Is the depletion force entropic? Molecular crowding beyond steric interactions

Crowding beyond excluded volume: A tale of two dimers

Protein-protein interactions are modulated by their environment. High macromolecular solute concentrations crowd proteins and shift equilibria between protein monomers and their assemblies. We aim to understand the mechanism of crowding by elucidating the molecular-level interactions that determine dimer stability. Using 19F-NMR spectroscopy, we studied the effects of various polyethylene glycols (PEGs) on the equilibrium thermodynamics of two protein complexes: a side-by-side and a domain-swap dimer. Analysis using our mean-field crowding model shows that, contrary to classic crowding theories, PEGs destabilize both dimers through enthalpic interactions between PEG and the monomers. The enthalpic destabilization becomes more dominant with increasing PEG concentration because the reduction in PEG mesh size with concentration diminishes the stabilizing effect of excluded volume interactions. Additionally, the partially folded domain-swap monomers fold in the presence of PEG, contributing to dimer stabilization at low PEG concentrations. Our results reveal that polymers crowd protein complexes through multiple conjoined mechanisms, impacting both their stability and oligomeric state.

The role of model crowders in the salt resistance of complex coacervates

Complex coacervation is the phase separation of oppositely charged polyelectrolytes, resulting in a polymer-dense coacervate phase and a polymer-depleted supernatant phase. Coacervation is crucial for many biological processes and novel synthetic materials, where the environment is often filled with other neutral molecules (crowders). Yet, the complex role of crowders in complex coacervation has not been studied systematically under controlled conditions. We performed coarse-grained molecular dynamics simulations of coacervation in the presence of polymeric crowders of varying concentrations and chain lengths. While short crowders do not have any significant effect on coacervation, larger crowders stabilize the coacervate against added salt, increasing its critical salt concentration. The change in critical salt concentration saturates for long crowders at a value determined by the crowder concentration. Rescaling all phase diagrams by their critical salt concentration leads to a collapse of the data, which demonstrates a universal phase behavior. Our simulation indicates that the inability of crowder chains to mix with the polyelectrolytes is the driving force behind crowding effects. These testable predictions provide a first step toward a comprehensive understanding of crowding effects in complex coacervation.

Calcium Cross-Linked Cellulose Nanofibrils: Hydrogel Design for Local and Controlled Nitric Oxide Release

Nitric oxide (NO) holds promise for wound healing due to its antimicrobial properties and role in promoting vasodilation and tissue regeneration. The local delivery of NO to target cells or organs offers significant potential in numerous biomedical applications, especially when NO donors are integrated into nontoxic viscous matrices. This study presents the development of robust cellulose nanofibril (CNF) hydrogels designed to control the release of nitric oxide (NO) generated in situ from a NO-donor molecule (S-nitrosoglutathione, GSNO) obtained from the nitrosation of its precursor molecule glutathione (GSH). CNF, efficiently isolated from sugar cane bagasse, exhibited a high aspect ratio and excellent colloidal stability in water. Although depletion forces could be observed upon the addition of GSH, this effect did not significantly alter the morphology of the CNF network at low GSH concentrations (<20 mM). Ionic cross-linking with Ca2+ resulted in nontoxic and robust hydrogels (elastic moduli ranging from 300 to 3000 Pa) at low CNF solid content. The release rate of NO from GSNO decreased in CNF from 1.61 to 0.40 mmol. L-1·h-1 when the nanofibril content raised from 0.3 to 1.0 wt %. The stabilization effect monitored for 16 h was assigned to hydrogel mesh size, which was easily tailored by modifying the concentration of CNF in the initial suspension. These results highlight the potential of CNF-based hydrogels in biomedical applications requiring a precise NO delivery.

Factor defining the effects of tetraalkylammonium chloride on stability, folding, and dynamics of horse cytochrome c

This article describes the molecular mechanism by which tetraalkylammonium chloride ([R4N]Cl: R- = methyl (Me), ethyl (Et), propyl (Pr),butyl (Bu)) modulates the stability, folding, and dynamics of cytochrome c (Cyt c). Analysis of [R4N]Cl effects on thermal/chemical denaturations, millisecond refolding/unfolding kinetics, and slow CO-association kinetics of Cyt c without and with denaturant providing some significant results: (i) [R4N]Cl decreasing the unfolding free energy estimated by thermodynamic and kinetic analysis of thermal/chemical denaturation curves and kinetic chevrons (Log kobs-[GdmCl]) of Cyt c, respectively (ii) hydrophobicity of R-group of [R4N]Cl, preferential inclusion of [R4N]Cl at the protein surface, and destabilizing enthalpic attractive interactions of [Me4N]Cl and steric entropic interactions of [Et4N]Cl,[Pr4N]Cl and [Bu4N]Cl with protein contribute to [R4N]Cl-induced decrease thermodynamic stability of Cyt c (iii) [R4N]Cl exhibits an additive effect with denaturant to decrease thermodynamic stability and refolding rates of Cyt c (iv) low concentrations of [R4N]Cl (≤ 0.5 M) constrain the motional dynamics while the higher concentrations (>0.75 M [R4N]Cl) enhance the structural-fluctuations that denture protein (v) hydrophobicity of R-group of [R4N]Cl alters the [denaturant]-dependent conformational stability, refolding-unfolding kinetics, and CO-association kinetics of Cyt c. Furthermore, the MD simulations depicted that the addition of 1.0 M of [R4N]Cl increased the conformational fluctuations in Cyt c leading to decreased structural stability in the order [Me4N]Cl < [Et4N]Cl < [Pr4N]Cl < [Bu4N]Cl consistent with the experimental results.

