Combining Diffusion NMR and Small-Angle Neutron Scattering Enables Precise Measurements of Polymer Chain Compression in a Crowded Environment

Impact of Cellular Crowding on Protein Structural Dynamics Investigated by EPR Spectroscopy

The study of how the intracellular medium influences protein structural dynamics and protein-protein interactions is a captivating area of research for scientists aiming to comprehend biomolecules in their native environment. As the cellular environment can hardly be reproduced in vitro, direct investigation of biomolecules within cells has attracted growing interest in the past two decades. Among magnetic resonances, site-directed spin labeling coupled to electron paramagnetic resonance spectroscopy (SDSL-EPR) has emerged as a powerful tool for studying the structural properties of biomolecules directly in cells. Since the first in-cell EPR experiment was reported in 2010, substantial progress has been made, and this Review provides a detailed overview of the developments and applications of this spectroscopic technique. The strategies available for preparing a cellular sample and the EPR methods that can be applied to cells will be discussed. The array of spin labels available, along with their strengths and weaknesses in cellular contexts, will also be described. Several examples will illustrate how in-cell EPR can be applied to different biological systems and how the cellular environment affects the structural and dynamic properties of different proteins. Lastly, the Review will focus on the future developments expected to expand the capabilities of this promising technique.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. In addition, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. Additionally, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation.

SIGNIFICANCE

Phase separation has emerged as a process of significant relevance to sorting macromolecules into distinct compartments, thereby enabling spatial and temporal control over cellular matter. Considerable effort is being invested into uncovering the driving forces that enable the separation of macromolecular solutions into coexisting phases. At its heart, this process is governed by the balance of macromolecule-solvent, inter-macromolecule, and solvent-solvent interactions. We show that the driving forces for phase separation, including the coefficients that measure interaction strengths between macromolecules, can be extracted by titrating the concentrations of crowders that enable macromolecules to phase separate at lower concentrations. Our work paves the way to leverage specific categories of measurements for quantitative characterizations of driving forces for phase separation.

Microscopic kinetic theory of the mean collision force of a particle moving in rarefied gases

The friction of an incident particle interacting with the background molecules is a cornerstone in the nonequilibrium dynamics and statistics. It is reported that the Stokes force may fail while the Brown particle's size is small enough. In this work, the mean collision force of a small classical particle moving through the rarefied gases is analyzed by the direct calculation of the mean decrease of particle's velocity by elastic collisions. As an example, a whole velocity space applicable mean collision force in Maxwell gas is obtained. A self-consistent solution is further provided based on the numerical simulations. Within the low speed limit, comparison of the friction and the Stokes force has been demonstrated. Although the two forces are both proportional to the speed of the particle, their coefficients are different. Unlike the linear speed dependence of Stokes force, the linear behavior in rarefied gases is broken with increasing the speed of incident particle, and a quadratic speed dependence is resulted in high speed. This work clarifies the nonequilibrium dynamics of microscopic particles moving in rarefied gases, and can improve our microscopic understanding of the collision force.

A simulation study on the subdiffusion of polymer chains in crowded environments containing nanoparticles

Polymer chains in crowded environments often show subdiffusive behavior. We adopt molecular dynamics simulations to study the conditions for the subdiffusion of polymer chains in crowded environments containing randomly distributed, immobile, attractive nanoparticles (NPs). The attraction is strong enough to adsorb polymer chains on NPs. The results show that subdiffusion occurs at a low concentration of polymer chains (c_p). A transition from subdiffusion to normal diffusion is observed when c_p exceeds the transition concentration , which increases with increasing concentration of NPs while decreases with increasing size of NPs. The high concentration and small size of NPs exert a big effect on the subdiffusion of polymer chains. The subdiffusive behavior of polymer chains can be attributed to the strong adsorption of polymer chains on the attractive NPs. For the subdiffusion case, polymer chains are adsorbed strongly on multiple NPs, and they diffuse via the NP-exchange diffusion mechanism. However for the normal diffusion case, polymer chains are either free or weakly adsorbed on one or a few NPs, and they diffuse mainly via the adsorption-and-desorption diffusion mechanism.

Testing the Stokes-Einstein relation with the hard-sphere fluid model

The Stokes-Einstein (SE) relation has been widely applied to quantitatively describe the Brownian motion. Notwithstanding, here we show that even for a simple fluid, the SE relation may fail over a wide range of the Brownian particle's size. Namely, although the SE relation could be a good approximation for a large enough Brownian particle, a significant error may appear when decreasing the Brownian particle's size down to several hundred times the size of the fluid molecules, and the error increases with the decrease of the Brownian particle's size. The cause is rooted in the fact that the kinetic contribution to the diffusion coefficient is inversely proportional to the squared radius of the Brownian particle. After excluding the kinetic contribution, we show that the applicable range of the SE relation is expanded significantly.

