Biomedical subjects

D Thirumalai

Publications and source records attributed to D Thirumalai.

At least 19 recordsLinked to original sources

PubMed2007

Intermediates and transition states in protein folding.

The complex role played by intermediates is dissected using experimental data on apomyoglobin (apoMb), simple theoretical concepts, and simulations of kinetics of simple minimal off-lattice models. The folding of moderate-to-large-sized proteins often occurs through passage of an ensemble of intermediates. In the case of apoMb there is dominant kinetic intermediate I that also occurs at equilibrium. The cooperativity of transition of U<-->I (U represents the ensemble of unfolded states) in apoMb at pH 4.0 is determined not only by the sequence but also by the anion concentration. Point mutations can substantially alter the cooperativity of formation of I. Another class of intermediates arise owing to bottlenecks in the rugged energy landscape that arises from topological frustration. As a result of the rough energy landscape, folding is predicted to follow the kinetic partitioning mechanism (KPM). According to KPM a fraction of molecules reaches the native state rapidly, while the remaining fraction is kinetically trapped in intermediates. The folding of lysozyme at pH 5.5 follows KPM. Our perspective also shows that the fraction of fast folding trajectories can be altered by changing pH, for example. These observations are clearly illustrated in simple off-lattice models of proteins. The simulations show that equilibrium intermediates occur "on-pathway" and have substantial probability to be revisited after the native state is reached, while kinetic intermediates are almost never sampled after native state is reached. In addition, kinetic intermediates are higher in free energy than equilibrium intermediates. We also discuss the consequences of multiple routes and intermediates on the transition state ensemble (TSE) in folding. Whenever multiple routes to the native state dominate, Phi-values can be larger than unity or less than zero. There appears to be a relationship between the diversity of structures in the denatured state ensemble and the extent to which the TSE is plastic. Simulations of beta-hairpins are used to illustrate these ideas.

Kinetics↗

PubMed2006

Dynamic competition between catch and slip bonds in selectins bound to ligands.

Atomic force measurements of unbinding rates (or off-rates) of ligands bound to a class of cell adhesion molecules from the selectin family show a transition from catch to slip bonds as the value of external force (f) is increased. At low forces (<10 pN), the unbinding rates decrease (catch regime), while, at high forces, the rates increase in accord with the Bell model (slip regime). The energy landscape underlying the catch-slip transition can be captured by a two-state model that considers the possibility of redistribution of population from the force-free bound state to the force-stabilized bound state. The excellent agreement between theory and experiments is used to extract the parameters characterizing the energy landscape of the complex by fitting the calculated curves to lifetime data (obtained at constant f) for the monomeric form of PSGL-1 (sPSGL-1). We used the constant force parameters to predict the distributions of unbinding times and unbinding forces as a function of the loading rate. The general two-state model, which also correctly predicts the absence of catch bonds in the binding of antibodies to selectins, is used to resolve the energy landscape parameters characterizing adhesive interactions of P- and L-selectins with physiological ligands such as sPSGL-1 and endoglycan and antibodies such as G1 and DREG56. Despite high sequence similarity, the underlying shapes of the energy landscape of P-selectin and L-selectin interacting with sPSGL-1 are markedly different. The underlying energy landscape of the selectin cell adhesion complex is sensitive to the nature of the ligand. The unified description of selectins bound to physiological ligands and antibodies in conjunction with experimental data can be used to extract the key parameters that describe the dynamics of cell adhesion complexes.

Binding, Competitive↗

PubMed2006

Monomer adds to preformed structured oligomers of Abeta-peptides by a two-stage dock-lock mechanism.

