Entropic Mechanism Research Articles

Single-molecule evidence of Entropic Pulling by Hsp70 chaperones.

Hsp70 chaperones are central components of the cellular network that ensures the structural quality of proteins. Despite crucial roles in processes such as protein disaggregation and protein translocation into organelles, their physical mechanism of action has remained hotly debated. To the best of our knowledge, no experimental data has directly proven any of the modelsproposed to date (Power Stroke, Brownian Ratchet, or Entropic Pulling) due to a lack of suitable methods. Here, we use nanopores, a powerful single-molecule tool, to investigate the mechanism of Hsp70s. We demonstrate that Hsp70s extract trapped polypeptide substrates from the nanopore by generating strong forces (equivalent to 46 pN over distances of 1 nm), that rely on the size of Hsp70. The findings provide unambiguous evidence of the Entropic Pulling mechanism, thus solving a long-standing debate, and proposing a potentially universal principle governing diverse cellular processes. Additionally, these results highlight the utility of biological nanopores for protein studies.

Competing gauge fields and entropically driven spin liquid to spin liquid transition in non-Kramers pyrochlores.

Gauge theories are powerful theoretical physics tools that allow complex phenomena to be reduced to simple principles and are used in both high-energy and condensed matter physics. In the latter context, gauge theories are becoming increasingly popular for capturing the intricate spin correlations in spin liquids, exotic states of matter in which the dynamics of quantum spins never ceases, even at absolute zero temperature. We consider a spin system on a three-dimensional pyrochlore lattice where emergent gauge fields not only describe the spin liquid behavior at zero temperature but crucially determine the system's temperature evolution, with distinct gauge fields giving rise to different spin liquid phases in separate temperature regimes. Focusing first on classical spins, in an intermediate temperature regime, the system shows an unusual coexistence of emergent vector and tensor gauge fields where the former is known from classical spin ice systems while the latter has been associated with fractonic quasiparticles, a peculiar type of excitation with restricted mobility. Upon cooling, the system transitions into a low-temperature phase where an entropic selection mechanism depopulates the degrees of freedom associated with the tensor gauge field, rendering the system spin-ice-like. We further provide numerical evidence that in the corresponding quantum model, a spin liquid with coexisting vector and tensor gauge fields has a finite window of stability in the parameter space of spin interactions down to zero temperature. Finally, we discuss the relevance of our findings for non-Kramers magnetic pyrochlore materials.

RNA's Dynamic Conformational Selection and Entropic Allosteric Mechanism in Controlling Cascade Protein Binding Events.

In the TAR RNA of immunodeficiency viruses, an allosteric communication exists between a distant loop and a bulge. The bulge interacts with the TAT protein vital for transactivating viral RNA, while the loop interacts with cyclin-T1, contingent on TAT binding. Through extensive atomistic and free energy simulations, we investigate TAR-TAT binding in nonpathogenic bovine immunodeficiency virus (BIV) and pathogenic human immunodeficiency virus (HIV). Thermodynamic analysis reveals enthalpically driven binding in BIV and entropically favored binding in HIV. The broader global basin in HIV is attributed to binding-induced loop fluctuation, corroborated by nuclear magnetic resonance (NMR), indicating classical entropic allostery onset. While this loop fluctuation affects the TAT binding affinity, it generates a binding-competent conformation that aids subsequent effector (cyclin-T1) binding. This study underscores how two structurally similar apo-RNA scaffolds adopt distinct conformational selection mechanisms to drive enthalpic and entropic allostery, influencing protein affinity in the signaling cascade.

An entropic expansion mechanism modulates small-molecule recognition by alpha-synuclein.

