Abstract
The heat shock protein 70 (Hsp70) chaperones, vital to the proper folding of proteins inside cells, consume ATP and require cochaperones in assisting protein folding. It is unclear whether Hsp70 can utilize the free energy from ATP hydrolysis to fold a protein into a native state that is thermodynamically unstable in the chaperone-free equilibrium. Here we present a model of Hsp70-mediated protein folding, which predicts that Hsp70, as a result of differential stimulation of ATP hydrolysis by its Hsp40 cochaperone, dissociates faster from a substrate in fold competent conformations than from one in misfolding-prone conformations, thus elevating the native concentration above and suppressing the misfolded concentration below their respective equilibrium values. Previous models would not make or imply these predictions, which are experimentally testable. Our model quantitatively reproduces experimental refolding kinetics, predicts how modulations of the Hsp70/Hsp40 chaperone system affect protein folding, and suggests new approaches to regulating cellular protein quality.
Introduction
The discovery of chaperones and their roles in assisting protein folding amended the long-held view that proteins spontaneously fold into their native structures1–3. Large, multi-domain proteins may take many hours to fold, or fail to fold properly altogether on their own2,4. ATP-consuming chaperones—including Hsp70s—provide critical assistance in the in vivo folding and the biological functions of broad sets of substrate proteins3. Extensive experimental studies have firmly established that the Hsp70 chaperones can greatly accelerate the folding of their substrate proteins5,6. Despite tremendous progress in the mechanistic studies of the Hsp70 chaperones2,7, including the development of theoretical models8–10, it remains unclear why ATP consumption is indispensable to these chaperones; enzymes do not need to consume free energy in catalyzing chemical reactions. Recently it was demonstrated that chaperones such as GroEL and Hsp70 depend on continuous ATP hydrolysis to maintain a protein in a native state that is thermodynamically unstable11, but it is unknown how Hsp70 can utilize the ATP free energy to alter the folding equilibrium. In addition, Hsp70s require Hsp40—also known as J proteins12— cochaperones in assisting protein folding. It is yet unexplained why cochaperones are absolutely necessary.
The Hsp70 chaperones, such as the bacterial DnaK, consist of an N-terminal nucleotide binding domain (NBD) and a C-terminal substrate binding domain (SBD). The Hsp70 SBD adopts an open conformation when its NBD is ATP-bound (we call the Hsp70 to be in the ATP-state), which allows the substrate to bind and unbind at high rates, whereas when the NBD is ADP-bound (ADP-state), the SBD changes to a closed conformation, rendering both binding and unbinding orders-of-magnitude slower6,13,14. Hsp70s have low basal ATP hydrolysis activities15. The Hsp40 cochaperones, such as the bacterial DnaJ, can drastically stimulate the ATPase activity of Hsp70 using their N-terminal J domain (JD)16,17, shared by all Hsp40s (hence the name J proteins)12. Hsp40s also have a C-terminal domain (CTD) that can bind to denatured proteins18,19. Both Hsp70 and Hsp40 recognize exposed hydrophobic sites7,20,21. As a result, they can distinguish different protein conformations using the corresponding difference in the exposed hydrophobic sites. For example, Hsp70 has been shown to bind to both unfolded and partially folded, near native protein structures, but not to native structures22,23. Hsp40 and Hsp70 may simultaneously bind to different segments of the same substrate molecule, and the consequent spatial proximity then facilitates the J domain binding to Hsp70 and accelerating its ATP hydrolysis24–26. Following ATP hydrolysis, the chaperone returns from the ADP-state to the ATP-state through nucleotide exchange, which is often catalyzed by nucleotide exchange factors (NEF) such as the bacterial GrpE27,28.
