Free energy reconstruction from nonequilibrium single-molecule pulling experiments

General theory for localizing the where and when of entropy production meets single-molecule experiments

The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in experiments where a fully resolved description allows direct access to such quantities. Complementary studies consider partially hidden, coarse-grained descriptions, in which the mean entropy production typically is not directly accessible but can be bounded in terms of observable quantities. Going beyond the mean, we introduce a fluctuating entropy production that applies to individual trajectories in a coarse-grained description under time-dependent driving. Thus, this concept is applicable to the broad and experimentally significant class of driven systems in which not all relevant states can be resolved. We provide a paradigmatic example by studying an experimentally verified protein unfolding process. As a consequence, the entire distribution of the coarse-grained entropy production rather than merely its mean retains spatial and temporal information about the microscopic process. In particular, we obtain a bound on the distribution of the physical entropy production of individual unfolding events.

Tribo-Chemical Reactions in DLC-Zirconia Sliding under Ethanol Gas Environment

A reactive force field (ReaxFF) molecular dynamics simulation is performed for the sliding of diamond-like carbon (DLC) and yttria-stabilized zirconia (YSZ) under an ethanol gas environment, motivated by the previous experiment of ultralow friction phenomenon (friction fade-out). We observe (i) dissociation of ethanol into ethoxy and hydrogen, both of which simultaneously adsorb on the YSZ surface, and (ii) dissociation of ethanol into ethyl and hydroxy, the former of which forms a bond with another ethanol molecule and the latter of which adsorbs on the DLC surface. Reaction (i) is enhanced by the sliding motion, but occurs even without it, while reaction (ii) only occurs during sliding with a sufficiently high load pressure. The potentials of mean force for the two reactions are also calculated combining the steered MD and Jarzynski equality. It is shown that the activation energies of reactions (i) and (ii) are significantly lowered by the YSZ and DLC surfaces, respectively, as compared to those in a vacuum. The resultant activation energy is higher for reaction (ii) than for reaction (i).

Acetylcholinesterase inhibitory activities of some flavonoids from the root bark of Pinus krempfii Lecomte: in vitro and in silico study

From the root bark of Pinus krempfii Lecomte, four flavonoids were isolated and evaluated for their inhibitory activities against AChE and BChE enzymes in vitro and in silico. Tectochrysin (1) was found to inhibit AChE with an IC50 value of 33.69 ± 2.80 μM. The docking study results also showed agreement with the in vitro test results. All four compounds also showed the best binding affinity for the AChE enzyme, characterised by binding energy (ΔG) values as low as -8.1 to -9.3 kcal/mol, in which, the compound tectochrysin had the best binding affinity for the AChE protein with a ΔG value of -9.329 kcal/mol. Tectochrysin (1) was also bound to the amino acid Phe295 of AChE with a bond length of 2.8 Å, similar to the control dihydrotanshinone-I. Galangin (2) also showed its in vitro inhibitory activity against BChE with an IC50 value of 82.21 ± 2.70 μM. In silico, it also had the best binding energy value of -9.072 kcal/mol with BChE and formed hydrogen bonds with the His438 (2.85 Å) residues of BChE like the positive control (tacrine). The steered molecular dynamics (SMD) simulation results of these two complexes revealed a mechanistic insight that the protein-ligand complexes showed stable trajectories throughout the 20 and 150 ns simulations. Moreover, the drug likeliness suggested that both flavonoids (1 and 2) were expected to be drug-like and have an LD50 toxicity level of 5. This study has contributed new results for drug discovery and the development of substances with neuroprotective effects, especially for the treatment of Alzheimer's disease.Communicated by Ramaswamy H. Sarma.

Imidazole[1,5-a]pyridine derivatives as EGFR tyrosine kinase inhibitors unraveled by umbrella sampling and steered molecular dynamics simulations

Although the use of the tyrosine kinase inhibitors (TKIs) has been proved that it can save live in a cancer treatment, the currently used drugs bring in many undesirable side-effects. Therefore, the search for new drugs and an evaluation of their efficiency are intensively carried out. Recently, a series of eighteen imidazole[1,5-a]pyridine derivatives were synthetized by us, and preliminary analyses pointed out their potential to be an important platform for pharmaceutical development owing to their promising actions as anticancer agents and enzyme (kinase, HIV-protease,…) inhibitors. In the present theoretical study, we further analyzed their efficiency in using a realistic scenario of computational drug design. Our protocol has been developed to not only observe the atomistic interaction between the EGFR protein and our 18 novel compounds using both umbrella sampling and steered molecular dynamics simulations, but also determine their absolute binding free energies. Calculated properties of the 18 novel compounds were in detail compared with those of two known drugs, erlotinib and osimertinib, currently used in cancer treatment. Inspiringly the simulation results promote three imidazole[1,5-a]pyridine derivatives as promising inhibitors into a further step of clinical trials.

