*Article* **Non-Equilibrium Protein Folding and Activation by ATP-Driven Chaperones**

**Huafeng Xu**

Roivant Sciences, New York, NY 10036, USA<EMAIL_ADDRESS>
**Abstract:** Recent experimental studies suggest that ATP-driven molecular chaperones can stabilize protein substrates in their native structures out of thermal equilibrium. The mechanism of such non-equilibrium protein folding is an open question. Based on available structural and biochemical evidence, I propose here a unifying principle that underlies the conversion of chemical energy from ATP hydrolysis to the conformational free energy associated with protein folding and activation. I demonstrate that non-equilibrium folding requires the chaperones to break at least one of four symmetry conditions. The Hsp70 and Hsp90 chaperones each break a different subset of these symmetries and thus they use different mechanisms for non-equilibrium protein folding. I derive an upper bound on the non-equilibrium elevation of the native concentration, which implies that non-equilibrium folding only occurs in slow-folding proteins that adopt an unstable intermediate conformation in binding to ATP-driven chaperones. Contrary to the long-held view of Anfinsen's hypothesis that proteins fold to their conformational free energy minima, my results predict that some proteins may fold into thermodynamically unstable native structures with the assistance of ATP-driven chaperones, and that the native structures of some chaperone-dependent proteins may be shaped by their chaperone-mediated folding pathways.

**Keywords:** chaperones; Hsp70; Hsp90; non-equilibrium; protein folding

**1. Introduction**

A commonly accepted view on protein folding is Anfinsen's thermodynamic hypothesis [1]: the native structure of a protein is uniquely determined by its amino acid sequence, and it is the conformation of the lowest free energy. According to this view, a free energy gap separates the native structure and the denatured conformations, and protein folding is accompanied by a negative free energy change [2]. A protein, left to its own device and given sufficient time, will fold spontaneously to its native structure.

We now know that many proteins depend on the assistance of molecular chaperones for folding into their functional structures inside cells [3–5]. ATP-driven chaperones such as GroEL/GroES [6–8], Hsp70 [9,10], and Hsp90 [11–17] represent an important class of chaperones that consume chemical energy in their functions. Biochemical and structural studies have established that these chaperones undergo a cycle powered by ATP hydrolysis through open and closed conformations [10,18–22]. These chaperones can rescue their protein substrates from misfolded or aggregated structures and accelerate their refolding to their native structures [23–27]. This role of ATP-driven chaperones does not contradict Anfinsen's thermodynamic hypothesis: proteins still fold into the most thermodynamically stable structures, but the chaperones enable them to do so within a physiologically reasonable time [28].

Recent experimental studies suggest that ATP-driven chaperones may play a thermodynamic role besides the kinetic one: they may stabilize proteins in their native structures out of thermal equilibrium, converting the chemical energy of ATP hydrolysis into the conformational free energy of their substrates [26,29]. Coincidental to these experimental studies, theoretical models were published around the same time that predicted such

**Citation:** Xu, H. Non-Equilibrium Protein Folding and Activation by ATP-Driven Chaperones. *Biomolecules* **2022**, *12*, 832. https://doi.org/ 10.3390/biom12060832

Academic Editor: Chrisostomos Prodromou

Received: 24 May 2022 Accepted: 13 June 2022 Published: 15 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

non-equilibrium stabilization [29–31]. In addition to quantitatively recapitulating the experimentally observed acceleration in folding kinetics, these models suggest that ATP-driven chaperones can maintain their protein substrates in their native structures at higher concentrations than thermodynamically permitted in the chaperone-free equilibrium. They explain why ATP hydrolysis is indispensable to the cellular functions of these chaperones, and in the case of Hsp70 [30] and Hsp90 [31], the critical roles of their respective cochaperones.

Here, I define non-equilibrium protein folding to be the phenomenon in which the native fraction of a protein is elevated by an energy-consuming process above its value in thermal equilibrium. Let *fN* = [*N*]/*P*0 be the steady state fraction of the protein substrate in its native structure in the presence of ATP-driven chaperones, and *fN*,*eq* = [*N*]*eq*/*P*0 be the native fraction in the chaperone-free equilibrium, where *P*0 is the total protein concentration and [*N*] is the concentration of the protein in its native structure. Non-equilibrium protein folding occurs if *fN* > *fN*,*eq*, which of course requires energy consumption. I will introduce the gain factor of non-equilibrium folding

$$\mathbf{g} \equiv \frac{f\_{\mathbf{N}}}{f\_{\mathbf{N},eq}} = \frac{[\mathbf{N}]}{[\mathbf{N}]\_{eq}} \tag{1}$$

which measures the extent of out-of-equilibrium stabilization of the native structure. A protein that primarily occupies the non-native structures in equilibrium (i.e., *fN*,*eq* < 0.5) but its native structure in the presence of ATP-driven chaperones (i.e., *fN* > 0.5) would contest Anfinsen's hypothesis.

Note that the native fraction in my definition of non-equilibrium folding includes only the free (i.e., not chaperone-bound) native protein because chaperones primarily bind to proteins that are at least partially unfolded [9,32]. There are, however, examples in which chaperone-bound proteins retain some native activity. For instance, glucocorticoid receptor (GR) can bind to its ligand when it is in complex with Hsp90 [33]. In this case, however, GR may still need to dissociate from Hsp90 to function as an active transcription factor. Thus, in this work, I will only consider non-equilibrium folding to a free, native protein.

Many mechanistic models have been proposed for chaperone-mediated protein folding [27,28,32,34–36]. One prevalent hypothesis regards the chaperones as unfoldases or holdases [37], in that their primary function is to rescue a misfolded or aggregated protein substrate and to hold it in an unfolded state. Upon release from the chaperones, the protein molecule has a certain probability of folding into its native structure [38]. Models based on this hypothesis provide an explanation of how ATP-driven chaperones accelerate the folding of the substrates to their inherently stable native structures, but they do not provide an explicit mechanism for the chaperones to transfer the chemical energy from ATP hydrolysis into the folding free energy of the substrate protein. It has been proposed that the ATP energy is used by the chaperones to achieve ultra-affinity in substrate binding [36].

It is often unclear whether a model will imply non-equilibrium protein folding (i.e., *g* > 1), when microscopic reversibility [31,39] is rigorously enforced. Based on thermodynamic principles, I have previously established one requirement of non-equilibrium protein folding: the substrate protein must undergo a conformational change when it is bound to the chaperone [31]. Supported by biochemical and structural evidence [40–42], this is a key assumption in my models of chaperone-mediated protein folding that couple the conformational dynamics of the protein substrate with the ATP-driven, open-close cycle of the chaperones (Figure 1).

In this work, I introduce an additional requirement that an ATP-driven chaperone must satisfy to perform non-equilibrium protein folding. Specifically, I demonstrate mathematically that an ATP-driven chaperone must break at least one of the four kinetic symmetry conditions (Conditions 1–4 in Section 3.1) to use the energy from ATP hydrolysis for outof-equilibrium stabilization of substrate proteins in their native structures. As discussed below, Hsp70, Hsp90, and GroEL/GroES each break a different subset of the symmetry conditions, thus they use different mechanisms to perform non-equilibrium folding. De-

spite the difference in their mechanistic details, I present a unifying principle by which symmetry breaking translates into non-equilibrium folding to the native structures.

**Figure 1.** A mechanistic model of chaperone-mediated non-equilibrium protein folding that couples the state cycle of the chaperone and the conformational dynamics of its substrate. The chaperone undergoes a cycle of open and closed conformations, driven by ATP hydrolysis and nucleotide exchange. The protein substrate can transition among four classes of conformations: Misfolded (*M*), Misfold-tending (*U*), Native-tending (*F*), and Native (*N*). The lengths of the reaction arrows signify the corresponding reaction rates. The red arrows indicate the predominant folding pathway.

In addition, I derive an upper bound on the extent to which an ATP-driven chaperone can elevate the native fraction of a substrate above its chaperone-free equilibrium value (Equation (56)). My results suggest that, for substantial non-equilibrium protein folding (i.e., *g* 1) to occur, the chaperone—with the possible exception of chaperonins such as GroEL/GroES—must bind to an unstable intermediate conformation of the substrate, and the substrate protein must fold slowly on its own.

Whether Anfinsen's hypothesis holds true for an individual protein can be experimentally tested by comparing the protein's activity in the presence and in the absence of functional ATP-driven chaperones; I have previously proposed new experiments that may provide such tests on Hsp70- and Hsp90-mediated folding [30,31]. In this work, I propose a potential proteomics-level experiment that may help identify proteins that depend on ATP-driven chaperones for maintenance of their native structures.

My models of non-equilibrium protein folding imply that the native structures of some proteins may be shaped by the chaperone-mediated folding pathways. They raise the possibility of discovering natural proteins—and engineering novel proteins—that adopt different conformations in the presence and absence of the chaperones.

#### *Assumptions and Notations*

To facilitate the exposition, I summarize the assumptions and notations in my model as follows:

• The substrate protein can convert among a set of conformations S, both when it is free in solution and when it is bound to the chaperone. I will use *M* to denote the misfolded/aggregated conformation and *N* the native conformation. In addition, I will consider two classes of intermediate conformations: the unfolded and misfold-tending (or aggregation-tending) conformation *U*, and the non-native but native-tending conformation *F*. To avoid a proliferation of symbols and to underscore the mechanistic commonality shared by protein folding and activation, in the discussion of kinase activation, I will use *M* to denote the inactive conformation, *N* the active conformation, *U* the inactive-tending conformation, and *F* the active-tending conformation.

• The chaperone can transition among a set of states I, each state *i* characterized by its conformational state (e.g., open or closed) and the numbers and the types (ATP vs ADP) of bound nucleotides.

My model includes the following reactions:

• The substrate in conformation *S* binds to the chaperone in state *i* with the association rate constant *ka*,*Si* and the dissociation rate constant *kd*,*Si*:

$$S + H\_i \xrightleftharpoons[k\_{d,Si}]{k\_{d,Si}} SH\_i \tag{2}$$

• The free substrate in solution converts between conformation *S* and conformation *S* 0 :

$$\mathcal{S} \xrightleftharpoons[k\_{S' \to S} \quad \mathcal{S}'] \tag{3}$$

The corresponding conformational equilibrium constant is

$$K\_{SS'} = \frac{k\_{S \to S'}}{k\_{S' \to S}} \tag{4}$$

• The substrate bound to the chaperone in state *i* converts between conformation *S* and conformation *S* 0 :

$$SH\_{\dot{l}} \xrightleftharpoons^{k\_{S \to S', j\_s}} S'H\_{\dot{l}} \tag{5}$$

• The chaperone transitions between state *i* and state *j* when it is bound to a substrate in conformation *S*:

$$\text{S}H\_{\text{i}} \xrightleftharpoons[k\_{S,i\to j}]{k\_{S,i\to j}} \text{S}H\_{\text{j}} \tag{6}$$

#### **2. Materials and Methods**

*2.1. Proof That Symmetry Breaking Is Required for Non-Equilibrium Protein Folding*

I will show that, under the symmetry conditions (Conditions 1–4 in Section 3.1), the steady state concentrations of the substrate satisfies, for any pair of conformations *S* and *S* 0 ,

$$k\_{S \to S'} [S] = k\_{S' \to S} [S'] \iff \frac{[S']}{[S]} = \frac{k\_{S \to S'}}{k\_{S' \to S}} = K\_{SS'} \tag{7}$$

where [*S*] (or [*S* 0 ]) is the concentration of the free substrate in conformation *S* (or *S* 0 ). Thus, the steady state ratio [*S* 0 ]/[*S*] is unchanged from that in the chaperonefree equilibrium [*S* 0 ]*eq*/[*S*]*eq* = *KSS*0 for any pair of conformations *S* and *S* 0 , including [*N*]/[*M*] = [*N*]*eq*/[*M*]*eq*, and the chaperone is unable to increase the native concentration of the substrate above that in the equilibrium.

