arXiv subjects

Changbong Hyeon

Publications and source records attributed to Changbong Hyeon.

At least 37 records · Page 2Linked to original sources

arXiv2019

Iterative Annealing Mechanism Explains the Functions of the GroEL and RNA Chaperones

Molecular chaperones are ATP-consuming biological machines, which facilitate the folding of proteins and RNA molecules that are kinetically trapped in misfolded states for long times. Unassisted folding occurs by the kinetic partitioning mechanism according to which folding to the native state, with low probability as well as misfolding to one of the many metastable states, with high probability, occur rapidly on similar time scales. GroEL is an all-purpose stochastic machine that assists misfolded substrate proteins (SPs) to fold. The RNA chaperones (CYT-19) help the folding of ribozymes that readily misfold. GroEL does not interact with the folded proteins but CYT-19 disrupts both the folded and misfolded ribozymes. Despite this major difference, the Iterative Annealing Mechanism (IAM) quantitatively explains all the available experimental data for assisted folding of proteins and ribozymes. Driven by ATP binding and hydrolysis and GroES binding, GroEL undergoes a catalytic cycle during which it samples three allosteric states, referred to as T (apo), R (ATP bound), and R'' (ADP bound). In accord with the IAM predictions, analyses of the experimental data shows that the efficiency of the GroEL-GroES machinery and mutants is determined by the resetting rate $k_{R''\rightarrow T}$, which is largest for the wild type GroEL. Generalized IAM accurately predicts the folding kinetics of Tetrahymena ribozyme and its variants. Chaperones maximize the product of the folding rate and the steady state native state fold by driving the substrates out of equilibrium. Neither the absolute yield nor the folding rate is optimized.

q-bio.BM↗

arXiv2019

Theoretical Perspectives on Biological Machines

Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and replicate DNA. A common aspect of these machines is that their functions are driven out of equilibrium. It is a challenge to provide a general framework for understanding the functions of biological machines, such as molecular motors, molecular chaperones, and helicases. Using these machines as prototypical examples, we describe a few general theoretical methods providing insights into their functions. Although the theories rely on coarse-graining of these complex systems they have proven useful in not only accounting for many in vitro experiments but also addressing questions such as how the trade-off between precision, energetic costs and optimal performances are balanced. However, many complexities associated with biological machines will require one to go beyond current theoretical methods. Simple point mutations in the enzyme could drastically alter functions, making the motors bi-directional or result in unexpected diseases or dramatically restrict the capacity of molecular chaperones to help proteins fold. These examples are reminders that while the search for principles of generality in biology is intellectually stimulating, one also ought to keep in mind that molecular details must be accounted for to develop a deeper understanding of processes driven by biological machines. Going beyond generic descriptions of in vitro behavior to making genuine understanding of in vivo functions will likely remain a major challenge for some time to come. The combination of careful experiments and the use of physical principles will be useful in elucidating the rules governing the workings of biological machines.

physics.bio-ph↗

arXiv2019

Energetic costs, precision, and efficiency of a biological motor in cargo transport

Molecular motors play pivotal roles in organizing the interior of cells. A motor efficient in cargo transport would move along cytoskeletal filaments with a high speed and a minimal error in transport distance (or time) while consuming a minimal amount of energy. The travel distance of the motor and its variance are, however, physically constrained by the free energy being consumed. A recently formulated \emph{thermodynamic uncertainty relation} offers a theoretical framework for the energy-accuracy trade-off relation ubiquitous in biological processes. According to the relation, a measure $\mathcal{Q}$, the product between the heat dissipated from a motor and the squared relative error in the displacement, has a minimal theoretical bound ($\mathcal{Q} \geq 2 k_B T$), which is approached when the time trajectory of the motor is maximally regular for a given amount of free energy input. Here, we use $\mathcal{Q}$ to quantify the transport efficiency of biological motors. Analyses on the motility data from several types of molecular motors reveal that $\mathcal{Q}$ is a complex function of ATP concentration and load ($f$). For kinesin-1, $\mathcal{Q}$ approaches the theoretical bound at $f\approx 4$ pN and over a broad range of ATP concentration (1 $μ$M - 10 mM), and is locally minimized at [ATP] $\approx$ 200 $μ$M. In stark contrast, this local minimum vanishes for a mutant that has a longer neck-linker, and the value of $\mathcal{Q}$ is significantly greater, which underscores the importance of molecular structure. Transport efficiencies of the biological motors studied here are semi-optimized under the cellular condition ([ATP] $\approx 1$ mM, $f=0-1$ pN). Our study indicates that among many possible directions of optimization, cytoskeletal motors are designed to operate at a high speed with a minimal error while leveraging their energy resources.