Aberrant misfolding and progressive aggregation of the intrinsically disordered protein, alpha-synuclein, is associated with the etiology of several neurodegenerative diseases. However, the structurally heterogeneous ensemble of alpha-synuclein precludes the implementation of conventional structure-based drug discovery methods with small molecules targeted to interact with a well-defined binding pocket. Here, by harnessing powerful framework of Markov State Models on unprecedentedly long millisecond atomistic simulation trajectories of monomeric alpha-synuclein interacting with the small-molecule drug fasudil, we identify exhaustive sets of metastable binding-competent states of alpha-synuclein. Characterisation and comparison of the metastable states in the presence and absence of the small molecule in the system indicate that interaction with the small molecule facilitates the protein to explore both more compact and more extended conformational states hitherto undetectable in neat water, thereby broadening the structural repertoire via an ‘entropy expansion’ mechanism. These states exhibit diverse modes of interaction with the small molecule involving the entirety of the protein, albeit the predominant interactions lie in the negatively charged C-terminal region. Subsequent simulation of dimerization process shows that fasudil can retard the self-aggregation propensity of the alpha-synuclein via creating multiple distinct states using similar entropic-expansion mechanism. In particular, due to presence of small molecules, conformations featuring aggregation-resistant long-range interactions are populated that has an inhibitory effect on the early dimerisation propensity of alpha-synuclein. This demonstrated ability of small-molecule illustrates its ensemble-modulatory effect on IDPs that can be effectively utilised for therapeutic strategies probing aggregation-related diseases.

TMAO Destabilizes RNA Secondary Structure via Direct Hydrogen Bond Interactions.

Trimethylamine N-oxide (TMAO) is an osmolyte that accumulates in cells in response to osmotic stress. TMAO stabilizes proteins by the entropic stabilization mechanism, which pictures TMAO as a nanocrowder that predominantly destabilizes the unfolded state. However, the mechanism of action of TMAO on RNA is much less understood. Here, we use all-atom molecular dynamics simulations to investigate how TMAO interacts with a 12-nt RNA hairpin with a high melting temperature, and an 8-nt RNA hairpin, which has a relatively fluid native basin in the absence of TMAO. The use of the two hairpins with different free energy of stabilization allows us to probe the origin of the destabilization effect of TMAO on RNA molecules without the possibility of forming tertiary interactions. We generated multiple trajectories using all-atom molecular dynamics (MD) simulations in explicit water by employing AMBER and CHARMM force fields, both in the absence and presence of TMAO. We observed qualitatively similar RNA-TMAO interaction profiles from the simulations using the two force fields. TMAO hydrogen bond interactions are largely depleted around the paired RNA bases and ribose sugars. In contrast, we show that the oxygen atom in TMAO, the hydrogen bond acceptor, preferentially interacts with the hydrogen bond donors in the solvent exposed bases, such as those in the stem-loop and the destabilized base stacks in the unfolded state, especially in the marginally stable 8-nt RNA hairpin. The predicted destabilization mechanism through TMAO-RNA hydrogen bond interactions could be tested using two-dimensional IR spectroscopy. Since TMAO does not significantly interact with the hydroxyl group of the ribose sugars, we predict that similar results must also hold for DNA.

Observed steric crowding at modest coverage requires a particular membrane-binding scheme or a complementary mechanism

Membrane shape transitions, including fusion and fission, play an important role in many biological processes. It is therefore essential to understand mechanisms of “curvature generation,” the mathematical quantification of membrane shape. Among the different mechanisms is the effect of steric pressure between proteins crowded on a surface. At a higher curvature, there is more space for the crowders and less steric pressure. Currently, the physical model of curvature induction by crowding views the proteins as being bound to the surface as a whole rather than to the underlying lipids. Here, we split the previously understood model into two pieces: first, the reduction in steric pressure due to reduced collisions between proteins, and second, the increased area available to the protein that is independent of other crowders. The cases are distinguished by how the crowder is attached to the membrane. When a protein is attached to a specific lipid, as is the case in a typical crowding experiment, one should not model its lateral entropy; this has already been accounted for by the underlying lipid. The Carnahan-Starling pressure includes this lateral entropy. The revised theory predicts that a purely entropic crowding mechanism is inconsistent with observations of reshaping at the lower range of surface coverage, suggesting that an additional mechanism is at play.

Realize Emergent Gravity to Generic Situations

We clarify the problem in which occasions can gravitational force be regarded emergent from thermodynamics, by proposing an entropic mechanism that can extract the entropic gradient existing in spacetime, due to the variation of the Casini–Bekenstein bound in specific quasi-static processes with the heat flux delta Q into the whole casual wedge. We explicitly formulate the derivation of inertial force as the emergent gravitational attraction from the Entanglement First Law. We find the saturation of the bound along with the vanishing relative entropy corresponds to the variation of minimal surface. To covariant meaning, it is the Bousso bound. Besides, this understanding is connected to recent Pennington’s work on Black Hole Information Paradox, suggesting a Page-Curve function origins from removing attraction by the external heat bath. Our theory from entanglement now overcomes several criticism towards Verlinde’s original entropic force proposal, and is able to co-exist with Susskind’s Complexity Tendency. This entropic mechanism reproduces the Newton’s Second Law in Rindler space and the gravitational force (together with derivation of the Einstein equation) beyond the near-horizon region, and can be adapted into AdS/CFT and other generic situations.