Polymer time crystal: Mechanical activation of reversible bonds by low-amplitude high frequency excitations

Reversible supramolecular bonds play an important role in materials science and in biological systems. The equilibrium between open and closed bonds and the association rate can be controlled thermally, chemically, by mechanical pulling, by ultrasound, or by catalysts. In practice, these intrinsic equilibrium methods either suffer from a limited range of tunability or may damage the material. Here, we present a nonequilibrium strategy that exploits the dissipative properties of the system to control and change the dynamic properties of sacrificial and reversible networks. We show theoretically and numerically how high-frequency mechanical oscillations of very low amplitude can open or close bonds. This mechanism indicates how reversible bonds could alleviate mechanical fatigue of materials especially at low temperatures where they are fragile. In another area, it suggests that the system can be actively modified by the application of ultrasound to induce gel-fluid transitions and to activate or deactivate adhesion properties.

Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model

Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.

Temperature fluctuations in mesoscopic systems

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equation with respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

Investigation of Rare Protein Conformational Transitions via Dissipation-Corrected Targeted Molecular Dynamics

To sample rare events, dissipation-corrected targeted molecular dynamics (dcTMD) applies a constant velocity constraint along a one-dimensional reaction coordinate s, which drives an atomistic system from an initial state into a target state. Employing a cumulant approximation of Jarzynski's identity, the free energy ΔG(s) is calculated from the mean external work and dissipated work of the process. By calculating the friction coefficient Γ(s) from the dissipated work, in a second step, the equilibrium dynamics of the process can be studied by propagating a Langevin equation. While so far dcTMD has been mostly applied to study the unbinding of protein-ligand complexes, here its applicability to rare conformational transitions within a protein and the prediction of their kinetics are investigated. As this typically requires the introduction of multiple collective variables {xj} = x, a theoretical framework is outlined to calculate the associated free energy ΔG(x) and friction Γ(x) from dcTMD simulations along coordinate s. Adopting the α-β transition of alanine dipeptide as well as the open-closed transition of T4 lysozyme as representative examples, the virtues and shortcomings of dcTMD to predict protein conformational transitions and the related kinetics are studied.

Theory of nonequilibrium asymptotic state thermodynamics: Interacting Ehrenfest urn ring as an example

A generalized class of the nonequilibrium state, called the nonequilibrium asymptotic state (NEAS), is proposed. The NEAS is constructed within the framework of Fokker-Planck equations in thermodynamic limit. Besides the usual equilibrium state and nonequilibrium steady state (NESS), the class of NEAS could also cover the nonequilibrium periodic state (NEPS) in which its dynamics shows periodicity, the nonequilibrium quasiperiodic state (NEQPS), and nonequilibrium chaotic state (NECS) in which its dynamics becomes chaotic. Based on the theory of NEAS thermodynamics, the corresponding thermodynamics of different NEASs could also be determined. Finally the interacting Ehrenfest urn ring model is used as an example to illustrate how different kinds of NEAS (equilibrium state, uniform NESS, nonuniform NESS, NEPS) in the three-urn case are identified in our framework. In particular, the thermodynamics of NEPS and its phase transitions to other types of NEAS are studied.

Experimental Test of the Jarzynski Equality in a Single Spin-1 System Using High-Fidelity Single-Shot Readouts

The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.

Stochastic Thermodynamics of a Quantum Dot Coupled to a Finite-Size Reservoir

In nanoscale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work, and entropy production in such systems is, however, missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctuating temperature of the reservoir. Based on a fluctuation theorem, we identify the appropriate entropy production that results in a thermodynamically consistent statistical description. We illustrate our results by analyzing the work production for a finite-size reservoir Szilard engine.

Hybridization Kinetics of miR-155 on Gold Surfaces as Investigated by Surface Plasmon Resonance and Atomic Force Spectroscopy

miRNAs are short noncoding RNA single strands, with a crucial role in several biological processes. miRNAs are dysregulated in several human diseases, and their detection is an important goal for diagnosis and screening. Innovative biosensors for miRNAs are commonly based on the hybridization process between a miRNA and its corresponding complementary strand (or suitable aptamers) immobilized onto an electrode surface forming a duplex. A detailed description of the hybridization kinetics in working conditions deserves a great deal of interest for the optimization of the biosensing process. Surface plasmon resonance (SPR) and atomic force spectroscopy (AFS) were applied to investigate the hybridization process between miR-155, a multifunctional miRNA that constitutes an important marker overexpressed in several diseases, and its complementary strand (antimiR-155), immobilized on the gold-coated surface of a commercial electrode. Under well-adjusted pH, ionic strength, surface coverage, and concentration, we found that miR-155 has a high affinity for antimiR-155 with kinetics well described by the 1:1 Langmuir model. Both techniques provided an association rate of about 104 M-1 s-1, while a dissociation rate of 10-5 and 10-4 s-1 was assessed by SPR and AFS, respectively. These results allowed us to establish optimized measurement running times for applications in biosensing. An analysis of AFS data also led us to evaluate the binding free energy for the duplex, which was found to be close to that of free molecules in solution. These results could guide in the implementation of fine-tuned working conditions of a biosensor for detecting miRNAs based on correspondent complementary strands.