Letting [*Hi* ] be the concentration of the chaperone in state *i* and [*SHi* ] the concentration of the substrate in conformation *S* bound to the chaperone in state *i*, the steady state condition for the reactions in Equations (2), (3), (5) and (6) is

$$0 = \frac{d[S]}{dt} \quad = \sum\_{i} (k\_{d,Si}[SH\_i] - k\_{a,Si}[H\_i][S]) + \sum\_{S'} (k\_{S' \to S}[S'] - k\_{S \to S'}[S])$$

$$0 = \frac{d[SH\_i]}{dt} \quad = \begin{array}{c} k\_{a,Si}[H\_i][S] - k\_{d,Si}[SH\_i] + \sum\_{j \neq i} (k\_{S,j \to i}[SH\_j] - k\_{S,j \to j}[SH\_i]) \\ + \sum\_{S'} (k\_{S' \to S,i}[S'H\_i] - k\_{S \to S',i}[SH\_i]) \end{array} \tag{8}$$

According to Condition 1, the ratio *ka*,*S* 0 *i*/*ka*,*Si* does not depend on *i*. I denote this ratio as

$$\frac{k\_{a,S'i}}{k\_{a,Si}} = \gamma\_{SS'} K\_{SS'}^{-1} \tag{9}$$

where *γSS*0 is a number that does not depend on *i*.

Consider a hypothetical, restricted system in which the substrate bound to the chaperone cannot change conformations (i.e., setting *kS*→*S* 0 ,*i* = 0 for all *i* and all pairs of *S* and *S* 0 in Equation (8)). Because the reaction *S S* 0 is not part of any energy consuming cycle in this restricted system, [*S* 0 ]/[*S*] = *KSS*0 [31]. Let {[*S*]} S {[*SHi* ]|*i* ∈ I} be the steady state concentrations of the substrate in conformation *S* in this restricted system, I will show that

$$\begin{bmatrix} \mathbf{S}' \end{bmatrix} \quad = \begin{array}{cc} \mathbf{K}\_{\mathbf{S}\mathbf{S}'} \begin{bmatrix} \mathbf{S} \end{bmatrix} \end{array} \tag{10}$$

$$\begin{bmatrix} \mathbf{S'} \mathbf{H}\_{\mathbf{i}} \end{bmatrix} \quad = \quad \gamma\_{S S'} [\mathbf{S} \mathbf{H}\_{\mathbf{i}}] \tag{11}$$

are the steady state concentrations of the substrate in conformation *S* 0 , and that [*SHi* ] and [*S* 0*Hi* ] satisfy

$$k\_{\mathbb{S}\rightarrow S',i}[SH\_i] - k\_{\mathbb{S}'\rightarrow S,i}[S'H\_i] = 0 \,\,\forall i \in \mathbb{I} \tag{12}$$

for the original *kS*→*S* 0 ,*i* > 0 and *kS* 0→*S*,*i* > 0. Thus, the steady state concentrations of the restricted system are also the solution to the original steady state condition in Equation (8), and Equation (7) holds (it is equivalent to Equation (10)).

To prove Equation (12), consider first an open state *i*. Thermodynamic cycle closure in the following reaction cycle (which does not consume chemical energy because the chaperone does not change state),

$$\begin{array}{ccccc} S & \xrightarrow{k\_{S \to S'}} & S'\\ S' + H\_i & \xrightarrow{k\_{a, S'\_i}} & S'H\_i\\ S'H\_i & \xrightarrow{k\_{S' \to S, i\_i}} & SH\_i\\ SH\_i & \xrightarrow{k\_{S \to S', i}} & SH\_i\\ SH\_i & \xrightarrow{k\_{d, S i\_i}} & S + H\_i \end{array} \tag{13}$$

implies that

$$\frac{k\_{S' \to S,i}}{k\_{S \to S',i}} \frac{k\_{a,S'i}}{k\_{d,S'i}} \frac{k\_{d,Si}}{k\_{a,Si}} K\_{SS'} = 1 \tag{14}$$

$$\begin{array}{lcl} \iff & k\_{S \to S',i} = k\_{S' \to S,i} K\_{S\mathcal{Y}} \frac{k\_{a\mathcal{Y}i}}{k\_{a,\mathcal{S}i}} \frac{k\_{d,\mathcal{S}i}}{k\_{d,\mathcal{S'}i}} = k\_{S' \to S,i} \gamma\_{\mathcal{SS'}} \text{ (\text{\textquotedblleft Equations (9) and (37))}\\ \implies & k\_{S' \to S,i} [S'H\_i] - k\_{S \to S',i} [SH\_i] \\ = & [SH\_i] \left(k\_{S' \to S,i} \gamma\_{\mathcal{SS'}} - k\_{S \to S',i} \right) \text{ (\textquotedblright Equation (11))}\\ = & 0 \end{array} \tag{15}$$

If *i* is a closed state such that *ka*,*Si* = *ka*,*S* 0 *i* = *kd*,*Si* = *kd*,*S* 0 *i* = 0, Equation (14) no longer holds. According to Condition 4, however, the chaperone can reversibly transition between *i* and an open state *j* without the consumption of chemical energy, and, according to Condition 3, the transition rates between *i* and *j* do not depend on the conformational state of the bound substrate, i.e.,

$$\frac{k\_{S',i\to j}}{k\_{S,i\to j}} = \frac{k\_{S',j\to i}}{k\_{S,j\to i}} = 1\tag{16}$$

Thus, thermodynamic cycle closure in the following reversible reaction cycle

$$\begin{array}{ll} \mathcal{S} & \xrightarrow{\xi\_{S\rightarrow S'}} & \mathcal{S}'\\ & \overbrace{k\_{S'\rightarrow S}}^{k\_{S\rightarrow S'j}} & \quad \mathcal{S}'\\ \mathcal{S}' + H\_{j} & \xrightarrow{k\_{a}S'\_{j}} & \mathcal{S}'H\_{j} \\ & S'H\_{j} & \xrightarrow{k\_{S',j\rightarrow i}} & S'H\_{i} \\ & & \overbrace{k\_{S'\rightarrow S,j}}^{k\_{S'\rightarrow S,j}} & SH\_{i} \\ & S'H\_{i} & \xrightarrow{k\_{S\rightarrow S',i}} & SH\_{j} \\ & SH\_{i} & \overbrace{k\_{S,i\rightarrow j}}^{k\_{S,i\rightarrow j}} & SH\_{j} \\ & SH\_{j} & \overbrace{k\_{a,S\_{j}}}^{k\_{d,S\_{j}}} & S + H\_{j} \end{array} \tag{17}$$

implies

$$\frac{k\_{S' \to S,i}}{k\_{S \to S',i}} \frac{k\_{S,j \to j}}{k\_{S,j \to i}} \frac{k\_{S',j \to i}}{k\_{S',j \to j}} \frac{k\_{a,S'j}}{k\_{d,S'j}} \frac{k\_{d,Sj}}{k\_{a,Sj}} \mathbf{K}\_{SS'} = \mathbf{1} \tag{18}$$

$$\frac{k\_{S' \to S,i}}{k\_{S \to S',i}} \frac{k\_{a,S'j}}{k\_{a,Sj}} \frac{k\_{d,Sj}}{k\_{d,S'j}} \mathbf{K}\_{SS'} = \mathbf{1} \tag{19} \tag{16}$$

$$\begin{array}{lcl} \implies & \underset{k\_{S}' \to S\_{J}'} \stackrel{\text{\tiny{\text{L}}\_{S}' \to S\_{J}'}}{k\_{S \to S',i}} \stackrel{\text{\tiny{\text{R}}\_{S}' \to S\_{J}'}}{k\_{S,S'}} \mathcal{K}\_{S S'} = 1 \; (\text{\textquotedblleft: Equation (16)}) \\ \implies & \underset{k\_{S \to S',i}}{k\_{S \to S',i}} \gamma\_{S S'} = 1 \; (\text{\textquotedblleft: Equations (9) and (37)}) \\ \implies & k\_{S' \to S,i} [S'H\_{i}] - k\_{S \to S',i} [SH\_{i}] \\ = & [SH\_{i}] \left(k\_{S' \to S,i} \gamma\_{S S'} - k\_{S \to S',i} \right) \text{ (\textquotedblright} \text{ : Equation (11))} \\ = & 0 \end{array} \tag{19}$$

Thus, Equation (12) is true for both open and closed states.

To prove that {[*S* 0 ]} S {[*S* 0*Hi* ]|*i* ∈ I} in Equations (10) and (11) satisfy the steady state condition Equation (8) (swapping *S* 0 and *S*), I only need to show that, for the reactions in Equations (2) and (6), the flux in each reaction involving the substrate in conformation *S* 0 is *γSS*0 times the flux of the corresponding reaction involving the substrate in conformation *S* because {[*S*]} S {[*SHi* ]|*i* ∈ I} satisfies Equation (8) and the reactions in Equations (3) and (5) have zero flux (Equations (10) and (12)).

Let *JS*,*ij* = *kS*,*i*→*j* [*SHi* ] − *kS*,*j*→*i* [*SHj* ] be the reactive flux of the state transition for the chaperone bound to a substrate in conformation *S* (Equation (6)) and *J a Si* = *ka*,*Si*[*Hi* ][*S*] − *kd*,*Si*[*SHi* ] be the reactive flux of the substrate in conformation *S* binding to the chaperone in state *i* (Equation (2)). The corresponding reactive fluxes for the substrate in conformation *S* 0 are

$$\begin{array}{rcl} \mathcal{I}\_{S',\vec{i}\vec{j}} &=& k\_{S',\vec{i}\to\vec{j}}[S'H\_{\vec{i}}] - k\_{S',\vec{j}\to\vec{i}}[S'H\_{\vec{j}}] \\ &=& \gamma\_{SS'}(k\_{S,\vec{i}\to\vec{j}}[SH\_{\vec{i}}] - k\_{S,\vec{j}\to\vec{i}}[SH\_{\vec{j}}]) \\ &=& \gamma\_{SS'}I\_{S,\vec{i}\vec{j}} \end{array} \text{( $\vec{r}$ -Equation (11) and Condition 3)} \quad \text{(20)}$$

and

$$\begin{array}{rcl}l\_{S'i}^{a} &=& k\_{aS'i}[H\_i][S'] - k\_{d,S'i}[S'H\_i] \\ &=& k\_{aS'i}[H\_i]K\_{S'}[S] - k\_{d,S'}\gamma\_{SS'}[SH\_i] \text{ ( $\cdot$ : Equations (10), (11) and (37))} \\ &=& \gamma\_{SS'}(k\_{a,Si}[H\_i][S] - k\_{d,Si}[SH\_i]) \text{ ( $\cdot$ : Equation (9))} \\ &=& \gamma\_{SS'}l\_{Si}^{a}\end{array} \tag{21}$$

Q.E.D.

#### *2.2. Derivation of the Upper Bound of the Native Concentration at the Steady State of Non-Equilibrium Folding*

To derive the upper bound in Equation (51), consider the reactions in Table 1. These are simplifications of the reactions in Equations (2), (3), (5) and (6): only a substrate in intermediate conformations *S* = *U*, *F* can bind to the chaperone (see Section 3.2.1), and only two chaperone states, open (*O*) and closed (*C*), are considered. The results hold as long as the substrate binds to all chaperone open states with the same association and dissociation rate constants, i.e.,

$$\begin{array}{rcl}k\_{a,Si} & = & k\_{a,S} \\ k\_{d,Si} & = & k\_{d,S} \; \forall \text{ open state } i \end{array} \tag{22}$$

**Table 1.** The reactions in chaperone-mediated protein folding. These reactions are depicted in Figure 1. ATP hydrolysis and nucleotide exchange occur and inject chemical energy in the chaperone cycle.

