arXiv subjects

Changbong Hyeon

Publications and source records attributed to Changbong Hyeon.

At least 73 records · Page 4Linked to original sources

arXiv2012

Chain Length Determines the Folding Rates of RNA

We show that the folding rates (k_F) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free energy barriers separating the folded and the unfolded states is Gaussian, which follows from central limit theorem arguments and polymer physics concepts, we show that k_F ~ k_0 exp(-alpha N^0.5). Remarkably, the theory fits the experimental rates spanning over seven orders of magnitude with k_0 ~ 1.0 (microsec)^{-1}. An immediate consequence of our finding is that the speed limit of RNA folding is about one microsecond just as it is in the folding of globular proteins.

cond-mat.soft↗

arXiv2011

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck-linker and clarify issues related the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.

physics.bio-ph↗

arXiv2011

Link between allosteric signal transduction and functional dynamics in a multi-subunit enzyme: S-adenosylhomocysteine hydrolase

S-adenosylhomocysteine hydrolase (SAHH), a cellular enzyme that plays a key role in methylation reactions including those required for maturation of viral mRNA, is an important drug target in the discovery of antiviral agents. While targeting the active site is a straightforward strategy of enzyme inhibition, evidences of allosteric modulation of active site in many enzymes underscore the molecular origin of signal transduction. Information of co-evolving sequences in SAHH family and the key residues for functional dynamics that can be identified using native topology of the enzyme provide glimpses into how the allosteric signaling network, dispersed over the molecular structure, coordinates intra- and inter-subunit conformational dynamics. To study the link between the allosteric communication and functional dynamics of SAHHs, we performed Brownian dynamics simulations by building a coarse-grained model based on the holo and ligand-bound structures. The simulations of ligand-induced transition revealed that the signal of intra-subunit closure dynamics is transmitted to form inter-subunit contacts, which in turn invoke a precise alignment of active site, followed by the dimer-dimer rotation that compacts the whole tetrameric structure. Further analyses of SAHH dynamics associated with ligand binding provided evidence of both induced fit and population shift mechanisms, and also showed that the transition state ensemble is akin to the ligand-bound state. Besides the formation of enzyme-ligand contacts at the active site, the allosteric couplings from the residues distal to the active site is vital to the enzymatic function.

q-bio.BM↗

arXiv2011

Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models

The distances over which biological molecules and their complexes can function range from a few nanometres, in the case of folded structures, to millimetres, for example during chromosome organization. Describing phenomena that cover such diverse length, and also time scales, requires models that capture the underlying physics for the particular length scale of interest. Theoretical ideas, in particular, concepts from polymer physics, have guided the development of coarse-grained models to study folding of DNA, RNA, and proteins. More recently, such models and their variants have been applied to the functions of biological nanomachines. Simulations using coarse-grained models are now poised to address a wide range of problems in biology.

cond-mat.soft↗

arXiv2011

Compaction and tensile forces determine the accuracy of folding landscape parameters from single molecule pulling experiments

We establish a framework for assessing whether the transition state location of a biopolymer, which can be inferred from single molecule pulling experiments, corresponds to the ensemble of structures that have equal probability of reaching either the folded or unfolded states (Pfold = 0.5). Using results for the forced-unfolding of a RNA hairpin, an exactly soluble model and an analytic theory, we show that Pfold is solely determined by s, an experimentally measurable molecular tensegrity parameter, which is a ratio of the tensile force and a compaction force that stabilizes the folded state. Applications to folding landscapes of DNA hairpins and leucine zipper with two barriers provide a structural interpretation of single molecule experimental data. Our theory can be used to assess whether molecular extension is a good reaction coordinate using measured free energy profiles.

cond-mat.soft↗

arXiv2010

Exploring the energy landscape of biopolymers using single molecule force spectroscopy and molecular simulations