Interaction of Synthetic Cannabinoid Receptor Agonists with Cannabinoid Receptor I: Insights into Activation Molecular Mechanism

Synthetic cannabinoid receptor agonists (SCRAs) have become a wide group of new psychoactive substances since the 2010s. For the last few years, the X-ray structures of the complexes of cannabinoid receptor I (CB1) with SCRAs as well as the complexes of CB1 with its antagonist have been published. Based on those data, SCRA-CB1 interactions are analyzed in detail, using molecular modeling and molecular dynamics simulations. The molecular mechanism of the conformational transformation of the transmembrane domain of CB1 caused by its interaction with SCRA is studied. These conformational changes allosterically modulate the CB1-Gi complex, providing activation of the Gi protein. Based on the X-ray-determined structures of the CB1-ligand complexes, a stable apo conformation of inactive CB1 with a relatively low potential barrier of receptor activation was modeled. For that model, molecular dynamic simulations of SCRA binding to CB1 led to the active state of CB1, which allowed us to explore the key features of this activation and the molecular mechanism of the receptor's structural transformation. The simulated CB1 activation is in accordance with the previously published experimental data for the activation at protein mutations or structural changes of ligands. The key feature of the suggested activation mechanism is the determination of the stiff core of the CB1 transmembrane domain and the statement that the entire conformational transformation of the receptor to the active state is caused by a shift of alpha helix TM7 relative to this core. The shift itself is caused by protein-ligand interactions. It was verified via steered molecular dynamics simulations of the X-ray-determined structures of the inactive receptor, which resulted in the active conformation of CB1 irrespective of the placement of agonist ligand in the receptor's active site.

Coenzyme Q10 trapping in mitochondrial complex I underlies Leber's hereditary optic neuropathy

How does a single amino acid mutation occurring in the blinding disease, Leber's hereditary optic neuropathy (LHON), impair electron shuttling in mitochondria? We investigated changes induced by the m.3460 G>A mutation in mitochondrial protein ND1 using the tools of Molecular Dynamics and Free Energy Perturbation simulations, with the goal of determining the mechanism by which this mutation affects mitochondrial function. A recent analysis suggested that the mutation's replacement of alanine A52 with a threonine perturbs the stability of a region where binding of the electron shuttling protein, Coenzyme Q10, occurs. We found two functionally opposing changes involving the role of Coenzyme Q10. The first showed that quantum electron transfer from the terminal Fe/S complex, N2, to the Coenzyme Q10 headgroup, docked in its binding pocket, is enhanced. However, this positive adjustment is overshadowed by our finding that the mobility of Coenzyme Q10 in its oxidized and reduced states, entering and exiting its binding pocket, is disrupted by the mutation in a manner that leads to conditions promoting the generation of reactive oxygen species. An increase in reactive oxygen species caused by the LHON mutation has been proposed to be responsible for this optic neuropathy.

Identifying inhibitors of NSP16-NSP10 of SARS-CoV-2 from large databases

The COVID-19 pandemic, which has already claimed millions of lives, continues to pose a serious threat to human health, requiring the development of new effective drugs. Non-structural proteins of SARS-CoV-2 play an important role in viral replication and infection. Among them, NSP16 (non-structured protein 16) and its cofactor NSP10 (non-structured protein 10) perform C2'-O methylation at the 5' end of the viral RNA, which promotes efficient virus replication. Therefore, the NSP16-NSP10 complex becomes an attractive target for drug development. Using a multi-step virtual screening protocol which includes Lipinski's rule, docking, steered molecular dynamics and umbrella sampling, we searched for potential inhibitors from the PubChem and anti-HIV databases. It has been shown that CID 135566620 compound from PubChem is the best candidate with an inhibition constant in the sub-μM range. The Van der Waals interaction was found to be more important than the electrostatic interaction in the binding affinity of this compound to NSP16-NSP10. Further in vitro and in vivo studies are needed to test the activity of the identified compound against COVID-19.Communicated by Ramaswamy H. Sarma.

Heat distribution in quantum Brownian motion

We investigate the heat statistics in a relaxation process of quantum Brownian motion described by the Caldeira-Leggett model. By employing the normal mode transformation and the phase-space formulation approach, we can analyze the quantum heat distribution within an exactly dynamical framework beyond the traditional paradigm of Born-Markovian and weak-coupling approximations. It is revealed that the exchange fluctuation theorem for quantum heat generally breaks down in the strongly non-Markovian regime. Our results may improve the understanding about the nonequilibrium thermodynamics of open quantum systems when the usual Markovian treatment is no longer appropriate.

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

Inferring equilibrium transition rates from nonequilibrium protocols

We develop a theory for inferring equilibrium transition rates from trajectories driven by a time-dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution function in terms of the equilibrium distribution function and the excess dissipation, we formulate a nonequilibrium transition state theory to estimate the rate enhancement over the equilibrium rate due to the nonequilibrium protocol. We demonstrate the utility of our theory in examples of pulling of harmonically trapped particles in one and two dimensions, as well as a semiflexible polymer with a reactive linker in three dimensions. We expect our purely thermodynamic approach will find use in both molecular simulation and force spectroscopy experiments.

Kinetic reconstruction of free energies as a function of multiple order parameters

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.

