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.

Solvent Effects on Structure and Screening in Confined Electrolytes.

Using classical density functional theory, we investigate the influence of solvent on the structure and ionic screening of electrolytes under slit confinement and in contact with a reservoir. We consider a symmetric electrolyte with implicit and explicit solvent models and find that spatially resolving solvent molecules is essential for the ion structure at confining walls, excess ion adsorption, and the pressure exerted on the walls. Despite this, we observe only moderate differences in the period of oscillations of the pressure with the slit width and virtually coinciding decay lengths as functions of the scaling variable σ_{ion}/λ_{D}, where σ_{ion} is the ion diameter and λ_{D} the Debye length. Moreover, in the electrostatic-dominated regime, this scaling behavior is practically independent of the relative permittivity and its dependence on the ion concentration. In contrast, the crossover to the hard-core-dominated regime depends sensitively on all three factors.

A screening of results on the decay length in concentrated electrolytes.

Screening of electrostatic interactions in room-temperature ionic liquids and concentrated electrolytes has recently attracted much attention as surface force balance experiments have suggested the emergence of unanticipated anomalously large screening lengths at high ion concentrations. Termed underscreening, this effect was ascribed to the bulk properties of concentrated ionic systems. However, underscreening under experimentally relevant conditions is not predicted by classical theories and challenges our understanding of electrostatic correlations. Despite the enormous effort in performing large-scale simulations and new theoretical investigations, the origin of the anomalously long-range screening length remains elusive. This contribution briefly summarises the experimental, analytical and simulation results on ionic screening and the scaling behaviour of screening lengths. We then present an atomistic simulation approach that accounts for the solvent and ion exchange with a reservoir. We find that classical density functional theory (DFT) for concentrated electrolytes under confinement reproduces ion adsorption at charged interfaces surprisingly well. With DFT, we study confined electrolytes using implicit and explicit solvent models and the dependence on the solvent's dielectric properties. Our results demonstrate how the absence vs. presence of solvent particles and their discrete nature affect the short and long-range screening in concentrated ionic systems.

Minimal Coarse-Grained Model for Immunoglobulin G: Diffusion and Binding under Crowding.

Immunoglobulin G (IgG) is the most common type of antibody found in blood and extracellular fluids and plays an essential role in our immune response. However, studies of the dynamics and reaction kinetics of IgG-antigen binding under physiological crowding conditions are scarce. Herein, we develop a coarse-grained model of IgG consisting of only six beads that we find minimal for a coarse representation of IgG's shape and a decent reproduction of its flexibility and diffusion properties measured experimentally. Using this model in Brownian dynamics simulations, we find that macromolecular crowding affects only slightly the IgG's flexibility, as described by the distribution of angles between the IgG's arms and stem. Our simulations indicate that, contrary to expectations, crowders slow down the translational diffusion of an IgG less strongly than they do for a smaller Ficoll 70, which we relate to the IgG's conformational size changes induced by crowding. We also find that crowders affect the binding kinetics by decreasing the rate of the first binding step and enhancing the second binding step.

Crowding-Regulated Binding of Divalent Biomolecules.

Macromolecular crowding affects biophysical processes as diverse as diffusion, gene expression, cell growth, and senescence. Yet, there is no comprehensive understanding of how crowding affects reactions, particularly multivalent binding. Herein, we use scaled particle theory and develop a molecular simulation method to investigate the binding of monovalent to divalent biomolecules. We find that crowding can increase or reduce cooperativity-the extent to which the binding of a second molecule is enhanced after binding a first molecule-by orders of magnitude, depending on the sizes of the involved molecular complexes. Cooperativity generally increases when a divalent molecule swells and then shrinks upon binding two ligands. Our calculations also reveal that, in some cases, crowding enables binding that does not occur otherwise. As an immunological example, we consider immunoglobulin G-antigen binding and show that crowding enhances its cooperativity in bulk but reduces it when an immunoglobulin G binds antigens on a surface.

Theory and Simulations of Ionic Liquids in Nanoconfinement.

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Less Is More: Can Low Quantum Capacitance Boost Capacitive Energy Storage?

We present a theoretical analysis of charge storage in electrochemical capacitors with electrodes based on carbon nanotubes. Using exact analytical solutions supported by Monte Carlo simulations, we show how the limitations of the electron density of states in such low-dimensional electrode materials may help boost the energy stored at increased voltages. While these counterintuitive predictions await experimental verification, they suggest exciting opportunities for enhancing energy storage by rational engineering of the electronic properties of low-dimensional electrodes.

How macromolecules softness affects diffusion under crowding.