Nonfibrillar soluble oligomers, which are intermediates in the transition from monomers to amyloid fibrils, may be the toxic species in Alzheimer's disease. To monitor the early events that direct assembly of amyloidogenic peptides we probe the dynamics of formation of (Abeta(16-22))(n) by adding a monomer to a preformed (Abeta(16-22))(n-1) (n = 4-6) oligomer in which the peptides are arranged in an antiparallel beta-sheet conformation. All atom molecular dynamics simulations in water and multiple long trajectories, for a cumulative time of 6.9 mus, show that the oligomer grows by a two-stage dock-lock mechanism. The largest conformational change in the added disordered monomer occurs during the rapid ( approximately 50 ns) first dock stage in which the beta-strand content of the monomer increases substantially from a low initial value. In the second slow-lock phase, the monomer rearranges to form in register antiparallel structures. Surprisingly, the mobile structured oligomers undergo large conformational changes in order to accommodate the added monomer. The time needed to incorporate the monomer into the fluid-like oligomer grows even when n = 6, which suggests that the critical nucleus size must exceed six. Stable antiparallel structure formation exceeds hundreds of nanoseconds even though frequent interpeptide collisions occur at elevated monomer concentrations used in the simulations. The dock-lock mechanism should be a generic mechanism for growth of oligomers of amyloidogenic peptides.

Amyloid beta-Peptides↗

PubMed2006

Dynamics of Asp23-Lys28 salt-bridge formation in Abeta10-35 monomers.

In the amyloid fibrils formed from long fragments of the amyloid beta-protein (Abeta-protein), the monomers are arranged in parallel and lie perpendicular to the fibril axis. The structure of the monomers satisfies the amyloid self-organization principle; namely, the low free energy state of the monomer maximizes the number of intra- and interpeptide contacts and salt bridges. The formation of the intramolecular salt bridge between Asp(D)23 and Lys(K)28 ensures that unpaired charges are not buried in the low-dielectric interior. We have investigated, using all-atom molecular dynamics simulations in explicit water, whether the D23-K28 interaction forms spontaneously in the isolated Abeta10-35 monomer. To validate the simulation protocol, we show, using five independent trajectories spanning a total of 100 ns, that the pKa values of the titratable groups are in good agreement with experimental measurements. The computed free energy disconnectvity graph shows that broadly the ensemble of compact random coil conformations can be clustered into four basins that are separated by free energy barriers ranging from 0.3 to 2.7 kcal/mol. There is significant residual structure in the conformation of the peptide in each of the basins. Due to the desolvation penalty, the structural motif with a stable turn involving the residues VGSN and a preformed D23-K28 contact is a minor component of the simulated structures. The extent of solvation of the peptides in the four basins varies greatly, which underscores the dynamical fluctuations in the monomer. Our results suggest that the early event in the oligomerization process must be the expulsion of discrete water molecules that facilitates the formation of interpeptide-interaction-driven stable structures with an intramolecular D23-K28 salt bridge and an intact VGSN turn.

Amyloid beta-Peptides↗

PubMed2006

Dynamics of allosteric transitions in GroEL.

The chaperonin GroEL-GroES, a machine that helps proteins to fold, cycles through a number of allosteric states, the T state, with high affinity for substrate proteins, the ATP-bound R state, and the R" (GroEL-ADP-GroES) complex. Here, we use a self-organized polymer 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 --> R transition, in which the apical domains undergo counterclockwise 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 -->R" 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" states are broad with the TSE for the T --> R transition being more plastic than the R --> R" TSE.

Allosteric Regulation↗

PubMed2006

Size, shape, and flexibility of RNA structures.

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration R(G), follows the Flory scaling law, namely, R(G)=5.5N(1/3) A, where N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity Delta and the shape S parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of Delta, we find that a large fraction of folded RNA structures are aspherical and the distribution of S values shows that RNA molecules are prolate (S>0). The flexibility of folded structures is characterized by the persistence length l(p). By fitting the distance distribution function P(r), that is computed using the coordinates of the folded RNA, to the wormlike chain model we extracted the persistence length l(p). We find that l(p) approximately 1.5N(0.33) A which might reflect the large separation between the free energies that stabilize secondary and tertiary structures. The dependence of l(p) on N implies that the average length of helices should increase as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of R(G), Delta, S, and l(p). The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.