Biodiversity of butterflies (Lepidoptera: Rhopalocera) in the protected landscape of Nandhour, Uttarakhand, India

An appraisal of butterfly species composition in terms of comparative diversity richness in various habitat types was conducted in and around the Nandhour Wildlife Sanctuary of Terai Arc landscape in Uttarakhand. During the two years of survey period (March 2018–February 2020), a total of 89 species of butterflies belonging to families Nymphalidae 43 species, Pieridae 15 species, Lycaenidae 13 species, Hesperiidae eight species, Papilionidae seven species, and Riodinidae three species were recorded, of which 46 species represented new records for the Nandhour Landscape. Butterfly diversity and richness were highest in dense moist & open dry riverine forests and lowest in human settlements & agricultural land. No significant differences in the number of species were found in moist mixed deciduous forest, subtropical Chir Pine forest, moist Bhabar Sal forest, moist Shiwalik Sal forest, and plantation forest. Eight species are endemic to the Indian Himalayan Region. 

Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics

Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic equations of motion, introduces time into the description of thermodynamic processes-which opens the way to fine control them. As a result, the field of finite-time thermodynamics of mesoscopic systems has blossomed. In this article, after introducing a few concepts of control for isolated mechanical systems evolving according to deterministic equations of motion, we review the different strategies that have been developed to realize finite-time state-to-state transformations in both over and underdamped regimes, by the proper design of time-dependent control parameters/driving. The systems under study are stochastic, epitomized by a Brownian object immersed in a fluid; they are thus strongly coupled to their environment playing the role of a reservoir. Interestingly, a few of those methods (inverse engineering, counterdiabatic driving, fast-forward) are directly inspired by their counterpart in quantum control. The review also analyzes the control through reservoir engineering. Besides the reachability of a given target state from a known initial state, the question of the optimal path is discussed. Optimality is here defined with respect to a cost function, a subject intimately related to the field of information thermodynamics and the question of speed limit. Another natural extension discussed deals with the connection between arbitrary states or non-equilibrium steady states. This field of control in stochastic thermodynamics enjoys a wealth of applications, ranging from optimal mesoscopic heat engines to population control in biological systems.

Hepatoprotective Effect of Millettia dielsiana: In Vitro and In Silico Study

In silico docking studies of 50 selected compounds from Millettia dielsiana Harms ex Diels (family Leguminosae) were docked into the binding pocket of the PI3K/mTOR protein. In there, compounds trans-3-O-p-hydroxycinnamoyl ursolic acid (1) and 5,7,4'-trihydroxyisoflavone 7-O-β-D-apiofuranosyl-(1→6)-β-D-glucopyranoside (2) are predicted to be very promising inhibitors against PI3K/mTOR. They direct their cytotoxic activity against Hepatocellular carcinoma with binding affinity (BA) values, the pulling work spent to the co-crystallized ligand from the binding site of PI3K/mTOR (W and F_max), and the non-equilibrium binding free energy (∆G_neq^Jar) as BA values = -9.237 and -9.083 kcal/mol, W = 83.5 ± 10.6 kcal/mol with F_max = 336.2 ± 45.3 pN and 126.6 ± 21.7 kcal/mol with F_max = 430.3 ± 84.0 pN, and ∆G_neq^Jar = -69.86074 and -101.2317 kcal/mol, respectively. In molecular dynamic simulation, the RMSD value of the PI3K/mTOR complex with compounds (1 and 2) was in the range of 0.3 nm to the end of the simulation. Therefore, the compounds (1 and 2) are predicted to be very promising inhibitors against PI3K/mTOR. The crude extract, ethyl acetate fraction and compounds (1 and 2) from Millettia dielsiana exhibited moderate to potent in vitro cytotoxicity on Hepatocellular carcinoma cell line with IC₅₀ values of 81.2 µg/mL, 60.4 µg/mL, 23.1 μM, and 16.3 μM, respectively, and showed relatively potent to potent in vitro antioxidant activity on mouse hepatocytes with ED₅₀ values of 24.4 µg/mL, 19.3 µg/mL, 30.7 μM, and 20.5 μM, respectively. In conclusion, Millettia dielsiana and compounds (1 and 2) are predicted to have very promising cytotoxic activity against Hepatocellular carcinoma and have a hepatoprotective effect.

Connections between efficient control and spontaneous transitions in an Ising model

A system can be driven between metastable configurations by a time-dependent driving protocol, which uses external control parameters to change the potential energy of the system. Here we investigate the correspondence between driving protocols that are designed to minimize work and the spontaneous transition paths of the system in the absence of driving. We study the spin-inversion reaction in a 2D Ising model, quantifying the timing of each spin flip and heat flow to the system during both a minimum-work protocol and a spontaneous transition. The general order of spin flips during the transition mechanism is preserved between the processes, despite the coarseness of control parameters that are unable to reproduce more detailed features of the spontaneous mechanism. Additionally, external control parameters provide energy to each system component to compensate changes in internal energy, showing how control parameters are tuned during a minimum-work protocol to counteract underlying energetic features. This paper supports a correspondence between minimum-work protocols and spontaneous transition mechanisms.