physics.bio-ph↗

arXiv2019

Compressing $Θ$-chain in slit geometry

When compressed in a slit of width $D$, a $Θ$-chain that displays the scaling of size $R_0$ (diameter) with respect to the number of monomers $N$, $R_0\sim aN^{1/2}$, expands in the lateral direction as $R_{\parallel}\sim a N^ν(a/D)^{2ν-1}$. Provided that the $Θ$ condition is strictly maintained throughout the compression, the well-known scaling exponent of $Θ$-chain in 2 dimensions, $ν=4/7$, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from $R_0/D<1$ to $R_0/D\gg 1$, $ν$ gradually deviates from $ν=1/2$ and plateaus at $ν=3/4$, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the $Θ$ condition under confinement because of two major effects. First, as the dimension is reduced from 3 to 2 dimensions, the contributions of higher order virial terms, which can be ignored in 3 dimensions at large $N$, become significant. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the second virial coefficient ($B_2$) changes from $B_2=0$ ($Θ$ condition) in free space to $B_2>0$ (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.

cond-mat.soft↗

arXiv2018

Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular Machines

Allosteric signaling in biological molecules, which may be viewed as specific action at a distance due to localized perturbation upon binding of ligands or changes in environmental cues, is pervasive in biology. Phenomenological MWC and KNF models galvanized research for over five decades, and these models continue to be the basis for describing the allostery in an array of systems. However, understanding allosteric signaling and the associated dynamics between distinct allosteric states is challenging. In this review, we first describe symmetry and rigidity as essential requirements for allosteric proteins. The general features, with MWC and KNF as two extreme scenarios, emerge when allosteric signaling is viewed from an energy landscape perspective. To go beyond the general theories, we describe computational tools to predict the network of residues that carry allosteric signals. Methods to obtain molecular insights into the dynamics of allosteric transitions are briefly mentioned. The utility of the methods is illustrated by applications to systems ranging from monomeric proteins to multisubunit proteins. Finally, the role allostery plays in the functions of ATP-consuming molecular machines, bacterial chaperonin GroEL and molecular motors, is described. Although universal molecular principles governing allosteric signaling do not exist, we can draw the following general conclusions. (1) Multiple pathways connecting allosteric states are highly heterogeneous. (2) Allosteric signaling is exquisitely sensitive to the architecture of the system, which implies that the capacity for allostery is encoded in the structure itself. (3) The mechanical modes that connect distinct allosteric states are robust to sequence variations. (4) Extensive investigations of allostery in Hemoglobin and more recently GroEL, show that a network of salt-bridge rearrangements serves as allosteric switches.

cond-mat.soft↗

arXiv2018

Thermodynamic uncertainty relation of interacting oscillators in synchrony

The thermodynamic uncertainty relation sets the minimal bound of the cost-precision trade-off relation for dissipative processes. Examining the dynamics of an internally coupled system that is driven by a constant thermodynamic force, we however find that the trade-off relation of a sub-system is not constrained by the minimal bound of conventional uncertainty relation. We made our point explicit by using an exactly solvable model of interacting oscillators. As the number (N) of interacting oscillators increases, the uncertainty bound of individual oscillators is reduced to 2k_B T/N upon full synchronization under strong coupling. The cost-precision trade-off for the sub-system is particularly relevant for sub-cellular processes where collective dynamics emerges from multiple energy-expending components interacting with each other.

cond-mat.stat-mech↗

arXiv2018

From Octopus to Dendrite - Semiflexible Polyelectrolyte Brush Condensates in Trivalent Counterion Solution

Interplay between counterion-mediated interaction and stiffness inherent to polymer chain can bring substantial complexity to the morphology and dynamics of polyelectrolyte brush condensates. Trivalent counterions induce collapse of flexible polyelectrolyte brushes, over a certain range of grafting density, into octopus-like surface micelles; however, if individual chains are rigid enough, the ion-mediated local nematic ordering assembles the brush chains into fractal-like dendritic condensates whose relaxation dynamics is significantly slower than that in the surface micelles. Notably, the trivalent ions condensed in the dendritic condensates are highly mobile displaying quasi-one-dimensional diffusion in parallel along the dendritic branches. Our findings in this study are potentially of great significance to understanding the response of cellular organization such as chromosomes and charged polysaccharides on membranes to the change in ionic environment.

cond-mat.soft↗

arXiv2018

Signaling Networks and Dynamics of Allosteric Transitions in Bacterial Chaperonin GroEL: Implications for Iterative Annealing of Misfolded Proteins