Hybrid Nanosystems for Biomedical Applications

Inorganic/organic hybrid nanosystems have been increasingly developed for their versatility and efficacy at overcoming obstacles not readily surmounted by nonhybridized counterparts. Currently, hybrid nanosystems are implemented for gene therapy, drug delivery, and phototherapy in addition to tissue regeneration, vaccines, antibacterials, biomolecule detection, imaging probes, and theranostics. Though diverse, these nanosystems can be classified according to foundational inorganic/organic components, accessory moieties, and architecture of hybridization. Within this Review, we begin by providing a historical context for the development of biomedical hybrid nanosystems before describing the properties, synthesis, and characterization of their component building blocks. Afterward, we introduce the architectures of hybridization and highlight recent biomedical nanosystem developments by area of application, emphasizing hybrids of distinctive utility and innovation. Finally, we draw attention to ongoing clinical trials before recapping our discussion of hybrid nanosystems and providing a perspective on the future of the field.

Effects of macromolecular crowding on the folding of a polymer chain: A Wang-Landau simulation study

A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.

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.

Altering the X-ray Scattering Contrast of Triton X-100 Micelles and Its Trapping in a Supercooled Solvent

The structure of core-shell micelles formed by nonionic surfactant Triton X-100 (TX-100) in a supercooled glucose-urea melt is investigated by contrast variation small-angle X-ray scattering (SAXS), small angle neutron scattering (SANS), and HR-TEM. Cooling a molten mixture of glucose-urea (weight ratio of 3:2) to room temperature yields a supercooled solvent without crystallization that can be used for trapping micelles of TX-100. By use of a combination of water and glucose-urea mixture at different proportions as solvent for micellization, the scattering length density (SLD) of the solvent can be tuned to match the shell contrast of the micelles. A systematic analysis of SAXS and SANS data with different SLD of solvent permits a quantitative evaluation of electron density profile of micelles in different matrices. The core of TX-100 micelles shows significant swelling in glucose-urea melt, as compared to that in water. The dimension and morphology of micelles were evaluated by scattering techniques and HR-TEM. Dynamic light scattering (DLS) studies suggest that, unlike micelles in water, the diffusion of micelles in supercooled glucose-urea melt decreased by several orders of magnitude.

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.

Simulation on diffusivity and statistical size of polymer chains in polymer nanocomposites

The dynamical and conformational properties of polymer chains are affected significantly by strongly attractive nanoparticles. The adsorption of polymer chains on nanoparticles not only reduces the dynamics but also changes the conformation of polymer chains. For orderly distributed nanoparticles of size roughly the same as the radius of gyration of polymer chains, the variation of the diffusivity is highly related to that of the statistical size and can be explained mainly from the adsorption of polymers. In particular, both the polymer's size and diffusivity reach the minimum when the number of polymer chains matches the number of nanoparticles where polymer chains are mostly adsorbed on separate nanoparticles. The behavior of diffusivity can be explained from the cooperation of polymer adsorption and nanoparticle-exchange motion. Adsorption of the polymer chain slows down the diffusion, whereas the nanoparticle-exchange motion accelerates the diffusion of polymer chains.

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Small-angle scattering (SAS; X-rays, neutrons, light) is being increasingly used to better understand the structure of fractal-based materials and to describe their interaction at nano- and micro-scales. To this aim, several minimalist yet specific theoretical models which exploit the fractal symmetry have been developed to extract additional information from SAS data. Although this problem can be solved exactly for many particular fractal structures, due to the intrinsic limitations of the SAS method, the inverse scattering problem, i.e., determination of the fractal structure from the intensity curve, is ill-posed. However, fractals can be divided into various classes, not necessarily disjointed, with the most common being random, deterministic, mass, surface, pore, fat and multifractals. Each class has its own imprint on the scattering intensity, and although one cannot uniquely identify the structure of a fractal based solely on SAS data, one can differentiate between various classes to which they belong. This has important practical applications in correlating their structural properties with physical ones. The article reviews SAS from several fractal models with an emphasis on describing which information can be extracted from each class, and how this can be performed experimentally. To illustrate this procedure and to validate the theoretical models, numerical simulations based on Monte Carlo methods are performed.