Limited-control optimal protocols arbitrarily far from equilibrium

Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and experimental contexts, systems often may only be controlled with a limited set of degrees of freedom. Here, going beyond slow- and fast-driving approximations employed in previous studies, we obtain exact finite-time optimal protocols for this limited-control setting. By working with deterministic Fokker-Planck probability density time evolution, we can frame the work-minimizing protocol problem in the standard form of an optimal control theory problem. We demonstrate that finding the exact optimal protocol is equivalent to solving a system of Hamiltonian partial differential equations, which in many cases admit efficiently calculable numerical solutions. Within this framework, we reproduce analytical results for the optimal control of harmonic potentials and numerically devise optimal protocols for two anharmonic examples: varying the stiffness of a quartic potential and linearly biasing a double-well potential. We confirm that these optimal protocols outperform other protocols produced through previous methods, in some cases by a substantial amount. We find that for the linearly biased double-well problem, the mean position under the optimal protocol travels at a near-constant velocity. Surprisingly, for a certain timescale and barrier height regime, the optimal protocol is also nonmonotonic in time.

Homeostatic and adaptive energetics: Nonequilibrium fluctuations beyond detailed balance in voltage-gated ion channels

Stochastic thermodynamics has largely succeeded in characterizing both equilibrium and far-from-equilibrium phenomena. Yet many opportunities remain for application to mesoscopic complex systems-especially biological ones-whose effective dynamics often violate detailed balance and whose microscopic degrees of freedom are often unknown or intractable. After reviewing excess and housekeeping energetics-the adaptive and homeostatic components of a system's dissipation-we extend stochastic thermodynamics with a trajectory class fluctuation theorem for nonequilibrium steady-state, nondetailed-balanced complex systems. We then take up the neurobiological examples of voltage-gated sodium and potassium ion channels to apply and illustrate the theory, elucidating their nonequilibrium behavior under a biophysically plausible action potential drive. These results uncover challenges for future experiments and highlight the progress possible understanding the thermodynamics of complex systems-without exhaustive knowledge of every underlying degree of freedom.

Computing Free Energies with Fluctuation Relations on Quantum Computers

As a central thermodynamic property, free energy enables the calculation of virtually any equilibrium property of a physical system, allowing for the construction of phase diagrams and predictions about transport, chemical reactions, and biological processes. Thus, methods for efficiently computing free energies, which in general is a difficult problem, are of great interest to broad areas of physics and the natural sciences. The majority of techniques for computing free energies target classical systems, leaving the computation of free energies in quantum systems less explored. Recently developed fluctuation relations enable the computation of free energy differences in quantum systems from an ensemble of dynamic simulations. While performing such simulations is exponentially hard on classical computers, quantum computers can efficiently simulate the dynamics of quantum systems. Here, we present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. We discuss under which conditions our approximation becomes exact, and under which conditions it serves as a strict upper bound. Furthermore, we successfully demonstrate a proof of concept of our algorithm using the transverse field Ising model on a real quantum processor. As quantum hardware continues to improve, we anticipate that our algorithm will enable computation of free energy differences for a wide range of quantum systems useful across the natural sciences.

Gecko Adhesion on Flat and Rough Surfaces: Simulations with a Multi-Scale Molecular Model

A multiscale modeling approach is used to develop a particle-based mesoscale gecko spatula model that is able to link atomistic simulations and mesoscale (0.44 µm) simulations. It is used to study the detachment of spatulae from flat as well as nanostructured surfaces. The spatula model is based on microscopical information about spatulae structure and on atomistic molecular simulation results. Target properties for the coarse-graining result from a united-atom model of gecko keratin in periodic boundary conditions (PBC), previously developed by the authors. Pull-off forces necessary to detach gecko keratin under 2D PBC parallel to the surface are previously overestimated when only a small region of a spatula is examined. It is shown here that this is due to the restricted geometry (i.e., missing peel-off mode) and not model parameters. The spatula model peels off when pulled away from a surface, both in the molecular picture of the pull-off process and in the force-extension curve of non-equilibrium simulations mimicking single-spatula detachment studied with atomic force microscopy equipment. The force field and spatula model can reproduce experimental pull-off forces. Inspired by experimental results, the underlying mechanism that causes pull-off forces to be at a minimum on surfaces of varying roughnesses is also investigated. A clear sigmoidal increase in the pull-off force of spatulae with surface roughness shows that adhesion is determined by the ratio between spatula pad area and the area between surface peaks. Experiments showed a correlation with root-mean-square roughness of the surface, but the results of this work indicate that this is not a causality but depends on the area accessible.

Decisive structural elements in water and ion permeation through mechanosensitive channels of large conductance: insights from molecular dynamics simulation

In this paper, a series of equilibrium molecular dynamics simulations (EMD), steered molecular dynamics (SMD), and computational electrophysiology methods are carried out to explore water and ion permeation through mechanosensitive channels of large conductance (MscL). This research aims to identify the pore-lining side chains of the channel in different conformations of MscL homologs by analyzing the pore size. The distribution of permeating water dipole angles through the pore domains enclosed by VAL21 and GLU104 demonstrated that water molecules are oriented toward the charged oxygen headgroups of GLU104 from their hydrogen atoms to retain this interaction in a stabilized fashion. Although, this behavior was not perceived for VAL21. Numerical assessments of the secondary structure clarified that, during the ion permeation, in addition to the secondary structure alterations, the structure of Tb-MscL would also undergo significant conformational changes. It was elucidated that VAL21, GLU104, and water molecules accomplish a fundamental task in ion permeation. The mentioned residues hinder ion permeation so that the pulling SMD force is increased remarkably when the ions permeate through the domains enclosed by VAL21 and GLU102. The hydration level and potassium diffusivity in the hydrophobic gate of the transmembrane domain were promoted by applying the external electric field. Furthermore, the implementation of an external electric field altered the distribution pattern for potassium ions in the system while intensifying the accumulation of Cl⁻ in the vicinity of ARG11 and ARG98.

