Entropic Trapping Research Articles

Dark State Concentration Dependent Emission and Dynamics of CdSe Nanoplatelet Exciton-Polaritons.

The recent surge of interest in polaritons has prompted fundamental questions about the role of dark states in strong light-matter coupling phenomena. Here, we systematically vary the relative number of dark states by controlling the number of stacked CdSe nanoplatelets confined in a Fabry-Pérot cavity. We find the emission spectrum to change significantly with an increasing number of nanoplatelets, with a gradual shift of the dominant emission intensity from the lower polariton branch to a manifold of dark states. Through accompanying calculations based on a kinetic model, this shift is rationalized by an entropic trapping of excitations by the dark state manifold, while a weak dark state dispersion due to local disorder explains their nonzero emission. Our results point toward the relevance of the dark state concentration to the optical and dynamical properties of cavity-embedded quantum emitters with ramifications for Bose-Einstein condensate formation, polariton lasing, polariton-based quantum transduction schemes, and polariton chemistry.

Free energy simulations unravel luciferin-chirality dependence in firefly bioluminescence—A pKa-controlled asymmetric catalysis

Firefly bioluminescence contains a series of complicated chemical reactions starting from the enzymatic oxidation of D-luciferin (D-LH2) by luciferase (Luc). Why firefly bioluminescence uses D-LH2 not L-LH2 has never been clearly interpreted. We theoretically investigated the two steps where LH2-chirality takes effect: adenylation of LH2 to adenylluciferin (ALU) with the aid of ATP and Mg2+, and deprotonation of ALU. Free energy simulations showed that both D- and L-LH2 react with ATP via a reversible SN2 reaction. The co-factor Mg2+ decreases the activation energy by an entropic trap. The theoretical estimated pKa of D-ALU (4.5) and L-ALU (22.2) in Luc, indicating deprotonation at the chiral carbon effectively occurs for D-ALU but not L-ALU under the physiological pH. This pKa-controlled asymmetric catalysis was further analyzed via the substrate-residue interactions. This work unravels the LH2-chirality dependence in firefly BL for the first time, and provides another residue-regulation strategy for designing BL systems and other asymmetric catalysts.

Influence of intracrystalline diffusion constraints enhanced by channel fluctuation on zeolite catalyst performance in isomerization and aromatization

In the realm of zeolite catalysis, understanding the role of intracrystalline diffusion constraints is of paramount significance, especially in the context of isomerization and aromatization reactions. This study delves deep into the structure-performance relationships, shedding light on the profound impact of channel fluctuation on isomerization and aromatization performance. Through meticulous analysis, we scrutinized the intracrystalline diffusion constraints of olefin intermediates integral to these reactions. ZSM-5, ZSM-22, Beta, and ZSM-12 zeolites, while possessing similar crystallinity, Si/Al ratio, acidity, and diffusion path length, display distinct channel fluctuations. Insightful in situ infrared desorption experiments coupled with molecular dynamic simulations underscore that these channel fluctuations intensify the intracrystalline diffusion constraints of olefin intermediates via an entropic trapping effect. Consequently, the isomers selectivity in n-octane isomerization adopts the sequence of Pt/Al2O3-ZSM-5 < Pt/Al2O3-ZSM-22 < Pt/Al2O3-Beta < Pt/Al2O3-ZSM-12, inversely correlating with channel fluctuation. This arises from the acceleration of undesired β-scission of olefin intermediates by intracrystalline diffusion constraints accentuated by channel fluctuation, leading to cracking by-products. Contrarily, the aromatic selectivity in 1-octene aromatization mirrors the opposite trend: ZSM-5 > ZSM-22 > Beta > ZSM-12, directly associating with channel fluctuation. This owes to the augmented intracrystalline diffusion constraints fostering the cyclization and hydrogen transfer of olefin intermediates, culminating in aromatic products. This study presents an in-depth investigation into how the diffusion constraints related to channel fluctuation influence product selectivity across different zeolite catalysts, offering valuable insights for future research and application in heterogeneous catalysis.

Interactions enhance dispersion in fluctuating channels via emergent flows

Understanding particle motion in narrow channels can guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of fluid-filled channel walls can slow down or increase the dispersion of tracer particles via entropic trapping in the wall bulges or hydrodynamic flows induced by wall fluctuations, respectively. Previous studies concentrated primarily on the case of a single Brownian tracer. Here, we address what happens when there is a large ensemble of interacting Brownian tracers – a common situation in applications. Introducing repulsive interactions between tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon reminiscent of that seen for single tracers in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of tracers numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Interactions between the fluctuating wall and the now-nearby particles then drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, our perturbation theory quantifies dispersion in generic advection–diffusion systems.