Effects of Polymer Architecture and Charged Molecular Crowders on Hydrophobic Polymer Collapse

Accounting for the crowding effects inside a living cell is crucial to obtain a comprehensive view of the biomolecular processes and designing responsive polymer-based materials for biomedical applications. These effects have long been synonymous with the entropic volume exclusion effects. The role of soft, attractive intermolecular interactions remains elusive. Here, we investigate the effects of model cationic and anionic hydrophobic molecular crowders on the collapse equilibrium of uncharged model polymers using molecular dynamics simulations. Particularly, the effect of polymer architecture is explored where a 50-bead linear polymer model (Poly-I) and a branched polymer model (Poly-II) with nonpolar side chains are examined. The collapse of Poly-I is found to be highly favorable than in Poly-II in neat water. Addition of anionic crowders strengthens hydrophobic collapse in Poly-I, whereas collapse of Poly-II is only slightly favored over that in neat water. The thermodynamic driving forces are quite distinct in water. Collapse of Poly-I is driven by the favorable polymer-solvent entropy change (due to loss of waters to bulk on collapse), whereas collapse of Poly-II is driven by the favorable polymer-solvent energy change (due to favorable intrapolymer energy). The anionic crowders support the entropic mechanism for Poly-I by acting like surfactants, redirecting water dipoles toward themselves, and preferentially adsorbing on the Poly-I surface. In the case of Poly-II, the anionic crowders are loosely bound to polymer side chains, and loss of crowders and waters to the bulk on polymer collapse reduces the entropic penalty, thereby making collapse free energy slightly more favorable than in neat water. The results indicate the discriminating behavior of anionic crowders to strengthen the hydrophobic collapse. It is related to the structuring of water molecules around the termini and the central region of the two polymers. The results address the modulation of hydrophobic hydration by weakly hydrated ionic hydrophobes at crowded concentrations.

Polyethylene Glycol Impacts Conformation and Dynamics of Escherichia coli Prolyl-tRNA Synthetase Via Crowding and Confinement Effects

Polyethylene glycol (PEG) is a flexible, nontoxic polymer commonly used in biological and medical research, and it is generally regarded as biologically inert. PEG molecules of variable sizes are also used as crowding agents to mimic intracellular environments. A recent study with PEG crowders revealed decreased catalytic activity of Escherichia coli prolyl-tRNA synthetase (Ec ProRS), where the smaller molecular weight PEGs had the maximum impact. The molecular mechanism of the crowding effects of PEGs is not clearly understood. PEG may impact protein conformation and dynamics, thus its function. In the present study, the effects of PEG molecules of various molecular weights and concentrations on the conformation and dynamics of Ec ProRS were investigated using a combined experimental and computational approach including intrinsic tryptophan fluorescence spectroscopy, atomic force microscopy, and atomistic molecular dynamic simulations. Results of the present study suggest that lower molecular weight PEGs in the dilute regime have modest effects on the conformational dynamics of Ec ProRS but impact the catalytic function primarily via the excluded volume effect; they form large clusters blocking the active site pocket. In contrast, the larger molecular weight PEGs in dilute to semidilute regimes have a significant impact on the protein's conformational dynamics; they wrap on the protein surface through noncovalent interactions. Thus, lower-molecular-weight PEG molecules impact protein dynamics and function via crowding effects, whereas larger PEGs induce confinement effects. These results have implications for the development of inhibitors for protein targets in a crowded cellular environment.

Co-Solutes Induced Changes in the Properties of Polymeric Solution and Water Dynamics

In this paper we are addressing the co-solute-induced changes in the properties of an aqueous solution of a block copolymer. Due to the preferential interaction of different co-solute with different regions of the block copolymer, the changes were observed in both the physical properties and water dynamics. The modulation of both the physical properties and water dynamics was monitored using different spectroscopic techniques. Different co-solutes affect micellar properties of copolymer to a different extent signifying their interactions with different regions within the copolymer. The solvent relaxation dynamics were also modulated with the additions of different co-solutes. The change in free-energy (ΔGbf) and rate constant for bound to free water interconversion (kbf) in a copolymeric micelle was calculated which gets affected by the addition of co-solutes. The calculated kbf suggests that betaine, sarcosine, TMAO, and GnHCl favor the ordering of water molecules around the micelle and are excluded from the micellar surface whereas, urea favors the formation of free-water molecules rather than the structurally ordered bound water molecules around the micelle by accumulating at the micellar surface. Among the added methylamines trimethylamine N-oxide affected the water dynamics and its kinetics most profoundly. The protective property of GnHCl was revealed.

Macromolecular Crowding Effect on Chitosan-Hyaluronic Acid Complexation and the Activity of Encapsulated Catalase

The associative phase separation of charged biomacromolecules plays a key role in many biophysical events that take place in crowded intracellular environments. Such natural polyelectrolyte complexation and phase separation often occur at nonstoichiometric charge ratios with the incorporation of bioactive proteins, which is not studied as extensively as those complexations at stoichiometric ratios. In this work, we investigated how the addition of a crowding agent (polyethylene glycol, PEG) affected the complexation between chitosan (CS) and hyaluronic acid (HA), especially at nonstoichiometric ratios, and the encapsulation of enzyme (catalase, CAT) by the colloidal complexes. The crowded environment promoted colloidal phase separation at low charge ratios, forming complexes with increased colloidal and dissolution stability, which resulted in a smaller size and polydispersity (PDI). The binding isotherms revealed that the addition of PEG greatly enhanced the ion-pairing strength (with increased ion-pairing equilibrium constant Ka from 4.92 × 104 without PEG to 1.08 × 106 with 200 g/L PEG) and switched the coacervation from endothermic to exothermic, which explained the promoted complexation and phase separation. At the stoichiometric charge ratio, the enhanced CS-HA interaction in crowded media generated a more solid-like coacervate phase with a denser network, slower chain relaxation, and higher modulus. Moreover, both crowding and complex encapsulation enhanced the activity and catalytic efficiency of CAT, represented by a 2-fold increase in catalytic efficiency (Kcat/Km) under 100 g/L PEG crowding and CS-HA complex encapsulation. This is likely due to the lower polarity in the microenvironment surrounding the enzyme molecules. By a systematic investigation of both nonstoichiometric and stoichiometric charge ratios under macromolecular crowding, this work provided new insights into the complexation between natural polyelectrolytes in a scenario closer to an intracellular environment.

