Conformational Transition Rates Research Articles

Probing conformational kinetics of catalase with and without magnetic field by single-entity collision electrochemistry

The conformational motions of enzymes are crucial for their catalytic activities, but these fluctuations are usually spontaneous and unsynchronized and thus difficult to obtain from ensemble-averaged measurements. Here, we employ label-free single-entity electrochemical measurements to monitor in real time the fluctuating enzymatic behavior of single catalase molecules toward the degradation of hydrogen peroxide. By probing the electrochemical signals of single catalase molecules at a carbon nanoelectrode, we were able to observe three distinct current traces that could be attributed to conformational changes on the sub-millisecond timescale. Whereas, nearly uniform single long peaks were observed for single catalase molecules under a moderate magnetic field due to the restricted conformational changes of catalase. By combining high-resolution current signals with a multiphysics simulation model, we studied the catalytic kinetics of catalase with and without a magnetic field, and further estimated the maximum catalytic rate and conformational transition rate. This work introduces a new complementary approach to existing single-molecule enzymology, giving further insight into the enzymatic reaction mechanism.

Fast Visualized Conformational Transition of Polyphenylacetylenes with Stepwise Tunable Circularly Polarized Luminescence.

Two novel poly(3,5-diamide substituted phenylacetylene)s bearing L- or D-alanine residues with a long alkyl chain were synthesized. In low polar or apolar solvents, the polymers adopted contracted cis-cisoid helix showing strong yellow fluorescence, which was transferred to stretched cis-transoid helix by adding polar solvents or decreasing temperature, accompanied with the disappearance of fluorescence. The critical conformational transition temperature could be readily tuned in a wide range by altering the content of polar solvent, and the conformational variation at molecular level could be directly read out via the change in fluorescent property. The synergistical participation of amide and ester groups in the formation of intramolecular hydrogen bonds accelerated the conformational transition rate, resulting in remarkable reduction of hysteresis. Moreover, the polymers displayed switchable CPL performance and the luminescent dissymmetry factor could be stepwise amplified by forming chiral aggregates or liquid crystalline structure. This study may open a new avenue for the development of controllable helical structure-based smart CPL materials.

Quantum computing for classical problems: variational quantum eigensolver for activated processes

The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker–Plank–Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is, therefore, a workhorse of physical chemistry. In this paper we report on the development and implementation of a variational quantum eigensolver to solve the Fokker–Planck–Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be effectively applied to classical systems, paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors with nearest-neighbour interactions. We provide a method to encode the probability distribution for a given conformation of the chain on a quantum computer and assess its scalability in terms of operations. A performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain which shows results in good agreement with the classical benchmark without any further addition of error mitigation techniques.

DNA Looping and DNA Conformational Fluctuations Can Accelerate Protein Target Search.

Protein searching and binding to specific sites on DNA is a fundamentally important process that marks the beginning of all major cellular transformations. While the dynamics of protein-DNA interactions in in vitro settings is well investigated, the situation is much more complex for in vivo conditions because the DNA molecules in live cells are packed into chromosomal structures where they are undergoing strong dynamic and conformational fluctuations. In this work, we present a theoretical investigation on the role of DNA looping and DNA conformational fluctuations in the protein target search. It is based on a discrete-state stochastic analysis that allows for explicit calculations of dynamic properties, which is also supplemented by Monte Carlo computer simulations. It is found that for stronger nonspecific interactions between DNA and proteins the search occurs faster on the DNA looped conformation in comparison with the unlooped conformation, and the fastest search is observed when the loop is formed near the target site. It is also shown that DNA fluctuations between the looped and unlooped conformations influence the search dynamics, and this depends on the magnitude of conformational transition rates and on which conformation is more energetically stable. Physical-chemical arguments explaining these observations are presented. Our theoretical study suggests that the geometry and conformational changes in DNA are additional factors that might efficiently control the gene regulation processes.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size.