Path Counting on Tree-like Graphs with a Single Entropic Trap: Critical Behavior and Finite Size Effects.

It is known that maximal entropy random walks and partition functions that count long paths on graphs tend to become localized near nodes with a high degree. Here, we revisit the simplest toy model of such a localization: a regular tree of degree p with one special node ("root") that has a degree different from all the others. We present an in-depth study of the path-counting problem precisely at the localization transition. We study paths that start from the root in both infinite trees and finite, locally tree-like regular random graphs (RRGs). For the infinite tree, we prove that the probability distribution function of the endpoints of the path is a step function. The position of the step moves away from the root at a constant velocity v=(p-2)/p. We find the width and asymptotic shape of the distribution in the vicinity of the shock. For a finite RRG, we show that a critical slowdown takes place, and the trajectory length needed to reach the equilibrium distribution is on the order of N instead of logp-1N away from the transition. We calculate the exact values of the equilibrium distribution and relaxation length, as well as the shapes of slowly relaxing modes.

Analysis of Megadalton-Sized DNA by Charge Detection Mass Spectrometry: Entropic Trapping and Shearing in Nanoelectrospray.

The analysis of nucleic acids by conventional mass spectrometry is complicated by counter ions which cause mass heterogeneity and limit the size of the DNA that can be analyzed. In this work, we overcome this limitation using charge detection mass spectrometry to analyze megadalton-sized DNA. Using positive mode electrospray, we find two dramatically different charge distributions for DNA plasmids. A low charge population that charges like compact DNA origami and a much higher charge population, with charges that extend over a broad range. For the high-charge population, the deviation between the measured mass and mass expected from the DNA sequence is consistently around 1%. For the low-charge population, the deviation is larger and more variable. The high-charge population is attributed to the supercoiled plasmid in a random coil configuration, with the broad charge distribution resulting from the rich variety of geometries the random coil can adopt. High-resolution measurements show that the mass distribution shifts to slightly lower mass with increasing charge. The low-charge population is attributed to a condensed form of the plasmid. We suggest that the condensed form results from entropic trapping where the random coil must undergo a geometry change to squeeze through the Taylor cone and enter an electrospray droplet. For the larger plasmids, shearing (mechanical breakup) occurs during electrospray or in the electrospray interface. Shearing is reduced by lowering the salt concentration.

Substantial Slowing of Electrophoretic Translocation of DNA through a Nanopore Using Coherent Multiple Entropic Traps.

One of the major challenges in the technology of sequencing DNA using single-molecule electrophoresis through a nanopore is to control the translocation of the macromolecule across the pore in order to allow sufficient time for accurate sequence reading at limited recording bandwidths. If the translocation speed is too fast, the signatures of the bases passing through the sensing region of the nanopore overlap in time, presenting difficulties in accurately identifying the bases in a sequential manner. Even though several strategies, such as enzyme ratcheting, have been implemented to reduce the translocation speed, the challenge to achieve a substantial reduction in the translocation speed continues to be of paramount significance. Toward achieving this goal, we have fabricated a nonenzymatic hybrid device that can reduce the translocation speed of long DNAs by more than 2 orders of magnitude, in comparison with the current status of the art. This device is made of a tetra-PEG hydrogel that is chemically anchored to the donor side of a solid-state nanopore. The idea behind this device is based on the recent discovery of the topologically frustrated dynamical state of confined polymers, whereby the front hydrogel matter of the hybrid device provides multiple entropic traps for a single DNA molecule holding it back against the electrophoretic driving force that pulls the DNA through the solid-state nanopore portion of the device. As a demonstration of slowing DNA translocation by a factor of about 500, we find the average translocation time realized in the present hybrid device for 3 kbp DNA as 23.4 ms, whereas the corresponding time for the bare solid-state nanopore under otherwise identical conditions is 0.047 ms. Our measurements on 1 kbp DNA and λ-DNA show that such a slowing down of DNA translocation with our hybrid device is general. An additional feature of our hybrid device is its incorporation of all features of the conventional gel electrophoresis to separate different DNA sizes in a clump of DNAs and to streamline them in an orderly and slow manner into the nanopore. Our results suggest the high potential of our hydrogel-nanopore hybrid device in further advancing the single-molecule electrophoresis technology to accurately sequence very large biological polymers.