A protein may fold to its native state, N, or go into a misfolded/aggregated—we will use these two terms interchangeably—state, M (Fig. 1a). It is unknown whether Hsp70 can use the free energy from ATP hydrolysis to drive its substrate toward the native state such that fN / fM > fN,eq / fM,eq, where fS is the fraction of the substrate in state S at the steady state of Hsp70-mediated folding, and fS,eq is the corresponding fraction at the folding equilibrium in the absence of the chaperone. Previous models9,29 mostly considered the chaperone as an unfoldase/holdase—which need not consume free energy—that pulls the substrate out of the misfolded state and holds it in an unfolded state. It was proposed that the free energy from ATP hydrolysis was used to achieve ultra-affinity in substrate binding8,30. As an unfoldase/holdase, Hsp70 would also pull the substrate out of the native state into the unfolded state; unless Hsp70 has a higher affinity for the native substrate than for the misfolded substrate, these models would predict fN / fMN,eq / fM,eq.
Here we propose a model of Hsp70-mediated protein folding, in which Hsp70 and Hsp40 together constitute a molecular machine that uses the free energy from ATP hydrolysis to actively drive a protein toward its native state, so that fN / fM > fN,eq / fM,eq. It suggests that without Hsp40, Hsp70 alone cannot change the ratio fN / fM from the equilibrium value fN,eq / fM,eq. Our model thus answers the question why Hsp70 requires both the Hsp40 cochaperones and ATP consumption in assisting protein folding. Our model explains the puzzling non-monotonic dependency of folding efficiency on the chaperone and cochaperone concentrations. It makes quantitative predictions on how protein folding is affected by modulations of the chaperone environment, including changes in the ATPase activity or the nucleotide exchange rate of Hsp70. These predictions may be readily tested by experiments, and inform rational approaches to manipulating chaperone-mediated protein folding.
Results
In our model (detailed in Methods), we consider two additional conformational states—besides the M and N states—of a protein: the unfolded and aggregation-prone state, U, and the fold-competent state, F. A protein in the F state is unfolded but poised to fold into the native state (Fig. 1a, b). Such intermediate states of folding have been observed experimentally4. Conformational transitions can occur between M and U, between U and F, and between F and N (Fig. 1b). We assume that a protein in the U state has more exposed hydrophobic sites than in the F state—which is consistent with the experimental observations4—and a protein in the M and N states has nearly zero such sites, as both folding and aggregation (including oligomerization) bury the protein’s hydrophobic sites (Fig. 1a).
Key to our model is the assumption that Hsp40, like Hsp70, has different affinities for the substrate in different conformations20, favoring conformations with more exposed hydrophobic sites. Thus Hsp70 and Hsp40 can bind to a substrate molecule in the U and F states—with higher affinities for the U state than for the F state—but not to one in the M and N states (Fig. 1b). A substrate in the U state is more likely to be Hsp40-bound than one in the F state. As a result, an Hsp70 molecule bound to a substrate molecule in the U state will on average have substantially higher ATP hydrolysis rate—because of the more probable cis stimulation by an Hsp40 molecule bound to the same substrate molecule—than if it is bound to a substrate molecule in the F state. If the nucleotide exchange rate is between these two hydrolysis rates, an Hsp70 bound to a substrate in the U state will be driven toward the ADP-state, where it slowly dissociates from the substrate, while an Hsp70 bound to a substrate in the F state will be driven toward the ATP-state, where it rapidly dissociates from the substrate. Acting like a Maxwell’s demon31, Hsp70 releases the fold-competent substrate but retains the aggregation-prone substrate, driving the folding along the reaction path of M → U → U · C · ATP → U · C · ADP → F · C · ADP → F C ATP → F → N (S C · X represents the complex between a substrate in conformation S and the chaperone C bound to nucleotide X = ATP, ADP) (Fig. 1b). One ATP molecule is consumed in this reaction path and the free energy is used to compel the substrate into the native state.