Models, Chemical↗

PubMed2006

Hydrophobic and ionic interactions in nanosized water droplets.

A number of situations such as protein folding in confined spaces, lubrication in tight spaces, and chemical reactions in confined spaces require an understanding of water-mediated interactions. As an illustration of the profound effects of confinement on hydrophobic and ionic interactions, we investigate the solvation of methane and methane decorated with charges in spherically confined water droplets. Free energy profiles for a single methane molecule in droplets, ranging in diameter (D) from 1 to 4 nm, show that the droplet surfaces are strongly favorable as compared to the interior. From the temperature dependence of the free energy in D = 3 nm, we show that this effect is entropically driven. The potentials of mean force (PMFs) between two methane molecules show that the solvent separated minimum in the bulk is completely absent in confined water, independent of the droplet size since the solute particles are primarily associated with the droplet surface. The tendency of methanes with charges (M(q+) and M(q-) with q(+) = |q(-)| = 0.4e, where e is the electronic charge) to be pinned at the surface depends dramatically on the size of the water droplet. When D = 4 nm, the ions prefer the interior whereas for D < 4 nm the ions are localized at the surface, but with much less tendency than for methanes. Increasing the ion charge to e makes the surface strongly unfavorable. Reflecting the charge asymmetry of the water molecule, negative ions have a stronger preference for the surface compared to positive ions of the same charge magnitude. With increasing droplet size, the PMFs between M(q+) and M(q-) show decreasing influence of the boundary owing to the reduced tendency for surface solvation. We also show that as the solute charge density decreases the surface becomes less unfavorable. The implications of our results for the folding of proteins in confined spaces are outlined.

Hydrogen Bonding↗

PubMed2006

Mechanical unfolding of RNA: from hairpins to structures with internal multiloops.

Mechanical unfolding of RNA structures, ranging from hairpins to ribozymes, using laser optical tweezer experiments have begun to reveal the features of the energy landscape that cannot be easily explored using conventional experiments. Upon application of constant force (f), RNA hairpins undergo cooperative transitions from folded to unfolded states whereas subdomains of ribozymes unravel one at a time. Here, we use a self-organized polymer model and Brownian dynamics simulations to probe mechanical unfolding at constant force and constant-loading rate of four RNA structures of varying complexity. For simple hairpins, such as P5GA, application of constant force or constant loading rate results in bistable cooperative transitions between folded and unfolded states without populating any intermediates. The transition state location (DeltaxFTS) changes dramatically as the loading rate is varied. At loading rates comparable to those used in laser optical tweezer experiments, the hairpin is plastic, with DeltaxFTS being midway between folded and unfolded states; whereas at high loading rates, DeltaxFTS moves close to the folded state, i.e., RNA is brittle. For the 29-nucleotide TAR RNA with the three-nucleotide bulge, unfolding occurs in a nearly two-state manner with an occasional pause in a high free energy metastable state. Forced unfolding of the 55 nucleotides of the Hepatitis IRES domain IIa, which has a distorted L-shaped structure, results in well-populated stable intermediates. The most stable force-stabilized intermediate represents straightening of the L-shaped structure. For these structures, the unfolding pathways can be predicted using the contact map of the native structures. Unfolding of a RNA motif with internal multiloop, namely, the 109-nucleotide prohead RNA that is part of the 29 DNA packaging motor, at constant value of rf occurs with three distinct rips that represent unraveling of the paired helices. The rips represent kinetic barriers to unfolding. Our work shows 1), the response of RNA to force is largely determined by the native structure; and 2), only by probing mechanical unfolding over a wide range of forces can the underlying energy landscape be fully explored.

Computer Simulation↗

PubMed2006

The different electronic natures displayed by the alkylthio groups in simple and higher conjugated aniline systems.