Deeper Insights into Mixed Crowding through Enzyme Activity, Dynamics, and Crowder Diffusion

Given the fact that the cellular interior is crowded by many different kinds of macromolecules, it is important that in vitro studies be carried out in the presence of mixed crowder systems. In this regard, we have used binary crowders formed by the combination of some of the commonly used crowding agents, namely, Ficoll 70, Dextran 70, Dextran 40, and PEG 8000 (PEG 8), to study how these affect enzyme activity, dynamics, and crowder diffusion. The enzyme chosen is AK3L1, an isoform of adenylate kinase. To investigate its dynamics, we have carried out three single point mutations (A74C, A132C, and A209C) with the cysteine residues being labeled with a coumarin-based solvatochromic probe [CPM: (7-diethylamino-3-(4-maleimido-phenyl)-4-methylcoumarin)]. Both enzyme activity and dynamics decreased in the binary mixtures as compared with the sum of the individual crowders, suggesting a reduction in excluded volume (in the mixture). To gain deeper insights into the binary mixtures, fluorescence correlation spectroscopy studies were carried out using fluorescein isothiocyanate-labeled Dextran 70 and tetramethylrhodamine-labeled AK3L1 as the diffusion probes. Diffusion in binary mixtures was observed to be much more constrained (relative to the sum of the individual crowders) for the labeled enzyme as compared to the labeled crowder showing different environments being faced by the two species. This was further confirmed during imaging of the phase-separated droplets formed in the binary mixtures having PEG as one of the crowding agents. The interior of these droplets was found to be rich in crowders and densely packed, as shown by confocal and digital holographic microscopy images, with the enzymes predominantly residing outside these droplets, that is, in the relatively less crowded regions. Taken together, our data provide important insights into various aspects of the simplest form of mixed crowding, that is, composed of just two components, and also hint at the enhanced complexity that the cellular interior presents toward having a detailed and comprehensive understanding of the same.

Depletion-Induced Self-Assembly of Colloidal Particles on a Solid Substrate

We investigate the depletion contributions to the self-assembly of microcolloids on solid substrates. The assembly is driven by the exclusion of nanoparticles and nonadsorbing polymers from the depletion zone between the microcolloids in the liquid and the underlying substrate. The model system consists of 1 μm polystyrene particles that we deposit on a flat glass slab in an electrolyte solution. Using polystyrene nanoparticles and poly(acrylic acid) polymers as depleting agents, we demonstrate in our experiments that nanoparticle concentrations of 0.5% (w/v) support well-ordered packing of microcolloids on glass, while the presence of polymers leads to irregular aggregate deposition structures. A mixture of nanoparticles and polymers enhances the formation of colloidal aggregate and particulate surface coverage compared to using the polymers alone as a depletion agent. Moreover, tuning the polymer ionization state from pH 4 to 9 modifies the polymer conformational state and radius of gyration, which in turn alters the microcolloid deposition from compact multilayers to flocculated structures. Our study provides entropic strategies for manipulating particulate assembly on substrates from dispersed to continuous coatings.

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.

Thermal properties of glycinin in crowded environments

Crowded environments, commonly found in the food system, are utilized to enhance the properties of soybean proteins. Despite their widespread application, little information exists regarding the impact of crowded environments on the denaturation behaviors of soybean proteins. In this study, we investigated how crowding agents with varying molecular weights, functional groups, and topology affect the denaturation behavior of glycinin under crowded conditions. The results reveal that thermal stability in PEG crowded environments is mainly influenced by both preferential hydration and binding. The stabilization is primarily enthalpy-driven, with aggregation contributing additional entropic stabilization. Specifically, ethylene glycol and diethylene glycol exhibit temperature-dependent, bilateral effects on glycinin stability. At the denaturation temperature, hydrophobic interactions play a predominant role, decreasing glycinin's thermal stability. However, at a molecular weight of 200 g/mol, there is a delicate balance between destabilizing and stabilizing effects, leading to no significant change in thermal stability. With the addition of PEG 400, 1000, and 2000, besides preferential hydration, additional hard-core repulsions between glycinin molecules enhance thermal stability. Methylation modification experiments demonstrated that 2-methoxyethyl ether exerted a more pronounced denaturing effect. Additionally, the cyclization of PEG 1000 decreased its stabilizing effect.

Bridging Soft Interaction and Excluded Volume in Crowded Milieu through Subtle Protein Dynamics

The impact of macromolecular crowding on biological macromolecules has been elucidated through the excluded volume phenomenon and soft interactions. However, it has often been difficult to provide a clear demarcation between the two regions. Here, using temperature-dependent dynamics (local and global) of the multidomain protein human serum albumin (HSA) in the presence of commonly used synthetic crowders (Dextran 40, PEG 8, Ficoll 70, and Dextran 70), we have shown the presence of a transition that serves as a bridge between the soft and hard regimes. The bridging region is independent of the crowder identity and displays no apparent correlation with the critical overlap concentration of the polymeric crowding agents. Moreover, the dynamics of domains I and II and the protein gating motion respond differently, thereby bringing to the fore the asymmetry underlying the crowder influence on HSA. In addition, solvent-coupled and decoupled protein motions indicate the heterogeneity of the dynamic landscape in the crowded milieu. We also propose an intriguing correlation between protein stability and dynamics, with increased global stability being accompanied by eased local domain motion.

Differential local ordering of mixed crowders determines effective size and stability of ss-DNA capped gold nanoparticle

Understanding the influence of a crowded intracellular environment on the structure and solvation of DNA functionalized gold nanoparticles (ss-DNA AuNP) is necessary for designing applications in nanomedicine. In this study, the effect of single (Gly, Ser, Lys) and mixture of amino acids (Gly+Ser, Gly+Lys, Ser+Lys) at crowded concentrations is examined on the structure of the ss-DNA AuNP using molecular dynamics simulations. Using the structural estimators such as pair correlation functions and ligand shell positional fluctuations, the solvation entropy is estimated. Combining the AuNP-solvent interaction energy with the solvation entropy estimates, the free energy of solvation of the AuNP in crowded solutions is computed. The solvation entropy favours the solvation free energy which becomes more favourable for larger effective size of AuNP in crowded solutions relative to that in water. The effective size of AuNP depends on the different propensity of the crowders to adsorb on Au surface, with the smallest crowder (Gly) having the highest propensity inducing the least effective AuNP size as compared to other single crowder solutions. In mixed crowded solutions of amino acids of variable size and chemistry, distinctive local adsorption of the crowders on the gold surface is observed that controls the additive or non-additive crowding effects which govern an increase (in Gly+Ser) or decrease (in Gly+Lys) in nanoparticle effective size respectively. The results shed light into the fundamental understanding of the influence of intracellular crowding on structure of ss-DNA AuNP and plausible employability of crowding as a tool to design programmable self-assembly of functionalized nanoparticles.