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Comparative Analyses of the Conformational Dynamics Between the Soluble and Membrane-Bound Cytokine Receptors

Cytokine receptors receive extracellular cues by binding with cytokines to transduce a signaling cascade leading to gene transcription in cells. Their soluble isoforms, functioning as decoy receptors, contain only the ectodomain. Whether the ectodomains of cytokine receptors at the membrane exhibit different conformational dynamics from their soluble forms is unknown. Using Stimulation-2 (ST2) as an example, we performed microsecond molecular dynamics (MD) simulations to study the conformational dynamics of the soluble and the membrane-bound ST2 (sST2 and ST2). Combined use of accelerated and conventional MD simulations enabled extensive sampling of the conformational space of sST2 for comparison with ST2. Using the interdomain loop conformation as the reaction coordinate, we built a Markov State Model to determine the slowest implied timescale of the conformational transition in sST2 and ST2. We found that the ectodomain of ST2 undergoes slower conformational relaxation but exhibits a faster rate of conformational transition in a more restricted conformational space than sST2. Analyses of the relaxed conformations of ST2 further suggest important contributions of interdomain salt-bridge interactions to the stabilization of different ST2 conformations. Our study elucidates differential conformational properties between sST2 and ST2 that may be exploited for devising strategies to selectively target each isoform.

Residual Structure of Intrinsically Disordered Transactivation Domains Regulates Their Binding Mechanisms to the TAZ1 Domain of CBP

The CREB binding protein (CBP) is a multifunctional transcription coactivator. The TAZ1 domain of CBP interacts with various intrinsically disordered transactivation domains (TADs), including CITED2, HIF-1α, p53, STAT2, and RelA. In our recent work, we found that the binding mechanisms of these five TADs can be divided into three groups by analyzing the conformational transition rate constants and binding free energy landscapes. Our work provides some clues suggesting that binding of TADs to TAZ1 is encoded by the TADs as well as templated by the TAZ1. The five TADs wrap around TAZ1 and form helical segments upon binding. Helical segments are important molecular recognition elements and their stability plays a role in regulating the binding process. In this work, we investigated the roles helical segments played in the binding processes of TADs with TAZ1 via molecular dynamics simulations using coarse-grained topology-based models. We first modulated the intramolecular interaction strength within TADs to increase or decrease their helicity. We then simulated the binding processes of TADs with various degree of helicity to TAZ1. Consistent with previous works on other protein complexes, increasing the TAD helicity generally increases the stability of the TAD/TAZ1 complex. However, since TAZ1 has four binding sites for TADs binding and a TAD molecule may contain multiple helical segments, the effect of individual helical segment varies significantly. Kinetic analysis also shows heterogeneous effects of helicity on the overall binding rate constant and conformational transition rate constants. Therefore, the current work further supports our previous finding that binding of TADs to TAZ1 is encoded by the TADs as well as templated by the TAZ1.

NMR Chemical Exchange Measurements Reveal That N6-Methyladenosine Slows RNA Annealing.

N6-Methyladenosine (m6A) is an abundant epitranscriptomic modification that plays important roles in many aspects of RNA metabolism. While m6A is thought to mainly function by recruiting reader proteins to specific RNA sites, the modification can also reshape RNA-protein and RNA-RNA interactions by altering RNA structure mainly by destabilizing base pairing. Little is known about how m6A and other epitranscriptomic modifications might affect the kinetic rates of RNA folding and other conformational transitions that are also important for cellular activity. Here, we used NMR R1ρ relaxation dispersion and chemical exchange saturation transfer to noninvasively and site-specifically measure nucleic acid hybridization kinetics. The methodology was validated on two DNA duplexes and then applied to examine how a single m6A alters the hybridization kinetics in two RNA duplexes. The results show that m6A minimally impacts the rate constant for duplex dissociation, changing koff by ∼1-fold but significantly slows the rate of duplex annealing, decreasing kon by ∼7-fold. A reduction in the annealing rate was observed robustly for two different sequence contexts at different temperatures, both in the presence and absence of Mg2+. We propose that rotation of the N6-methyl group from the preferred syn conformation in the unpaired nucleotide to the energetically disfavored anti conformation required for Watson-Crick pairing is responsible for the reduced annealing rate. The results help explain why in mRNA m6A slows down tRNA selection and more generally suggest that m6A may exert cellular functions by reshaping the kinetics of RNA conformational transitions.