Systematic studies based on 1H NMR and 13C NMR indicated that the alkylthio group behaves as a weak electron-withdrawing group in a simple aniline system like 2-butylthioaniline, while the same alkylthio group clearly acted as a resonance electron-donating group in higher conjugated aniline trimer systems, like butylthio-substituted PDA (mono-PDA) and dibutylthio-substituted PDA (2,6-diPDA). The formation of 2,6-diPDA as the major byproduct during the preparation of mono-PDA from PDI and butane-1-thiol provided additional support for the resonance electron donating nature of the butylthio group in these aniline trimer systems. Furthermore, CV studies also clearly indicated that the redox potential E degrees (vs. SCE) of the aniline trimer systems decreased with the increase in the number of butylthio groups, further confirming the electron-donating nature of the butylthio group in these higher conjugated trimer systems.

Journal Article↗

PubMed2006

Low-frequency normal modes that describe allosteric transitions in biological nanomachines are robust to sequence variations.

By representing the high-resolution crystal structures of a number of enzymes using the elastic network model, it has been shown that only a few low-frequency normal modes are needed to describe the large-scale domain movements that are triggered by ligand binding. Here we explore a link between the nearly invariant nature of the modes that describe functional dynamics at the mesoscopic level and the large evolutionary sequence variations at the residue level. By using a structural perturbation method (SPM), which probes the residue-specific response to perturbations (or mutations), we identify a sparse network of strongly conserved residues that transmit allosteric signals in three structurally unrelated biological nanomachines, namely, DNA polymerase, myosin motor, and the Escherichia coli chaperonin. Based on the response of every mode to perturbations, which are generated by interchanging specific sequence pairs in a multiple sequence alignment, we show that the functionally relevant low-frequency modes are most robust to sequence variations. Our work shows that robustness of dynamical modes at the mesoscopic level is encoded in the structure through a sparse network of residues that transmit allosteric signals.

Allosteric Regulation↗

PubMed2006

Counterion charge density determines the position and plasticity of RNA folding transition states.

The self-assembly of RNA structure depends on the interactions of counterions with the RNA and with each other. Comparison of various polyamines showed that the tertiary structure of the Tetrahymena ribozyme is more stable when the counterions are small and highly charged. By monitoring the folding kinetics of the ribozyme as a function of polyamine concentration, we now find that the charge density of the counterions determines the positions of the folding transition states. The transition state ensemble (TSE) between U and N moves away from the native state as the counterion valence and charge density increase, as predicted by the Hammond postulate. The TSE is broader and less structured when the RNA is refolded in polyamines rather than Mg2+. That the charge density of the counterions determines the plasticity of the TSE demonstrates the importance of interactions among condensed counterions for the self-assembly of RNA structures. We propose that the major barrier to RNA folding is dominated by entropy changes when counterion charge density is low and enthalpy differences when it is high.

Animals↗

PubMed2006

Kinetics of interior loop formation in semiflexible chains.

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison with the case are in excellent agreement with explicit Brownian dynamics simulations of wormlike chain (WLC) model. The interior looping times (tauIC) can be greatly altered in the cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then tauIC increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (tauc) and interior looping (tauIC) times greatly increase at low ionic concentration. Because both tauc and tauIC are determined essentially by the effective persistence length [lp(R)] we computed lp(R) by varying the range of the repulsive interaction between the monomers. For short range interactions lp(R) nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.

Algorithms↗

PubMed2006

Residues in substrate proteins that interact with GroEL in the capture process are buried in the native state.