Macromolecular Crowding and DNA: Bridging the Gap between In Vitro and In Vivo

The cellular environment is highly crowded, with up to 40% of the volume fraction of the cell occupied by various macromolecules. Most laboratory experiments take place in dilute buffer solutions; by adding various synthetic or organic macromolecules, researchers have begun to bridge the gap between in vitro and in vivo measurements. This is a review of the reported effects of macromolecular crowding on the compaction and extension of DNA, the effect of macromolecular crowding on DNA kinetics, and protein-DNA interactions. Theoretical models related to macromolecular crowding and DNA are briefly reviewed. Gaps in the literature, including the use of biologically relevant crowders, simultaneous use of multi-sized crowders, empirical connections between macromolecular crowding and liquid-liquid phase separation of nucleic materials are discussed.

How it feels in a cell

Life emerges from thousands of biochemical processes occurring within a shared intracellular environment. We have gained deep insights from in vitro reconstitution of isolated biochemical reactions. However, the reaction medium in test tubes is typically simple and diluted. The cell interior is far more complex: macromolecules occupy more than a third of the space, and energy-consuming processes agitate the cell interior. Here, we review how this crowded, active environment impacts the motion and assembly of macromolecules, with an emphasis on mesoscale particles (10-1000 nm diameter). We describe methods to probe and analyze the biophysical properties of cells and highlight how changes in these properties can impact physiology and signaling, and potentially contribute to aging, and diseases, including cancer and neurodegeneration.

Not Always Sticky: Specificity of Protein Stabilization by Sugars Is Conferred by Protein-Water Hydrogen Bonds

Solutes added to buffered solutions directly impact protein folding. Protein stabilization by cosolutes or crowders has been shown to be largely driven by protein-cosolute volume exclusion complemented by chemical and soft interactions. By contrast to previous studies that indicate the invariably destabilizing role of soft protein-sugar attractions, we show here that soft interactions with sugar cosolutes are protein-specific and can be stabilizing or destabilizing. We experimentally follow the folding of two model miniproteins that are only marginally stable but in the presence of sugars and polyols fold into representative and distinct secondary structures: β-hairpin or α-helix. Our mean-field model reveals that while protein-sugar excluded volume interactions have a similar stabilizing effect on both proteins, the soft interactions add a destabilizing contribution to one miniprotein but further stabilize the other. Using molecular dynamics simulations, we link the soft protein-cosolute interactions to the weakening of direct protein-water hydrogen bonding due to the presence of sugars. Although these weakened hydrogen bonds destabilize both the native and denatured states of the two proteins, the resulting contribution to the folding free energy can be positive or negative depending on the amino acid sequence. This study indicates that the significant variation between proteins in their soft interactions with sugar determines the specific response of different proteins, even to the same sugar.

Molecular Crowders Can Induce Collapse in Hydrophilic Polymers via Soft Attractive Interactions

A comprehensive understanding of protein folding and biomolecular self-assembly in the intracellular environment requires obtaining a microscopic view of the crowding effects. The classical view of crowding explains biomolecular collapse in such an environment in terms of the entropic solvent excluded volume effects subjected to hard-core repulsions exerted by the inert crowders, neglecting their soft chemical interactions. In this study, the effects of nonspecific, soft interactions of molecular crowders in regulating the conformational equilibrium of hydrophilic (charged) polymers are examined. Using advanced molecular dynamics simulations, collapse free energies of an uncharged, a negatively charged, and a charge-neutral 32-mer generic polymer are computed. The strength of the polymer-crowder dispersion energy is modulated to examine its effect on polymer collapse. The results show that the crowders preferentially adsorb and drive the collapse of all three polymers. The uncharged polymer collapse is opposed by the change in solute-solvent interaction energy but is overcompensated by the favorable change in the solute-solvent entropy as observed in hydrophobic collapse. However, the negatively charged polymer collapses with a favorable change in solute-solvent interaction energy due to reduction in the dehydration energy penalty as the crowders partition to the polymer interface and shield the charged beads. The collapse of a charge-neutral polymer is opposed by the solute-solvent interaction energy but is overcompensated by the solute-solvent entropy change. However, for the strongly interacting crowders, the overall energetic penalty decreases since the crowders interact with polymer beads via cohesive bridging attractions to induce polymer collapse. These bridging attractions are found to be sensitive to the binding sites of the polymer, since they are absent in the negatively charged or uncharged polymers. These interesting differences in thermodynamic driving forces highlight the crucial role of the chemical nature of the macromolecule as well as of the crowder in determining the conformational equilibria in a crowded milieu. The results emphasize that the chemical interactions of the crowders should be explicitly considered to account for the crowding effects. The findings have implications in understanding the crowding effects on the protein free energy landscapes.

The conformational phase diagram of neutral polymers in the presence of attractive crowders

Extensive coarse-grained molecular dynamics simulations are performed to investigate the conformational phase diagram of a neutral polymer in the presence of attractive crowders. We show that, for low crowder densities, the polymer predominantly shows three phases as a function of both intra-polymer and polymer-crowder interactions: (1) weak intra-polymer and weak polymer-crowder attractive interactions induce extended or coil polymer conformations (phase E), (2) strong intra-polymer and relatively weak polymer-crowder attractive interactions induce collapsed or globular conformations (phase CI), and (3) strong polymer-crowder attractive interactions, regardless of intra-polymer interactions, induce a second collapsed or globular conformation that encloses bridging crowders (phase CB). The detailed phase diagram is obtained by determining the phase boundaries delineating the different phases based on an analysis of the radius of gyration as well as bridging crowders. The dependence of the phase diagram on strength of crowder-crowder attractive interactions and crowder density is clarified. We also show that when the crowder density is increased, a third collapsed phase of the polymer emerges for weak intra-polymer attractive interactions. This crowder density-induced compaction is shown to be enhanced by stronger crowder-crowder attraction and is different from the depletion-induced collapse mechanism, which is primarily driven by repulsive interactions. We also provide a unified explanation of the observed re-entrant swollen/extended conformations of the earlier simulations of weak and strongly self-interacting polymers in terms of crowder-crowder attractive interactions.