Sourcing curvature modes with entropy perturbations in non-singular bouncing cosmologies

The observed temperature fluctuations in the cosmic microwave background can be traced back to primordial curvature modes that are sourced by adiabatic and/or entropic matter perturbations. In this paper, we explore the entropic mechanism in the context of non-singular bouncing cosmologies. We show that curvature modes are naturally generated during `graceful exit,' i.e., when the smoothing slow contraction phase ends and the universe enters the bounce stage. Here, the key role is played by the kinetic energy components that come to dominate the energy density and drive the evolution towards the cosmological bounce.

Entropic Inhibition: How the Activity of a AAA+ Machine Is Modulated by Its Substrate-Binding Domain.

ClpB is a tightly regulated AAA+ disaggregation machine. Each ClpB molecule is composed of a flexibly attached N-terminal domain (NTD), an essential middle domain (MD) that activates the machine by tilting, and two nucleotide-binding domains. The NTD is not well-characterized structurally and is commonly considered to serve as a dispensable substrate-binding domain. Here, we use single-molecule FRET spectroscopy to directly monitor the real-time dynamics of ClpB’s NTD and reveal its unexpected autoinhibitory function. We find that the NTD fluctuates on the microsecond time scale, and these dynamics result in steric hindrance that limits the conformational space of the MD to restrict its tilting. This leads to significantly inhibited ATPase and disaggregation activities of ClpB, an effect that is alleviated upon binding of a substrate protein or the cochaperone DnaK. This entropic inhibition mechanism, which is mediated by ultrafast motions of the NTD and is not dependent on any strong interactions, might be common in related ATP-dependent proteases and other multidomain proteins to ensure their fast and reversible activation.

Small-Molecule Targeted Aβ42 Aggregate Degradation: Negatively Charged Small Molecules Are More Promising than the Neutral Ones.

Heavy evidence has confirmed that Aβ42 oligomers are the most neurotoxic aggregates and play a critical role in the occurrence and development of Alzheimer's disease by causing functional neuron death, cognitive damage, and dementia. Disordered Aβ42 oligomers are challenging therapeutic targets, and no drug is currently in clinical use that modifies the properties of their monomeric states. Here, a negatively charged molecule (ER), rather than the neutral TS1 one, is identified by a molecular dynamics simulation method to be more capable of binding and sequestering the intrinsically disordered amyloid-β peptide Aβ42 in its soluble pentameric state as well as its monomeric components. Results reveal that the ERs interact with Aβ and inhibit the primary nucleation pathways in its aggregation process in entropic expansion mechanism for both Aβ42 and Aβ40 oligomers but with opposite characteristics of hydrophobic surface area (HSA). The interaction between Aβ42 oligomer and either charged ER or neutral TS1/TS0 characterizes decreased HSA, and the decrease in ER-involved case is highly visible, consistent with the observations from in silico and in vitro studies. By contrast, the presence of these inhibitors causes the HSA of Aβ40 oligomer to change undetectably and there is even a bit of increase in the histidine isomerized Aβ40 oligomer. The HSA distinction between Aβ42 and Aβ40 oligomer is possibly derived from the different effects of M35-inhibitor interaction, which is analogous to the effect of M35 oxidation. In comparison with the neutral TS1/TS0 inhibitors, ER is more prone to bind the residues located in the central (β1) and C-terminal (β2) regions of Aβ42 peptide, two key nucleation regions for Aβ intramolecular folding, intermolecular aggregation, and assembly. Notably, ER can strongly bind the charged residues, such as K16, K28, D23, to greatly disturb the potential stabilizer (e.g., salt-bridge, etc.) in metastable Aβ42 oligomers and protofibrils. These results illustrate the strategy of overcoming Alzheimer's disease from inhibiting its early stage Aβ aggregation with two kinds of small molecules to alter their behavior for therapeutic purposes and strongly recommend paying more attention to the engineering and development of negatively charged inhibitors, the long-term underappreciated ones, targeting the early stage Aβ aggregates.

Water-Mediated Interactions Determine Helix Formation of Peptides in Open Nanotubes.