Signal transmission at the molecular level in many biological complexes occurs through allosteric transitions. They describe the response a complex to binding of ligands at sites that are spatially well separated from the binding region. We describe the Structural Perturbation Method (SPM), based on phonon propagation in solids, that can be used to determine the signal transmitting allostery wiring diagram (AWD) in large but finite-sized biological complexes. Applications to the bacterial chaperonin GroEL-GroES complex shows that the AWD determined from structures also drive the allosteric transitions dynamically. Both from a structural and dynamical perspective these transitions are largely determined by formation and rupture of salt-bridges. The molecular description of allostery in GroEL provides insights into its function, which is quantitatively described by the Iterative Annealing Mechanism. Remarkably, in this complex molecular machine, a deep connection is established between the structures, reaction cycle during which GroEL undergoes a sequence of allosteric transitions, and function in a self-consistent manner.

q-bio.BM↗

arXiv2017

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

Using Brownian motion in periodic potentials $V(x)$ tilted by a force $f$, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation $q$, and in order to limit the output fluctuation within a relative uncertainty $ε$, at least $2k_BT/ε^2$ of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium ($f\ll V'(x)$) but also at far-from-equilibrium $(f\gg V'(x))$, more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particle is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a new bound of nonequilibrium fluctuations that the variance of dissipated heat ($σ_q^2$) increases with its mean ($μ_q$) and cannot be smaller than $2k_BTμ_q$.

cond-mat.stat-mech↗

arXiv2017

Heterogeneous morphology and dynamics of polyelectrolyte brush condensates in trivalent counterion solution

Recent experiments have shown that trivalent ion, spermidine$^{3+}$, can provoke lateral microphase segregation in DNA brushes. Using molecular simulations and simple theoretical arguments, we explore the effects of trivalent counterions on polyelectrolyte brushes. At a proper range of grafting density, polymer size, and ion concentration, the brush polymers collapse heterogeneously into octopus-like surface micelles. Remarkably, the heterogeneity in brush morphology is maximized and the relaxation dynamics of chain and condensed ion are the slowest at the 1:3 stoichiometric concentration of trivalent ions to polyelectrolyte charge. A further increase of trivalent ion concentration conducive to a charge inversion elicits modest reswelling and homogenizes the morphology of brush condensate. Our study provides a new insight into the origin of the diversity in DNA organization in cell nuclei as well as the ion-dependent morphological variation in polyelectrolyte brush layer of biological membranes.

cond-mat.soft↗

arXiv2016

Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States

Theoretical analysis, which maps single molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related to each other. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1 whose dynamics is confined on one-dimensional tracks is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers thermodynamic basis to understand the heat enhanced self-diffusion of exothermic enzymes.

q-bio.SC↗

arXiv2016

Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm - Variational Bayes-double chain Markov model (VB-DCMM) - to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na$^+$ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA.

q-bio.QM↗

arXiv2016

Effects of dimethyl sulfoxide on surface water near phospholipid bilayers

Despite much effort to probe the properties of dimethyl sulfoxide (DMSO) solution, effects of DMSO on water, especially near plasma membrane surfaces still remain elusive. By performing molecular dynamics (MD) simulations at varying DMSO concentrations ($X_{\text{DMSO}}$), we study how DMSO affects structural and dynamical properties of water in the vicinity of phospholipid bilayers. As proposed by a number of experiments, our simulations confirm that DMSO induces dehydration from bilayer surfaces and disrupts the H-bond structure of water. However, DMSO enhanced water diffusivity at solvent-bilayer interfaces, an intriguing discovery reported by a spin-label measurement, is not confirmed in our simulations. In order to resolve this discrepancy, we examine the location of the spin-label (Tempo), relative to the solvent-bilayer interface. In accord with the evidence in the literature, our simulations, which explicitly model Tempo-PC, find that the Tempo moiety is equilibrated at $\sim 8-10$ Å \emph{below} the bilayer surface. Furthermore, the DMSO-enhanced surface water diffusion is confirmed only when water diffusion is analyzed around the Tempo moiety that is immersed below the bilayer surface, which implies that the experimentally detected signal of water using Tempo stems from the interior of bilayers, not from the interface. Our analysis finds that the increase of water diffusion below the bilayer surface is coupled to the increase of area per lipid with an increasing $X_{\text{DMSO}}$ $(\lesssim 10\text{ mol\%})$. Underscoring the hydrophobic nature of Tempo moiety, our study calls for careful re-evaluation of the use of Tempo in the measurement on lipid bilayer surfaces.

cond-mat.soft↗

arXiv2016

Ripping RNA by Force using Gaussian Network Models

Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in the context of proteins have shown that topology plays is the major determinant of the unfolding landscapes. By building on this finding we study the responses of RNA molecules to force by adapting Gaussian network model (GNM) that represents RNAs using a bead-spring network with isotropic interactions. Cross-correlation matrices of residue fluctuations, which are analytically calculated using GNM even upon application of mechanical force, show distinct allosteric communication as RNAs rupture. The model is used to calculate the force-extension curves at full thermodynamic equilibrium, and the corresponding unfolding pathways of four RNA molecules subject to a quasi-statically increased force.Our study finds that the analysis using GNM captures qualitatively the unfolding pathway of \emph{T}. ribozyme elucidated by the optical tweezers measurement. However, the simple model is not sufficient to capture subtle features, such as bifurcation in the unfolding pathways or the ion effects, in the forced-unfolding of RNAs.