Resolving the enthalpy of protein stabilization by macromolecular crowding

Proteins in the cellular milieu reside in environments crowded by macromolecules and other solutes. Although crowding can significantly impact the protein folded state stability, most experiments are conducted in dilute buffered solutions. To resolve the effect of crowding on protein stability, we use 19 F nuclear magnetic resonance spectroscopy to follow the reversible, two-state unfolding thermodynamics of the N-terminal Src homology 3 domain of the Drosophila signal transduction protein drk in the presence of polyethylene glycols (PEGs) of various molecular weights and concentrations. Contrary to most current theories of crowding that emphasize steric protein-crowder interactions as the main driving force for entropically favored stabilization, our experiments show that PEG stabilization is accompanied by significant heat release, and entropy disfavors folding. Using our newly developed model, we find that stabilization by ethylene glycol and small PEGs is driven by favorable binding to the folded state. In contrast, for larger PEGs, chemical or soft PEG-protein interactions do not play a significant role. Instead, folding is favored by excluded volume PEG-protein interactions and an exothermic nonideal mixing contribution from release of confined PEG and water upon folding. Our results indicate that crowding acts through molecular interactions subtler than previously assumed and that interactions between solution components with both the folded and unfolded states must be carefully considered.

Effect of tubulin self-association on GTP hydrolysis and nucleotide exchange reactions

We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. Both reactions are relevant for microtubule (MT) dynamics. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied by determining the concentrations of tubulin-free and tubulin-bound GTP and GDP. We observed no GTP hydrolysis below the critical conditions for MT assembly (either below the critical tubulin concentration and/or at low temperature), despite the assembly of tubulin 1D curved oligomers and single-rings, showing that their assembly did not involve GTP hydrolysis. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Cryo-TEM images showed that GTP-tubulin 1D oligomers were curved also at 36 °C. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to determine the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites. This conclusion may have implications on the dynamics at the tip of the MT plus end.

Crowded Environment Regulates the Coacervation of Biopolymers via Nonspecific Interactions

The membrane-less organelles (MLOs) with subcompartments are formed via liquid-liquid phase separation (LLPS) in the crowded cell interior whose background molecules are up to 400 mg/mL. It is still a puzzle how the background molecules regulate the formation, dynamics, and functions of MLOs. Using biphasic coacervate droplets formed by poly(l-lysine) (PLL), quaternized dextran (Q-dextran), and single-stranded oligonucleotides (ss-oligo) as a model of MLO, we online monitored the LLPS process in Bovine Serine Albumin (BSA) solution up to 200.0 mg/mL. Negatively charged BSA is able to form complex or coacervate with positively charged PLL and Q-dextran and thus participates in the LLPS via nonspecific interactions. Results show that BSA effectively regulates the LLPS by controlling the phase distribution, morphologies, and kinetics. With increasing BSA concentration, the spherical biphasic droplets evolve in sequence into phase-inverted flower-like structure, worm-like chains, network structures, and confined coacervates. Each kind of morphology is formed via its own specific growth and fusion pathway. Our work suggests that MLOs could be controlled solely by the crowded environment and provides a further step toward understanding the life process in cell.

Revitalizing an important field in biophysics: The new frontiers of molecular crowding

Taking into account the presence of the crowded environment of a macromolecule has been an important goal of biology over the past 20 years. Molecular crowding affects the motions, stability and the kinetic behaviour of proteins. New powerful approaches have recently been developed to study molecular crowding, some of which make use of the synchrotron radiation light. The meeting "New Frontiers in Molecular Crowding" was organized in July 2022at the European Synchrotron Radiation facility of Grenoble to discuss the new frontiers of molecular crowding. The workshop brought together researchers from different disciplines to highlight the new developments of the field, including areas where new techniques allow the scientists to gain unprecedently expected information. A key conclusion of the meeting was the need to build an international and interdisciplinary research community through enhanced communication, resource-sharing, and educational initiatives that could let the molecular crowding field flourish further.

Crowder-directed interactions and conformational dynamics in multistimuli-responsive intrinsically disordered protein

The consequences of crowding on the dynamic conformational ensembles of intrinsically disordered proteins (IDPs) remain unresolved because of their ultrafast motion. Here, we report crowder-induced interactions and conformational dynamics of a prototypical multistimuli-responsive IDP, Rec1-resilin. The effects of a range of crowders of varying sizes, forms, topologies, and concentrations were examined using spectroscopic, spectrofluorimetric, and contrast-matching small- and ultrasmall-angle neutron scattering investigation. To achieve sufficient neutron contrast against the crowders, deuterium-labeled Rec1-resilin was biosynthesized successfully. Moreover, the ab initio "shape reconstruction" approach was used to obtain three-dimensional models of the conformational assemblies. The IDP revealed crowder-specific systematic extension and compaction with the level of macromolecular crowding. Last, a robust extension-contraction model has been postulated to capture the fundamental phenomena governing the observed behavior of IDPs. The study provides insights and fresh perspectives for understanding the interactions and structural dynamics of IDPs in crowded states.

Crowding-Induced Spatial Organization of Gene Expression in Cell-Sized Vesicles

Cell-free protein synthesis is an important tool for studying gene expression and harnessing it for applications. In cells, gene expression is regulated in part by the spatial organization of transcription and translation. Unfortunately, current cell-free approaches are unable to control the organization of molecular components needed for gene expression, which limits the ability to probe and utilize its effects. Here, we show, using complementary computational and experimental approaches, that macromolecular crowding can be used to control the spatial organization and translational efficiency of gene expression in cell-sized vesicles. Computer simulations and imaging experiments reveal that, as crowding is increased, DNA plasmids become localized at the inner surface of vesicles. Ribosomes, in contrast, remain uniformly distributed, demonstrating that crowding can be used to differentially organize components of gene expression. We further carried out cell-free protein synthesis reactions in cell-sized vesicles and quantified mRNA and protein abundance. At sufficiently high levels of crowding, we observed localization of mRNA near vesicle surfaces, a decrease in translational efficiency and protein abundance, and anomalous scaling of protein abundance as a function of vesicle size. These results are consistent with high levels of crowding causing altered spatial organization and slower diffusion. Our work demonstrates a straightforward way to control the organization of gene expression in cell-sized vesicles and provides insight into the spatial regulation of gene expression in cells.