Water-mediated interactions (WMIs) play diverse roles in molecular biology. They are particularly relevant in geometrically confined spaces such as the interior of the chaperonin, at the interface between ligands and their binding partners, and in the ribosome tunnel. Inspired in part by the geometry of the ribosome tunnel, we consider confinement effects on the stability of peptides. We describe results from replica exchange molecular dynamics simulations of a system containing a 23-alanine or 23-serine polypeptide confined to nonpolar and polar nanotubes in the gas phase and when open to a water reservoir. We quantify the effect of water in determining the preferred conformational states of these polypeptides by calculating the difference in the solvation free energy for the helix and coil states in the open nanotube in the two phases. Our simulations reveal several possibilities. We find that nanoscopic confinement preferentially stabilizes the helical state of polypeptides with hydrophobic side chains, which is explained by the entropic stabilization mechanism proposed on the basis of polymer physics. Polypeptide chains with hydrophilic side chains can adopt helical structures within nanotubes, but helix formation is sensitive to the nature of the nanotube due to WMIs. We elaborate on the potential implications of our findings to the stability of peptides in the ribosome tunnel.

Pluronic-coated nanoparticles for enhanced spatial distribution and increased softness of nanocomposite hydrogels

Several factors govern the improvement in the mechanical, thermal, and conductive properties, when a nanoscale filler is incorporated into a polymer matrix. These factors include the concentration, size of the filling, distribution, etc. In this research, we present how to improve the distribution of nanoparticles using nanoparticles stabilized with block copolymers of different molar masses. For this purpose, Pluronic L35 and Pluronic F68 copolymers were used to stabilize nanoparticles in order to improve their distribution in a hydrogel of poly(2-hydroxyethyl methacrylate) through an entropic mechanism of interfacial control. The nanoparticles were labelled with fluorescein, and using confocal fluorescence microscopy, it was quantitatively demonstrated that both stabilizers led to a more homogeneous distribution. The nanocomposite hydrogels presented interesting viscoelastic properties. While the hydrogels stabilized with Pluronic L35 did not present significant changes in the rheological properties (e.g. stiffness and shear thinning), the most significant rheological effects were observed for the hydrogels prepared with Pluronic F68-stabilized nanoparticles. These hydrogels exhibited a diminution in the shear complex modulus, viscosity, and critical shear rate to give rise to the shear-thinning region, which was attributed to the differences in the molar masses of the stabilizers and favoured slipping of polymer chains because of unfavourable wetting with the stabilizer coating.

Finite-size effects in exponential random graphs

Abstract In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density $p<0.5$ or as the single cluster at $p>0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N>N^{*}(p),$ the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

Molecular Mechanisms of Membrane Curvature Sensing by a Disordered Protein.

The ability of proteins to sense membrane curvature is essential for the initiation and assembly of curved membrane structures. Established mechanisms of curvature sensing rely on proteins with specific structural features. In contrast, it has recently been discovered that intrinsically disordered proteins, which lack a defined three-dimensional fold, can also be potent sensors of membrane curvature. How can an unstructured protein sense the structure of the membrane surface? Many disordered proteins that associate with membranes have two key physical features: a high degree of conformational entropy and a high net negative charge. Binding of such proteins to membrane surfaces results simultaneously in a decrease in conformational entropy and an increase in electrostatic repulsion by anionic lipids. Here we show that each of these effects gives rise to a distinct mechanism of curvature sensing. Specifically, as the curvature of the membrane increases, the steric hindrance between the disordered protein and membrane is reduced, leading to an increase in chain entropy. At the same time, increasing membrane curvature increases the average separation between anionic amino acids and lipids, creating an electrostatic preference for curved membranes. Using quantitative imaging of membrane vesicles, our results demonstrate that long disordered amino acid chains with low net charge sense curvature predominately through the entropic mechanism. In contrast, shorter, more highly charged amino acid chains rely largely on the electrostatic mechanism. These findings provide a roadmap for predicting and testing the curvature sensitivity of the large and diverse set of disordered proteins that function at cellular membranes.

The Physics of Entropic Pulling: A Novel Model for the Hsp70 Motor Mechanism.