SmFRET Probing Reveals Substrate-Dependent Conformational Dynamics of E. coli Multidrug MdfA

Bacterial multidrug-resistance transporters of the major facilitator superfamily are distinguished by their extraordinary ability to bind structurally diverse substrates, thus serving as a highly efficient tool to protect cells from multiple toxic substances present in their environment, including antibiotic drugs. However, details of the dynamic conformational changes of the transport cycle involved remain to be elucidated. Here, we used the single-molecule fluorescence resonance energy transfer technique to investigate the conformational behavior of the Escherichia coli multidrug transporter MdfA under conditions of different substrates, pH, and alkali metal ions. Our data show that different substrates exhibit distinct effects on both the conformational distribution and transition rate between two major conformations. Although the cationic substrate tetraphenylphosphonium favors the outward-facing conformation, it has less effect on the transition rate. In contrast, binding of the electroneutral substrate chloramphenicol tends to stabilize the inward-facing conformation and decreases the transition rate. Therefore, our study supports the notion that the MdfA transporter uses distinct mechanisms to transport electroneutral and cationic substrates.

Conformational analysis of replica exchange MD: Temperature-dependent Markov networks for FF amyloid peptides.

Recent molecular modeling methods using Markovian descriptions of conformational states of biomolecular systems have led to powerful analysis frameworks that can accurately describe their complex dynamical behavior. In conjunction with enhanced sampling methods, such as replica exchange molecular dynamics (REMD), these frameworks allow the systematic and accurate extraction of transition probabilities between the corresponding states, in the case of Markov state models, and of statistically-optimized transition rates, in the case of the corresponding coarse master equations. However, applying automatically such methods to large molecular dynamics (MD) simulations, with explicit water molecules, remains limited both by the initial ability to identify good candidates for the underlying Markovian states and by the necessity to do so using good collective variables as reaction coordinates that allow the correct counting of inter-state transitions at various lag times. Here, we show that, in cases when representative molecular conformations can be identified for the corresponding Markovian states, and thus their corresponding collective evolution of atomic positions can be calculated along MD trajectories, one can use them to build a new type of simple collective variable, which can be particularly useful in both the correct state assignment and in the subsequent accurate counting of inter-state transition probabilities. In the case of the ubiquitously used root-mean-square deviation (RMSD) of atomic positions, we introduce the relative RMSD (RelRMSD) measure as a good reaction coordinate candidate. We apply this method to the analysis of REMD trajectories of amyloid-forming diphenylalanine (FF) peptides-a system with important nanotechnology and biomedical applications due to its self-assembling and piezoelectric properties-illustrating the use of RelRMSD in extracting its temperature-dependent intrinsic kinetics, without a priori assumptions on the functional form (e.g., Arrhenius or not) of the underlying conformational transition rates. The RelRMSD analysis enables as well a more objective assessment of the convergence of the REMD simulations. This type of collective variable may be generalized to other observables that could accurately capture conformational differences between the underlying Markov states (e.g., distance RMSD, the fraction of native contacts, etc.).

A Multi-Scale Model for Insulin Self-Association Rates and Oligomerization Kinetics

Insulin, a therapeutic protein, can aggregate during manufacture and is considered detrimental to its quality. Early identification of aggregation inducing factors would be an essential aspect concerning the design of mitigation strategies during manufacturing processes. The time-scales and length-scales relevant for aggregation makes the use of all-atom (AA) explicit solvent simulations for prediction of aggregation thermodynamics and/or kinetics very difficult. Since aggregation is mainly driven by non-native interactions, we have used the physics based MARTINI coarse grained model to model protein-protein interactions. In an earlier work we had identified aggregation-prone, partially folded intermediates (PFIs) of insulin. Here we have employed a transient-complex model to determine self-association rate of native insulin (N) and the PFIs of insulin. To this end, a set of most probable conformations of the N-PFI complex were first obtained using docking and scoring on basis of MMPBSA energies. These docked complexes were then refined by separating the N and PFI monomers translationally followed by long molecular dynamics simulations. In two sets of test cases we show that the binding interface of the final N-PFI complex is similar in both the AA simulations and CG-MARTINI simulations with elastic network constraints. We hypothesize that this N-PFI complex can be taken as the diffusion limited transient state for the insulin homodimer on aggregation pathway. We use the TransComp server to calculate association rates for formation of this diffusion limited complex. The dimer association rates and monomer conformational transition rates are used to determine all the rates for formation of various small oligomeric species on insulin aggregation pathway. These rates are then input to a kinetic monte carlo (KMC) scheme to determine oligomerization kinetics of insulin.

Structure and dynamics of GPCR signaling complexes.