The extent to which Hsp70 biases protein folding can be quantified by the excess free energy: ΔΔG ≡ R T (ln(fN / fM) - ln(fN,eq / fM,eq)), where R is the gas constant and T the temperature. A positive excess free energy requires not that more chaperones bind to the substrate in the U state than to the substrate in the F state, which is true and reflected in previous models, but that an individual chaperone molecule, when bound to a substrate, resides longer on it if the substrate is in the U state than if it is in the F state. For this, Hsp70 needs both ATP consumption and a cochaperone: it can be shown algebraically (see Methods) and numerically (Fig. 1c) that without cochaperones, ΔΔG = 0. These predictions are consistent with the results from the single molecule experiment of DnaK-mediated refolding32, where DnaK alone in the presence of ATP was unable to alter the ratio of the misfolded and folded fractions.
We applied our model to the analysis of DnaK/DnaJ/GrpE-mediated refolding of luciferase5 and its variant LucDHis629. Most of the relevant kinetic parameters for this bacterial Hsp70 system have been carefully determined experimentally33 (Table 1). Our model quantitatively reproduces the experimentally observed refolding kinetics under various conditions, capturing the slow spontaneous refolding and denaturation of luciferase, the acceleration of refolding with chaperone assistance, and the necessity of GrpE (Fig. 2a, b). The refolding speed and yield reach a maximum at the DnaK concentration of 1μM, which is captured by our model (Fig. 2b, c). The intermediate conformations U and F in our model may correspond to the experimentally identified intermediate conformations I2 and I1 of luciferase4: the free energy difference between N and F at 25 °C, according to the fitted parameters, is 20 kJ/mol, close to the experimental value of 15 kJ/mol between N and I1, measured at 10 °C. Consistent with previous experimental observations29, our model suggests that the Hsp70-accelerated refolding proceeds in two steps: 1) rapid unfolding of the misfolded substrate, stabilized by the ADP-bound DnaK, followed by 2) slow conversion to the native state (Fig. 3a).
At the steady state, the reactive flux along the ATP-driven cycle U → U C ATP → U C · ADP → F · C · ADP → F · C · ATP → F (→ U) (Fig. 3b) keeps the protein folding out of equilibrium, elevating the native population above and suppressing the misfolded population below their respective equilibrium values (Fig. 2c). The excess free energy at the steady state always increases with increasing DnaK concentrations, but the native population reaches a maximum and then decreases (Fig. 2c), because at high DnaK concentrations, the substrate is trapped in the DnaK-bound state and thus prevented from folding into the native state.
The model parameters fit to the refolding experiments. of LucDHis6 (Fig. 4). In the initial minutes of refolding, approximately 150 ATP molecules are consumed to refold one LucDHis6 (Fig. 4a), which is reasonably close to the experimental result of ~50 ATP molecules consumed per refolded LucDHis6 when the stoichiometry of DnaK:LucDHis6 is 1:1, significantly higher than the experimental number of ~5 when LucDHis6 is in excess of DnaK, and significantly lower than the estimates of > 1000 for many other substrates in other experiments29,34–36. The discrepancy between the model and the experimental results may be partially attributable to the approximations in our model and the inaccuracies in the input kinetic parameters. ATP hydrolysis continues at the steady state and the free energy is utilized to promote the native state and suppress the misfolded state (Fig. 4b, c). As [DnaK] exceeds 1 µM, the ATP consumption rate increases rapidly without commensurate increase in the excess free energy. Our analysis thus suggests that DnaK may be most free energy efficient at maintaining protein folding out-of-equilibrium when its concentration is in the sub-micromolar range, a prediction that may be tested experimentally.
Our model suggests that Hsp70 can keep a protein folded even if it thermodynamically favors aggregation. The chaperone is thus able to play a critical role in maintaining protein conformations, not just in the folding of nascent chains37. Higher DnaK concentrations are required to suppress aggregation at increasing substrate concentrations (Fig. 5a) or at decreasing substrate stabilities (Fig. 5b). This may explain how cells that overexpress DnaK can tolerate higher numbers of mutations in the chaperone’s substrates38. Because the excess free energy plateaus at high chaperone concentrations (Fig. 2c), our results imply a limit on the chaperones’capacity to prevent aggregation, in that there exists a threshold of aggregation tendency (Fig. 5a, b, the black arrows) above which the chaperone can no longer maintain high levels of native concentrations and prevent aggregation at the same time.