Let

$$J\_{FL} = k\_{F \to \mathcal{U}}[F] - k\_{\mathcal{U} \to F}[\mathcal{U}] \tag{23}$$

be the reactive flux from *F* to *U*. At the steady state, there is no net flux into or out of any molecular species, implying

$$\begin{array}{rcl} \text{J}\_{\text{FL}} &=& k\_{a,\text{II}}[\text{U}][O] - k\_{d,\text{II}}[\text{UO}]\\ &=& k\_{d,\text{F}}[\text{FO}] - k\_{a,\text{F}}[\text{F}][O] \end{array} \tag{24}$$

Because no external chemical energy is consumed in the reaction cycle of

$$\mathcal{U} + \mathcal{O} \rightleftharpoons \mathcal{U}\\ \mathcal{O} \rightleftharpoons \mathcal{F}\\ \mathcal{O} \rightleftharpoons \mathcal{F} + \mathcal{O} \rightleftharpoons \mathcal{U} + \mathcal{O}, \tag{25}$$

we have

$$\frac{k\_{F \to IL,O}}{k\_{IL \to F,O}} \cdot \frac{k\_{a,F}}{k\_{d,F}} \cdot \frac{k\_{d,II}}{k\_{a,II}} \cdot \frac{k\_{IL \to F}}{k\_{F \to II}} = 1 \tag{26}$$

Thus,

$$\begin{array}{ccl} \frac{k\_{F \to II,O}[\text{FO}]}{k\_{II \to F,O}[\text{LO}]} &=& \frac{k\_{F \to II,O}}{k\_{II \to F,O}} \cdot \frac{k\_{a,F}}{k\_{d,F}} \cdot \frac{k\_{d,II}}{k\_{a,II}} \cdot \frac{k\_{II \to F}}{k\_{F \to II}}\\ &\cdot \frac{k\_{d,F}[\text{FO}]}{k\_{a,F}[F][\text{O}]} \cdot \frac{k\_{a,II}[\text{II}][\text{O}]}{k\_{d,II}[\text{IO}]} \cdot \frac{k\_{F \to II}[F]}{k\_{II \to F}[\text{II}]}\\ &=& \frac{k\_{d,F}[\text{FO}]}{k\_{d,F}[F][\text{O}]} \cdot \frac{k\_{a,II}[\text{II}][\text{O}]}{k\_{d,II}[\text{IO}]} \cdot \frac{k\_{F \to II}[F]}{k\_{U \to F}[\text{II}]} \end{array} \tag{27}$$

If *JFU* in Equations (23) and (24) is positive, all three ratios on the right-hand side of Equation (27) are greater than 1; if *JFU* < 0, they are all smaller than 1. Thus, the reactive flux

$$J\_{\rm UF,O} = k\_{\rm UI \to F,O} \left[ \rm LO \right] - k\_{F \to \rm UI,O} \left[ \rm FO \right] \tag{28}$$

must be of the opposite sign of *JFU*.

If the chaperone drives the substrate toward the native structure, we have [*F*]/[*U*] > *KF* = *kU*→*F*/*kF*→*U*, implying *JFU* > 0 and *JUF*,*O* < 0. Because the flux from conformation *F* to *U* in free substrates must balance the total flux from conformation *U* to *F* in chaperonebound substrates, the steady state reactive flux of the reaction *UC FC*

$$J\_{\rm UF,C} = k\_{\rm U \to F,\mathcal{C}}[\rm lLC] - k\_{F \to lL,\mathcal{C}}[\rm FC] \tag{29}$$

satisfies

$$J\_{\rm FL} = J\_{\rm UF,C} + J\_{\rm UF,O} < J\_{\rm UF,C} \tag{50}$$

Thus,

$$\begin{aligned} &k\_{F \to II}[F] - k\_{U \to F}[\mathcal{U}] < k\_{\mathcal{U} \to F, \mathcal{C}}[\mathcal{U}\mathcal{C}] - k\_{F \to \mathcal{U}, \mathcal{C}}[\mathcal{F}\mathcal{C}]\\ &\implies \quad k\_{F \to \mathcal{U}}[F] < k\_{\mathcal{U} \to F}\left([\mathcal{U}] + \frac{k\_{\mathcal{U} \to F, \mathcal{C}}}{k\_{\mathcal{U} \to F}}[\mathcal{U}\mathcal{C}]\right) \equiv k\_{\mathcal{U} \to F}([\mathcal{U}] + \mathfrak{a}[\mathcal{U}\mathcal{C}])\\ &\implies \quad [\mathcal{F}] < K\_{F} \cdot \max(1, \mathfrak{a}) \cdot ([\mathcal{U}] + [\mathcal{U}\mathcal{C}]) \end{aligned} \tag{31}$$

We also have, per Equations (23) and (24),

$$\begin{array}{lcl}\hline & J\_{\rm FU} = k\_{F \to \rm U}[F] - k\_{\rm L \to F}[\mathcal{U}] = k\_{a,\rm II}[O][\mathcal{U}] - k\_{d,\rm II}[\mathcal{U}O] < k\_{a,\rm II}[O][\mathcal{U}]\\ \implies & (k\_{\rm II \to F} + k\_{a,\rm II}[O])[\mathcal{U}] > k\_{F \to \rm U}[F] \end{array} \tag{32}$$

At the steady state, there is no net flux in *M U* or in *F N*, thus

$$\begin{array}{rcl}[M] &=& \mathcal{K}\_M[\mathcal{U}]\\ [N] &=& \mathcal{K}\_N[\mathcal{F}]\end{array} \tag{33}$$

Because

$$[M] + [\mathcal{U}] + [\mathcal{U}\mathcal{C}] + [F] + [N]
 & \left( K\_\mathcal{F}^{-1} \max(1, a)^{-1} + 1 \right) \left[ \mathcal{F} \right] + \left[ M \right] + \left[ N \right] \text{ (: Equation (31))} \\ &= & \left( K\_\mathcal{F}^{-1} \max(1, a)^{-1} + 1 \right) \left[ \mathcal{F} \right] + K\_\mathcal{M} \left[ \mathcal{U} \right] + K\_\mathcal{N} \left[ \mathcal{F} \right] \\ &> & \left( K\_\mathcal{F}^{-1} \max(1, a)^{-1} + 1 \right) \left[ \mathcal{F} \right] + K\_\mathcal{M} \frac{k\_\mathcal{F} \to \mathcal{U}}{k\_{\mathcal{U}\mathcal{U}\to\mathcal{F}} + k\_\mathcal{a} \mu \mathcal{I} \left[ \mathcal{O} \right]} \left[ \mathcal{F} \right] + k\_\mathcal{N} \left[ \mathcal{F} \right] \tag{32} \end{aligned} \tag{35}$$

Thus,

$$\mathbb{E}\left[F\right] < \left(K\_M K\_F^{-1} \left(1 + \frac{k\_{d,II}[O]}{k\_{dI \to F}}\right)^{-1} + K\_F^{-1} \max(1, a)^{-1} + 1 + K\_N\right)^{-1} P\_0 \tag{36}$$

and plugging in Equation (33) yields the upper bound in Equation (51).

#### **3. Results**

#### *3.1. Non-Equilibrium Folding Requires Kinetic Symmetry Breaking*

I present a set of four symmetry conditions that, if all satisfied, forbids an ATPdriven chaperone from elevating the native concentration [*N*] of its substrate above the chaperone-free equilibrium concentration [*N*]*eq*. A chaperone must break at least one of these symmetry conditions to be able to convert chemical energy into non-equilibrium

stabilization of the native structure of the substrate. As I discuss below, different chaperones break different symmetry conditions, corresponding to different mechanisms of non-equilibrium protein folding and activation. The symmetry conditions are as follows:

$$k\_{d,Si} = k\_{d,i} \tag{37}$$

for all open state *i* and for all conformation *S*.

In Section 2.1 of Materials and Methods, I prove that, if these four symmetry conditions are all satisfied, the ratio between the concentrations of the free substrate in any two conformations—say, *S* and *S* 0—at the chaperone-mediated steady state is unchanged from that in the chaperone-free equilibrium, i.e., [*S* 0 ]/[*S*] = [*S* 0 ]*eq*/[*S*]*eq*, which implies [*N*]/[*M*] = [*N*]*eq*/[*M*]*eq*. Because chaperone-binding reduces the total concentration of the free substrate, the native concentration of the free substrate will be lower in the presence of chaperones than in the absence of chaperones, i.e., *g* < 1. (As noted in the Introduction, I only consider non-equilibrium folding to a free native protein.)

The above results regarding symmetry conditions hold for an arbitrary number of substrate conformations. For simplicity, I will assume only four representative conformations in the substrate, S = {*M* ≡ misfolded, *U* ≡ misfold-tending, *F* ≡ native-tending, *N* ≡ native}, in the following discussion.

#### 3.1.1. Requisites for Breaking the Binding and Unbinding Symmetries (Conditions 1 and 2)

The binding symmetry, Condition 1, is trivially satisfied if there is only one open chaperone state to which the substrate binds, or if the substrate binding rate does not depend on the chaperone state, i.e., *ka*,*Si* = *ka*,*S*. Note that the substrate in different conformations *S* may bind to the chaperone at different rates *ka*,*S*, e.g., the substrate in an unfolded structure may bind to the chaperone faster than the substrate in a near-native structure, which is a common assumption in models of chaperone-mediated folding [34], but this conformation-selective binding alone does not permit non-equilibrium folding (defined by *g* > 1).

Condition 1 is approximately satisfied if the substrate in different conformations and the chaperone in different states bind using the same interface. In this case, the association rate constant is approximately

$$k\_{a,Si} = p\_S \times f\_{\dot{\imath}} \times k\_a \tag{38}$$

where *pS* is the probability that the binding surface on the substrate becomes accessible in conformation *S*, *fi* is the probability that the binding surface on the chaperone is accessible in state *i*, and *ka* is the intrinsic binding rate between the two binding surfaces once exposed (Equation (38) assumes that the conformational fluctuations exposing and occluding the binding surfaces are fast compared to the overall binding). The ratio

$$\frac{k\_{a,S'i}}{k\_{a,Si}} = \frac{p\_{S'}}{p\_S} \tag{39}$$

thus satisfies Condition 1.

Condition 1 is violated if the substrate binds to different binding surfaces on the chaperone depending on both the substrate conformation and the chaperone (open) state. This requires that the chaperone possesses multiple open states in which different binding

surfaces are exposed. There has not been experimental demonstration of any ATP-driven chaperone breaking this symmetry condition.

The unbinding symmetry, Condition 2, is approximately satisfied if the chaperone binds to the substrate in different conformations using the same binding interface. The symmetry is broken if the substrate in different conformations form different protein–protein interactions with the chaperone.

In one limit of such binding interface change, the substrate in the misfold-tending conformation *U* with a slow dissociation rate *kd*,*U* may bind to the open chaperone and, after the chaperone closes, change to the native-tending conformation *F* in which its chaperone-binding surface is lost, so that, when the chaperone opens again after the ATPdriven cycle, the substrate unbinds rapidly with a fast dissociation rate *kd*,*F kd*,*U*. This may happen in chaperones that can retain a substrate without a contact interface while allowing the bound substrate to change conformation from *U* to *F*. Hsp90 and GroEL/ES are two such examples: Hsp90 clamps its client kinase between its closed homo dimer with a central hole that may accommodate substantial conformational changes in the client [31,42], and GroEL/ES holds the substrate in its cavity, inside which the substrate may fold [43]. These two chaperones may break Condition 2 by this mechanism and thus perform non-equilibrium protein folding.

Cochaperones that simultaneously bind to the chaperone and to the misfold-tending, but not the native-tending, conformation of the substrate may help break Condition 2. When the substrate in the misfold-tending conformation is bound to the cochaperone, the substrate–cochaperone complex together has an extended chaperone-binding surface with contributions from both the substrate and the cochaperone, which decreases the substrate's dissociation rate from the chaperone. Binding to and unbinding from the cochaperone, a substrate in the misfold-tending conformation has, in effect, a slower dissociation rate than the substrate in the native-tending conformation. One case in point may be that of Cdc37-assisted kinase activation by Hsp90, as discussed in the following.

3.1.2. Cdc37 Enables Hsp90 to Differentiate between the Active-Tending and Inactive-Tending Conformations of a Client Kinase

Cdc37 is a cochaperone that specializes in assisting Hsp90 to activate client kinases [32,44,45]. Experimental evidence suggests that Cdc37 binds to a locally unfolded conformation of the client kinase [46], and that Cdc37 can simultaneously bind to a client kinase and Hsp90 [42,47,48]. Based on the cryo-EM structure of the Hsp90-kinase-Cdc37 complex [42] (Figure 2A), I have previously proposed a simple mechanism for Cdc37 to distinguish between the inactive-tending (*U*) and active-tending (*F*) kinase conformations, binding to the former with higher affinity than to the latter: in the inactive-tending conformation, the disordered DFG-loop of the kinase does not interfere with Cdc37 binding, whereas, in the active-tending conformation, the DFG-loop may be ordered into a configuration that results in steric clashes with Cdc37 [31] (Figure 2B,C). Thus, Cdc37 can help Hsp90 retain an inactive-tending client more than an active-tending client, and the effective rate of dissociation from Hsp90 is higher for a client in the active-tending conformation than for a client in the inactive-tending conformation (Figure 2D,E), breaking symmetry Condition 2.