G-protein-coupled receptors (GPCRs) relay numerous extracellular signals by triggering intracellular signaling through coupling with G proteins and arrestins. Recent breakthroughs in the structural determination of GPCRs and GPCR-transducer complexes represent important steps toward deciphering GPCR signal transduction at a molecular level. A full understanding of the molecular basis of GPCR-mediated signaling requires elucidation of the dynamics of receptors and their transducer complexes as well as their energy landscapes and conformational transition rates. Here, we summarize current insights into the structural plasticity of GPCR-G-protein and GPCR-arrestin complexes that underlies the regulation of the receptor's intracellular signaling profile.

Molecular dynamics simulation of the glass transition temperature of fullerene filled cis-1,4-polybutadiene nanocomposites

In this work, the effect of the fullerene (C60) weight fraction and PB-C60 interaction on the glass transition temperature (T g) of polymer chains has been systemically investigated by adopting the united atom model of cis-1,4-poly(butadiene) (cis-PB). Various chain dynamics properties, such as atom translational mobility, bond/segment reorientation dynamics, torsional dynamics, conformational transition rate and dynamic heterogeneity of the cis-PB chains, are analyzed in detail. It is found that T g could be affected by the C60 weight fraction due to its inhibition effect on the mobility of the cis-PB chains. However, T g is different, which depends on different dynamics scales. Among the chain dynamics properties, T g is the lowest from atom translational mobility, while it is the highest from the dynamic heterogeneity. In addition, T g can be more clearly distinguished from the dynamic heterogeneity; however, the conformational transition rate seems to be not very sensitive to the C60 weight fraction compared with others. For pure cis-PB chains, T g and the activation energy in this work can be compared with those of other polymers. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T g. The activation energy below T g is lower than that above T g. This work can help to understand the effect of the C60 on the dynamic properties and glass transition temperature of the cis-PB chains from different scales.

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

ABSTRACTIn this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (Tg) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding Tg. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the Tg of the PB chains gradually increases. Depending on the chain structure and the calculation method, the Tg of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below Tg. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above Tg, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 1005–1016

How to Distinguish Conformational Selection and Induced Fit Based on Chemical Relaxation Rates

Protein binding often involves conformational changes. Important questions are whether a conformational change occurs prior to a binding event (‘conformational selection’) or after a binding event (‘induced fit’), and how conformational transition rates can be obtained from experiments. In this article, we present general results for the chemical relaxation rates of conformational-selection and induced-fit binding processes that hold for all concentrations of proteins and ligands and, thus, go beyond the standard pseudo-first-order approximation of large ligand concentration. These results allow to distinguish conformational-selection from induced-fit processes—also in cases in which such a distinction is not possible under pseudo-first-order conditions—and to extract conformational transition rates of proteins from chemical relaxation data.

Protein Allostery and Conformational Dynamics.

The functions of many proteins are regulated through allostery, whereby effector binding at a distal site changes the functional activity (e.g., substrate binding affinity or catalytic efficiency) at the active site. Most allosteric studies have focused on thermodynamic properties, in particular, substrate binding affinity. Changes in substrate binding affinity by allosteric effectors have generally been thought to be mediated by conformational transitions of the proteins or, alternatively, by changes in the broadness of the free energy basin of the protein conformational state without shifting the basin minimum position. When effector binding changes the free energy landscape of a protein in conformational space, the change affects not only thermodynamic properties but also dynamic properties, including the amplitudes of motions on different time scales and rates of conformational transitions. Here we assess the roles of conformational dynamics in allosteric regulation. Two cases are highlighted where NMR spectroscopy and molecular dynamics simulation have been used as complementary approaches to identify residues possibly involved in allosteric communication. Perspectives on contentious issues, for example, the relationship between picosecond-nanosecond local and microsecond-millisecond conformational exchange dynamics, are presented.