Hsp70s use ATP to generate forces that disassemble protein complexes and aggregates, and that translocate proteins into organelles. Entropic pulling has been proposed as a novel mechanism, distinct from the more familiar power-stroke and Brownian ratchet models, for how Hsp70s generate these forces. Experimental evidence supports entropic pulling, but this model may not be well understood among scientists studying these systems. In this review we address persistent misconceptions regarding the dynamics of proteins in solution that contribute to this lack of understanding, and we clarify the basic physics of entropic pulling with some simple analogies. We hope that increased understanding of the entropic pulling mechanism will inform future efforts to characterize how Hsp70s function as motors, and how they coordinate with their regulatory cochaperones in mechanochemical cycles that transduce the energy of ATP hydrolysis into physical changes in their protein substrates.

Synergy between intrinsically disordered domains and structured proteins amplifies membrane curvature sensing

The ability of proteins to sense membrane curvature is essential to cellular function. All known sensing mechanisms rely on protein domains with specific structural features such as wedge-like amphipathic helices and crescent-shaped BAR domains. Yet many proteins that contain these domains also contain large intrinsically disordered regions. Here we report that disordered domains are themselves potent sensors of membrane curvature. Comparison of Monte Carlo simulations with in vitro and live-cell measurements demonstrates that the polymer-like behavior of disordered domains found in endocytic proteins drives them to partition preferentially to convex membrane surfaces, which place fewer geometric constraints on their conformational entropy. Further, proteins containing both structured curvature sensors and disordered regions are more than twice as curvature sensitive as their respective structured domains alone. These findings demonstrate an entropic mechanism of curvature sensing that is independent of protein structure and illustrate how structured and disordered domains can synergistically enhance curvature sensitivity.

Coupled Brownian motors

A set of coupled Brownian motors—resulting from a noise-induced phase transition generated through an entropic mechanism, and formerly studied in mean-field approximation—is numerically integrated by Heun’s method. The results add much insight to the mean-field ones, allowing interpretation of the underlying mechanisms. It turns out that the low-noise boundary of the ordered phase obtained in mean-field approximation lies near a region where the order parameter is negative. Hints of bistability and negative mobility around F = 0 are seen in two cases, and anomalous hysteresis is confirmed in one case.

Verlinde’s emergent gravity in an [formula omitted]-dimensional, non-additive Tsallis’ scenario

This paper brings together four distinct but very important physical notions: (1) Entropic force, (2) Entropy-along-a-curve, (3) Tsallis’ q-statistics, and (4) Emergent gravitation. We investigate the non additive, classical (Tsallis’) q-statistical mechanics of a phase-space curve in n dimensions (3 dimensions, in particular). We focus attention on an entropic force mechanism that yields a simple realization of it, being able to mimic interesting effects such as confinement, hard core, and asymptotic freedom, typical of high energy physics.

Structural disorder of plasmid-encoded proteins in Bacteria and Archaea

BackgroundIn the last decade and a half it has been firmly established that a large number of proteins do not adopt a well-defined (ordered) structure under physiological conditions. Such intrinsically disordered proteins (IDPs) and intrinsically disordered (protein) regions (IDRs) are involved in essential cell processes through two basic mechanisms: the entropic chain mechanism which is responsible for rapid fluctuations among many alternative conformations, and molecular recognition via short recognition elements that bind to other molecules. IDPs possess a high adaptive potential and there is special interest in investigating their involvement in organism evolution.ResultsWe analyzed 2554 Bacterial and 139 Archaeal proteomes, with a total of 8,455,194 proteins for disorder content and its implications for adaptation of organisms, using three disorder predictors and three measures. Along with other findings, we revealed that for all three predictors and all three measures (1) Bacteria exhibit significantly more disorder than Archaea; (2) plasmid-encoded proteins contain considerably more IDRs than proteins encoded on chromosomes (or whole genomes) in both prokaryote superkingdoms; (3) plasmid proteins are significantly more disordered than chromosomal proteins only in the group of proteins with no COG category assigned; (4) antitoxin proteins in comparison to other proteins, are the most disordered (almost double) in both Bacterial and Archaeal proteomes; (5) plasmidal proteins are more disordered than chromosomal proteins in Bacterial antitoxins and toxin-unclassified proteins, but have almost the same disorder content in toxin proteins.ConclusionOur results suggest that while disorder content depends on genome and proteome characteristics, it is more influenced by functional engagements than by gene location (on chromosome or plasmid).

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards–Wilkinson equation with non-conserved noise and the Mullins–Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This ‘renormalization’ of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.