Reconciling theories of chaperonin accelerated folding with experimental evidence

Abstract

For the last 20 years, a large volume of experimental and theoretical work has been undertaken to understand how chaperones like GroEL can assist protein folding in the cell. The most accepted explanation appears to be the simplest: GroEL, like most other chaperones, helps proteins fold by preventing aggregation. However, evidence suggests that, under some conditions, GroEL can play a more active role by accelerating protein folding. A large number of models have been proposed to explain how this could occur. Focused experiments have been designed and carried out using different protein substrates with conclusions that support many different mechanisms. In the current article, we attempt to see the forest through the trees. We review all suggested mechanisms for chaperonin-mediated folding and weigh the plausibility of each in light of what we now know about the most stringent, essential, GroEL-dependent protein substrates.

Appendices

Appendix A: Estimating the fraction of time proteins are exposed to the cytosol

In an earlier work, we developed a formula to describe the folding of any protein in the presence of chaperones which cyclically unfold their substrates [148]. We used this to prove that the iterative annealing model (IAM) is not optimal for, and does not explain, the chaperonin-mediated folding of aggregate-prone substrates. Instead, an optimal chaperonin would bind to its substrates only once, releasing it only upon folding, lending support to the Anfinsen cage model. Unfortunately, many simplifying assumptions were made; for example, we ignored the fact that proteins interact with a variety of chaperones other than GroEL, and we ignored the fact that some proteins remain bound to the chaperone over multiple ATPase cycles. We also implicitly assumed that sufficient GroEL chaperonins are present to handle demand, and we ignored transient stress. However, the conclusions of that study remain valid when these assumptions are relaxed. In the sections that follow we briefly review and generalize these kinetic arguments.

The many-cycle assumption

As explained earlier [21, 148], chaperonins like GroEL can reduce the time that proteins spend unprotected in the cytosol before folding by a fraction (denoted f _bulk) which can be estimated from the ratios of the average time spent bound and unbound from GroEL during each cycle:

$$ f_{\text{bulk}} = {\frac{{\left\langle {t_{\text{unbound}} } \right\rangle }}{{\left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{bound}} } \right\rangle }}} $$

(1)

To justify this, we must assume that proteins undergo many cycles of binding to GroEL and release into the cytosol before folding, as suggested by [16, 80, 91, 102]. Here 〈〉 denotes the average, and t _bound is the total time spent bound to the chaperone (while either immobilized or protected).

$$ \left\langle {t_{\text{bound}} } \right\rangle = \left\langle {t_{\text{hold}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle $$

(2)

(See Figs. 1 and 2, for definitions of t _unbound, t _hold, and t _protect.) We considered what happens if you abandon this assumption in “The stationary iterative annealing model”.

Substrates do not always unbind from GroEL

A complication arises due the fact that some GroEL substrates (rhodanese) do not unbind during every ATPase cycle [7, 12, 180]. Suppose that f _ub indicates the probability that the protein substrate can successfully unbind itself from GroEL once the GroES lid departs. (This occurs following ATP hydrolysis; see Figs. 1, caption and 2). If so, then in that case it will require 1/f _ub cycles for the protein to successfully free itself from GroEL, on average, (note: 1/f _ub ≥ 1). This means it would remain bound to GroEL for a duration of approximately (〈t _bound〉 + 〈t _unbound〉)/f _ub seconds, instead of 〈t _bound〉 seconds. (Minor correction: We note that during the first of these 1/f _ub cycles, the protein is initially unbound, so to be precise, we should not have included one of these “unbound” time intervals.)

Once finally released, if the protein has not yet folded, it will have to rebind to GroEL requiring t _unbound seconds. As long as this process occurs multiple times before folding, the arguments we have made so far continue to apply, and we can replace 〈t _bound〉 in Eq. 1, with 〈t _unbound〉 (1/f _ub − 1) + 〈t _bound〉/f _ub. (The “−1” comes from the correction discussed above.) This yields:

$$ f_{\text{bulk}} = f_{\text{ub}} \times {\frac{{\left\langle {t_{\text{unbound}} } \right\rangle }}{{\left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{bound}} } \right\rangle }}} $$

(3)

For example, rhodanese in vitro escapes GroEL every four cycles on average (f _ub ≈ 0.25), frequently enough so that it probably escapes GroEL a couple times before folding [180]. Rhodanese is an extraordinarily slow folder, requiring 7 min to fold on average [20], corresponding to 7–60 full, two-ring ATPase cycles and consuming at least 130 molecules of ATP [149].