A Minimalistic Kinetic Model for Amyloid Self-Assembly

Amyloid aggregation is a phenomenon in which proteins/peptides self-assemble into highly ordered structures that are associated with diseases (e.g. Alzheimer's and Parkinson's) as well as several native biological functions. A wide range of proteins/peptides can form these structures while displaying remarkable phenomenological similarities, both structural and kinetic. Thus, there is a need for a unifying framework that would enable a better understanding of the phenomenon of amyloid formation. In the current work, we develop a coarse-grained model for amyloid formation that accounts for experimentally known phenomenon like polymerization, depolymerization (under different polymer-states) and the conformational transition of monomers during aggregation. The model is analytically solvable, and can be simulated for timescales and lengthscales that are biologically relevant. Our mathematical model and kinetic Monte carlo simulations shed light on the vital signatures of amyloid growth, including a plausible explanation for the concentration-independence of fibril growth velocities at large free-monomer concentrations. Interestingly, our simulations also reveal the relationship between the heterogeneity in filament lengths (variances) and the rate of conformational transition. The length fluctuation data suggest that an increased rate of conformational transition not only alters the extent of fluctuation in filament lengths, but also the timescales at which the heterogeneity is maximum. Using our analytical expressions for aggregation and beta-sheet growth velocities, we predict a multi-phasic behavior of proteins/peptides in response to varying kinetic parameters. Our model also captures other interesting aspects of amyloid growth including the potential of growing fibrils to generate mechanical forces and the experimentally observed phenomenon of intermittent nature of filament growth. Overall, the study could significantly augment our fundamental understanding of the complex phenomenon of amyloid aggregation.

Resolving Conformational Switches in the Protease Ftsh using Single-Molecule FRET

FtsH is a homohexameric AAA+ protease embedded in the prokaryote membrane, where it recognizes, unfolds, translocates and lyses protein substrates. Previous crystal structural data of Thermotoga maritima FtsH in an ADP-bound and an apo-state showed an ATPase and a protease domain linked by a flexible unresolved hinge, facilitating a large conformational change upon ADP binding. The current model of the chemo-mechanical cycle was inferred from these two crystal structures and describes FtsH with a power stroke mechanism, whereby the energy released by ATP hydrolysis is converted into a conformational switch. To date, this mechanism could not be observed experimentally. Here, we use single-molecule Förster Resonance Energy Transfer (smFRET) to study FtsH in real time. Our assay involved the vesicle encapsulation of unlabeled and double-labeled monomers to promote self-assembled FtsH hexamers. Total Internal Reflection Fluorescence (TIRF) microscopy of the immobilized molecules allowed us to collect kinetic information of conformational changes. Data analysis based on hidden Markov modeling resolved distinct conformational states, transition coordinates and transition rates. Surprisingly, without nucleotide, an FtsH monomer adopted four distinct conformational states, undergoing highly dynamic interconversion on the second timescale. Thus, FtsH performed stochastic transitions independently of an energy source, but rather using thermal activation. Upon binding of ATP, the number of conformational states remained identical, however, presence of ATP reduced some barriers of the free energy landscape. A homolog mutation in FtsH, A359V, of the pathogenic mutation A510V in paraplegin displayed an additional further closed conformational state, which was highly populated in the presence of ATP. We propose that this highly populated state could reflect the malfunctioning of the pathogenic mutation in paraplegin.

Both protein dynamics and ligand concentration can shift the binding mechanism between conformational selection and induced fit.

This study aimed to shed light on the long debate over whether conformational selection (CS) or induced fit (IF) is the governing mechanism for protein-ligand binding. The main difference between the two scenarios is whether the conformational transition of the protein from the unbound form to the bound form occurs before or after encountering the ligand. Here we introduce the IF fraction (i.e., the fraction of binding events achieved via IF), to quantify the binding mechanism. Using simulations of a model protein-ligand system, we demonstrate that both the rate of the conformational transition and the concentration of ligand molecules can affect the IF fraction. CS dominates at slow conformational transition and low ligand concentration. An increase in either quantity results in a higher IF fraction. Despite the many-body nature of the system and the involvement of multiple, disparate types of dynamics (i.e., ligand diffusion, protein conformational transition, and binding reaction), the overall binding kinetics over wide ranges of parameters can be fit to a single exponential, with the apparent rate constant exhibiting a linear dependence on ligand concentration. The present study may guide future kinetics experiments and dynamics simulations in determining the IF fraction.

Stochastic dynamics of electrical membrane with voltage-dependent ion channel fluctuations

A Brownian-ratchet–like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable , representing mobile membrane charge density, and a discrete variable Kt representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson–type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing an Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, the membrane charge Qm is a more natural dynamic variable than the potential Vm; our formalism treats Qm-dependent conformational transition rates as intrinsic parameters. Therefore, in principle, vs. Vm is experimental-protocol–dependent, e.g., different from voltage or charge clamping measurements. For constant membrane capacitance per unit area Cm and neglecting the membrane potential induced by gating charges, , and HH's formalism is recovered. The presence of two types of ions, with different channels and reversal potentials, gives rise to a nonequilibrium steady state with positive entropy production ep. For rapidly fluctuating channels, an expression for ep is obtained.