**Figure 2.** Cochaperone Cdc37 enables a client kinase in different conformations to unbind from Hsp90 at different rates. (**A**) the Hsp90-Cdk4-Cdc37 complex structure (PDB: 5FWM). The closed Hsp90 homo dimer clamps a partially unfolded Cdk4 kinase, and Cdc37 simultaneously binds to Cdk4 and Hsp90; (**B**) Cdc37 can bind to the kinase in the inactive-tending conformation; (**C**) steric clashes prevent Cdc37 from binding to the kinase in the active-tending conformation, due to its DFG-loop configuration and other conformational features; (**D**) Cdc37 helps to retain an inactivetending kinase molecule inside the open Hsp90, resulting in slow unbinding of the kinase from the Hsp90. The bipartite interaction by NTD and CTD of Cdc37 with the kinase may result in the encirclement of a Hsp90 protomer by the Cdc37-kinase complex, preventing the latter from slipping off Hsp90. (**E**) Without Cdc37, an active-tending kinase molecule unbinds rapidly from the open Hsp90. (**F**) Alternatively, the loss of the interaction between the NTD of Cdc37 and the C-lobe of an active-tending kinase breaks the bipartite interaction between Cdc37 and the kinase, resulting in the release of the Cdc37-kinase complex from Hsp90.

This mechanism implies the following reaction path of Hsp90-mediated kinase activation:

$$\begin{aligned} \text{U} & \xrightleftharpoons \text{Udc37} \xrightarrow{+ \text{Hsp90}\_{\text{open}}} \text{Hsp90}\_{\text{open}} \cdot \text{U} \cdot \text{Cdc37} \rightleftharpoons \text{Hsp90}\_{\text{closed}} \cdot \text{U} \cdot \text{Cdc37} \\ \xrightleftharpoons \text{Hsp90}\_{\text{closed}} \cdot \text{U} & \xrightleftharpoons \text{Hsp90}\_{\text{closed}} \cdot \text{F} \xrightleftharpoons \text{Hsp90}\_{\text{open}} \cdot \text{F} \xrightleftharpoons \text{Hsp90}\_{\text{open}} \cdot \text{F} \end{aligned} \tag{40}$$

Clearly, this mechanism requires that Cdc37 can dissociate from the Hsp90-kinase complex after Hsp90 closes. This requirement is indeed consistent with the observed structure of the Hsp90-kinase-Cdc37 complex: the closed Hsp90 clamps the client kinase between its N- and C-lobes to prevent the kinase from unbinding, but Cdc37 wraps around the exterior of Hsp90 so that it can disengage from the closed Hsp90 (Figure 2A).

Both the N-terminal domain (NTD) and the C-terminal domain (CTD) of Cdc37 bind to the partially unfolded kinase [49,50]. Individually, NTD and CTD bind to the kinase with low affinities [50] (on the order of 100 µM), but the bipartite interaction between the complete Cdc37 and the kinase results in sub-micromolar affinity. Based on the cryo-EM structure of the Hsp90-kinase-Cdc37 complex, the bipartite interaction may lead to the encirclement of a Hsp90 protomer by the kinase-Cdc37 binary complex, thus preventing the kinase from slipping off Hsp90 (Figure 2D). As discussed above, the NTD of Cdc37 may not bind to the active-tending conformation of the kinase. This not only substantially diminishes the affinity of Cdc37 to the kinase (CTD alone binds with over two-hundred-fold lower affinity), it also breaks the encirclement of the Hsp90 protomer by the Cdc37-kinase binary complex, potentially allowing the latter to dissociate rapidly from Hsp90 (Figure 2F), followed by the conversion of the kinase to the active conformation.

A puzzling observation is that Cdc37 binds to both the inactive B-Raf kinase and the active B-Raf mutant B-RafV600E (which has the valine at position 600 mutated to a glutamate) with similar affinities [51]: *KD* = 1.0 µM for the wild-type B-Raf and *KD* = 0.4 µM for the mutant B-RafV600E [50]. This can be explained by the above proposal that Cdc37 binds with high affinity to the inactive-tending conformation of the kinase but with comparatively negligible affinity to the other conformations. Consider the conformational equilibrium among the inactive (*M*), the inactive-tending (*U*), the active-tending (*F*), and the active (*N*) conformations:

$$\mathcal{M} \xrightleftharpoons^{K\_{M\_{\succ}}^{-1}} \mathcal{U} \xrightleftharpoons^{K\_{\overset{\mathcal{K}\_{\succ}}}} \mathcal{F} \xrightleftharpoons^{K\_{\overset{\mathcal{K}\_{\overset{\mathcal{K}\_{\succ}}}}}} \mathcal{N} \tag{41}$$

If Cdc37 binds to the inactive-tending conformation *U* with a conformation-specific dissociation constant *K* ∗ *D* , the apparent experimentally measured dissociation constant of Cdc37 binding to the kinase is

$$\begin{array}{rcl} \mathbb{K}\_{\text{D}} &=& \frac{[P][\text{Cdc37}]}{[\text{U} \cdot \text{Cdc37}]} \\ &=& \frac{[P]}{[\text{U}]} \cdot \frac{[\text{U}][\text{Cdc37}]}{[\text{U} \cdot \text{Cdc37}]} \\ &=& \frac{\mathbb{K}\_{\text{M}} \text{K}\_{\text{F}}^{-1} + \text{K}\_{\text{F}}^{-1} + 1 + \text{K}\_{\text{N}}}{\text{K}\_{\text{F}}^{-1}} \cdot \text{K}\_{\text{D}}^{\*} \end{array} \tag{42}$$

where *P* represents the kinase in any conformation.

The equilibrium active fraction, on the other hand, is

$$[N]\_{eq} / P\_0 = \frac{K\_N}{K\_M K\_F^{-1} + K\_F^{-1} + 1 + K\_N} \tag{43}$$

Thus, it is possible for the wild-type and the mutant kinase to have very different active fractions [*N*]*eq*/*P*0 yet similar *KD*'s. For example, the hypothetical sets of equilibrium constants in Table 2 would be consistent with the observed Cdc37 affinities of the wild-type B-Raf and the V600E mutant and with the mechanistic hypothesis [52] that the mutation destabilizes the inactive and—less so—the inactive-tending conformation (thus decreasing *KM* and increasing *KF*).

**Table 2.** A hypothetical set of equilibrium constants that are consistent with the measured Cdc37 affinities of the wild-type B-raf and the V600E mutant. The dissociation constants are similar between the inactive wild-type and the active mutant.

3.1.3. Cochaperone Hsp40 Enables Differential ATP Hydrolysis by Hsp70 Bound to a Substrate in Different Conformations

Hsp70-mediated protein folding is an example of breaking symmetry Condition 3. The Hsp70 chaperones, such as the bacterial DnaK, adopts an open conformation when its nucleotide binding domain (NBD) is occupied by ATP. Upon ATP hydrolysis, Hsp70 changes to a closed conformation [53,54] (Figure 3A). By itself, Hsp70 has a low basal ATP hydrolysis rate, but the J domain from the Hsp40 cochaperones—also known as J proteins—can stimulate Hsp70 and drastically increase its ATP hydrolysis rate [55,56].

Both Hsp40 and Hsp70 bind to exposed hydrophobic sites on a substrate protein [57,58] (Figure 3A–C). Consequently, a substrate with multiple exposed hydrophobic sites may simultaneously bind to an Hsp70 and an Hsp40. This induces the proximity between the chaperone and the cochaperone, resulting in accelerated ATP hydrolysis in Hsp70 and its transition to the closed state. Because a substrate in the misfold-tending conformation often exposes more hydrophobic sites than a substrate in the native-tending conformation [59], an Hsp70 bound to the former is more likely to be stimulated by a nearby Hsp40 bound to the same substrate molecule than an Hsp70 bound to the latter. By recruiting Hsp40 to accelerate the ATP hydrolysis in Hsp70, a substrate in the misfold-tending conformation induces a higher rate of transition by Hsp70 from the open state to the closed state than a substrate in the native-tending conformation, i.e., *kU*,open→closed > *kF*,open→closed, breaking symmetry Condition 3 (Figure 3D,E).

**Figure 3.** Cochaperone Hsp40 enables Hsp70 to change the balance between its open and closed states in response to the conformation of a bound substrate. (**A**) the ATP-bound, open state of Hsp70, which allows rapid binding and unbinding of the substrate; (**B**) the ADP-bound, closed state of Hsp70, with slow binding and unbinding of the substrate. SBD: substrate binding domain. (**C**) the structure of the Hsp40 cochaperone, including CTD that can bind to exposed hydrophobic sites on a substrate and the J domain that can stimulate the ATP hydrolysis of Hsp70. (**D**) An Hsp70 bound to a misfold-tending substrate molecule with many exposed hydrophobic sites is likely to be in proximity to an Hsp40 bound to the same substrate molecule, thus the Hsp70 will be stimulated in ATP hydrolysis, which drives the Hsp70 to its ADP-bound, closed state. (**E**) An Hsp70 bound to a native-tending substrate molecule with few exposed hydrophobic sites is unlikely to have a nearby Hsp40 and thus unlikely to be stimulated in ATP hydrolysis, and nucleotide exchange drives the Hsp70 toward its ATP-bound, open state.

As a result of this symmetry breaking, an Hsp70 bound to a substrate in the misfoldtending conformation is more likely to be closed than one bound to a substrate in the native-tending conformation. Thus, a substrate is on average more quickly released from the Hsp70 if it is in the native-tending conformation than if it is in the misfold-tending conformation. This difference biases the substrate toward the native conformation [30].

3.1.4. Hsp70 and Hsp90 Perform Non-Equilibrium Folding by Preferentially Releasing Substrate Proteins in Native-Tending Conformations

The cochaperone Cdc37 helps break symmetry Condition 2 in Hsp90-mediated kinase activation. The cochaperone Hsp40 helps break symmetry Condition 3 in Hsp70-mediated protein folding. Despite breaking different symmetries, Hsp70 and Hsp90 share the same kinetic consequence: both chaperones release a bound substrate in the native-tending (*F*) conformation faster than a bound substrate in the misfold-tending (*U*) conformation.

and

To see how this kinetic asymmetry promotes the native concentration, consider first a system in which the symmetry conditions are satisfied (Figure 4A). A substrate in the *U* conformation binds to the chaperone faster than a substrate in the *F* conformation. As a result, the reactive flux through the ATP-driven cycle of a chaperone bound to a substrate in the *U* conformation is higher than that through the cycle of a chaperone bound to a substrate in the *F* conformation. However, kinetic symmetry ensures that, at the steady state, the flux of *U* binding to the chaperone is the same as the flux of *U* unbinding from the chaperone; the same holds true for *F* binding to and unbinding from the chaperone, and there is no net flux between *U* and *F*. Under the symmetry conditions, there are two parallel, independent chaperone cycles with respective reactive fluxes:

$$\mathcal{S}\_{\mathcal{S}\text{+Hsp}} = (\mathcal{S} \to \mathcal{S} \cdot \text{Hsp} \to \mathcal{S} \cdot \{\text{states of Hsp} \cdot \cdots \} \to \mathcal{S} \cdot \text{Hsp} \to \mathcal{S}) \text{ for } \mathcal{S} = \mathcal{U}, \mathcal{F}, \tag{44}$$

*JU*+Hsp > *JF*+Hsp (45)

**Figure 4.** Reactive flux in chaperone-mediated non-equilibrium protein folding. (**A**) Under the symmetry conditions, there are two independent ATP-driven chaperone cycles: one with a higher reactive flux for a substrate in the misfold-tending (*U*) conformation (left) and one with a lower reactive flux for a substrate in the native-tending (*F*) conformation (right). There is no net flux between the substrate's two conformations, and the ratio [*F*]/[*U*] is the same as its chaperone-free equilibrium value. (**B**) Cochaperones break the kinetic symmetry. The release of a substrate in the *U* conformation from the chaperone is inhibited: Cdc37 assists Hsp90 with retaining the substrate and Hsp40 stimulates ATP hydrolysis and closure of Hsp70. This restricts the reactive flux to release a substrate in the *U* conformation, forcing a partial diversion of the flux to the conformation conversion from *U* · Hsp to *F* · Hsp and resulting in a net reactive flux of *U* → *U* · Hsp → *F* · Hsp → *F* → *U* (red cycle), which elevates the ratio [*F*]/[*U*] above its chaperone-free equilibrium value.