In recent years, single molecule force techniques have opened a new avenue to decipher the folding landscapes of biopolymers by allowing us to watch and manipulate the dynamics of individual proteins and nucleic acids. In single molecule force experiments, quantitative analyses of measurements employing sound theoretical models and molecular simulations play central role more than any other field. With a brief description of basic theories for force mechanics and molecular simulation technique using self-organized polymer (SOP) model, this chapter will discuss various issues in single molecule force spectroscopy (SMFS) experiments, which include pulling speed dependent unfolding pathway, measurement of energy landscape roughness, the in uence of molecular handles in optical tweezers on measurement and molecular motion, and folding dynamics of biopolymers under force quench condition.

q-bio.BM↗

arXiv2010

Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.

cond-mat.soft↗

arXiv2009

Urea destabilizes RNA by forming stacking interactions and multiple hydrogen bonds with nucleic acid bases

Urea titration of RNA by urea is an effective approach to investigate the forces stabilizing this biologically important molecule. We used all atom molecular dynamics simulations using two urea force fields and two RNA constructs to elucidate in atomic detail the destabilization mechanism of folded RNA in aqueous urea solutions. Urea denatures RNA by forming multiple hydrogen bonds with the RNA bases and has little influence on the phosphodiester backbone. Most significantly we discovered that urea engages in stacking interactions with the bases. We also estimate, for the first time, m-value for RNA, which is a measure of the strength of urea-RNA interactions. Our work provides a conceptual understanding of the mechanism by which urea enhances RNA folding rates.

q-bio.BM↗

arXiv2009

Refolding dynamics of stretched biopolymers upon force quench

Single molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench, using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, $τ_F$, depends asymmetrically on $δf_S = f_S - f_m$ and $δf_Q = f_m - f_Q$ where $f_S$ ($f_Q$) is the stretch (quench) force, and $f_m$ is the transition mid-force of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, $R(t)$, occurs in three stages: a rapid initial decrease in the extension is followed by a plateau, and finally an abrupt reduction in $R(t)$ that occurs as the native state is approached. The duration of the plateau increases as $λ=τ_Q/τ_F$ decreases (where $τ_Q$ is the time in which the force is reduced from $f_S$ to $f_Q$). Variations in the mechanisms of force quench relaxation as $λ$ is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in $R(t)$. The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding.

physics.bio-ph↗

arXiv2009

Kinesin's backsteps under mechanical load

Kinesins move processively toward the plus end of microtubules by hydrolyzing ATP for each step. From an enzymatic perspective, the mechanism of mechanical motion coupled to the nucleotide chemistry is often well explained using a single-loop cyclic reaction. However, several difficulties arise in interpreting kinesin's backstepping within this framework, especially when external forces oppose the motion of kinesin. We review evidence, such as an ATP-independent stall force and a slower cycle time for backsteps, that has emerged to challenge the idea that kinesin backstepping is due to ATP synthesis, i.e., the reverse cycle of kinesin's forward-stepping chemomechanics. Supplementing the conventional single-loop chemomechanics with routes for ATP-hydrolyzing backward steps and nucleotide-free steps, especially under load, gives a better physical interpretation of the experimental data on backsteps.

physics.bio-ph↗

arXiv2008

Force Dependent Hopping Rates of RNA Hairpins can be Estimated from Accurate Measurement of the Folding Landscapes

The sequence-dependent folding landscapes of nucleic acid hairpins reflect much of the complexity of biomolecular folding. Folding trajectories, generated using single molecule force clamp experiments by attaching semiflexible polymers to the ends of hairpins have been used to infer their folding landscapes. Using simulations and theory, we study the effect of the dynamics of the attached handles on the handle-free RNA free energy profile $F^o_{eq}(z_m)$, where $z_m$ is the molecular extension of the hairpin. Accurate measurements of $F^o_{eq}(z_m)$ requires stiff polymers with small $L/l_p$, where $L$ is the contour length of the handle, and $l_p$ is the persistence length. Paradoxically, reliable estimates of the hopping rates can only be made using flexible handles. Nevertheless, we show that the equilibrium free energy profile $F^o_{eq}(z_m)$ at an external tension $f_m$, the force ($f$) at which the folded and unfolded states are equally populated, in conjunction with Kramers' theory, can provide accurate estimates of the force-dependent hopping rates in the absence of handles at arbitrary values of $f$. Our theoretical framework shows that $z_m$ is a good reaction coordinate for nucleic acid hairpins under tension.