Block Copolymer of Flexible and Semi-Flexible Block Confined in Nanopost Array

Coarse-grained molecular dynamics simulations of a diblock copolymer consisting of a flexible and semi-flexible block in a dense array of parallel nanoposts with a square lattice packing were performed. The mutual interactions between the two blocks of the confined diblock chain were investigated through a comparison of their size, structure, and penetration among nanoposts with the corresponding separate chains. The geometry of a nanopost array was varied at constant post separation or at constant width of the passage between nanoposts. The size of a single interstitial volume was comparable to or smaller than the size of the diblock chain. A comparison of the blocks with their separate analogous chains revealed that the mutual interactions between the blocks were shielded by the nanoposts and, thus, the blocks behaved independently. At constant passage width, competitive effects of the axial chain extension in interstitial volumes and the lateral chain expansion among interstitial volumes led to a nonmonotonic behavior of the axial span. The position of the maximum in the span plotted against the filling fraction for a diblock chain was dictated by the semi-flexible block. The semi-flexible block penetrates among the nanoposts more readily and the expansion of the whole diblock copolymer is governed by the semiflexible block. The main findings were explained using the free energy arguments when an interstitial volume was approximated by a channel geometry and a passage aperture by a slit geometry. Detail knowledge of controlled conformational behavior in a compartmentalized environment can contribute to new processes in the storage and retrieval of information.

Influence of solvent quality on conformations of crowded polymers

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute the average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of the polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

Towards developing principles of protein folding and dynamics in the cell

Proteins must fold and function in the immensely complex environment of a cell, i.e. the cytoplasm-this is far from the ideal test-tube setting of a dilute solution. Here we review the advances in protein folding and dynamics inside the cell. In developing principles of protein behavior in vivo, we also begin to understand the organization and dynamics of the cytoplasm, unifying the single protein scale with the many-protein architectures at the subcellular scale. Our group has significantly contributed to this frontier by characterizing the effect of macromolecular crowding on the distribution of protein conformations. Additionally, we provide a personal perspective on becoming a theoretical biological physicist in the era of interdisciplinary research that has been greatly influenced by Dr Kamal Shukla. We also share our view on the future direction of protein folding inside a cell.

Realization of a stable, monodisperse water-in-oil droplet system with micro-scale and nano-scale confinement for tandem microscopy and diffusion NMR studies

In this work we generate stable and monodisperse water-in-oil emulsions using a co-flowing geometry that produced droplet sizes between 13 μm and 250 μm. The drops survived transfer to NMR tubes and were stable for at least 26 hours, enabling the performance of pulsed-field-gradient NMR experiments in addition to microscopy. The drops sizes achieved as a function of flow rate agree well with a simple model for droplet generation: this yields a precise measure of the interfacial tension. The design of a cell mimetic environment with nano-scale confinement has also been demonstrated with diffusion measurements on macromolecules (PEG and Ficoll70) within droplets that are further structured internally using agarose gel networks. Containing the agarose gel in droplets appears to provide very reproducible and homogeneous network environments, enabling quantitative agreement of Ficoll70 dynamics with a theoretical model, with no fit parameters, and, with PEG, yielding a systematic polymer-size dependent slowing down in the network. This is in contrast with bulk agarose, where identical macromolecular diffusion measurements indicate the presence of heterogeneities with water pockets.

The effect of hydrodynamic interactions on nanoparticle diffusion in polymer solutions: a multiparticle collision dynamics study

The diffusion of nanoparticles (NPs) in polymer solutions is studied by a combination of a mesoscale simulation method, multiparticle collision dynamics (MPCD), and molecular dynamics (MD) simulations. We investigate the long-time diffusion coefficient D as well as the subdiffusive behavior in the intermediate time region. The dependencies of both D and subdiffusion factor α on NP size and polymer concentration, respectively, are explicitly calculated. Particular attention is paid to the role of hydrodynamic interaction (HI) in the NP diffusion dynamics. Our simulation results show that the long-time diffusion coefficients satisfy perfectly the scaling relation found by experimental observations. Meanwhile, the subdiffusive factor decreases with the increase in polymer concentration but is of little relevance to the NP size. By parallel simulations with and without HI, we reveal that HI will generally enhance D, while the enhancement effect is non-monotonous with increasing polymer concentration, and it becomes most pronounced at semidilute concentrations. With the aid of a scaling law based on the diffusive activation energy model, we understand that HI affects diffusion through decreasing the diffusive activation energy on the one hand while increasing the effective diffusion size on the other. In addition, HI will certainly influence the subdiffusive behavior of the NP, leading to a larger subdiffusion exponent.