Effect of solvent gradient inside the entropic trap on polymer migration.

By employing the exact enumeration technique on the lattice model of a polymer, we study the migration of the polymer chain across an entropic trap in a quasiequilibrium condition and explore the effect of solvent gradient present in the entropic trap which acts both parallel and perpendicular to the direction of migration. The Fokker-Planck formalism utilizes the free energy landscape of a polymer chain across the channel in the presence of the entropic trap to calculate the migration time. It is revealed that the migration is fast when the solvent gradient acts along the migration axis (i.e., x axis) inside the channel in comparison to the channel having the entropic trap. We report here for the first time that the entropic trap makes the migration faster at a certain value of solvent gradient. We also study the effect of transverse solvent gradient (along the y axis) inside the trap and investigate the structural changes of the polymer during migration through the channel. We observe the nonmonotonic dependence of migration time on the solvent gradient.

Entropic stochastic resonance induced by a transverse driving force.

The phenomenon of entropic stochastic resonance (ESR) is investigated with the presence of a time-periodic force in the transverse direction. Simulation results manifest that the ESR can survive even if there is no static bias force in any direction, just if a transverse driving field is applied. In the weak noise region, the transverse driving force leads to a giant-suppression of the escape rate from one well to another, i.e. the entropic trapping. The increase in noise intensity will eliminate this suppression and induce the ESR phenomenon. An alternative quantity, called the mean free flying time, is also proposed to characterize the ESR as well as the conventional spectral power amplification. The ESR can be modulated conveniently by the transverse periodic force, which implies an alternative method for controlling the dynamics of small-scale systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Activated nanoscale actin-binding domain motion in the catenin–cadherin complex revealed by neutron spin echo spectroscopy

As the core component of the adherens junction in cell-cell adhesion, the cadherin-catenin complex transduces mechanical tension between neighboring cells. Structural studies have shown that the cadherin-catenin complex exists as an ensemble of flexible conformations, with the actin-binding domain (ABD) of α-catenin adopting a variety of configurations. Here, we have determined the nanoscale protein domain dynamics of the cadherin-catenin complex using neutron spin echo spectroscopy (NSE), selective deuteration, and theoretical physics analyses. NSE reveals that, in the cadherin-catenin complex, the motion of the entire ABD becomes activated on nanosecond to submicrosecond timescales. By contrast, in the α-catenin homodimer, only the smaller disordered C-terminal tail of ABD is moving. Molecular dynamics (MD) simulations also show increased mobility of ABD in the cadherin-catenin complex, compared to the α-catenin homodimer. Biased MD simulations further reveal that the applied external forces promote the transition of ABD in the cadherin-catenin complex from an ensemble of diverse conformational states to specific states that resemble the actin-bound structure. The activated motion and an ensemble of flexible configurations of the mechanosensory ABD suggest the formation of an entropic trap in the cadherin-catenin complex, serving as negative allosteric regulation that impedes the complex from binding to actin under zero force. Mechanical tension facilitates the reduction in dynamics and narrows the conformational ensemble of ABD to specific configurations that are well suited to bind F-actin. Our results provide a protein dynamics and entropic explanation for the observed force-sensitive binding behavior of a mechanosensitive protein complex.

Optimizing on-chip concentration of DNA molecules against a nanoslit barrier

On-chip concentration method for deoxyribonucleic acid (DNA) molecules is preconcentrating DNA molecules before analyses using nanometer-sized structures formed in a microchannel and is effective in improving the sensitivity in DNA analyses using microfluidic devices. Although accurate and predictive theoretical models of concentration profile and concentration factor in on-chip concentration can be used for designing nanostructures and optimizing conditions for concentration, there has been few studies on models. In our previous study, we presented a method of on-chip concentration of DNA molecules using a nanoslit, which is a smaller gap than the diameter of random-coiled DNA molecules. This method is based on the principle of an entropic trap, and we achieved DNA concentration by controlling the applied voltage. In this study, we developed theoretical models of concentration profile and concentration factor in on-chip concentration for DNA molecules using a nanoslit. We conducted concentration experiments of lambda DNA (λ DNA) using our fabricated chip device with a 25-nm nanoslit. The theoretical results of our models were in good agreement with these experimental results. Based on our theoretical models, we determined the optimal applied voltage to be 0.95 V for maximizing the concentration factor in λ DNA concentration by using our chip device.