cond-mat.soft↗

arXiv2007

Kinetics of Loop Formation in Polymer Chains

We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is $τ_c\sim τ_0 N^2$ (where $τ_0$ is a microscopic time scale and $N$ is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when $a$, the capture radius for contact formation, exceeds $b$, the average distance between two connected beads. Simulations also show that, when $a < b$, $τ_c\sim N^{α_τ}$, where $1.5<{α_τ}\le 2$ in the range $7<N<200$ used in the simulations. By using a diffusion coefficient that is dependent on the length scales $a$ and $b$ (with $a<b$), which captures the two-stage mechanism by which looping occurs when $a < b$, we obtain an analytic expression for $τ_c$ that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for $N < 100$ the values of $τ_c$ decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for $τ_c$ to a power law in $N$ ($τ_c\sim N^{α_τ}$) show that $α_τ$ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain.

cond-mat.soft↗

arXiv2007

Mechanical control of the directional stepping dynamics of the kinesin motor

Among the multiple steps constituting the kinesin's mechanochemical cycle, one of the most interesting events is observed when kinesins move an 8-nm step from one microtubule (MT)-binding site to another. The stepping motion that occurs within a relatively short time scale (~100 microsec) is, however, beyond the resolution of current experiments, therefore a basic understanding to the real-time dynamics within the 8-nm step is still lacking. For instance, the rate of power stroke (or conformational change), that leads to the undocked-to-docked transition of neck-linker, is not known, and the existence of a substep during the 8-nm step still remains a controversial issue in the kinesin community. By using explicit structures of the kinesin dimer and the MT consisting of 13 protofilaments (PFs), we study the stepping dynamics with varying rates of power stroke (kp). We estimate that 1/kp <~ 20 microsec to avoid a substep in an averaged time trace. For a slow power stroke with 1/kp>20 microsec, the averaged time trace shows a substep that implies the existence of a transient intermediate, which is reminiscent of a recent single molecule experiment at high resolution. We identify the intermediate as a conformation in which the tethered head is trapped in the sideway binding site of the neighboring PF. We also find a partial unfolding (cracking) of the binding motifs occurring at the transition state ensemble along the pathways prior to binding between the kinesin and MT.

cond-mat.soft↗

arXiv2007

Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {sufficiently large} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $ \sim f$ for small $f$, and $ \sim f^{2/3}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for $\la Z\ra$ as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.

cond-mat.soft↗

arXiv2007

Internal strain regulates the nucleotide binding site of the kinesin leading head

In the presence of ATP, kinesin proceeds along the protofilament of microtubule by alternated binding of two motor domains on the tubulin binding sites. Since the processivity of kinesin is much higher than other motor proteins, it has been speculated that there exists a mechanism for allosteric regulation between the two monomers. Recent experiments suggest that ATP binding to the leading head domain in kinesin is regulated by the rearward strain built on the neck-linker. We test this hypothesis by explicitly modeling a $C_α$-based kinesin structure whose both motor domains are bound on the tubulin binding sites. The equilibrium structures of kinesin on the microtubule show disordered and ordered neck-linker configurations for the leading and the trailing head, respectively. The comparison of the structures between the two heads shows that several native contacts present at the nucleotide binding site in the leading head are less intact than those in the binding site of the rear head. The network of native contacts obtained from this comparison provides the internal tension propagation pathway, which leads to the disruption of the nucleotide binding site in the leading head. Also, using an argument based on polymer theory, we estimate the internal tension built on the neck-linker to be f~(12-15) pN. Both of these conclusions support the experimental hypothesis.