We have used a bioinformatic approach to predict the natural substrate proteins for the Escherichia coli chaperonin GroEL based on two simple criteria. Natural substrate proteins should contain binding motifs similar in sequence to the mobile loop peptide of GroES that displaces the binding motif during the chaperonin cycle. Secondly, each substrate protein should contain multiple copies of the binding motif so that the chaperonin can perform "work" on the substrate protein. To validate these criteria, we have used a database of 252 proteins that have been experimentally shown to interact with the chaperonin machinery in vivo. More than 80% are identified by these criteria. The binding motifs of all 79 proteins in the database with a known three-dimensional structure are buried (<50% solvent-accessible surface area) in the native state. Our results show that the binding motifs are inaccessible in the native state but become solvent-exposed in unfolded state, thus enabling GroEL to distinguish between unfolded and native states. The structures of the binding motif in the native states of the substrate proteins include alpha-helices, beta-strands, and random coils. The diversity of secondary structures implies that there are large and varied conformational transitions in the recognition motifs after their displacement by the mobile loops of GroES.

Binding Sites↗

PubMed2006

Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy: theory and applications.

We present, to our knowledge, a new theory that takes internal dynamics of proteins into account to describe forced-unfolding and force-quench refolding in single molecule experiments. In the current experimental setup (using either atomic force microscopy or laser optical tweezers) the distribution of unfolding times, P(t), is measured by applying a constant stretching force f(S) from which the apparent f(S)-dependent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy to map the parameters of the energy landscape of proteins. In force correlation spectroscopy, the joint distribution P(T, t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant f(S) separated by release periods T during which the force is quenched to f(Q) < f(S). During the release period, the protein can collapse to a manifold of compact states or refold. We show that P(T, t) at various f(S) and f(Q) values can be used to resolve the kinetics of unfolding as well as formation of native contacts. We also present methods to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P(T, t). The theory and a wormlike chain model for the unfolded states allows us to obtain the persistence length l(p) and the f(Q)-dependent relaxation time, giving us an estimate of collapse timescale at the single molecular level, in the coil states of the polypeptide chain. Thus, a more complete description of landscape of protein native interactions can be mapped out if unfolding time data are collected at several values of f(S) and f(Q). We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein (S1) with beta-sheet architecture for several values of f(S), T, and f(Q) = 0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.

Biomechanical Phenomena↗

PubMed2006

Forced-unfolding and force-quench refolding of RNA hairpins.

Nanomanipulation of individual RNA molecules, using laser optical tweezers, has made it possible to infer the major features of their energy landscape. Time-dependent mechanical unfolding trajectories, measured at a constant stretching force (f(S)) of simple RNA structures (hairpins and three-helix junctions) sandwiched between RNA/DNA hybrid handles show that they unfold in a reversible all-or-none manner. To provide a molecular interpretation of the experiments we use a general coarse-grained off-lattice Gō-like model, in which each nucleotide is represented using three interaction sites. Using the coarse-grained model we have explored forced-unfolding of RNA hairpin as a function of f(S) and the loading rate (r(f)). The simulations and theoretical analysis have been done both with and without the handles that are explicitly modeled by semiflexible polymer chains. The mechanisms and timescales for denaturation by temperature jump and mechanical unfolding are vastly different. The directed perturbation of the native state by f(S) results in a sequential unfolding of the hairpin starting from their ends, whereas thermal denaturation occurs stochastically. From the dependence of the unfolding rates on r(f) and f(S) we show that the position of the unfolding transition state is not a constant but moves dramatically as either r(f) or f(S) is changed. The transition-state movements are interpreted by adopting the Hammond postulate for forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to the two ends, show that the value of the unfolding force increases (especially at high pulling speeds) as the length of the handles increases. The pathways for refolding of RNA from stretched initial conformation, upon quenching f(S) to the quench force f(Q), are highly heterogeneous. The refolding times, upon force-quench, are at least an order-of-magnitude greater than those obtained by temperature-quench. The long f(Q)-dependent refolding times starting from fully stretched states are analyzed using a model that accounts for the microscopic steps in the rate-limiting step, which involves the trans to gauche transitions of the dihedral angles in the GAAA tetraloop. The simulations with explicit molecular model for the handles show that the dynamics of force-quench refolding is strongly dependent on the interplay of their contour length and persistence length and the RNA persistence length. Using the generality of our results, we also make a number of precise experimentally testable predictions.