Diffusion in a macromolecularly crowded environment is essential for many intracellular processes, from metabolism and catalysis to gene transcription and translation. So far, theoretical and experimental work has focused on anomalous subdiffusion, and the effects of interactions, shapes, and composition, while the compactness or softness of macromolecules has received less attention. Herein, we use Brownian dynamics simulations to study how the softness of crowders affects macromolecular diffusion. We find that in most cases, soft crowders slow down the diffusion less effectively than hard crowders like Ficoll. For instance, at a 30% occupied volume fraction, the diffusion in Ficoll70 is about 20% slower than in soft crowders of the same size. However, our simulations indicate that elongated macromolecules, such as double-stranded DNA pieces, can diffuse comparably or even faster in hard crowders. We relate these effects to the volume excluded by soft and hard crowders to different tracers. Our results show that the softness and shape of macromolecules are crucial factors determining diffusion under crowding, relevant to diverse intracellular environments.

Mechanisms and Effects of Substrate Channelling in Enzymatic Cascades.

Substrate or metabolite channelling is a transfer of intermediates produced by one enzyme to the sequential enzyme of a reaction cascade or metabolic pathway, without releasing them entirely into bulk. Despite an enormous effort and more than three decades of research, substrate channelling remains the subject of continuing debates and active investigation. Herein, we review the benefits and mechanisms of substrate channelling in vivo and in vitro. We discuss critically the effects that substrate channelling can have on enzymatic cascades, including speeding up or slowing down reaction cascades and protecting intermediates from sequestration and enzymes' surroundings from toxic or otherwise detrimental intermediates. We also discuss how macromolecular crowding affects substrate channelling and point out the galore of open questions.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.

Ionic screening in bulk and under confinement.

Recent experiments have shown that the repulsive force between atomically flat, like-charged surfaces confining room-temperature ionic liquids or concentrated electrolytes exhibits an anomalously large decay length. In our previous publication [J. Zeman, S. Kondrat, and C. Holm, Chem. Commun. 56, 15635 (2020)], we showed by means of extremely large-scale molecular dynamics simulations that this so-called underscreening effect might not be a feature of bulk electrolytes. Herein, we corroborate these findings by providing additional results with more detailed analyses and expand our investigations to ionic liquids under confinement. Unlike in bulk systems, where screening lengths are computed from the decay of interionic potentials of mean force, we extract such data in confined systems from cumulative charge distributions. At high concentrations, our simulations show increasing screening lengths with increasing electrolyte concentration, consistent with classical liquid state theories. However, our analyses demonstrate that-also for confined systems-there is no anomalously large screening length. As expected, the screening lengths determined for ionic liquids under confinement are in good quantitative agreement with the screening lengths of the same ionic systems in bulk. In addition, we show that some theoretical models used in the literature to relate the measured screening lengths to other observables are inapplicable to highly concentrated electrolytes.

Capacitive energy storage in single-file pores: Exactly solvable models and simulations.

Understanding charge storage in low-dimensional electrodes is crucial for developing novel ecologically friendly devices for capacitive energy storage and conversion and water desalination. Exactly solvable models allow in-depth analyses and essential physical insights into the charging mechanisms. So far, however, such analytical approaches have been mainly limited to lattice models. Herein, we develop a versatile, exactly solvable, one-dimensional off-lattice model for charging single-file pores. Unlike the lattice model, this model shows an excellent quantitative agreement with three-dimensional Monte Carlo simulations. With analytical calculations and simulations, we show that the differential capacitance can be bell-shaped (one peak), camel-shaped (two peaks), or have four peaks. Transformations between these capacitance shapes can be induced by changing pore ionophilicity, by changing cation-anion size asymmetry, or by adding solvent. We find that the camel-shaped capacitance, characteristic of dilute electrolytes, appears for strongly ionophilic pores with high ion densities, which we relate to charging mechanisms specific to narrow pores. We also derive a large-voltage asymptotic expression for the capacitance, showing that the capacitance decays to zero as the inverse square of the voltage, C ∼ u-2. This dependence follows from hard-core interactions and is not captured by the lattice model.

Capillary Ionization and Jumps of Capacitive Energy Stored in Mesopores.

We study ionic liquid-solvent mixtures in slit-shaped nanopores wider than a few ion diameters. Using a continuum theory and generic thermodynamic reasoning, we reveal that such systems can undergo a capillary ionization transition. At this transition, the pores spontaneously ionize or deionize upon infinitesimal changes of temperature, slit width, or voltage. Our calculations show that a voltage applied to a pore may induce a capillary ionization, which-counterintuitively-is followed by a re-entrant deionization as the voltage increases. We find that such ionization transitions produce sharp jumps in the accumulated charge and stored energy, which may find useful applications in energy storage and heat-to-energy conversion.

Controlled deposition of nanoparticles with critical Casimir forces.

Nanocrystal assembly represents the key fabrication step to develop next-generation optoelectronic devices with properties defined from the bottom-up. Despite numerous efforts, our limited understanding of nanoscale interactions has so far delayed the establishment of assembly conditions leading to reproducible superstructure morphologies, therefore hampering integration with large-scale, industrial processes. In this work, we demonstrate the deposition of a layer of semiconductor nanocrystals on a flat and unpatterned silicon substrate as mediated by the interplay of critical Casimir attraction and electrostatic repulsion. We show experimentally and rationalize with Monte Carlo and molecular dynamics simulations how this assembly process can be biased towards the formation of 2D layers or 3D islands and how the morphology of the deposited superstructure can be tuned from crystalline to amorphous. Our findings demonstrate the potential of the critical Casimir interaction to direct the growth of future artificial solids based on nanocrystals as the ultimate building blocks.