GROEL/ES Buffers Entropic Traps in Folding Pathway during Evolution of a Model Substrate

The folding landscape of proteins can change during evolution with the accumulation of mutations that may introduce entropic or enthalpic barriers in the protein folding pathway, making it a possible substrate of molecular chaperones in vivo. Can the nature of such physical barriers of folding dictate the feasibility of chaperone-assistance? To address this, we have simulated the evolutionary step to chaperone-dependence keeping GroEL/ES as the target chaperone and GFP as a model protein in an unbiased screen. We find that the mutation conferring GroEL/ES dependence in vivo and in vitro encode an entropic trap in the folding pathway rescued by the chaperonin. Additionally, GroEL/ES can edit the formation of non-native contacts similar to DnaK/J/E machinery. However, this capability is not utilized by the substrates in vivo. As a consequence, GroEL/ES caters to buffer mutations that predominantly cause entropic traps, despite possessing the capacity to edit both enthalpic and entropic traps in the folding pathway of the substrate protein.

Rapidly Forming Early Intermediate Structures Dictate the Pathway of Capsid Assembly.

There are ∼1030 possible intermediates on the assembly path from hepatitis B capsid protein dimers to the 120-dimer capsid. If every intermediate was tested, assembly would often get stuck in an entropic trap and essentially every capsid would follow a unique assembly path. Yet, capsids assemble rapidly with minimal trapped intermediates, a realization of the Levinthal paradox. To understand the fundamental mechanisms of capsid assembly, it is critical to resolve the early stages of the reaction. We have used time-resolved small angle X-ray scattering, which is sensitive to solute size and shape and has millisecond temporal resolution. Scattering curves were fit to a thermodynamically curated library of assembly intermediates, using the principle of maximum entropy. Maximum entropy also provides a physical rationale for the selection of species. We found that the capsid assembly pathway was exquisitely sensitive to initial assembly conditions. With the mildest conditions tested, the reaction appeared to be two-state from dimer to 120-dimer capsid with some dimers-of-dimers and trimers-of-dimers. In slightly more aggressive conditions, we observed transient accumulation of a decamer-of-dimers and the appearance of 90-dimer capsids. In conditions where there is measurable kinetic trapping, we found that highly diverse early intermediates accumulated within a fraction of a second and propagated into long-lived kinetically trapped states (≥90-mer). In all cases, intermediates between 35 and 90 subunits did not accumulate. These results are consistent with the presence of low barrier paths that connect early and late intermediates and direct the ultimate assembly path to late intermediates where assembly can be paused.

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 $p&amp;lt;0.5$ or as the single cluster at $p&amp;gt;0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N&amp;gt;N^{*}(p),$ 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 $N&amp;gt;N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

Machine learning for analysing ab initio molecular dynamics simulations

Post-calculation analyses are often required to extract physical insights from ab initio molecular dynamics simulations. In the present work, we use different machine learning classifiers to take a new perspective on the decomposition reaction of dioxetane. Upon thermally activated decomposition, dioxetane can form products in an electronically excited state and can thus chemiluminesce. Simulated dynamics trajectories exhibit both successful and frustrated dissociations. As an exhaustive and systematic study of the decomposition mechanism “by hand” is beyond feasibility, machine learning models have been employed to study the relevant nuclear distortions governing molecular dissociation. According to all classifiers used in the study, the two sets of geometries differ by the in-phase planarisation of the two formaldehyde moieties. New insights are obtained from this analysis: if both moieties are not planar enough when the dissociation is attempted, it is frustrated and the molecule remains trapped. The postponing of the decomposition reaction by the so-called entropic trap enhances the chemiexcitation efficiency.

Entropic Trapping of DNA with a Nanofiltered Nanopore.

