernels and generates the salient feature of time-dependent diffusion dynamics reported in the experimental measurements of biomolecules. The dressed diffusion model provides one quantitative aspect for future endeavors in this rapid-growing field.

Crowding-Induced Uncompetitive Inhibition of Lactate Dehydrogenase: Role of Entropic Pushing

The cell is an extremely complex environment, notably highly crowded, segmented, and confining. Overall, there is overwhelming and ever-growing evidence that to understand how biochemical reactions proceed in vivo, one cannot separate the biochemical actors from their environment. Effects such as excluded volume, obstructed diffusion, weak nonspecific interactions, and fluctuations all team up to steer biochemical reactions often very far from what is observed in ideal conditions. In this paper, we use Ficoll PM70 and PEG 6000 to build an artificial crowded milieu of controlled composition and density in order to assess how such environments influence the biocatalytic activity of lactate dehydrogenase (LDH). Our measurements show that the normalized apparent affinity and maximum velocity decrease in the same fashion, a behavior reminiscent of uncompetitive inhibition, with PEG resulting in the largest reduction. In line with previous studies on other enzymes of the same family, and in agreement with the known role of a surface loop involved in enzyme isomerization and regulation of access to the active site, we suggest that the crowding matrix interferes with the conformational ensemble of the enzyme. This likely results in both impaired enzyme-complex isomerization and thwarted product release. Molecular dynamics simulations confirm that excluded-volume effects lead to an entropic force that effectively tends to push the loop closed, thereby effectively shifting the conformational ensemble of the enzyme in favor of a more stable complex isoform. Overall, our study substantiates the idea that most biochemical kinetics cannot be fully explained without including the subtle action of the environment where they take place naturally, in particular accounting for important factors such as excluded-volume effects and also weak nonspecific interactions when present, confinement, and fluctuations.

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).

A Unified Description of Intrinsically Disordered Protein Dynamics under Physiological Conditions Using NMR Spectroscopy

Intrinsically disordered proteins (IDPs) are flexible biomolecules whose essential functions are defined by their dynamic nature. Nuclear magnetic resonance (NMR) spectroscopy is ideally suited to the investigation of this behavior at atomic resolution. NMR relaxation is increasingly used to detect conformational dynamics in free and bound forms of IDPs under conditions approaching physiological, although a general framework providing a quantitative interpretation of these exquisitely sensitive probes as a function of experimental conditions is still lacking. Here, measuring an extensive set of relaxation rates sampling multiple-time-scale dynamics over a broad range of crowding conditions, we develop and test an integrated analytical description that accurately portrays the motion of IDPs as a function of the intrinsic properties of the crowded molecular environment. In particular we observe a strong dependence of both short-range and long-range motional time scales of the protein on the friction of the solvent. This tight coupling between the dynamic behavior of the IDP and its environment allows us to develop analytical expressions for protein motions and NMR relaxation properties that can be accurately applied over a vast range of experimental conditions. This unified dynamic description provides new insight into the physical behavior of IDPs, extending our ability to quantitatively investigate their conformational dynamics under complex environmental conditions, and accurately predicting relaxation rates reporting on motions on time scales up to tens of nanoseconds, both in vitro and in cellulo.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Nonuniform Crowding Enhances Transport

The cellular cytoplasm is crowded with macromolecules and other species that occupy up to 40% of the available volume. Previous studies have reported that for high crowder molecule concentrations, colloidal tracer particles have a dampened diffusion due to the higher solution viscosity. However, these studies employed uniform distributions of crowder molecules. We report a scenario, previously unexplored experimentally, of increased tracer transport driven by a nonuniform concentration of crowder macromolecules. In gradients of a polymeric crowder, tracer particles undergo transport several times higher than that of their bulk diffusion rate. The direction of the transport is toward regions of lower crowder concentration. Mechanistically, hard-sphere interactions and the resulting volume exclusion between the tracer and crowder increase the effective diffusion by inducing a convective motion of tracers, which we explain through modeling. Strikingly, soft deformable particles show even greater enhancement in transport in crowder gradients compared to similarly sized hard particles. Overall, this demonstration of enhanced transport in nonuniform distributions of crowders is anticipated to clarify aspects of multicomponent intracellular transport.

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.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Effect of protein-protein interactions and solvent viscosity on the rotational diffusion of proteins in crowded environments

The rotational diffusion of a protein in the presence of protein crowder molecules was analyzed via computer simulations. Cluster formation as a result of transient intermolecular contacts was identified as the dominant effect for reduced rotational diffusion upon crowding. The slow-down in diffusion was primarily correlated with direct protein-protein contacts rather than indirect interactions via shared hydration layers. But increased solvent viscosity due to crowding contributed to a lesser extent. Key protein-protein contacts correlated with a slow-down in diffusion involve largely interactions between charged and polar groups suggesting that the surface composition of a given protein and the resulting propensity for forming interactions with surrounding proteins in a crowded cellular environment may be the major determinant of its diffusive properties.