Base Sequence↗

PubMed2006

Effect of finite size on cooperativity and rates of protein folding.

We analyze the dependence of cooperativity of the thermal denaturation transition and folding rates of globular proteins on the number of amino acid residues, N, using lattice models with side chains, off-lattice Go models, and the available experimental data. A dimensionless measure of cooperativity, Omega(c) (0 < Omega(c) < infinity), scales as Omega(c) approximately N(zeta). The results of simulations and the analysis of experimental data further confirm the earlier prediction that zeta is universal with zeta = 1 + gamma, where exponent gamma characterizes the susceptibility of a self-avoiding walk. This finding suggests that the structural characteristics in the denaturated state are manifested in the folding cooperativity at the transition temperature. The folding rates k(F) for the Go models and a dataset of 69 proteins can be fit using k(F) = k(F)0 exp(-cN(beta)). Both beta = 1/2 and 2/3 provide a good fit of the data. We find that k(F) = k(F)0 exp(-cN(1/2)), with the average (over the dataset of proteins) k(F)0 approximately (0.2 micros)(-1) and c approximately 1.1, can be used to estimate folding rates to within an order of magnitude in most cases. The minimal models give identical N dependence with c approximately 1. The prefactor for off-lattice Go models is nearly 4 orders of magnitude larger than the experimental value.

Hot Temperature↗

PubMed2006

Dynamic transition in tRNA is solvent induced.

Dynamics of tRNA was studied using neutron scattering spectroscopy. Despite vast differences in the architecture and backbone structure of proteins and RNA, hydrated tRNA undergoes the dynamic transition at the same temperature as hydrated lysozyme. The similarity of the dynamic transition in RNA and proteins supports the idea that it is solvent induced. Because tRNA essentially has no methyl groups, the results also suggest that methyl groups are not the main contributor of the dynamic transition in biological macromolecules. However, they may explain strong differences in the dynamics of tRNA and lysozyme observed at low temperatures.

Journal Article↗

PubMed2006

Nanopore-protein interactions dramatically alter stability and yield of the native state in restricted spaces.

We have studied the stability and the yield of the folded WW domains in a spherical nanopore to provide insights into the changes in the folding characteristics due to interactions of the polypeptide (SP) with the walls of the pore. Using different models for the interactions between the nanopore and the polypeptide chain we have obtained results that are relevant to a broad range of experiments. (a) In the temperature and the strength of the SP-pore interaction plane (lambda), there are four "phases," namely, the unfolded state, the native state, the molten globule phase (MG), and the surface interaction-stabilized (SIS) state. The MG and SIS states are populated at moderate and large values of lambda, respectively. For a fixed pore size, the folding rates vary non-monotonically as lambda is varied with a maximum at lambda approximately 1 at which the SP-nanopore interaction is comparable to the stability of the native state. At large lambda values, the WW domain is kinetically trapped in the SIS states. Using multiple sequence alignment, we conclude that similar folding mechanism should be observed in other WW domains as well. (b) To mimic the changes in the nature of the allosterically driven SP-GroEL interactions we consider two models for the dynamic Anfinsen cage (DAC). In DAC1, the SP-cavity interaction cycles between hydrophobic (lambda>0) and hydrophilic (lambda=0) with a period tau. The yield of the native state is a maximum for an optimum value of tau=tau(OPT). At tau=tau(OPT), the largest yield of the native state is obtained when tau(H) approximately tau(P) where tau(H)(tau(P)) is the duration for which the cavity is hydrophobic (hydrophilic). Thus, in order to enhance the native state yield, the cycling rate, for a given loading rate of the GroEL nanomachine, should be maximized. In DAC2, the volume of the cavity is doubled (as happens when ATP and GroES bind to GroEL) and the SP-pore interaction simultaneously changes from hydrophobic to hydrophilic. In this case, we find greater increase in yield of the native state compared to DAC1 at all values of tau.

Mathematics↗