Measuring Structural Changes in Cytochrome c under Crowded Conditions Using In Vitro and In Silico Approaches

It is known from in vitro studies that macromolecular crowding in the cell effects protein structure, stability and function; but predictive studies are relatively unexplored. There are few reports where the effect of various crowder mixtures has been exploited to discern their combined effect on the structural stability of proteins. These studies are more significant because their effect can mimicked with in vivo conditions, where the environment is heterogeneous. Effects of two crowders, polyethylene glycol (PEG 400 Da), and its monomer ethylene glycol (EG) alone and in mixture on the structural stability of cytochrome c (cyt c) were determined using various spectroscopic and bioinformatics tools. The main conclusions of our study are (i) the monomer EG has a kosmotropic effect on the protein (stabilizes the protein), and has no significant effect on the tertiary structure; (ii) PEG 400 destabilizes the structure as well as the stability of the protein; and (iii) EG counteracts the destabilizing effect of PEG 400. From this investigation, it seems evident that proteins may fold or unfold in the crowded environment of the cell where various interactions assist them to maintain their structure for their functions. Bioinformatics approaches were also used to support all of the in vitro observations. Cyt c is functional protein; if the structure of the protein is modulated due to change in the environment its nature of function will also change. Our research addresses the question by modulating the environment around the protein, and the macromolecule (protein) conformation dynamics and interaction study via in vitro and in silico approaches which indirectly compares with that of the environment in-cellular milieu, which is highly crowded.

Analysis of the effect of 1-Allyl-3-Methylimidazolium chloride on thermodynamic stability, folding kinetics, and motional dynamics of horse cytochrome c

1-allyl-3-methylimidazolium chloride (AMIMCl) acts as a potential green solvent for proteins. The present work provides a possible pathway by which the structural, kinetic, thermodynamic, and folding properties of horse cytochrome c (cyt c) are affected in green aqueous-AMIMCl systems. Analysis of the effect of AMIMCl on thermodynamic stability, refolding/unfolding kinetics, and motional dynamics of cyt c provided important information, (i) AMIMCl decreases the thermodynamic stability of reduced cyt c and also strengthens the guanidinium chloride (GdmCl)-mediated decrease in thermodynamic stability of protein, (ii) AMIMCl reduces the thermal-fluctuation of Met80-containing omega-loop of natively-folded compact state of carbonmonoxycytochrome c (MCO-state) due to polyfunctional interactions between the AMIM⁺ and different groups of protein, (iii) AMIMCl shifts the kinetic chevron plot, ln k_obs[GdmCl] to the lower concentration of GdmCl, (iv) AMIMCl shifts the refolding and unfolding limps to vertically downwards and upwards, respectively, and (v) AMIMCl reducing the unfolding free energy estimated by both thermodynamic and kinetic analysis.

Programmable Multimodal Optothermal Manipulation of Synthetic Particles and Biological Cells

Optical manipulation of tiny objects has benefited many research areas ranging from physics to biology to micro/nanorobotics. However, limited manipulation modes, intense lasers with complex optics, and applicability to limited materials and geometries of objects restrict the broader uses of conventional optical tweezers. Herein, we develop an optothermal platform that enables the versatile manipulation of synthetic micro/nanoparticles and live cells using an ultralow-power laser beam and a simple optical setup. Five working modes (i.e., printing, tweezing, rotating, rolling, and shooting) have been achieved and can be switched on demand through computer programming. By incorporating a feedback control system into the platform, we realize programmable multimodal control of micro/nanoparticles, enabling autonomous micro/nanorobots in complex environments. Moreover, we demonstrate in situ three-dimensional single-cell surface characterizations through the multimodal optothermal manipulation of live cells. This programmable multimodal optothermal platform will contribute to diverse fundamental studies and applications in cellular biology, nanotechnology, robotics, and photonics.

Mechanism of Osmolyte Stabilization-Destabilization of Proteins: Experimental Evidence

In this work, we investigated the influence of stabilizing (N,N,N-trimethylglycine) and destabilizing (urea) osmolytes on the hydration spheres of biomacromolecules in folded forms (trpzip-1 peptide and hen egg white lysozyme—hewl) and unfolded protein models (glycine—GLY and N-methylglycine—NMG) by means of infrared spectroscopy. GLY and NMG were clearly limited as minimal models for unfolded proteins and should be treated with caution. We isolated the spectral share of water changed simultaneously by the biomacromolecule/model molecule and the osmolyte, which allowed us to provide unambiguous experimental arguments for the mechanism of stabilization/destabilization of proteins by osmolytes. In the case of both types of osmolytes, the decisive factor determining the equilibrium folded/unfolded state of protein was the enthalpy effect exerted on the hydration spheres of proteins in both forms. In the case of stabilizing osmolytes, enthalpy was also favored by entropy, as the unfolded state of a protein was more entropically destabilized than the folded state.

Camel back shaped Kirkwood-Buff Integrals

Some binary mixtures, such as specific alcohol-alkane mixtures, or even water-tbutanol, exhibit two humps "camel back" shaped KBI. This is in sharp contrast with usual KBI of binary mixtures having a single extremum. This extremum is interpreted as the region of maximum concentration fluctuations, and usually occurs in binary mixtures presenting appreciable micro-segregation, and corresponds to where the mixture exhibit a percolation of the two species domains. In this paper, it is shown that two extrema occur in binary mixtures when one species forms "meta-particle" aggregates, the latter which act as a meta-species, and have their own concentration fluctuations, hence their own KBI extremum. This "meta-extremum" occurs at low concentration of the aggregate-forming species (such as alcohol in alkane), and is independant of the other usual extremum observed at mid volume fraction occupancy. These systems are a good illustration of the concept of the duality between concentration fluctuations and micro-segregation.

Reentrant transitions in a mixture of small and big particles interacting via soft repulsive potential

We report an observation of a temperature-controlled reentrant transition in simulations of mixtures of small and big particles interacting via a soft repulsive potential in two dimensions. As temperature increases, the system passes from a fluid mixture, to a crystal of big particles in a fluid of small particles, and back to a fluid mixture. Solidification is driven by entropy gain of small particles which overcomes the free-energy cost of confining big ones. Melting results from enhanced interpenetration of particles at high temperature which reduces the entropic forces that stabilize the crystal.