However, there is no net flux between *U* and *F*:

$$f\_{\rm UF} = k\_{\rm UI \to F}[\mathcal{U}] - k\_{F \to \mathcal{U}}[F] = 0 \tag{46}$$

Thus, the ratio between *F* and *U* is unchanged from the chaperone-free equilibrium:

$$\frac{[F]}{[\mathcal{U}]} = \frac{k\_{\mathcal{U} \to F}}{k\_{F \to \mathcal{U}}} = \mathcal{K}\_{\mathcal{U}F} = \frac{[F]\_{eq}}{[\mathcal{U}]\_{eq}} \tag{47}$$

Symmetry breaking disrupts the independence between this pair of chaperone cycles. The release of a substrate in the *U* conformation from the chaperone is inhibited: in the case of Hsp90, Cdc37 helps the chaperone retain the bound client kinase; in the case of Hsp70, Hsp40-stimulated ATP hydrolysis and closure in Hsp70 diminish the reactive flux to re-open the chaperone (Figure 4B). This forces part of the reactive flux in *JU*+HSP after the binding of the substrate to be diverted into the reactive flux of conformation conversion in the bound substrate:

$$J\_{\rm ll-Hsp} \to \text{ $F$ -Hsp} \tag{48}$$

This in turn leads to a corresponding increase in the reactive flux of the chaperone's release of the substrate in the *F* conformation, which increases [*F*] such that

$$\frac{[F]}{[\mathcal{U}]} > \frac{[F]\_{eq}}{[\mathcal{U}]\_{eq}} \tag{49}$$

Thus, symmetry breaking biases the substrate toward the native-tending conformation and elevates the native concentration.

3.1.5. The Potential Role of Sequential Hydrolyses of Multiple ATPs in the Chaperone Cycle

Breaking symmetry Condition 4 permits a net reactive flux along the following path that promotes the native-tending conformation *F* over the misfold-tending conformation *U*:

$$\begin{array}{c} \begin{array}{c} \begin{array}{c} + \text{Hsp} \\ \end{array} \longrightarrow \begin{array}{c} \begin{array}{c} \text{Hsp} \\ \end{array} \end{array} \end{array} \begin{array}{c} \begin{array}{c} \text{ATP} \rightarrow \text{ADP} + \text{Pi} \\ \end{array} \longrightarrow \begin{array}{c} \begin{array}{c} \text{Hsp} \\ \end{array} \end{array} \begin{array}{c} \begin{array}{c} \text{ATP} \rightarrow \text{ADP} + \text{Pi} \\ \end{array} \end{array} \begin{array}{c} \begin{array}{c} \text{Hsp} \\ \end{array} \end{array} \longrightarrow \begin{array}{c} \begin{array}{c} \text{Hsp} \\ \end{array} \end{array} \end{array} \end{array} \tag{50}$$

A non-zero net flux of *U* · Hspclosed → *F* · Hspclosed does not violate thermodynamic cycle closure in this case because the reaction cycle in Equation (17) is no longer reversible—ATP hydrolysis occurs and chemical energy is consumed in that cycle—and thus Equations (18) and (19) no longer hold.

To break symmetry Condition 4, at least one closed state of the chaperone must be separated from all the open states by ATP hydrolysis. This requires at least two ATP to be hydrolyzed sequentially—not synchronously—per chaperone cycle, and the substrate has to change conformation between two ATP hydrolyses. Examples include Hsp90 that hydrolyzes two ATP molecules sequentially in its cycle [60] and the group II chaperonins in eukaryotes—such as TRiC/CCT—that hydrolyzes up to eight ATPs sequentially [61,62]. The role of such sequential ATP hydrolysis—and the consequent symmetry breaking of Condition 4—in non-equilibrium protein folding is an open question.

#### *3.2. An Upper Bound of Non-Equilibrium Protein Folding and Its Implications*

Having established the symmetry breaking requirements for non-equilibrium folding, I now derive an upper bound on the folding capacity of an ATP-driven chaperone. The key result is

$$\mathbb{E}\left[N\right] < \frac{K\_N}{K\_M K\_F^{-1} \left(1 + \frac{k\_{a,II}[O]}{k\_{l\to F}}\right)^{-1} + K\_F^{-1} \max(1, a)^{-1} + 1 + K\_N} P\_0 \tag{51}$$

where [*O*] is the concentration of free chaperone in the open state, the equilibrium constants *KN*, *KM*, and *KF*, the kinetic rate constants *kU*→*F* and *ka*,*U*, and their corresponding reactions are summarized in Table 1, and

$$\alpha \equiv \frac{k\_{\rm II \to F,C}}{k\_{\rm II \to F}} \tag{52}$$

is an acceleration factor to indicate any potential rate change in conformation conversion when the substrate is bound to the closed chaperone. The proof of Equation (51) is given in Section 2.2 of Methods and Materials.

Equation (51) gives a general upper bound applicable to any ATP-driven chaperone. The folding capacity of a specific type of chaperone needs to be calculated by detailed models [30,31], but it cannot exceed that given by Equation (51). This result allows an analysis of the common key factors in non-equilibrium folding without considering the mechanistic details of specific chaperones.

Introducing a combined equilibrium constant for the reaction *U K*˜ *F* −)\*− (*F* + *N*)

$$\tilde{\mathcal{K}}\_{\mathcal{F}} \equiv \frac{[\mathcal{F}]\_{eq} + [\mathcal{N}]\_{eq}}{[\mathcal{U}]\_{eq}} = (1 + \mathcal{K}\_N)\mathcal{K}\_{\mathcal{F}} \tag{53}$$

The upper bound in Equation (51) can be written as

$$\mathbb{E}\left[N\right] < \frac{1}{\mathbb{K}\_M \tilde{\mathbb{K}}\_F^{-1} \left(1 + \frac{k\_{al}l(\mathcal{O})}{k\_{l\mid l \to F}}\right)^{-1} + \tilde{\mathbb{K}}\_F^{-1} \max(1, a)^{-1} + 1} \cdot \frac{\mathbb{K}\_N}{1 + \mathcal{K}\_N} P\_0 \tag{54}$$

Compare this to the native concentration in the chaperone-free equilibrium

$$\begin{array}{rcl} [N]\_{\ell q} &=& \frac{K\_N}{\pounds\_M \mathcal{K}\_F^{-1} + \mathcal{K}\_F^{-1} + 1 + \mathcal{K}\_N} P\_0 \\ &=& \frac{1}{\mathcal{K}\_M \mathcal{K}\_F^{-1} + \mathcal{K}\_F^{-1} + 1} \cdot \frac{\mathcal{K}\_N}{1 + \mathcal{K}\_N} P\_0 \end{array} \tag{55}$$

The non-equilibrium gain factor is thus bounded by

$$\log = \frac{[N]}{[N]\_{\varepsilon q}} < \frac{\mathbb{K}\_M \tilde{\mathbb{K}}\_F^{-1} + \tilde{\mathbb{K}}\_F^{-1} + 1}{\mathbb{K}\_M \tilde{\mathbb{K}}\_F^{-1} \left(1 + \frac{k\_{d, \mathrm{II}}[O]}{k\_{\mathrm{II} \to F}}\right)^{-1} + \tilde{\mathbb{K}}\_F^{-1} \max(1, \mathfrak{a})^{-1} + 1} \tag{56}$$

3.2.1. Chaperones Bind to Unstable Intermediate Conformations of Substrates to Drive Non-Equilibrium Folding

An implication of Equation (56) is that ATP-driven chaperones must bind to an intermediate unfolded conformation (*U*) of the substrate, not to the misfolded conformation (*M*) itself, to perform non-equilibrium folding, unless the conformation conversion of a substrate is accelerated when bound to the chaperone (i.e., *kU*→*F*,*C* > *kU*→*F* hence *α* > 1). This can be demonstrated by contradiction. If the substrate does not have an intermediate misfold-tending conformation and the chaperone directly binds to the misfolded conformation, i.e., *M* and *U* are the same, Equation (51) reduces to (by setting *KM* = 0)

$$\mathbb{E}\left[N\right] < \left(\tilde{K}\_F^{-1} \max(1, \mathfrak{a})^{-1} + 1\right)^{-1} \cdot \frac{K\_N}{1 + K\_N} P\_0 \tag{57}$$

and the upper bound of the non-equilibrium gain factor becomes

$$g < \frac{\tilde{K}\_F^{-1} + 1}{\tilde{K}\_F^{-1} \max(1, \alpha)^{-1} + 1} \tag{58}$$

In the absence of a mechanism for the substrate to accelerate its conformation conversion when it is bound to the chaperone (*α* ≤ 1), *g* ≤ 1, the chaperone cannot elevate the native concentration.

To my knowledge, accelerated folding of protein substrates when bound to a chaperone has only been reported for the GroEL/GroES chaperonins [43,63–67]. In general, steric hindrance from the chaperone is more likely to impede rather than to accelerate conformation conversions in a bound substrate; this impedance was observed for the rhodanese

protein trapped in GroEL/GroES by a single-molecule experiment [68]. For Hsp90 and Hsp70, there has not been any experimental demonstration that a substrate exhibits faster conformation conversions when bound to the chaperone than when free in the solution. This suggests that chaperones, with the potential exceptions of chaperonins, must bind to intermediate unfolded conformations of the substrate proteins to drive non-equilibrium protein folding.

Assuming *α* ≤ 1, the upper bound on the non-equilibrium gain factor becomes

$$\mathcal{g} < \mathcal{g}\_{\text{max}} = \frac{\mathcal{K}\_M \left(\tilde{\mathcal{K}}\_F + 1\right)^{-1} + 1}{\mathcal{K}\_M \left(\tilde{\mathcal{K}}\_F + 1\right)^{-1} \left(1 + \frac{k\_{d, \mathcal{U}}[O]}{k\_{\mathcal{U} \to F}}\right)^{-1} + 1} \tag{59}$$

For the gain factor to substantially exceed 1, the following must be true:

$$\left(K\_{\rm M}(\tilde{\mathbf{K}}\_{\rm F} + 1)\right)^{-1} \gg 1 \implies K\_{\rm M} \gg 1\tag{60}$$

Equation (60) implies that the intermediate conformation *U* to which the chaperone binds must be intrinsically unstable, and it will predominantly convert to the misfolded conformation *M* in the absence of the chaperone. This result is intuitive: if the chaperone binds to a dominant conformation of the substrate, it will trap a substantial fraction of the substrate and hinder its folding to the native structure. As a result, the chaperone will be unable to elevate the native concentration. The difficulty to observe the chaperone-binding conformations in biophysical experiments [69] attests to their transiency.

#### 3.2.2. Chaperones Stabilize the Native Structures of Slow-Folding Proteins

Non-equilibrium folding also requires, as implied by Equation (59) and *g* 1,

$$\frac{k\_{a,II}[O]}{k\_{U \to F}} \gg 1 \iff k\_{U \to F} \ll k\_{a,II}[O] \tag{61}$$

Taken together, Equations (60) and (61) suggest that chaperones stabilize the native structures of slow-folding proteins. Assuming the binding rate constant to be on the order of *ka*,*U* ∼ 106 /M/s, the spontaneous (i.e., without chaperones) refolding rate of the protein, which is approximately *K* −1 *M kU*→*F*, should be much slower than 1 /s to admit effective non-equilibrium folding by chaperones at a concentration of [*O*] ∼ 1 µM.

#### 3.2.3. ATP-Driven Chaperones Buffer Destabilizing Mutations

About 18% of protein molecules in the cell harbor at least one missense mutation due to errors in translation [70]. In addition, proteins incur mutations due to germline and somatic gene polymorphism [71]. Given that about 30–40% of random substitutions disrupt protein functions [72,73], most probably by loss-of-folding [74,75], it is likely that many cellular protein molecules have compromised thermal stability and the native structures of some will not be the free energy minima. ATP-driven chaperones may buffer such destabilizing mutations [76,77] and maintain the native concentrations of these proteins by non-equilibrium folding [30].