Graphical representation of the most determinant pore-lining side chains of Tb-MscL along with the solid surfaces depicting the spatial shape of the interior pore.

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.

Antibody-nanobody combination increases their neutralizing activity against SARS-CoV-2 and nanobody H11-H4 is effective against Alpha, Kappa and Delta variants

The global spread of COVID-19 is devastating health systems and economies worldwide. While the use of vaccines has yielded encouraging results, the emergence of new variants of SARS-CoV-2 shows that combating COVID-19 remains a big challenge. One of the most promising treatments is the use of not only antibodies, but also nanobodies. Recent experimental studies revealed that the combination of antibody and nanobody can significantly improve their neutralizing ability through binding to the SARS-CoV-2 spike protein, but the molecular mechanisms underlying this observation remain largely unknown. In this work, we investigated the binding affinity of the CR3022 antibody and H11-H4 nanobody to the SARS-CoV-2 receptor binding domain (RBD) using molecular modeling. Both all-atom steered molecular dynamics simulations and coarse-grained umbrella sampling showed that, consistent with the experiment, CR3022 associates with RBD more strongly than H11-H4. We predict that the combination of CR3022 and H11-H4 considerably increases their binding affinity to the spike protein. The electrostatic interaction was found to control the association strength of CR3022, but the van der Waals interaction dominates in the case of H11-H4. However, our study for a larger set of nanobodies and antibodies showed that the relative role of these interactions depends on the specific complex. Importantly, we showed Beta, Gamma, Lambda, and Mu variants reduce the H11-H4 activity while Alpha, Kappa and Delta variants increase its neutralizing ability, which is in line with experiment reporting that the nanobody elicited from the llama is very promising for fighting against the Delta variant.

Computed Three-Dimensional Atomic Force Microscopy Images of Biopolymers Using the Jarzynski Equality

Three-dimensional atomic force microscopy (3D-AFM) has resolved three-dimensional distributions of solvent molecules at solid-liquid interfaces at the subnanometer scale. This method is now being extended to the imaging of biopolymer assemblies such as chromosomes or proteins in cells, with the expectation of being able to resolve their three-dimensional structures. Here, we have developed a computational method to simulate 3D-AFM images of biopolymers by using the Jarzynski equality. It is found that some parts of the fiber structure of biopolymers are indeed resolved in the 3D-AFM image. The dependency of 3D-AFM images on the vertical scanning velocity is investigated, and optimum scanning velocities are found. It is also clarified that forces in nonequilibrium processes are measured in 3D-AFM measurements when the dynamics of polymers are slower than the scanning of the probe.

A topological fluctuation theorem

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

While topology is crucial in complex systems, stochastic thermodynamics uncovers universal constraints for non-equilibrium fluctuations. The authors combine these two areas and formulate a fluctuation theorem for the heat dissipated along closed loops in vortex force fields, which is found to be topologically protected.

Multidimensional minimum-work control of a 2D Ising model

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and thus decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations, and significantly reducing resistance and hence work.

Cocktail of REGN Antibodies Binds More Strongly to SARS-CoV-2 Than Its Components, but the Omicron Variant Reduces Its Neutralizing Ability

A promising approach to combat Covid-19 infections is the development of effective antiviral antibodies that target the SARS-CoV-2 spike protein. Understanding the structures and molecular mechanisms underlying the binding of antibodies to SARS-CoV-2 can contribute to quickly achieving this goal. Recently, a cocktail of REGN10987 and REGN10933 antibodies was shown to be an excellent candidate for the treatment of Covid-19. Here, using all-atom steered molecular dynamics and coarse-grained umbrella sampling, we examine the interactions of the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein with REGN10987 and REGN10933 separately as well as together. Both computational methods show that REGN10933 binds to RBD more strongly than REGN10987. Importantly, the cocktail binds to RBD (simultaneous binding) more strongly than its components. The dissociation constants of REGN10987-RBD and REGN10933-RBD complexes calculated from the coarse-grained simulations are in good agreement with the experimental data. Thus, REGN10933 is probably a better candidate for treating Covid-19 than REGN10987, although the cocktail appears to neutralize the virus more efficiently than REGN10933 or REGN10987 alone. The association of REGN10987 with RBD is driven by van der Waals interactions, while electrostatic interactions dominate in the case of REGN10933 and the cocktail. We also studied the effectiveness of these antibodies on the two most dangerous variants Delta and Omicron. Consistent with recent experimental reports, our results confirmed that the Omicron variant reduces the neutralizing activity of REGN10933, REGN10987, and REGN10933+REGN10987 with the K417N, N440K, L484A, and Q498R mutations playing a decisive role, while the Delta variant slightly changes their activity.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