q-bio.BM↗

arXiv2006

Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments

Single molecule mechanical unfolding experiments are beginning to provide profiles of the complex energy landscape of biomolecules. In order to obtain reliable estimates of the energy landscape characteristics it is necessary to combine the experimental measurements with sound theoretical models and simulations. Here, we show how by using temperature as a variable in mechanical unfolding of biomolecules in laser optical tweezer or AFM experiments the roughness of the energy landscape can be measured without making any assumptions about the underlying reaction oordinate. The efficacy of the formalism is illustrated by reviewing experimental results that have directly measured roughness in a protein-protein complex. The roughness model can also be used to interpret experiments on forced-unfolding of proteins in which temperature is varied. Estimates of other aspects of the energy landscape such as free energy barriers or the transition state (TS) locations could depend on the precise model used to analyze the experimental data. We illustrate the inherent difficulties in obtaining the transition state location from loading rate or force-dependent unfolding rates. Because the transition state moves as the force or the loading rate is varied it is in general difficult to invert the experimental data unless the curvature at the top of the one dimensional free energy profile is large, i.e the barrier is sharp. The independence of the TS location on force holds good only for brittle or hard biomolecules whereas the TS location changes considerably if the molecule is soft or plastic. We also comment on the usefulness of extension of the molecule as a surrogate reaction coordinate especially in the context of force-quench refolding of proteins and RNA.

cond-mat.soft↗

arXiv2006

Dynamics of allosteric transitions in GroEL

The chaperonin GroEL-GroES, a machine which helps some proteins to fold, cycles through a number of allosteric states, the $T$ state, with high affinity for substrate proteins (SPs), the ATP-bound $R$ state, and the $R^{\prime\prime}$ ($GroEL-ADP-GroES$) complex. Structures are known for each of these states. Here, we use a self-organized polymer (SOP) model for the GroEL allosteric states and a general structure-based technique to simulate the dynamics of allosteric transitions in two subunits of GroEL and the heptamer. The $T \to R$ transition, in which the apical domains undergo counter-clockwise motion, is mediated by a multiple salt-bridge switch mechanism, in which a series of salt-bridges break and form. The initial event in the $R \to R^{\prime\prime}$ transition, during which GroEL rotates clockwise, involves a spectacular outside-in movement of helices K and L that results in K80-D359 salt-bridge formation. In both the transitions there is considerable heterogeneity in the transition pathways. The transition state ensembles (TSEs) connecting the $T$, $R$, and $R^{\prime\prime}$ states are broad with the the TSE for the $T \to R$ transition being more plastic than the $R\to R^{\prime\prime}$ TSE. The results suggest that GroEL functions as a force-transmitting device in which forces of about (5-30) pN may act on the SP during the reaction cycle.

q-bio.BM↗

arXiv2006

Pathways and kinetic barriers in mechanical unfolding and refolding of RNA and proteins

Using self-organized polymer models, we predict mechanical unfolding and refolding pathways of ribo-zymes, and the green fluorescent protein. In agreement with experiments, there are between six and eight unfolding transitions in the Tetrahymena ribozyme. Depending on the loading rate, the number of rips in the force-ramp unfolding of the Azoarcus ribozymes is between two and four. Force-quench refolding of the P4-P6 subdomain of the Tetrahymena ribozyme occurs through a compact intermediate. Subsequent formation of tertiary contacts between helices P5b-P6a and P5a/P5c-P4 leads to the native state. The force-quench refolding pathways agree with ensemble experiments. In the dominant unfolding route, the N-terminal a helix of GFP unravels first, followed by disruption of the N terminus b strand. There is a third intermediate that involves disruption of three other strands. In accord with experiments, the force-quench refolding pathway of GFP is hierarchic, with the rate-limiting step being the closure of the barrel.

q-bio.BM↗