Superionic Liquids in Conducting Nanoslits: Insights from Theory and Simulations.

Mapping the theory of charging supercapacitors with nanostructured electrodes on known lattice models of statistical physics is an interesting task, aimed at revealing generic features of capacitive energy storage in such systems. The main advantage of this approach is the possibility to obtain analytical solutions that allow new physical insights to be more easily developed. But how general the predictions of such theories could be? How sensitive are they to the choice of the lattice? Herein, we address these questions in relation to our previous description of such systems using the Bethe-lattice approach and Monte Carlo simulations. Remarkably, we find a surprisingly good agreement between the analytical theory and simulations. In addition, we reveal a striking correlation between the ability to store energy and ion ordering inside a pore, suggesting that such ordering can be beneficial for energy storage.

Conformation-changing enzymes and macromolecular crowding.

We study how crowding affects the activity and catalysis-enhanced diffusion of enzymes and passive tracers by employing a fluctuating-dumbbell model of conformation-changing enzymes. Our Brownian dynamics simulations reveal that the diffusion of enzymes depends qualitatively on the type of crowding. If only enzymes are present in the system, the catalysis-induced enhancement of the enzyme diffusion - somewhat counter-intuitively - increases with crowding, while it decreases if crowding is due to inert particles. For the tracers, the diffusion enhancement increases with increasing the enzyme concentration. We also show how the enzyme activity is reduced by crowding and propose a simple expression to describe this reduction. Our results highlight subtle effects at play concerning enzymatic activity and macromolecular transport in crowded systems, such as, e.g., the interior of living cells.

Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate.

Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few kBT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.

How to speed up ion transport in nanopores.

Electrolyte-filled subnanometre pores exhibit exciting physics and play an increasingly important role in science and technology. In supercapacitors, for instance, ultranarrow pores provide excellent capacitive characteristics. However, ions experience difficulties in entering and leaving such pores, which slows down charging and discharging processes. In an earlier work we showed for a simple model that a slow voltage sweep charges ultranarrow pores quicker than an abrupt voltage step. A slowly applied voltage avoids ionic clogging and co-ion trapping-a problem known to occur when the applied potential is varied too quickly-causing sluggish dynamics. Herein, we verify this finding experimentally. Guided by theoretical considerations, we also develop a non-linear voltage sweep and demonstrate, with molecular dynamics simulations, that it can charge a nanopore even faster than the corresponding optimized linear sweep. For discharging we find, with simulations and in experiments, that if we reverse the applied potential and then sweep it to zero, the pores lose their charge much quicker than they do for a short-circuited discharge over their internal resistance. Our findings open up opportunities to greatly accelerate charging and discharging of subnanometre pores without compromising the capacitive characteristics, improving their importance for energy storage, capacitive deionization, and electrochemical heat harvesting.

Bulk ionic screening lengths from extremely large-scale molecular dynamics simulations.

Recent experiments have reported anomalously large screening lengths of interactions between charged surfaces confining concentrated electrolytes and ionic liquids. Termed underscreening, this effect was ascribed to bulk properties of dense ionic systems. Herein, we study bulk ionic screening with extremely large-scale molecular dynamics simulations, allowing us to assess the range of distances relevant to the experiments. Our results yield two screening lengths satisfying distinct scaling relations. However, with an accuracy of 10-5kBT in interionic potentials of mean force, we find no signs of underscreening, suggesting that other than bulk effects might be at play in the experiments.

Macromolecular Crowding: How Shape and Interactions Affect Diffusion.

A significant fraction of the cell volume is occupied by various proteins, polysaccharides, nucleic acids, etc., which considerably reduces the mobility of macromolecules. Theoretical and experimental work so far have mainly focused on the dependence of the mobility on the occupied volume, while the effect of a macromolecular shape received less attention. Herein, using fluorescence correlation spectroscopy (FCS) and Brownian dynamics (BD) simulations, we report on a dramatic slowdown of tracer diffusion by cylindrically shaped double-stranded (ds) DNAs (16 nm in length). We find, for instance, that the translational diffusion coefficient of a streptavidin tracer is reduced by about 60% for a volume fraction of dsDNA as low as just 5%. For comparison, for a spherical crowder (Ficoll70) the slowdown is only 10% at the same volume fraction and 60% reduction occurs at a volume fraction as high as 35%. BD simulations reveal that this reduction can be attributed to a larger volume excluded to a tracer by dsDNA particles, as compared with spherical Ficoll70 at the same volume fraction, and to the differences in the tracer-crowder attractive interactions. In addition, we find using BD simulations that rotational diffusion of dsDNA is less affected by the crowder shape than its translational motion. Our results show that diffusion in crowded systems is determined not merely by the occupied volume fraction, but that the shape and interactions can determine diffusion, which is relevant to the diverse intracellular environments inside living cells.