Molecularly resolved, label-free nucleic acid sensing at solid-liquid interface using non-ionic DNA analogues

Nucleic acid-based biosensors, where the capture probe is a nucleic acid, e.g., DNA or its synthetic analogue xeno nucleic acid (XNA), offer interesting ways of eliciting clinically relevant information from hybridization/dehybridization signals. In this respect, the application of XNA probes is attractive since the drawbacks of DNA probes might be overcome. Within the XNA probe repertoire, peptide nucleic acid (PNA) and morpholino (MO) are promising since their backbones are non-ionic. Therefore, in the absence of electrostatic charge repulsion between the capture probe and the target nucleic acid, a stable duplex can be formed. In addition, these are nuclease-resistant probes. Herein, we have tested the molecularly resolved nucleic acid sensing capacity of PNA and MO capture probes using a fluorescent label-free single molecule force spectroscopy approach. As far as single nucleobase mismatch discrimination is concerned, both PNA and MO performed better than DNA, while the performance of the MO probe was the best. We propose that the conformationally more rigid backbone of MO, compared to the conformationally flexible PNA, is an advantage for MO, since the probe orientation can be made more upright on the surface and therefore MO can be more effectively accessed by the target sequences. The performance of the XNA probes has been compared to that of the DNA probe, using fixed nucleobase sequences, so that the effect of backbone variation could be investigated. To our knowledge, this is the first report on molecularly resolved nucleic acid sensing by non-ionic capture probes, here, MO and PNA.

Improved nucleic acid sensing in terms of single nucleobase mismatch discrimination, as achieved by the surface-confined non-ionic PNA and MO capture probes, is exemplified by single molecule force spectroscopy.

Reconstruction of the Free Energy Profile for SUMO1 from Nonequilibrium Single-Molecule Pulling Experiments

Free energy profiles form the cornerstone in the study of protein folding and function. In this study, the free energy profile of SUMO1 protein is directly reconstructed using an extension of the Jarzynski equality from atomic force microscope (AFM) based single-molecule force spectroscopy (SMFS) experiments. SUMO1 is a ubiquitin-like posttranslational modifier protein having a β clamp motif in its structure, imparting it with mechanical stability. We use the Jarzynski equality to obtain the equilibrium free energy profile from repeated nonequilibrium single-molecule pulling experiments. Indeed, the free energy values determined by the Jarzynski equality are lesser than the normal work average at all extensions. The free energy profiles constructed for the two velocities (100 and 400 nm/s) overlap with each other. The unfolding free energy barrier is estimated to be ∼7.5 kcal/mol. We anticipate that the Jarzynski equality can be applied in a similar manner to other ubiquitin-like proteins to extract their differences in the free energy profile, and hence, the effect of sequence diversity of structurally homologous proteins on the free energy landscape can be studied.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Extraction of kinetics from equilibrium distributions of states using the Metropolis Monte Carlo method

The Metropolis Monte Carlo (MMC) method is used to extract reaction kinetics from a given equilibrium distribution of states of a complex system. The approach is illustrated by the folding/unfolding reaction for two proteins: a model β-hairpin and α-helical protein α_{3}D. For the β-hairpin, the free energy surfaces (FESs) and free energy profiles (FEPs) are employed as the equilibrium distributions of states, playing a role of the potentials of mean force to determine the acceptance probabilities of new states in the MMC simulations. Based on the FESs and PESs for a set of temperatures that were simulated with the molecular dynamics (MD) method, the MMC simulations are performed to extract folding/unfolding rates. It has been found that the rate constants and first-passage time (FPT) distributions obtained in the MMC simulations change with temperature in good agreement with those from the MD simulations. For α_{3}D protein, whose equilibrium folding/unfolding was studied with the single-molecule FRET method [Chung et al., J. Phys. Chem. A 115, 3642 (2011)1089-563910.1021/jp1009669], the FRET-efficiency histograms at different denaturant concentrations were used as the equilibrium distributions of protein states. It has been found that the rate constants for folding and unfolding obtained in the MMC simulations change with denaturant concentration in reasonable agreement with the constants that were extracted from the photon trajectories on the basis of theoretical models. The simulated FPT distributions are single-exponential, which is consistent with the assumption of two-state kinetics that was made in the theoretical models. The promising feature of the present approach is that it is based solely on the equilibrium distributions of states, without introducing any additional parameters to perform simulations, which suggests its applicability to other complex systems.

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Molecular dynamics study of the internalization of cell-penetrating peptides containing unnatural amino acids across membranes

Peptide-based delivery systems that deliver target molecules into cells have been gaining traction. These systems need cell-penetrating peptides (CPPs), which have the remarkable ability to penetrate into biological membranes and help internalize different cargoes into cells through the cell membranes. The molecular internalization mechanism and structure-function relationships of CPPs are not clear, although the incorporation of nonproteinogenic amino acids such as α-aminoisobutyric acid (Aib) has been reported to increase their helicity, biostability and penetration efficiencies. Here, we used molecular dynamics to study two Aib-containing CPPs, poly(LysAibAla)₃ (KAibA) and poly(LysAibGly)₃ (KAibG), that previously showed high cell internalization efficiency. KAibA and KAibG displayed the lowest internalization energies among the studied CPPs, showing distinct internalization mechanisms depending on the lipid composition of the model membranes. The presence of Aib residues allows these CPPs to adopt amphipathic folding to efficiently penetrate through the membranes. Elucidating how Aib incorporation affects CPP-membrane binding and interactions is beneficial for the design of CPPs for efficient intracellular delivery.