Macromolecular Crowding Is More than Hard-Core Repulsions

Cells are crowded, but proteins are almost always studied in dilute aqueous buffer. We review the experimental evidence that crowding affects the equilibrium thermodynamics of protein stability and protein association and discuss the theories employed to explain these observations. In doing so, we highlight differences between synthetic polymers and biologically relevant crowders. Theories based on hard-core interactions predict only crowding-induced entropic stabilization. However, experiment-based efforts conducted under physiologically relevant conditions show that crowding can destabilize proteins and their complexes. Furthermore, quantification of the temperature dependence of crowding effects produced by both large and small cosolutes, including osmolytes, sugars, synthetic polymers, and proteins, reveals enthalpic effects that stabilize or destabilize proteins. Crowding-induced destabilization and the enthalpic component point to the role of chemical interactions between and among the macromolecules, cosolutes, and water. We conclude with suggestions for future studies. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Cosolutes Modify Alkaline Phosphatase Catalysis through Osmotic Stress and Crowding Mechanisms

Examining the effects of different cosolutes on in vitro enzyme kinetics yielded glimpses into their potential behavior when functioning in their natural, complex, in vivo milieu. Viewing cosolute in vitro influences on a model enzyme, calf intestinal alkaline phosphatase, as a combination of competitive and uncompetitive behaviors provided quantitative insights into their effects on catalysis. Observed decreases in the apparent specificity constant, K _asp, caused by the presence of polyethylene glycols or betaine in the reaction solution, indicated interference with enzyme-substrate complex formation. This competitive inhibition appeared to be driven by osmotic stress. Dextran 6 K and sucrose strongly impeded the subsequent conversion of the bound substrate into a free product, which was marked by sharp reductions in V _max, uncompetitive inhibition. For the same step, smaller noncarbohydrate cosolutes, triethylene glycol, polyethylene glycol 400, and betaine, also behaved as uncompetitive inhibitors but to a lesser extent. However, polyethylene glycol 8000 and 20,000 were uncompetitive activators, increasing V _max. Polyethylene glycol of molecular weight 1000 displayed intermediate effects between these two groups of noncarbohydrate cosolutes. These results suggested that crowding has a strong influence on free product formation. The combination of competitive and uncompetitive effects and mixed behaviors, caused by the cosolutes on calf intestinal alkaline phosphatase kinetics, was consistent with the trends seen in similar enzyme-cosolute studies. It is proposed that the double-displacement mechanism of alkaline phosphatases, shared by many other enzymes, could be the root of this general observation.

Macromolecular crowding effects on electrostatic binding affinity: Fundamental insights from theoretical, idealized models

The crowded cellular environment can affect biomolecular binding energetics, with specific effects depending on the properties of the binding partners and the local environment. Often, crowding effects on binding are studied on particular complexes, which provide system-specific insights but may not provide comprehensive trends or a generalized framework to better understand how crowding affects energetics involved in molecular recognition. Here, we use theoretical, idealized molecules whose physical properties can be systematically varied along with samplings of crowder placements to understand how electrostatic binding energetics are altered through crowding and how these effects depend on the charge distribution, shape, and size of the binding partners or crowders. We focus on electrostatic binding energetics using a continuum electrostatic framework to understand effects due to depletion of a polar, aqueous solvent in a crowded environment. We find that crowding effects can depend predictably on a system's charge distribution, with coupling between the crowder size and the geometry of the partners' binding interface in determining crowder effects. We also explore the effect of crowder charge on binding interactions as a function of the monopoles of the system components. Finally, we find that modeling crowding via a lowered solvent dielectric constant cannot account for certain electrostatic crowding effects due to the finite size, shape, or placement of system components. This study, which comprehensively examines solvent depletion effects due to crowding, complements work focusing on other crowding aspects to help build a holistic understanding of environmental impacts on molecular recognition.

Polymer brush-induced depletion interactions and clustering of membrane proteins

We investigate the effect of mobile polymer brushes on proteins embedded in biological membranes by employing both Asakura-Oosawa type of theoretical model and coarse-grained molecular dynamics simulations. The brush polymer-induced depletion attraction between proteins changes non-monotonically with the size of brush. The depletion interaction, which is determined by the ratio of the protein size to the grafting distance between brush polymers, increases linearly with the brush size as long as the polymer brush height is shorter than the protein size. When the brush height exceeds the protein size, however, the depletion attraction among proteins is slightly reduced. We also explore the possibility of the brush polymer-induced assembly of a large protein cluster, which can be related to one of many molecular mechanisms underlying recent experimental observations of integrin nanocluster formation and signaling.

Using Microemulsions: Formulation Based on Knowledge of Their Mesostructure

Microemulsions, as thermodynamically stable mixtures of oil, water, and surfactant, are known and have been studied for more than 70 years. However, even today there are still quite a number of unclear aspects, and more recent research work has modified and extended our picture. This review gives a short overview of how the understanding of microemulsions has developed, the current view on their properties and structural features, and in particular, how they are related to applications. We also discuss more recent developments regarding nonclassical microemulsions such as surfactant-free (ultraflexible) microemulsions or ones containing uncommon solvents or amphiphiles (like antagonistic salts). These new findings challenge to some extent our previous understanding of microemulsions, which therefore has to be extended to look at the different types of microemulsions in a unified way. In particular, the flexibility of the amphiphilic film is the key property to classify different microemulsion types and their properties in this review. Such a classification of microemulsions requires a thorough determination of their structural properties, and therefore, the experimental methods to determine microemulsion structure and dynamics are reviewed briefly, with a particular emphasis on recent developments in the field of direct imaging by means of electron microscopy. Based on this classification of microemulsions, we then discuss their applications, where the application demands have to be met by the properties of the microemulsion, which in turn are controlled by the flexibility of their amphiphilic interface. Another frequently important aspect for applications is the control of the rheological properties. Normally, microemulsions are low viscous and therefore enhancing viscosity has to be achieved by either having high concentrations (often not wished for) or additives, which do not significantly interfere with the microemulsion. Accordingly, this review gives a comprehensive account of the properties of microemulsions, including most recent developments and bringing them together from a united viewpoint, with an emphasis on how this affects the way of formulating microemulsions for a given application with desired properties.