Elucidating the kinetics of DNA passage through a solid-state nanopore is a fertile field of research, and mechanisms for controlling capture, passage, and trapping of biopolymers are likely to find numerous technological applications. Here we present a nanofiltered nanopore device, which forms an entropic cage for DNA following first passage through the nanopore, trapping the translocated DNA and permitting recapture for subsequent reanalysis and investigation of kinetics of passage under confinement. We characterize the trapping properties of this nanodevice by driving individual DNA polymers into the nanoscale gap separating the nanofilter and the pore, forming an entropic cage similar to a "two pores in series" device, leaving polymers to diffuse in the cage for various time lengths, and attempting to recapture the same molecule. We show that the cage results in effectively permanent trapping when the radius of gyration of the target polymer is significantly larger than the radii of the pores in the nanofilter. We also compare translocation dynamics as a function of translocation direction in order to study the effects of confinement on DNA just prior to translocation, providing further insight into the nanopore translocation process. This nanofiltered nanopore device realizes simple fabrication of a femtoliter nanoreactor in which to study fundamental biophysics and biomolecular reactions on the single-molecule level. The device provides an electrically-permeable single-molecule trap with a higher entropic barrier to escape than previous attempts to fabricate similar structures.

Anomalous packing and dynamics of a polymer chain confined in a static porous environment.

Polymers in confined porous environments are ubiquitous throughout biology, physics, materials science, and engineering. Several experiments have suggested that in some porous environments, chain dynamics can become extremely slow. While phenomenological explanations exist, the exact mechanisms for these slow dynamics have not been fully characterized. In this work, we initiate a joint simulation-theory study to investigate chain packing and dynamics in a static porous environment. The main theoretical concept is the free energy of the chain partitioning into several chambers of the porous environment. Both the theoretical results and Langevin dynamics simulations show that chain packing in each of the chambers is predominantly independent of chain length; it is determined by the maximal packing of segments in each chamber. Dynamically, short chains (compared to the chamber size) become trapped in a single chamber and dynamics become extremely slow, characteristic of an Ogston sieving-like behavior. For longer chains, on the other hand, a hierarchy of slow dynamics is observed due to entropic trapping, characterized by sub-diffusive behavior and a temporary plateau in the mean square displacement. Due to the slow nature of the dynamics, the inevitable long-time diffusive behavior of the chains is not captured by our simulations. Theoretically, the slow dynamics are understood in terms of a free energy barrier required to thread the chain from one chamber to the next. There is overall qualitative and quantitative agreement between simulations and theory. This work provides foundations for a better understanding of how chain dynamics are affected by porous environments.

Dispersion in two-dimensional periodic channels with discontinuous profiles.

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., ε = a/L is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in ε and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in ε. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

Transport and dispersion across wiggling nanopores

The transport of fluids at the nanoscale has achieved major breakthroughs over recent years1–4; however, artificial channels still cannot match the efficiency of biological porins in terms of fluxes or selectivity. Pore shape agitation—due to thermal fluctuations or in response to external stimuli—is believed to facilitate transport in biochannels5–9, but its impact on transport in artificial pores remains largely unexplored. Here we introduce a general theory for transport through thermally or actively fluctuating channels, which quantifies the impact of pore fluctuations on confined diffusion in terms of the spectral statistics of the channel fluctuations. Our findings demonstrate a complex interplay between transport and surface wiggling: agitation enhances diffusion via the induced fluid flow, but spatial variations in pore geometry can induce a slowing down via entropic trapping, in full agreement with molecular dynamics simulations and existing observations from the literature. Our results elucidate the impact of pore agitation in a broad range of artificial and biological porins, but also, at larger scales, in vascular motion in fungi, intestinal contractions and microfluidic surface waves. These results open up the possibility that transport across membranes can be actively tuned by external stimuli, with potential applications to nanoscale pumping, osmosis and dynamical ultrafiltration.

Entropic Trapping of a Singly Charged Molecule in Solution.

We demonstrate the ability to confine a single molecule in solution by spatial modulation of its local configurational entropy. Previously we established electrostatic trapping of a charged macromolecule by geometric tailoring of a repulsive electrical interaction potential in a parallel plate system. However, since the lifetime of the trapped state depends exponentially on the electrical charge of the molecule, the electrostatic interaction alone is often insufficient in magnitude to stably confine molecules carrying a net charge of magnitude ≤5 e. Here we show that the configurational entropy of a thermally fluctuating molecule in a geometrically modulated system can be exploited to spatially confine weakly charged molecules in solution. Measurement of the configurational entropy contribution reveals good agreement with theoretical expectations. This additional translational contribution to the total free energy facilitates direct optical imaging and measurement of the effective charge of molecules on the size scale of ∼1 nm and a charge as low as 1 e, physical properties comparable with those of a monovalent ion in solution.