The missense mutations may alter one or more of the transition rates and the equilibrium constants in protein folding dynamics: e.g., it may decrease the thermal stability of the protein by increasing *KM*, decreasing *kU*→*F* or increasing *kF*→*U* (hence decreasing *KF* = *kU*→*F*/*kF*→*U*), or decreasing *KN*. Assuming *α* ≤ 1 as discussed above, the maximum native concentration mediated by a chaperone is

$$\begin{array}{rcl} [N]\_{\max} &=& g\_{\max}[N]\_{eq} \\\\ &=& \frac{1}{K\_{\text{M}}(\text{\$\tilde{\mathcal{K}}\_{\text{F}}\$+1\$)^{-1}\left(1+\frac{k\_{\text{d}}[\text{O}]}{K\_{\text{M}}+F}\right)^{-1}+1}\frac{1}{1+\mathcal{K}\_{\text{F}}^{-1}}\frac{K\_{\text{N}}}{1+K\_{\text{N}}}P\_{\text{O}} \end{array} \tag{62}$$

Equation (62) suggests that the capacity of ATP-driven chaperones to buffer a destabilizing mutation depends on both the wild-type substrate's folding kinetics and how the mutation alters the kinetic parameters (Figure 5). For instance, chaperones may be more effective in buffering mutations that slow down the transition from the misfold-tending conformation (*U*) to the native-tending conformation (*F*)—i.e., decreasing *kU*→*F* by e.g., stabilizing the *U* conformation—than mutations that destabilize the native state by decreasing *KN*. Such differential buffering may play a role in selecting tolerated genetic variations and shaping their consequences in human disease [78].

**Figure 5.** The capacity of ATP-driven chaperones to maintain elevated native fractions in response to destabilizing mutations in a protein substrate. The kinetic parameters of the wild-type protein are *KM* = 102 , *KF* = 10, *KN* = 102 , *kU*→*F* = 0.1 s −1 , and *ka* = 106 M−1 · s −1 ; the concentration of the open chaperone is set to [*O*] = 1 µM.

#### **4. Discussion**

Breaking the symmetry Conditions 1–4 is necessary but on its own is insufficient for non-equilibrium folding. *g* > 1 often requires both substantial deviation from the symmetry conditions and other enabling kinetic conditions, as exemplified by Equation (56). Detailed mechanistic models [30,31] are needed to quantitatively predict the extent of nonequilibrium folding. Nonetheless, these symmetry conditions can help assess whether a proposed mechanism of chaperone function will imply non-equilibrium folding.

Unlike equilibrium protein folding, the native yield of non-equilibrium protein folding depends not only on the equilibrium constants but also on the kinetic parameters of the folding reactions and the chaperone cycle. The native concentration of a substrate may change in response to the modulation of the step-wise kinetics of the chaperone cycle [30,31,79] by cochaperones [80], by mutations [81,82] and post-translational modifications [83,84] in the chaperones, and by pharmacological molecules [85]. Such modulations may be used by the cell to regulate proteostasis. They may also offer therapeutic opportunities.

Given both the theoretical models and the experimental evidence suggesting that ATP-driven chaperones can stabilize the native or active structures of substrate proteins out of the thermal equilibrium, Anfinsen's hypothesis does not *need* to be true for protein folding in cells. ATP-driven chaperones may not only kinetically accelerate the folding of proteins to thermodynamically stable native structures, but also actively fold some proteins to native structures that are thermodynamically unstable.

Most proteins have evolved to be marginally stable [86,87]. If ATP-driven chaperones can indeed buffer destabilizing mutations and maintain the native structures and functions of unstable mutants, as discussed in Section 3.2.3, it is then plausible that the native structures of some proteins may have become thermodynamically unstable as a consequence of this chaperone-buffered evolution. They may not stay folded on their own, but depend on the energy-consuming chaperones to maintain their native structures.

How many proteins in a cell take exception to Anfinsen's hypothesis and depend on non-equilibrium folding by a particular ATP-driven chaperone? Emerging proteomics techniques may help answer this question. For example, cell lysates may be subject to proteolytic digestion [88] and the resulting products analyzed by mass spectrometry (MS), identifying proteins with permissible digestion sites, which approximately reflect their state of folding [89]. This proteolysis-MS assay may be repeated for lysates incubated with chaperone inhibitors [90,91] or chaperone agonists [85]. Proteins more susceptible to proteolysis in the presence of chaperone inhibitors—and less susceptible in the presence of chaperone agonists—are candidates that may depend on the chaperone for non-equilibrium folding to their native structures. The lysates should be incubated in the presence of protein synthesis inhibitors so that the analysis can isolate the chaperone's effects on *maintaining* the native structures of its substrates from its effects on the folding of their nascent chains; the former demonstrates non-equilibrium stabilization of thermodynamically unfavorable native structures while the latter may be attributable to kinetic acceleration of protein folding. This analysis may be more applicable to GroEL/GroES and Hsp70 than to Hsp90 because the latter mediates the late-stage folding and activation of its substrates [33,92], which may not be associated with significant changes in the protein disorder detectable by the proteolysis-MS assay.

#### *Implications for Protein Native Structures and Their Folding Pathways*

My model of non-equilibrium protein folding and activation suggests the tantalizing possibility that ATP-driven chaperones may play a role in shaping the native structures of some proteins. Consistent with a previous experimental demonstration that chaperones alter the folding pathway of a substrate protein [93], my model implies that an ATP-driven chaperone may bias a substrate protein to fold along pathways that expose few cochaperone binding sites during folding, with consequences for the resulting structures.

Consider two conformations *M* and *N* of a substrate protein, where *M* is the free energy minimum but associated with a folding pathway inhibited by the chaperone, and *N* has a higher free energy but can be reached through a folding pathway uninhibited by the chaperone (Figure 6). The protein will fold into its free energy minimum conformation *M* in the absence of the chaperone, but, if the chaperone-induced pathway bias is sufficiently strong, it will fold into the alternative conformation *N* in the presence of the chaperone. Note that *M* can be an ensemble of rapidly inter-converting conformations, such as in intrinsically disordered proteins (IDP) or intrinsically disordered protein regions [94–98]. Can ATP-driven chaperones fold some IDPs into well-ordered structures?

It has been proposed that some proteins may fold into native structures that are more kinetically accessible than conformations of the lowest free energy [99]. Indeed, experimental observations have been reported that synonymous codon substitutions result in conformational changes in the translated proteins, due to kinetic changes in the co-translational folding of the nascent chain on the ribosome [100–103]. These results are consistent with the idea that the native structures of some proteins may be determined by kinetics rather than thermodynamics. One implication is that the solution to the structure prediction problem for such proteins in cell may depend on the solution to the protein folding problem, and in-cell protein folding may be an active, energy-dependent process [104]. Predicting the cellular conformation of these proteins—in the presence of ATP-driven chaperones—may require the search for folding pathways that limit the exposures of cochaperone-binding, e.g., hydrophobic, sites.

**Figure 6.** An ATP-driven chaperone (Hsp) may favor the protein folding pathway that exposes few cochaperone binding sites and drive the protein to a different conformation (*N*) than its most stable conformation (*M*) in the absence of the chaperone.

#### **5. Conclusions**

In this work, I have proposed a theoretical framework to analyze non-equilibrium protein folding by ATP-driven chaperones. The symmetry breaking conditions may help determine whether a chaperone—by a proposed mechanism of action—can convert the energy from ATP hydrolysis to the out-of-equilibrium stabilization of the native structures of its substrate proteins. I have discussed how Hsp70 and Hsp90 may have broken different symmetries and how the symmetry breaking enables them to perform non-equilibrium protein folding and activation. My models predict that some proteins may fold to native structures that do not correspond to the free energy minima, and that their native structures may be shaped by the chaperone-mediated folding pathways. These predictions may be tested by experiments, some of which I have suggested above.

**Funding:** This research received no external funding.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

#### **References**

## *Review* **Hsp90 and Associated Co-Chaperones of the Malaria Parasite**

**Tanima Dutta 1,2,3, Harpreet Singh 4 , Adrienne L Edkins 5 and Gregory L Blatch 1,2,5,6,\***

**Abstract:** Heat shock protein 90 (Hsp90) is one of the major guardians of cellular protein homeostasis, through its specialized molecular chaperone properties. While Hsp90 has been extensively studied in many prokaryotic and higher eukaryotic model organisms, its structural, functional, and biological properties in parasitic protozoans are less well defined. Hsp90 collaborates with a wide range of co-chaperones that fine-tune its protein folding pathway. Co-chaperones play many roles in the regulation of Hsp90, including selective targeting of client proteins, and the modulation of its ATPase activity, conformational changes, and post-translational modifications. *Plasmodium falciparum* is responsible for the most lethal form of human malaria. The survival of the malaria parasite inside the host and the vector depends on the action of molecular chaperones. The major cytosolic *P. falciparum* Hsp90 (PfHsp90) is known to play an essential role in the development of the parasite, particularly during the intra-erythrocytic stage in the human host. Although PfHsp90 shares significant sequence and structural similarity with human Hsp90, it has several major structural and functional differences. Furthermore, its co-chaperone network appears to be substantially different to that of the human host, with the potential absence of a key homolog. Indeed, PfHsp90 and its interface with cochaperones represent potential drug targets for antimalarial drug discovery. In this review, we critically summarize the current understanding of the properties of Hsp90, and the associated cochaperones of the malaria parasite.

**Keywords:** *Plasmodium falciparum*; heat shock proteins; cytosolic Hsp90; ATPase; co-chaperones; client proteins

### **1. Introduction**

To combat cellular stress, an elevated expression of chaperones, many of which are heat shock proteins, is observed [1]. In eukaryotes, heat shock protein 90 (Hsp90) and heat shock protein 70 (Hsp70) are the most prominent chaperone families. Together, Hsp90 and Hsp70 collaborate to ensure protein homeostasis by capturing client proteins and facilitating productive folding [2]. Hsp90 has essential functions in cell growth and differentiation, apoptosis, signal transduction, and cell–cell communication [3]. Hsp90 isoforms exist in organisms ranging from bacteria (where it is known as HtpG) to protozoa to higher eukaryotes. Although Hsp90 is not essential for cell survival in the bacterium *Escherichia coli*, it is important for the survival of *Shewanella oneidensis* under heat stress [4]. It is indispensable for viability in the yeast *Saccharomyces cerevisiae* [5], while in higher eukaryotes the Hsp90β, but not the Hsp90α, isoform is essential for survival [6–9]. Hsp90 plays a central

**Citation:** Dutta, T.; Singh, H.; Edkins, A.L.; Blatch, G.L. Hsp90 and Associated Co-Chaperones of the Malaria Parasite. *Biomolecules* **2022**, *12*, 1018. https://doi.org/ 10.3390/biom12081018

Academic Editor: Chrisostomos Prodromou

Received: 12 June 2022 Accepted: 17 July 2022 Published: 22 July 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

role in many cellular networks, along with buffering environmental conditions to promote evolutionary fitness [10].

*Plasmodium falciparum* is responsible for the most lethal form of human malaria, taking 627,000 lives worldwide in 2020 [11]. Infection begins with a female mosquito injecting sporozoites into human blood. Following the mosquito's 'blood meal', the successful colonization of the liver by sporozoites initiates the parasite life cycle in humans, followed by erythrocyte invasion, which accounts for the pathology of malaria [12,13]. The development of sporozoites takes place within hepatocytes, where they mature into schizonts and then merozoites, which are released and rapidly invade erythrocytes [13,14]. The intra-erythrocytic stage results in alterations of the infected host cells that cause them to adhere to the cell walls of capillaries, thereby preventing them from clearing through the spleen. This structural change poses a risk for the human host, since clusters of infected erythrocytes can create a blockage in blood circulation. After the intra-erythrocytic stage, the gametocyte-infected stage develops, which can infect the mosquito upon blood ingestion [12]. The motile ookinetes penetrates the midgut wall of the mosquito, developing into "oocysts". These cysts then release sporozoites, which migrate to the mosquito's salivary glands and can again infect the human host [12]. During the intra-erythrocytic stage, high temperatures are induced and, therefore, parasite proteins and membranes require cytoprotection for the maintenance of their integrity [15]. Survival of the malaria parasite inside the host and the vector depends on the action of molecular chaperones. The emergence of resistance to the most commonly used antimalarial drugs, coupled with the difficulty in producing an effective vaccine, resulted in an urgent need to develop drugs targeted against novel chemotherapeutic targets [16–18].