Impact of PROTAC Linker Plasticity on the Solution Conformations and Dissociation of the Ternary Complex

The conformational behavior of a small molecule free in solution is important to understand the free energy of binding to its target. This could be of special interest for proteolysis-targeting chimeras (PROTACs) due to their often flexible and lengthy linkers and the need to induce a ternary complex. Here, we report on the molecular dynamics (MD) simulations of two PROTACs, MZ1 and dBET6, revealing different linker conformational behaviors. The simulation of MZ1 in dimethyl sulfoxide (DMSO) agrees well with the nuclear magnetic resonance study, providing strong support for the relevance of our simulations. To further understand the role of linker plasticity in the formation of a ternary complex, the dissociation of the complex von Hippel-Lindau-MZ1-BRD4 is investigated in detail by steered simulations and is shown to follow a two-step pathway. Interestingly, both MZ1 and dBET6 display in water, a tendency toward an intramolecular lipophilic interaction between the two warheads. The hydrophobic contact of the two warheads would prevent them from binding to their respective proteins and might have an effect on the efficacy of induced cellular protein degradation. However, conformations featuring this hydrophobic contact of the two warheads are calculated to be marginally more favorable.

Preaveraging description of polymer nonequilibrium stretching

This article focuses on a preaveraging description of polymer nonequilibrium stretching, where a single polymer undergoes a transient process from equilibrium to nonequilibrium steady state by pulling one chain end. The preaveraging method combined with mode analysis reduces the original Langevin equation to a simplified form for both a stretched steady state and an equilibrium state, even in the presence of self-avoiding repulsive interactions spanning a long range. However, the transient stretching process exhibits evolution of a hierarchal regime structure, which means a qualitative temporal change in probabilistic distributions assumed in preaveraging. We investigate the preaveraging method for evolution of the regime structure with consideration of the nonequilibrium work relations and deviations from the fluctuation-dissipation relation.

Critical point for demixing of binary hard spheres

We use a two-level simulation method to analyze the critical point associated with demixing of binary hard-sphere mixtures. The method exploits an accurate coarse-grained model with two- and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble and matching to the universal form for the 3D Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions and the geometry of the underlying hard-sphere packings.

Water Dynamics in a Peptide-appended Pillar[5]arene Artificial Channel in Lipid and Biomimetic Membranes

Peptide-appended Pillar[5]arene (PAP) is an artificial water channel that can be incorporated into lipid and polymeric membranes to achieve high permeability and enhanced selectivity for angstrom-scale separations [Shen et al. Nat. Commun.9:2294 (2018)]. In comparison to commonly studied rigid carbon nanotubes, PAP channels are conformationally flexible, yet these channels allow a high water permeability [Y. Liu and H. Vashisth Phys. Chem. Chem. Phys.21:22711 (2019)]. Using molecular dynamics (MD) simulations, we study water dynamics in PAP channels embedded in biological (lipid) and biomimetic (block-copolymer) membranes to probe the effect of the membrane environment on water transport characteristics of PAP channels. We have resolved the free energy surface and local minima for water diffusion within the channel in each type of membrane. We find that water follows single file transport with low free-energy barriers in regions surroundings the central ring of the PAP channel and the single file diffusivity of water correlates with the number of hydrogen bonding sites within the channel, as is known for other sub-nm pore-size synthetic and biological water channels [Horner et al. Sci. Adv.1:e1400083 (2015)].

Similarity of extremely rare nonequilibrium processes to equilibrium processes

For system coupled to heat baths, typical nonequilibrated processes, e.g., induced by varying an external parameter without waiting for equilibration in between, are very different from the corresponding equilibrium infinitely slow processes. Nevertheless, there are connections between equilibrium and nonequilibrated behaviors, e.g., the theorems of Jarzynski and Crooks, which relate the distribution P(W) of nonequilibrium work to the free energy differences ΔF. Here we study the naturally arising question, whether those relevant but rare trajectories, which exhibit these work values, show a higher degree of similarity to equilibrium. For convenience, we have chosen a simple model of RNA secondary structures (or single-stranded DNA), here modeling a medium-size hairpin structure, under influence of a varying external force. This allows us to measure the work W during the resulting fast unfolding and refolding processes within Monte Carlo simulations, i.e., in nonequilibrium. Also we sample numerically efficiently directly in exact equilibrium, for comparison. Using a sophisticated large-deviation algorithm, we are able to measure work distributions with high precision down to probabilities as small as 10^{-46}, enabling us to verify the Crooks and Jarzynski theorems. Furthermore, we analyze force-extension curves and the configurations of the secondary structures during unfolding and refolding for typical equilibrium processes and nonequilibrated processes. We find that the nonequilibrated processes where the work values are close to those which are most relevant for applying Crooks and Jarzynski theorems, respectively, but which occur with exponential small probabilities, are most and quite similar to the equilibrium processes.