We note that sometimes unbinding does not occur multiple times before folding. For example, in vivo (or in the presence of a crowding agent), rhodanese typically remains bound to GroEL until folding [7]. In that case, the situation is fundamentally different, and we have to consider the issues raised in “The stationary iterative annealing model”. Equation 3 does not apply to rhodanese in vivo. We note that this is not an issue for many stringent GroEL substrates. Others (like RuBisCo) unbind from GroEL after every ATPase cycle (f _ub ≈ 1) [16].

Under steady-state conditions

In the absence of stress (“steady-state”) conditions (see “The steady-state assumption”), it is more relevant to consider:

$$ f_{\text{bulk}}^{\text{ss}} = f_{\text{ub}} \times {\frac{{\left\langle {t_{\text{unbound}} } \right\rangle }}{{\left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle }}} $$

(4)

During the time interval (〈t _hold〉) that proteins are either bound to the open GroEL trans ring, or bound to auxiliary chaperones like DnaK/J, they are unable to fold or aggregate and for all practical purposes, they are immobilized (although they may in fact be able to move). Under steady-state conditions we neglect to consider any time spent by the protein in these “immobilized” states; in other words, we have substituted 〈t _hold〉 = 0 into Eqs. 2, 3. Temporary delays (no matter how long) which have no other effect than to immobilize the protein, should have no effect on a protein’s likelihood of eventually folding or aggregating; that is, assuming the risk of aggregation in the bulk remains constant over time. We note that under steady-state conditions, the concentration of denatured proteins, and rate of aggregation, should not fluctuate significantly over time, at least not during the time for most proteins to fold. (See “The steady-state assumption” for details. We elaborate further in “Why should we ignore immobile states?”.)

Since 〈t _unbound〉 is typically far more rapid than 〈t _protect〉, this is a considerable reduction (f ^ss_bulk  ≪ 1).

The role of HSP70/HSP40 and other ancillary chaperones

For GroEL substrates, it appears that other chaperones such as trigger factor, HSP70/40 (DnaK/J) and their associated nucleotide exchange factors (GrpE), prevent unfolded protein chains from aggregating as they wait for GroEL [3, 13, 23, 25]. After being ejected from GroEL, proteins that are still unfolded are likely to bind to chaperones like DnaK/J before rebinding to GroEL. The average of the total time that proteins spend unprotected in the bulk during this time (represented by 〈t _unbound〉) is a complicated function of the DnaK/J, GrpE, and dimeric trigger factor concentrations, in addition to the nucleotide binding, release, and hydrolysis rates (for example, see [75]), not to mention the length of the substrate protein (as suggested by [134]). However, as far as GroEL substrates are concerned, the only role of these auxiliary chaperones is to reduce 〈t _unbound〉. Whether they are successful is a separate issue, and it does not effect our conclusion regarding the optimal behavior of GroEL. Equations 1, 3, and 4 still remain remain valid, regardless of the presence of other chaperones.

Appendix B: The steady-state assumption

As mentioned in the "Introduction", GroEL/ES performs maintenance duties in the cell and is always present at high concentrations, even in the absence of external stress [5]. Under non-stress, steady-state conditions, it seems reasonable to assume that concentration of each species of protein remains roughly constant over time; or at least these concentrations do not fluctuate significantly during the course of a single folding event. This is important for understanding the mechanism of GroEL.

Under steady-state conditions, the only way to reduce aggregation is to reduce the concentration of non-native proteins in the cell, which can only be done by reducing the average time each protein spends unprotected in the cytosol (“bulk”) before folding, 〈t _bulk〉 [148, 197]. During this time, proteins are susceptible to aggregation. It is convenient to think of this as the product of the average folding time 〈t _F〉 (under dilute conditions), and the fraction of that time which is spent in the bulk f _bulk.

$$ \left\langle {t_{\text{bulk}} } \right\rangle = \left\langle {t_{\text{F}} } \right\rangle \times f_{\text{bulk}} $$

(5)

In this way, we can compare the benefits of folding acceleration (reducing 〈t _F〉) with the benefits of sequestration/encapsulation (reducing f _bulk).