Polarization induced control of optical trap potentials in binary liquids

We illustrate control of a polarized laser optical trapping potential landscape through the nonideal mixing of binary liquids. The inherent trapping potential asymmetry (ITPA) present in the trapping region results from the asymmetric intensity distribution in focal volume due to the high numerical aperture objective lens. Experimentally, we show that this ITPA effect can be modified and/or removed by the use of binary liquid mixtures. From our femtosecond optical tweezers experiments, we determine the topograph of the trapping potential base on the fluctuation-dissipation theorem. Additionally, the Brownian motion of the trapped bead is sensitive to the frictional force (FF) of the surroundings that is exerted by clusters of water and alcohol binary mixture through extended hydrogen bonding. Thus, using these two effects, ITPA and FF of the medium, we have shown that one can indeed modify the effective trapping potential landscape. Water-alcohol binary mixtures display a nonlinear dependence on the microrheological properties of the solvent composition as a result of rigid cluster formation. Volumetrically, at about 30% methanol in water binary mixture, the trapping asymmetry is minimal. In this particular binary mixture composition, the hydrophobic part of the methanol molecule is surrounded by ‘cages’ of water molecules. Enhanced H-bonding network of water molecules results in higher viscosity, which contributes to the higher frictional force. Increased viscosity decreases the degree of anisotropy due to hindered dipolar rotation. However, at higher methanol concentrations, the methanol molecules are no longer contained within the water cages and are free to move, which decrease their overall bulk viscosity. Thus, for pure solvents, experimentally measured anisotropy matches quite well with the theoretical prediction, but this fails in case of the binary mixtures due to the increased frictional force exerted by binary mixtures that result from the formation of cage-like structures.

Microviscosity in E. coli Cells from Time-Resolved Linear Dichroism Measurements

A protein's folding or function depends on its mobility through the viscous environment that is defined by the presence of macromolecules throughout the cell. The relevant parameter for this mobility is microviscosity-the viscosity on a time and distance scale that is important for protein folding/function movements. A quasi-null, ultrasensitive time-resolved linear dichroism (TRLD) spectroscopy is proving to be a useful tool for measurements of viscosity on this scale, with previous in vitro studies reporting on the microviscosities of crowded environments mimicked by high concentrations of different macromolecules. This study reports the microviscosity experienced by myoglobin in the E. coli cell's heterogeneous cytoplasm by using TRLD to measure rotational diffusion times. The results show that photolyzed deoxyMb ensembles randomize through environment-dependent rotational diffusion with a lifetime of 34 ± 6 ns. This value corresponds to a microviscosity of 2.82 ± 0.42 cP, which is consistent with previous reports of cytoplasmic viscosity in E. coli. The results of these TRLD studies in E. coli (1) provide a measurement of myoglobin mobility in the cytoplasm, (2) taken together with in vitro TRLD studies yield new insights into the nature of the cytoplasmic environment in cells, and (3) demonstrate the feasibility of TRLD as a probe of intracellular viscosity.

Temperature dependent FCS studies using a long working distance objective: Viscosities of supercooled liquids and particle size

In this work, we describe new experimental setups for Fluorescence Correlation Spectroscopy (FCS) where a long working distance objective is used. Using these setups, FCS measurements in a broad temperature range for a small sample volume of about 50 μl can be performed. The use of specially designed cells and a dry long working distance objective was essential for avoiding temperature gradients in the sample. The performance of the new setups and a traditional FCS setup with immersion objectives is compared. The FCS data in combination with the Stokes-Einstein (SE) relation were used to obtain the values of the nanoviscosity of a fluid. We show for selected molecular van der Waals supercooled liquids that despite the fact that in these systems, a characteristic length scale can be defined, the nanoviscosity obtained from FCS is in a very good agreement with the macroscopic (rheometric) viscosity of the sample in a broad temperature range. This result corroborates the applicability of the SE relation to supercooled liquids at temperatures above 1.2 T_g. We also show that the temperature dependent size of thermoresponsive microgel particles can be determined by FCS using the designed cells and a long working distance objective in a broader size range without a need to use the correction procedure since the size correction is proportional to the square of the ratio of the hydrodynamic radius to the confocal volume size.