Our model suggests that Hsp70 only drives the folding of proteins with sufficiently slow conversion between U and F states (Fig. 5c, d, e), implying that Hsp70 substrates tend to be slow refolding proteins (Fig. 5d). If the conversion between U and F is too fast, the chaperone diminishes, rather than increases, the native fraction in comparison to the chaperone-free equilibrium. As the conversion slows, the chaperone drives the steady state native fraction higher, but at the price of longer refolding time (Fig. 5e), a trade-off reminiscent of that between speed and specificity in the kinetic proofreading mechanism39,40, where the expenditure of free energy (such as from ATP or GTP consumptions) is utilized to increase the specificity of chemical reactions.
Our model explains the observation that folding is less efficient at both low and high DnaJ concentrations15 (Fig. 6a). At low DnaJ concentrations, ATP hydrolysis is slow, and nucleotide exchange drives DnaK toward the ATP-state, in which it dissociates from the substrate rapidly and thus unable to prevent aggregation. At high DnaJ concentrations, a large fraction of the substrate in the U state is bound to DnaJ. These DnaJ-bound substrate molecules are trapped in the U state, unable to progress toward the F state, resulting in diminished folding.
Our model also explains the observation that folding decreases at both low and high GrpE concentrations27 (Fig. 6b). For the chaperone to effectively assist folding, nucleotide exchange should be much slower than ATP hydrolysis when the chaperone binds to a substrate in the U state, but much faster than ATP hydrolysis when it binds to a substrate in the F state, so that the chaperone is driven toward the ADP-state in the former case, and toward the ATP-state in the latter case (Fig. 1b). At low GrpE concentrations, nucleotide exchange is slow, leaving DnaK bound to the substrate in the F state predominantly in the ADP-state—as reflected by the low population of F · C · ATP (Fig. 6b), slowing its dissociation from the substrate and thus preventing the latter from folding to the native state. At high GrpE concentrations, nucleotide exchange is fast, and DnaK is driven into the ATP-state and does not stay bound to the substrate in the U state long enough—as reflected by the decreasing population of U · C · ADP (Fig. 6b)— to prevent the substrate from aggregation. To maximize substrate folding, higher nucleotide exchange rate should accompany higher stimulated ATP hydrolysis rate (Fig. 6c, d, e).
Our model predicts that Hsp70 chaperones with higher Hsp40-stimulated ATP hydrolysis rates can drive substrate folding to higher native fractions (Fig. 6e), at the cost of higher free energy expenditure (Fig. 6f). This result explains a previous experimental observation that a small molecule that enhances ATP hydrolysis by Hsp40-bound Hsp70 can induce higher yields of substrate folding41. Modulation of the ATP hydrolysis or the nucleotide exchange rates by small molecules may represent a therapeutic opportunity in the treatment of misfolding- or proteostasis-related diseases42.
Discussion
Our model makes two distinct predictions that subject it to future experimental tests and possible falsification. First, it predicts that some thermodynamically unstable substrates depend on continuous Hsp70 assistance to maintain their native structures, and such a substrate in the steady state of Hsp70-mediated folding will gradually lose its native structure upon disruption of the chaperone system. Second, it predicts that an Hsp70 molecule bound to a substrate molecule will dissociate faster if subsequently the substrate molecule folds into the native state than if the substrate molecule misfolds, and such a difference will vanish in the absence of Hsp40. The second prediction may be tested by single molecule experiments23,32, if, for instance, separate fluorescence signals are available to detect Hsp70-substrate binding and substrate folding.