Effect of imidazolium based ionic liquids on CO-association dynamics and thermodynamic stability of Ferrocytochrome c

Analysis of kinetic and thermodynamic parameters measured for CO-association reaction of Ferrocytochrome c (Ferrocyt c) under variable concentrations of 1-butyl-3-methylimidazolium with varying anion ([Bmim]X) (X = Cl^-, I^-, Br^-, HSO₄^-) at pH 7 revealed that the low concentration of [Bmim]X (≤0.5 M) constrains the CO-association dynamics of Ferrocyt c and typically follows the order: [Bmim]HSO₄ > [Bmim]Cl > [Bmim]Br > [Bmim]I. At relatively higher concentrations (>0.5), the chaotropic action of [Bmim]⁺ dominates which consequently increases the thermal-fluctuations responsible to denature the protein and thus accelerates the speed of CO-association reaction. Analysis of thermal denaturation curves of Ferrocyt c measured at different concentrations of [Bmim]X revealed that the [Bmim]X decreases the thermodynamic stability of protein and typically follows the order: [Bmim]I > [Bmim]Br > [Bmim]Cl > [Bmim]CH₃COO > [Bmim]HSO₄, demonstrating that the effect of [Bmim]X on thermodynamic stability of protein is not in accordance to Hofmeister series effect of anions because instead of increasing the kosmotropic anion carrying [Bmim]X ([Bmim]CH₃COO and [Bmim]HSO₄) also decreases the thermodynamic stability of protein.

Investigating the Effects of Molecular Crowding on the Kinetics of Protein Aggregation

The thermodynamics and kinetics of protein folding and protein aggregation in vivo are of great importance in numerous scientific areas including fundamental biophysics research, nanotechnology, and medicine. However, these processes remain poorly understood in both in vivo and in vitro systems. Here we extend an established model for protein aggregation that is based on the kinetic equations for the moments of the polymer size distribution by introducing macromolecular crowding particles into the model using scaled-particle and transition-state theories. The model predicts that the presence of crowders can either speed up, cause no change to, or slow down the progress of the aggregation compared to crowder-free solutions, in striking agreement with experimental results from nine different amyloid-forming proteins that utilized dextran as the crowder. These different dynamic effects of macromolecular crowding can be understood in terms of the change of excluded volume associated with each reaction step.

Small crowder interactions can drive hydrophobic polymer collapse as well as unfolding

Biomolecules evolve and function in the intracellular crowded environment that is densely packed with macromolecules. Yet, a microscopic understanding of the effects of such an environment on the conformational preferences of biomolecules remains elusive. While prior investigations have attributed crowding effects mainly to the excluded volume (size) effects of the crowders, very little is known about the effects exerted due to their chemical interactions. In this study, crowding effects of tri-alanine peptides on the collapse equilibria of generic hydrophobic polymer are investigated using molecular dynamics simulations. The role of weak, non-specific, attractive polymer-crowder interactions in modulating the polymer collapse equilibria is examined. The results highlight that crowding effects can lead to polymer compaction as well as unfolding depending on the strength of polymer-crowder interaction energy. Strongly interacting crowders weaken hydrophobic collapse (or unfold the polymer) at high volume fractions and induce polymer collapse only under dilute conditions. Weakly interacting crowders induce polymer collapse at all crowder concentrations. Interestingly, the thermodynamic driving forces for polymer collapse are remarkably different in the two cases. Strongly and weakly interacting crowders induce collapse by preferential adsorption and preferential depletion respectively. The findings provide new insights into the possible effects of interplay of intermolecular interactions in a crowded environment. The results have implications in understanding the impact of crowding in altering free energy landscapes of proteins.

Interactions Under Crowding Milieu: Chemical-Induced Denaturation of Myoglobin is Determined by the Extent of Heme Dissociation on Interaction with Crowders

Generally, in vivo function and structural changes are studied by probing proteins in a dilute solution under in vitro conditions, which is believed to be mimicking proteins in intracellular milieu. Earlier, thermal-induced denaturation of myoglobin, in the milieu of crowder molecule showed destabilization of the metal protein. Destabilization of protein by thermal-induced denaturation involves a large extrapolation, so, the reliability is questionable. This led us to measure the effects of macromolecular crowding on its stability by chemical-induced denaturation of the protein using probes like circular dichroism and absorption spectroscopy in the presence of dextran 70 and ficoll 70 at various pHs (acidic: 6.0, almost neutral: 7.0 and basic: 8.0). Observations showed that the degree of destabilization of myoglobin was greater due to ficoll 70 as compared to that of dextran 70 so it can be understood that the nature of the crowder or the shape of the crowder has an important role towards the stability of proteins. Additionally, the degree of destabilization was observed as pH dependent, however the pH dependence is different for different crowders. Furthermore, isothermal titration calorimetry and molecular docking studies confirmed that both the crowders (ficoll and dextran) bind to heme moiety of myoglobin and a single binding site was observed for each.

Depletion force between disordered linear macromolecules

When two macromolecules come very near in a fluid, the surrounding molecules, having finite volume, are less likely to get in between. This leads to a pressure difference manifesting as an entropic attraction, called depletion force. Here we calculate the density profile of liquid molecules surrounding a disordered rigid macromolecules modeled as a random arrangement of hard spheres on a linear backbone. We analytically determine the position dependence of the depletion force between two such disordered molecules by calculating the free energy of the system. We then use molecular dynamics simulations to obtain the depletion force between stiff disordered polymers as well as flexible ones and compare the two against each other. We also show how the disorder averaging can be handled starting from the inhomogenous reference interaction site model equations.

A microfluidic study of synergic liquid–liquid extraction of rare earth elements

A membrane based liquid–liquid extraction microfluidic device coupled with X-ray fluorescence enables the first quantification of free energies of transfer dependence for a complex mixture of rare earth elements and iron using synergic extractants.

Weak Chemical Interactions That Drive Protein Evolution: Crowding, Sticking, and Quinary Structure in Folding and Function

In recent years, better instrumentation and greater computing power have enabled the imaging of elusive biomolecule dynamics in cells, driving many advances in understanding the chemical organization of biological systems. The focus of this Review is on interactions in the cell that affect both biomolecular stability and function and modulate them. The same protein or nucleic acid can behave differently depending on the time in the cell cycle, the location in a specific compartment, or the stresses acting on the cell. We describe in detail the crowding, sticking, and quinary structure in the cell and the current methods to quantify them both in vitro and in vivo. Finally, we discuss protein evolution in the cell in light of current biophysical evidence. We describe the factors that drive protein evolution and shape protein interaction networks. These interactions can significantly affect the free energy, ΔG, of marginally stable and low-population proteins and, due to epistasis, direct the evolutionary pathways in an organism. We finally conclude by providing an outlook on experiments to come and the possibility of collaborative evolutionary biology and biophysical efforts.