Interfacial Properties and Hopping Diffusion of Small Nanoparticle in Polymer/Nanoparticle Composite with Attractive Interaction on Side Group

The diffusion dynamics of fullerene (C 60 ) in unentangled linear atactic polystyrene (PS) and polypropylene (PP) melts and the structure and dynamic properties of polymers in interface area are investigated by performing all-atom molecular dynamics simulations. The comparison of the results in two systems emphasises the influence of local interactions exerted by polymer side group on the diffusion dynamics of the nanoparticle. In the normal diffusive regime at long time scales, the displacement distribution function (DDF) follows a Gaussian distribution in PP system, indicating a normal diffusion of C 60 . However, we observe multiple peaks in the DDF curve for C 60 diffusing in PS melt, which indicates a diffusion mechanism of hopping of C 60 . The attractive interaction between C 60 and phenyl ring side groups are found to be responsible for the observed hopping diffusion. In addition, we find that the C 60 is dynamically coupled with a subsection of a tetramer on PS chain, which has a similar size with C 60 . The phenyl ring on PS chain backbone tends to have a parallel configuration in the vicinity of C 60 surface, therefore neighbouring phenyl rings can form chelation effect on the C 60 surface. Consequently, the rotational dynamics of phenyl ring and the translational diffusion of styrene monomers are found to be slowed down in this interface area. We hope our results can be helpful for understanding of the influence of the local interactions on the nanoparticle diffusion dynamics and interfacial properties in polymer/nanoparticle composites.

Insight into the fission mechanism by quantitative characterization of Drp1 protein distribution in the living cell

One of the main players in the process of mitochondrial fragmentation is dynamin-related protein 1 (Drp1), which assembles into a helical ring-like structure on the mitochondria and facilitates fission. The fission mechanism is still poorly understood and detailed information concerning oligomeric form of Drp1, its cellular distribution and the size of the fission complex is missing. To estimate oligomeric forms of Drp1 in the cytoplasm and on the mitochondria, we performed a quantitative analysis of Drp1 diffusion and distribution in gene-edited HeLa cell lines. This paper provides an insight into the fission mechanism based on the quantitative description of Drp1 cellular distribution. We found that approximately half of the endogenous GFP-Drp1 pool remained in the cytoplasm, predominantly in a tetrameric form, at a concentration of 28 ± 9 nM. The Drp1 mitochondrial pool included many different oligomeric states with equilibrium distributions that could be described by isodesmic supramolecular polymerization with a K_d of 31 ± 10 nM. We estimated the average number of Drp1 molecules forming the functional fission complex to be approximately 100, representing not more than 14% of all Drp1 oligomers. We showed that the upregulated fission induced by niclosamide is accompanied by an increase in the number of large Drp1 oligomers.

Nanorheology of Entangled Polymer Melts

We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.

Scale-dependent rotational diffusion of nanoparticles in polymer solutions

It is shown that the rotational diffusivity of nanoparticles in polymer solutions spanning the dilute to semi-dilute regimes deviates from the predictions of the Stokes-Einstein (SE) relationship, and that this deviation can be explained by the existence of a polymer depletion layer with the viscosity of the bath solvent. The measurements of the rotational diffusion coefficient of poly(ethylene glycol) (PEG) grafted magnetic nanoparticles in PEG solutions spanning the dilute to semi-dilute regimes and a wide range of polymer molecular weights were obtained from the dynamic magnetic response of the nanoparticles to alternating magnetic fields. Experimental rotational diffusion coefficient values were compared with those predicted by the SE relation using the macroscopic viscosity of the polymer solutions and the hydrodynamic radius of the nanoparticles. Deviations between experimental and SE rotational diffusivity values were observed for nanoparticles in polymer solutions where the radius of gyration of the polymer exceeded the hydrodynamic radius of the particles. A simple model for the rotational hydrodynamic drag on a particle surrounded by a polymer depletion layer was found to describe the experimental rotational diffusivities well, suggesting that the observed phenomenon arises due to the formation of a polymer depletion layer around the nanoparticles.

Crowding in Cellular Environments at an Atomistic Level from Computer Simulations

The effects of crowding in biological environments on biomolecular structure, dynamics, and function remain not well understood. Computer simulations of atomistic models of concentrated peptide and protein systems at different levels of complexity are beginning to provide new insights. Crowding, weak interactions with other macromolecules and metabolites, and altered solvent properties within cellular environments appear to remodel the energy landscape of peptides and proteins in significant ways including the possibility of native state destabilization. Crowding is also seen to affect dynamic properties, both conformational dynamics and diffusional properties of macromolecules. Recent simulations that address these questions are reviewed here and discussed in the context of relevant experiments.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.

A new scaling for the rotational diffusion of molecular probes in polymer solutions

In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study.

Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm

Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology.

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue-residue interaction.

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C₁₂E₈ (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales-from diffusion of molecular probes to macroscopic viscous flow-we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.

Nano-demixing as a novel strategy for magnetic field responsive systems: the case of dibutyl phosphate/bis(2-ethylhexyl)amine systems

Pure surfactant liquids and their binary mixtures, owing to the amphiphilic nature of the molecules involved, can exhibit nano-segregation and peculiar transport properties with the formation of magnetic field-responsive supramolecular structures.