In support of the first prediction above, a recent experiment has demonstrated that luciferase at 37 °C can be kept active by the DnaK/DnaJ/GrpE chaperone system when there is sufficient ATP, but it rapidly loses its activity when ATP is depleted by the addition of apyrase11. Here, based on our model, we propose an alternative experiment, which avoids the complication that apyrase also affects the luciferase assay: Hsp70-mediated maintenance of luciferase activity may be disrupted by inhibiting the simultaneous binding of Hsp40 to Hsp70 and the substrate protein, which can be implemented, for example, by adding a J-domain (e.g., DnaJ with its CTD deleted) in excess to the chaperone system.
Methods
Model of Hsp70-mediated protein folding
We denote Hsp70 as C, Hsp40 (J protein) as J, and the NEF as E. [Y] denotes the solution concentration of the molecular species Y. There are four types of reactions explicitly considered in our model (Fig. 1b):
1) Hsp70 binding to the substrate.
2) Conformational transitions of the substrate. An Hsp70-free substrate can adopt any of the four conformational states
The chaperone-bound substrate can only be in and transition between the U and F states
3) ATP hydrolysis.
4) Nucleotide exchange.
The details of the kinetic rates of the above reactions are described below.
Hsp70 binding to the substrate
The association rate constant of Hsp70 binding to a substrate in state , is determined by the number of accessible binding sites, , in that conformation: is the association rate constant of the chaperone binding to a fully accessible binding site, and X = ATP, ADP. The dissociation rate constant of Hsp70 from the substrate, kd,C.x, does not depend on the substrate conformation, but depends on whether nucleotide X = ATP or ADP is bound. Experimentally, and . We assume .
Conformational transitions of the substrate
The transition rates between conformations S and S’ are different between a chaperone-free substrate and a chaperone-bound substrate (Fig. 1b). The condition of thermodynamic cycle closure dictates that
Because Hsp40 has different affinities for different substrate conformations, the transition rates between the conformations will depend on whether the substrate is bound to Hsp40. We treat the effects of Hsp40 on the reactions implicitly by making the affected rate constants dependent on the solution Hsp40 concentration [J] (see below).
For the transition , we assume that the bound chaperone does not hinder the substrate to go from the F state to the U state, because a binding site available in the F state is most likely also available in the U state (based on the assumption . Thus we take . It follows from thermodynamic cycle closure that the rate of the reverse transition—we use the superscript dagger to indicate that they are influenced by the presence of Hsp40—is
We take the rate of aggregation to be proportional to the substrate concentration:
The rates (for S = F, M) depend on the affinities of Hsp40 for the substrate in different conformational states. For simplicity, we assume that Hsp40 only binds to the substrate in the U state, and consequently only the Hsp40-free substrate can change from conformation U to F or M. The corresponding transition rates are
where kU→ S is the rate of transition U → S (for S = F, M) for an Hsp40-free substrate, pJ is the probability that the substrate is Hsp40-bound, and is the binding constant of Hsp40 for the conformational state S.
Hsp40-substrate binding
To keep our model simple, we do not explicitly consider the kinetics of binding and unbinding between Hsp40 and the substrate, and make the approximation that they are always at equilibrium. The key assumption of our model is that the fold-competent conformation F is much less accessible to Hsp40 than the aggregation-prone conformation U, i.e., . To reduce the number of unknown parameters, we take , i.e., the binding of Hsp40 to the fold-competent conformation is negligible, as in our derivation of the transition rates above. We also neglect subtleties such as that the J domain may bind with different affinities to Hsp70 in the ATP- and ADP-states43. The above approximations may contribute to quantitative differences between the predictions of our model and the experimental observations, particularly in predicting how folding changes with Hsp40 concentrations. The binding and unbinding of Hsp40 to the substrate and to Hsp70 can be explicitly included in our model at the cost of greater complexity and additional fitting parameters, but our simplified treatment above is adequate for the key results in this work.