Appendix C: A review of the effects of iterative denaturation

It is useful to ask: under what conditions would iterative denaturation speed up protein folding? Rephrasing earlier arguments [77, 104], let:

$$ \begin{aligned} t = & {\text{the time that has elapsed since the protein was first introduced into the cytosol in its unfolded state}} \\ P(t) = & {\text{the probability that the polymer has not yet reached a folding-committed conformation after time }}t{\text{ has elapsed under dilute conditions in the absence of chaperones}} \\ \end{aligned} $$

Assuming that the only effect a chaperone has on the protein is to completely denature it once every τ _D s then the probability that the protein has not yet folded after N cycles of binding and release from the chaperone is [P(τ _D)]^N. In order for a protein to benefit from chaperone cycling:

$$ P(N\tau_{\text{D}} ) > \left[ {P(\tau_{\text{D}} )} \right]^{N} $$

(6)

For any protein which folds with a single well defined folding rate ($k_{\text{F}}$, for example, two-state folders, or proteins with only short-lived intermediates) P(t) must resemble a decaying exponential $(P(t) = e^{{ - k_{\text{F}}t }})$. For these proteins, P(Nτ _D) = [P(τ _D)]^N. Only proteins for which P(t) decays more slowly at long times (for example, proteins which can fall into kinetic traps) can satisfy this inequality.

It is possible to predict the average folding time, 〈t ^ss_F 〉 in the presence of iterative denaturation (at frequency λ ^ss_D ) for any protein, assuming the folding kinetics of that protein (under dilute conditions, P(t)) are known [148]:

$$ \left\langle {t_{\text{F}}^{\text{ss}} } \right\rangle = {\frac{1}{{\lambda_{\text{D}}^{\text{ss}} }}}\left[ {\left( {\lambda_{\text{D}}^{\text{ss}} \int\limits_{0}^{\infty } {P(t)e^{{ - \lambda_{\text{D}}^{\text{ss}} t}} } \,{\text{d}}t} \right)^{ - 1} - 1} \right]^{ - 1} $$

(7)

P(t) can be measured directly from bulk experiments, for example using florescence resonance energy transfer spectroscopy, or using enzyme assays applied to aliquots taken at regular intervals. By substituting $P(t) = e^{{ - k_{\text{F}}t }}$, we can see again that proteins with two-state folding kinetics (rate $k_{\text{F}}$ s⁻¹) would not benefit from iterative denaturation (in agreement with [104]).

The frequency of denaturation, λ ^ss_D , refers to the frequency at which proteins are denatured as a result of ATP-driven chaperonin binding and release: Specifically:

$$ \lambda_{\text{D}}^{\text{ss}} \approx 1/\left\langle {\tau_{\text{D}}^{\text{ss}} } \right\rangle \quad {\text{where:}} $$

(8)

$$ \left\langle {\tau_{\text{D}}^{\text{ss}} } \right\rangle = \left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle $$

(9)

$$ = \left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle + \left\langle {t_{\text{hold}} } \right\rangle \ldots {\text{ in the limit that}}\left\langle {t_{\text{hold}} } \right\rangle \to 0 $$

(10)

The “ss” superscripts are to remind us that under steady-state conditions, we should not consider the time proteins spend while immobilized during each cycle 〈t _hold〉 (See “Why should we ignore immobile states?”. Note that the actual folding time 〈t _F〉 can be inferred from 〈t ^ss_F 〉 by estimating the fraction of time a protein would have spent immobilized while folding. See Eq. 11 of “Why should we ignore immobile states?”)