There is evidence from saturation-scale mutagenesis screening that all the Hsp90 genes of the malaria parasite are essential [19]. Furthermore, the major cytosolic *P. falciparum* Hsp90 (PfHsp90) is highly expressed during the intra-erythrocytic stage of the parasite life cycle, induced by stress, and plays an essential role in parasite survival and development [7]. Using in vitro cell culture studies, geldanamycin (GA) was found to be highly effective at inhibiting the growth of parasite-infected erythrocytes, and causing an arrest at the ring stage [7,20]. Assuming that PfHsp90 was the primary target of GA, these findings suggest that PfHsp90 plays an important role in malaria parasite growth in erythrocytes [7,20]. In addition, given that transition from early ring to metabolically active trophozoites is regulated by temperature changes, PfHsp90 was also proposed as a major player in the malaria parasite's response to heat shock, and the establishment of infection in erythrocytes [21,22]. Indeed, frequent febrile episodes elevate the level of PfHsp90 expression, and GA inhibition studies suggest that PfHsp90 assists in malaria parasite survival during febrile episodes [23,24]. Interestingly, PfHsp90 is also shown to be essential for liver stage development [25]. Overall, these findings suggest that PfHsp90 is an ideal anti-malaria drug target.

#### **2. Hsp90: Chaperone Activity and Its Conformational Changes**

Cytosolic Hsp90 architecture is conserved from bacteria to humans with slight modifications, which are critical for functional differences between Hsp90 paralogs and orthologs [26]. The most common structural feature of all Hsp90 homologs is the presence of an N-terminal nucleotide-binding domain (NTD), along with a C-terminal domain (CTD) and a middle domain (MD) [27] (Figures 1 and 2; Protein Data Bank [PDB] identification [ID] codes: 5FWK and 5FWM). Hsp90 functions as a molecular machine to capture and promote the folding of client proteins through conformational changes regulated by AT-Pase activity and protein–protein interactions [28]. ATP binds the Hsp90 NTD, and ATP hydrolysis is catalyzed by the NTD and MD. The NTD and MD are joined by a charged linker sequence, which is important for inter-domain communication during chaperone activity [29].

co-chaperones [34].

The MD also carries the binding site for Hsp90 clients and co-chaperones. The CTD allows the constitutive dimerization of Hsp90 through two C-terminal helices forming a four-helix bundle [30,31]. One of the most prominent features of Hsp90 chaperone activity is the formation of a V-shape dimer, which helps in the transient N-terminal dimerization that is required for ATP hydrolysis [32] (Figure 1). A C-terminal MEEVD motif is present in all cytosolic Hsp90 paralogs, and is the main site of binding to tetratricopeptide repeat (TPR)-containing co-chaperones [33]. Co-chaperones of eukaryotic Hsp90s typically outnumber their respective chaperones, forming complexes with Hsp90 and their client proteins, to promote efficient protein folding and fine-tuning chaperone functions to maintain cellular homeostasis (Figure 1). Consequently, new approaches to inhibit the function of the Hsp90 complex have focused on the disruption of protein–protein interactions with

**Figure 1.** Regulation of the Hsp90 chaperone cycle by co-chaperones. Progression of client proteins through the Hsp90-mediated chaperone folding pathway is regulated by co-chaperones, which act at defined stages in the cycle. Co-chaperones may regulate Hsp90 association with clients, ATPase activity, conformational changes, and post-translational modifications. When inactive, Hsp90 is constitutively dimerized at the C-terminus but not the N-terminus. Entry of client proteins is facilitated by co-chaperones including the Hsp70/Hsp90 organizing protein Hop, which regulates transfer of clients from Hsp70 by binding simultaneously to Hsp70 and Hsp90), to form the intermediate complexes. Hop is conserved in *Plasmodium falciparum* (PfHop, PF3D7\_1434300). Kinase clients require the kinase-specific co-chaperone Cdc37; however, a Cdc37-encoding gene has not been identified in the *P. falciparum* genome. On ATP binding, Hsp90 undergoes N-terminal dimerization, and the client protein associates with the middle domain of Hsp90. Bindings of other co-chaperones, including peptidyl-prolyl cis–trans isomerases (PPIase) and protein phosphatase 5 (PP5), associate to form the asymmetric Hsp90 complexes. The *P. falciparum* genome encodes a PP5 isoform (PfPP5, **Figure 1.** Regulation of the Hsp90 chaperone cycle by co-chaperones. Progression of client proteins through the Hsp90-mediated chaperone folding pathway is regulated by co-chaperones, which act at defined stages in the cycle. Co-chaperones may regulate Hsp90 association with clients, ATPase activity, conformational changes, and post-translational modifications. When inactive, Hsp90 is constitutively dimerized at the C-terminus but not the N-terminus. Entry of client proteins is facilitated by co-chaperones including the Hsp70/Hsp90 organizing protein Hop, which regulates transfer of clients from Hsp70 by binding simultaneously to Hsp70 and Hsp90, to form the intermediate complexes. Hop is conserved in *Plasmodium falciparum* (PfHop, PF3D7\_1434300). Kinase clients require the kinase-specific co-chaperone Cdc37; however, a Cdc37-encoding gene has not been identified in the *P. falciparum* genome. On ATP binding, Hsp90 undergoes N-terminal dimerization, and the client protein associates with the middle domain of Hsp90. Bindings of other co-chaperones, including peptidyl-prolyl cis–trans isomerases (PPIase) and protein phosphatase 5 (PP5), associate to form the asymmetric Hsp90 complexes. The *P. falciparum* genome encodes a PP5 isoform (PfPP5, PF3D7\_1355500) and multiple PPIase isoforms (PfFKBP35, PF3D7\_1247400; PfCns1, PF3D7\_1108900; and PfCyp40, PF3D7\_1111800). These co-chaperones regulate the post-translational modification and maturation of Hsp90 complexes. Early co-chaperones subsequently dissociate from the complex to be replaced by p23, which stabilizes the late closed Hsp90 complex and the client within the complex, and inhibits ATPase activity. Two homologs of p23 are encoded in the *P. falciparum* genome (Pfp23A, PF3D7\_1453700; and Pf23B, PF3D7\_0927000). ATP hydrolysis is stimulated by binding of Aha1, resulting in release of the client protein and a return of Hsp90 to the inactive conformation. The *P. falciparum* genome encodes a single Aha1 isoform (PfAha1, PF3D7\_0306200). Image created with BioRender.com.

The MD also carries the binding site for Hsp90 clients and co-chaperones. The CTD allows the constitutive dimerization of Hsp90 through two C-terminal helices forming a four-helix bundle [30,31]. One of the most prominent features of Hsp90 chaperone activity is the formation of a V-shape dimer, which helps in the transient N-terminal dimerization that is required for ATP hydrolysis [32] (Figure 1). A C-terminal MEEVD motif is present in all cytosolic Hsp90 paralogs, and is the main site of binding to tetratricopeptide repeat (TPR) containing co-chaperones [33]. Co-chaperones of eukaryotic Hsp90s typically out-number their respective chaperones, forming complexes with Hsp90 and their client proteins, to promote efficient protein folding and fine-tuning chaperone functions to maintain cellular homeostasis (Figure 1). Consequently, new approaches to inhibit the function of the Hsp90 complex have focused on the disruption of protein–protein interactions with cochaperones [34].

Hsp90 modulates the stability of several essential cellular proteins, and is a conserved regulator of key protein kinases and nuclear receptors that control the cell cycle and signal transduction events [35–37]. The NTD is rich in β-strands and forms a nucleotide-binding pocket sharing a Bergerat fold with members of the GHKL superfamily (gyrase subunit B [GyrB], histidine kinase, and DNA mismatch repair protein MutL) [38]. This domain can be inhibited competitively by small molecule inhibitors, which target the ATP binding site and, as such, compete with ATP for binding [38–40]. The NTD and MD of Hsp90 undergo key conformational changes, bringing the γ-phosphate of ATP closer to key residues in the MD (e.g., Arg380 in yeast Hsp82), which triggers ATP hydrolysis [41]. Also, Hsp90 has a much higher affinity for ADP than ATP, suggesting that it requires a threshold cellular ATP:ADP ratio for ATPase activity [39,42,43]. In general, all Hsp90s bound to ATP can associate with unfolded/partially folded client proteins. Subsequently, the lid region closes over the ATP binding pocket, and the NTD dimerizes, adopting a closed conformation. The association of the MD in the Hsp90 dimer alters the position of the MD catalytic loop promoting ATP hydrolysis (Figure 1). Upon ATP hydrolysis, the client protein is released to fold spontaneously [2]. The Hsp90 homodimer returns to the unbound open conformation, and is primed for subsequent rounds of ATP hydrolysis and protein folding [38].

#### **3.** *P. falciparum* **Hsp90s**

The *P. falciparum* genome contains four Hsp90 genes, encoding the following PfHsp90 proteins: PfHsp90 (cytosol; PF3D7\_0708400), PfTrap1/PfHsp90\_M (mitochondrion; PF3D7\_ 1118200), PfGrp94 (endoplasmic reticulum; PF3D7\_1222300), and PfHsp90\_A (apicoplast; PF3D7\_1443900) [44]. Low resolution structural studies suggest that PfHsp90 exists in solution as elongated and flexible dimers [37] (Figure 2). While PfHsp90 shares significant sequence and structural similarity with its eukaryotic homologs, particularly cytosolic human Hsp90β (hHsp90), and contains all the characteristic domains (NTD, charged linker region, MD, CTD, and C-terminal dimerization domain ending in a MEEVD motif), it has several key structural and functional differences [45–47] (Figure 2). In particular, the ATP-binding pocket of PfHsp90 is more hydrophobic, constricted, and basic, relative to hHsp90 [48]. Biochemical studies on PfHsp90 report that, in comparison to hHsp90, it binds ATP with higher affinity (by 30%), is a more active ATPase (with six-fold higher activity), and has significantly higher catalytic efficiency (*k*cat/*Km* of 16.2 × 10−5 min−1 µM−1 ) [49]. While basal ATPase kinetics and, ultimately, the speed of the chaperone cycle are important factors, they are not sufficient for efficient client protein folding by Hsp90 [50,51]. There is evidence that the dwelling time between the open and closed conformations of Hsp90 is critical to ensuring appropriate client protein interaction [50] (Figure 1); and, hence, more detailed biophysical studies are required on PfHsp90. Interestingly, PfHsp90 has a highly (negatively) charged, flexible linker region that is substantially longer than that of hHsp90 [52]. Domain swapping experiments introducing the charged linker from PfHsp90 into yeast or human Hsp90 lead to chimeric proteins, which support viability in yeast but have reduced ATPase activity, and reduced interaction with client proteins and some co-chaperones [52]. It remains to be determined how the intrinsic biochemical properties of PfHsp90 are regulated by different client proteins and their associated cochaperones. Nevertheless, these initial biochemical findings suggest that the PfHsp90

chaperone cycle may be capable of rapid client protein turnover, which would be highly advantageous to parasite survival under the stressful conditions experienced in the human host. Furthermore, these unique architectural and biochemical features of PfHsp90 suggest that it is a prime drug target for structure-based anti-malarial drug discovery [53]. be highly advantageous to parasite survival under the stressful conditions experienced in the human host. Furthermore, these unique architectural and biochemical features of PfHsp90 suggest that it is a prime drug target for structure-based anti-malarial drug discovery [53].

biochemical properties of PfHsp90 are regulated by different client proteins and their associated co-chaperones. Nevertheless, these initial biochemical findings suggest that the PfHsp90 chaperone cycle may be capable of rapid client protein turnover, which would