physics.bio-ph↗

arXiv2016

Ultraslow water-mediated transmembrane interactions regulate the activation of A$_{\text{2A}}$ adenosine receptor

Water molecules inside G-protein coupled receptor have recently been spotlighted in a series of crystal structures. To decipher the dynamics and functional roles of internal waters in GPCR activity, we studied A$_{\text{2A}}$ adenosine receptor using $μ$sec-molecular dynamics simulations. Our study finds that the amount of water flux across the transmembrane (TM) domain varies depending on the receptor state, and that the water molecules of the TM channel in the active state flow three times slower than those in the inactive state. Depending on the location in solvent-protein interface as well as the receptor state, the average residence time of water in each residue varies from $\sim\mathcal{O}(10^2)$ psec to $\sim\mathcal{O}(10^2)$ nsec. Especially, water molecules, exhibiting ultraslow relaxation ($\sim\mathcal{O}(10^2)$ nsec) in the active state, are found around the microswitch residues that are considered activity hotspots for GPCR function. A continuous allosteric network spanning the TM domain, arising from water-mediated contacts, is unique in the active state, underscoring the importance of slow waters in the GPCR activation.

q-bio.BM↗

arXiv2016

Directly measuring single molecule heterogeneity using force spectroscopy

One of the most intriguing results of single molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active conformations. The structural differences between these conformations may be subtle, but each distinct state can be remarkably long-lived, with random interconversions between states occurring only at macroscopic timescales, fractions of a second or longer. Though we now have proof of functional heterogeneity in a handful of systems---enzymes, motors, adhesion complexes---identifying and measuring it remains a formidable challenge. Here we show that evidence of this phenomenon is more widespread than previously known, encoded in data collected from some of the most well-established single molecule techniques: AFM or optical tweezer pulling experiments. We present a theoretical procedure for analyzing distributions of rupture/unfolding forces recorded at different pulling speeds. This results in a single parameter, quantifying the degree of heterogeneity, and also leads to bounds on the equilibration and conformational interconversion timescales. Surveying ten published datasets, we find heterogeneity in five of them, all with interconversion rates slower than 10 s$^{-1}$. Moreover, we identify two systems where additional data at realizable pulling velocities is likely to find a theoretically predicted, but so far unobserved cross-over regime between heterogeneous and non-heterogeneous behavior. The significance of this regime is that it will allow far more precise estimates of the slow conformational switching times, one of the least understood aspects of functional heterogeneity.

q-bio.BM↗

arXiv2016

Contact statistics highlight distinct organizing principles of proteins and RNA

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, $P(s)$ as a function of the arc length $s$, decay in power-law $\sim s^{-γ}$ over the intermediate range of $s$, $10\lesssim s\lesssim 110$. We found that the contact probability scaling exponent is $γ\approx 1.11$ for large RNA ($N>110$), $γ\approx 1.41$ for small sized RNA ($N<110$), and $γ\approx 1.65$ for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of $γ$ value from $γ=1.5$ for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large sized RNA ($N\gtrsim 110$) adopt crumpled structures, partitioned into modular multi-domains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of $γ\approx 1$ for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.

cond-mat.soft↗

arXiv2015

Confinement-induced glassy dynamics in a model for chromosome organization

Recent experiments showing scaling of the intrachromosomal contact probability, $P(s)\sim s^{-1}$ with the genomic distance $s$, are interpreted to mean a self-similar fractal-like chromosome organization. However, scaling of $P(s)$ varies across organisms, requiring an explanation. We illustrate dynamical arrest in a highly confined space as a discriminating marker for genome organization, by modeling chromosome inside a nucleus as a homopolymer confined to a sphere of varying sizes. Brownian dynamics simulations show that the chain dynamics slows down as the polymer volume fraction ($ϕ$) inside the confinement approaches a critical value $ϕ_c$. The universal value of $ϕ_c^{\infty}\approx 0.44$ for a sufficiently long polymer ($N\gg 1$) allows us to discuss genome dynamics using $ϕ$ as a single parameter. Our study shows that the onset of glassy dynamics is the reason for the segregated chromosome organization in human ($N\approx 3\times 10^9$, $ϕ\gtrsimϕ_c^{\infty}$), whereas chromosomes of budding yeast ($N\approx 10^8$, $ϕ<ϕ_c^{\infty}$) are equilibrated with no clear signature of such organization.

cond-mat.soft↗