The chaperone-mediated folding of aggregate prone substrates

Recall that under steady-state conditions, chaperones ability to prevent aggregation is entirely determined by how much chaperones reduce the time proteins spend in the bulk before folding, 〈t _bulk〉 = 〈t _F〉 × f _bulk = 〈t ^ss_F 〉 × f ^ss_bulk (See “Why should we ignore immobile states?”.) Reducing the value of 〈t _bulk〉 reduces aggregation and increases the yield. If we restrict ourselves further to the set of proteins which do not remain bound during every ATPase cycle, then we can use Eq. 4. Substituting it, along with Eqs. 7 and 10, results in a formula for 〈t _bulk〉 which decreases as the cycle frequency λ ^ss_D  ≈ 1/(〈t _bound〉 + 〈t _protect〉) decreases; the result is proportional to Eq. 7 from [148]. In other words, for this broad set of proteins, GroEL/ES should cycle slowly (maximize 〈t _protect〉). There is no incentive to cycle rapidly, except perhaps to free up chaperones and assist the folding of other proteins. This contradicts the conclusion of the traditional IAM. Again, the cycle for GroEL/ES requires on the order of 10¹ s.

Appendix D: Why should we ignore immobile states?

Simple kinetics models of GroEL/ES behavior assume that the entire time a protein is bound to GroEL it is either able to continue folding [148], or immobilized [113]. In reality, proteins may spend a fraction of their time with GroEL mobile or immobilized. However, under steady-state conditions, these immobile states have no effect. Increasing or decreasing the duration of these frozen states do not tip the balance toward one outcome (folding) or the other (aggregation), at least not under steady-state conditions when, presumably, the rate of transition to either of these outcomes is not changing over time.

Motivating example

We have argued Eqs. 12 and 4 without providing an algebraic proof. If it helps the reader, we can motivate Eqs. 12, and 4, by calculating both 〈t ^ss_F 〉 and f ^ss_bulk , and show that their product remains equal to 〈t _bulk〉 from Eq. 5:

To motivate this with a concrete example, it is convenient to imagine a hypothetical chaperone system which does not immobilize its substrates, (〈t _bulk〉 = 0), and which otherwise behaves exactly like the GroEL/ES-DnaK/J chaperone system in all other respects, denaturing protein substrates with every ATPase cycle. Of course, the resulting reduction in time spent bound to the chaperone might free up chaperones and increase chaperone availability. However, we ignore this effect here. Here, we imagine a hypothetical chaperone for which 〈t _unbound〉 and 〈t _protect〉 remain unaffected as 〈t _hold〉 → 0.

〈t ^ss_F 〉 and f ^ss_bulk denote the folding time, and fraction of time spent in the bulk, folding under the influence of this new hypothetical chaperone system (with 〈t _hold〉 = 0). The formula for f ^ss_bulk is given in Eq. 4 of “Estimating the fraction of time proteins are exposed to the cytosol”. The formula for 〈t ^ss_F 〉 is given in Eq. 7 of “A review of the effects of iterative denaturation”. How does this 〈t ^ss_F 〉 compare with the real folding time in vivo, 〈t _F〉?

In the presence of this hypothetical chaperone system, proteins would fold faster because they no longer have to spend a certain fraction of each cycle immobilized and waiting. Assuming many cycles of binding and release, this should reduce the folding time by the fraction of time proteins are not immobilized during each cycle (shown in parenthesis in Eq. 11).

$$ \left\langle {t_{\text{F}}^{\text{ss}} } \right\rangle = \left\langle {t_{\text{F}} } \right\rangle \times \left( {{\frac{{\left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle }}{{\left\langle {t_{\text{unbound}} } \right\rangle + \left\langle {t_{\text{hold}} } \right\rangle + \left\langle {t_{\text{protect}} } \right\rangle }}}} \right) $$

(11)

Multiplying Eqs. 4 and 11, and substituting Eq. 2, recovers Eqs. 3 and 5:

$$ \left\langle {t_{\text{bulk}} } \right\rangle = \left\langle {t_{\text{F}}^{\text{ss}} } \right\rangle \times f_{\text{bulk}}^{\text{ss}} $$

(12)

This shows that ignoring immobilized states (or equivalently, setting 〈t _hold〉 = 0) has no effect on 〈t _bulk〉. Under the influence of such a chaperone, proteins would spend the same amount of time in the bulk before folding 〈t _bulk〉, and would be no more or less likely to aggregate. Thus, a hypothetical chaperone without immobilized states would prevent just as much aggregation as a real chaperone (under steady-state conditions). Hence, we can justifiably ignore these immobilized states.