ATP hydrolysis
The Hsp40-stimulated Hsp70 ATP hydrolysis rate, , can be orders-of-magnitude higher than the unstimulated basal rate . The ATP hydrolysis rate of Hsp70 bound to the substrate in the F state is simply , following our approximation that no Hsp40 binds to the substrate in the F state. When Hsp70 is bound to the substrate in the U state, its average rate of ATP hydrolysis, given the solution Hsp40 concentration, [J], can be approximated by
where being the association and dissociation rates of J domain binding to Hsp70, and [J]eff being the effective concentration of a substrate-bound Hsp40 molecule around an Hsp70 molecule bound to the same substrate molecule. The first term on the right hand side is the steady state rate of catalysis, weighted by the probability pJ that an Hsp40 is bound to the substrate and thus present to catalyze the hydrolysis. Here we assume a high ATP concentration such that ATP binding to Hsp70 is fast compared to other steps in ATP hydrolysis.
NEF-catalyzed nucleotide exchange
Because of the high concentration of ATP in cells and in the refolding experiments, we treat this reaction as irreversible. The reaction proceeds in three steps: 1) dissociation of ADP, 2) binding of ATP, and 3) conformational change of Hsp70 from the closed conformation in the ADP-state to the open conformation in the ATP-state. The conformational equilibrium between the open and closed conformations may be influenced by Hsp40 binding to Hsp7044, but this effect is not considered in our model for simplicity and lack of experimental parameters. In absence of the nucleotide exchange factor, the rate limiting step in the reaction is the dissociation of ADP, with the rate constant kd,ADP, whereas when catalyzed by the NEF, the rate limiting step is the conformational change, with rate constant kC 27,45. The overall rate of reaction at a given NEF concentration, [E], is then approximately
where being the association and dissociation rates of NEF binding to Hsp70. The temperature dependence of kC for DnaK has been determined to satisfy the Arrhenius equation: , where R = 8.314 J/mol/K is the gas constant.
Solving the kinetic equations
To simplify the calculations of refolding kinetics, we make the approximation that the solution concentrations of Hsp70, Hsp40, and NEF remain constant throughout the refolding process, which is true if they are in large excess of the substrate-bound chaperone, cochaperone, and NEF. Under this approximation, refolding kinetics is described by a set of linear ordinary differential equations, which are solved by the technique of eigenvalue decomposition of the rate matrix. This simplification allows quick and robust fitting of the folding kinetic parameters to the experimental refolding data. The steady state calculations do not use this approximation.
Proof that without cochaperones Hsp70 cannot alter the population ratio between the native and the misfolded states
Consider a hypothetical, single-conformation substrate s and a reference reaction cycle of chaperone binding , ATP hydrolysis , and nucleotide exchange (s · C · ADP + ATP → s · C ATP + ADP), where the ATP-bound and ADP-bound chaperones bind to s with the rate constants , respectively. Let be the fractions of the hypothetical substrate that are chaperone-free (s), bound to an ATP-bound chaperone (s · C · ATP), and bound to an ADP-bound chaperone (s · C · ADP), respectively, at the steady state of this reaction cycle. For the real substrate in Hsp70-mediated folding, let fS and fS·C·X (X = ATP, ADP) be the fractions of the free and the C · X-bound substrates in conformation S, and let fS,eq be the fraction of the substrate in conformation S at the folding equilibrium in the absence of the chaperones. It can be verified that
where
are the steady state solutions to the kinetic equations, given the condition of thermodynamic cycle closure. Thus the ratio is not altered by the chaperone, despite the free energy expenditure of ATP hydrolysis. This holds true for all numbers of intermediate states, so long as the ATP hydrolysis and the nucleotide exchange rates of the chaperone do not depend on the conformational state of the bound substrate.
Author Contributions
HX designed and performed the research and wrote the paper.