*Biomolecules* **2022**, *11*, x FOR PEER REVIEW 5 of 16

**Figure 2.** Domain organization and structural view of hHsp90β and PfHsp90. (**A**). Domain organization of hHsp90β (top) and PfHsp90 (bottom). Structure of full-length dimeric (**B**). hHsp90β and (**C**). PfHsp90 proteins as cartoons. ATP bound to the N-terminal domain (NTD) is shown as red spheres. The two Hsp90 monomers in the models are colored purple and blue. (**D**). hHsp90β and (**E**). PfHsp90 NTD as surface. The surface (with 60% transparency) is colored according to element type and it also depicts the arrangement of secondary structure elements (red color) as cartoons. The bound ATP molecule is represented as sticks, colored according to the element type. Full-length 3D structures of hHsp90β and PfHsp90 were modeled with SWISS-MODEL (SWISS-MODEL: homology modelling of protein structures and complexes. Available online: https://swissmodel.expasy.org/ [accessed on 12 June 2022]) using PDB files 5FWK and 5FWM, respectively, as templates. NTD: N-terminal domain; L: linker region; MD: middle domain; and CTD: C-terminal domain. Element coloring scheme uses red, blue, grey, and yellow for oxygen, nitrogen, carbon, and phosphorous, respectively. Images for 3D structures were rendered using UCSF Chimera 1.10.1 (UCSF Chimera—a visualization system for exploratory research and analysis. Available online: https://www.cgl.ucsf.edu/chimera/ [accessed on 12 June 2022]), while the linear domain layout image was rendered using IBS 1.0 (IBS: an illustrator for the presentation and visualization of biological sequences. Available online: http://ibs.biocuckoo.org/ [accessed on 12 June 2022]). **Figure 2.** Domain organization and structural view of hHsp90β and PfHsp90. (**A**). Domain organization of hHsp90β (**top**) and PfHsp90 (**bottom**). Structure of full-length dimeric (**B**). hHsp90β and (**C**). PfHsp90 proteins as cartoons. ATP bound to the N-terminal domain (NTD) is shown as red spheres. The two Hsp90 monomers in the models are colored purple and blue. (**D**). hHsp90β and (**E**). PfHsp90 NTD as surface. The surface (with 60% transparency) is colored according to element type and it also depicts the arrangement of secondary structure elements (red color) as cartoons. The bound ATP molecule is represented as sticks, colored according to the element type. Full-length 3D structures of hHsp90β and PfHsp90 were modeled with SWISS-MODEL (SWISS-MODEL: homology modelling of protein structures and complexes. Available online: https://swissmodel.expasy.org/ [accessed on 12 June 2022]) using PDB files 5FWK and 5FWM, respectively, as templates. NTD: N-terminal domain; L: linker region; MD: middle domain; and CTD: C-terminal domain. Element coloring scheme uses red, blue, grey, and yellow for oxygen, nitrogen, carbon, and phosphorous, respectively. Images for 3D structures were rendered using UCSF Chimera 1.10.1 (UCSF Chimera—a visualization system for exploratory research and analysis. Available online: https://www.cgl.ucsf.edu/chimera/ [accessed on 12 June 2022]), while the linear domain layout image was rendered using IBS 1.0 (IBS: an illustrator for the presentation and visualization of biological sequences. Available online: http://ibs.biocuckoo.org/ [accessed on 12 June 2022]).

While co-chaperones of hHsp90 are extensively studied [53], and informed anti-cancer drug discovery [34], there are relatively few studies on PfHsp90 co-chaperones. Increasing our understanding of how PfHsp90 and its co-chaperones interact would greatly assist the development of novel anti-malarial therapies. Table 1 provides a comparison of the known co-chaperones of PfHsp90 to those of hHsp90, and in the following sections these proteins are explored in further detail.

**Table 1.** Co-chaperones of Hsp90 in *Homo sapiens* and *Plasmodium falciparum*.

#### **4. PfHop (Hsp70–Hsp90 Organizing Protein; PF3D7\_1434300)**

As in other eukaryotes, the PfHsp70 and PfHsp90 protein folding pathways intersect to facilitate the folding of key proteins involved in diverse cellular pathways [22,46]. The interaction between Hsp70 and Hsp90 is regulated by Hop, which has been extensively characterized in the human system [68]. Both Hsp70 and Hsp90 possess C-terminally located EEVD motifs that interact with Hop via its multiple TPR domains [33]. Hop is not required for chaperone-mediated protein folding by Hsp70 and Hsp90 [69], but rather plays an important regulatory role for progression of client proteins through the chaperone cycle [70] (Figure 1). Of the six Hsp70-like proteins encoded by the *P. falciparum* genome, only the cytosol-nuclear localized chaperone PfHsp70-1 possesses the EEVD motif [71], which is crucial for interaction between Hsp70 and Hop. A Hop homologue (PF14\_0324) was identified in the *P. falciparum* genome by Acharya and co-workers [44] (Table 1). Overall structural conservation was reported in PfHop, with some variations in the TPR regions [54]. Less conserved segments of Hop outside its TPR domains are shown to influence the overall

conformation of the helical turns of the TPR domains, therefore, imparting unique structural features to Hop molecules from different species [72]. Immunofluorescence studies show PfHop to be localized with PfHsp70 and PfHsp90 in the parasite, and PfHsp70-1 complexes contained both PfHsp90 and PfHop by co-immunoprecipitation analysis [54]. PfHop co-localizes with the cytosolic chaperones PfHsp70-1 and PfHsp90 at the blood stages of the malaria parasite, and PfHop is stress-inducible [73,74]. Employing far western, surface plasmon resonance (SPR) and co-immunoprecipitation studies, a direct interaction between PfHop and PfHsp70-1 was identified, which was favored in the presence of ADP rather than ATP [73]. Recent studies on PfHop employing synchrotron radiation circular dichroism (SRCD) and small-angle X-ray scattering reveal that PfHop is a monomeric and elongated protein [55]. PfHop is also found to be unstable at temperatures higher than 40 ◦C in comparison to its functional partner, PfHsp70-1, which is known to be stable at temperatures as high as 80 ◦C [55,75].

#### **5. PfTah1 (TPR-Containing Protein Associated with Hsp90; PF3D7\_0213500) and PfPih1 (Protein Interacting with Hsp90; PF3D7\_1235000)**

The R2TP complex is an important multiprotein complex involved in multiple cellular process such as snoRNP biogenesis, PIKK signaling, RNA polymerase II assembly, and apoptosis [56]. Within the R2TP complex, the specialized Pih1 co-chaperone tightly interacts with Rvb1/Rvb2 and with another specialized co-chaperone Tah1 to form the R2TP macromolecular complex. The R2TP complex further interacts with Hsp90 to form the R2TP–Hsp90 complex [56]. A genome-wide screening of *P. falciparum* led to the identification of PfPih1 and PfTah1, which associate with PfHsp90 to form the *Plasmodium* R2TP–Hsp90 complex [47,56] (Table 1). The R2TP complex plays a vital role in both cancer cell proliferation in humans and rapid multiplication of *P. falciparum* [56].

#### **6. Immunophilins: PfCyp40 (Cyclophilin 40/PF3D7\_1111800) and PfFKBP35 (FK506-Binding Protein 35/PF3D7\_1247400)**

Immunophilins are known for their characteristic peptidyl-prolyl cis–trans isomerase (PPI) activity [76]. Cyclophilin 40 (Cyp40) and FK506-binding proteins (FKBPs) were discovered in 1989 as the major receptors of the immunosuppressive drugs Cyclosporine-A and FK506 (tacrolimus), respectively [77,78]. PPIs play an accessory role with the Hsp90 protein folding machinery, and are part of diverse intracellular signaling pathways, ranging from steroid receptors to regulatory tyrosine kinases, critical in cell cycle control [79,80]. In humans, Cyp40, along with FK506-binding proteins FKBP51 and FKBP52, are also components of steroid receptor complexes [81–83]. All three immunophilins (Cyp40, FKBP51, and FKBP52) have conserved N-termini for immunophilin function and a C-terminal domain containing TPR motifs involved in protein–protein interaction [83,84]. They all target Hsp90 through their conserved C-terminal region to form separate steroid receptor complexes containing Hsp90 (Figure 1). Smith and co-workers (1990) [85] explained the dynamic model of steroid receptor assembly, in which the high affinity hormone-binding form of the receptor was regulated through interactions between Hsc70 and Hsp90. The immunophilins are known to regulate the activity of steroid hormone receptors, and their interaction depends on the type of steroid hormone receptor to be activated. FKBP51 preferentially interacts with progesterone and glucocorticoid receptor complexes, while Cyp40 tends to accumulate with estrogen receptor complexes [86]. Mining of the *P. falciparum* 3D7 genome reveals eight putative cyclophilin chaperones with four α-like and four β-like subunits [87]. No *Plasmodium* export element (PEXEL) motifs were found in any of the putative cyclophilins co-chaperones. It was observed that only two have PPIase activity, but all of them prevent aggregation of a model substrate, and are implicated in heat shock resistance in *P. falciparum* [88]. *P. falciparum* Cyp40 (PfCyp40; Table 1) has a predicted C-terminal trans-membrane domain and no export signal [81]. Most of the PfCyps are identified as having no signal peptide and, therefore, would most likely be found in the parasite cytoplasm [89]. Similar to the mammalian counterpart, two PPIase monomers of PfCyp40 are predicted to interact with dimeric PfHsp90 [90].

One of the most highly expressed co-chaperones of hHsp90 across a range of tissues is FKBP38, a membrane-anchored protein distributed predominantly in mitochondria [91,92]. *P. falciparum* FKBP35 (PfFKBP35; Table 1), a putative FKBP38 homologue, is shown to be functional in that it exhibits PPIase activity that is sensitive to inhibition by FK506 and Rap [93]. Pull-down assays reveal that PfFKBP35 interacts with PfHsp90 through its TPR domain, suggesting that PfFKBP35 is a co-chaperone of PfHsp90 [94]. There is limited information on the exact mechanism of inhibitors such as FK506 in the interaction between PfFKBP35 and PfHsp90. PfFKBP35 itself might be responsible for the antimalarial effects of FK506 and Rap. Pharmaco-dynamics analysis suggests that both FK506 and Rap have similar effects on different intra-erythrocytic stages in culture and kinetics of killing or irreversible growth arrest of parasites [95]. Furthermore, X-ray and NMR crystallography experiments show slight differences between PfFKBP35 and another human PPI, FKBP12, which could be critical in the designing of inhibitors that selectively inhibit PfFKBP35 [96]. The structural differences were detected in the β5–β6 segment of the PPIase domain, where PfFKBP35 contains a conserved cysteine and serine residue at amino acid positions 106 and 109, respectively, instead of a histidine (H87) and isoleucine (I90) residue at the corresponding position in human FKBP12, which presents as an architectural FKBP domain. Another study on the design of small molecules, targeting these conserved C106/C105 and S109/S108 residues in PfFKBP35/*Plasmodium vivax* FKBP35 (PvFKBP35) to achieve selectivity, identified a novel ligand D44 (N-(2-Ethylphenyl)-2-(3H-imidazao [4, 5-b] pyridin-2-ylsulfanyl)-acetamide) with potent inhibitory activity against PfFKBP35 [97]. D44 displays approximately 100-fold higher selectivity towards the inhibition of *Plasmodium* FKBPs over human FKBPs (FKBP12 and FKBP52). Structural analysis reveals that the high selectivity towards *Plasmodium* FKBPs is attributed to improved proximity between D44 and the conserved C106/C105 and S109/S108 amino acid residues in PfFKBP35/PvFKBP35. In addition, another study proposed the incorporation of a bulky hydrophobic group at C-11 of FK506, to induce steric clashes with the residues H87 and I90 in FKBP12, as a potential strategy for engineering inhibitors that are selective towards PfFKBP35, while avoiding off-target effects on human FKBP12 [98].

#### **7. Pfp23A (PF3D7\_1453700) and Pfp23B (PF3D7\_0927000)**

The late stage co-chaperone p23 binds to the N-terminal domain of Hsp90, and is important for promoting the closed client-bound conformation of Hsp90 and inhibiting ATPase activity [70] (Figure 1). Pfp23, a 34-kDa phosphoprotein, is highly expressed and phosphorylated in the trophozoite stage of *P. falciparum* intra-erythrocytic development [99]. GST pull-down assays reveal the role of Pfp23 as a co-chaperone of PfHsp90, and this chaperone-co-chaperone interaction is dependent on the presence of ATP [61]. This is similar to the association between Sba1 (p23 yeast homologue) and yeast Hsp90 [100]. More recently, two small acidic co-chaperones, p23 orthologues, were identified in the *P. falciparum* genome [62] (Table 1). It was revealed that Pfp23A and Pfp23B show 13% identity between themselves, and 20% identity with human p23. It was found that Pfp23A has higher thermal stability in comparison to Pfp23B, suggesting structural and functional variability [62]. Both Pfp23A and Pfp23B could inhibit PfHsp90 ATPase activity, although Pfp23A was more effective [62], and although both could prevent aggregation of model substrate proteins (malate dehydrogenase, citrate synthase, and luciferase), the isoforms showed preferences for model client proteins [62]. Site-directed mutagenesis experiments by Chua et al. [61] identified the conserved residues K91, H93, W94, and K96 in Pfp23 as critical for interaction with PfHsp90. Pfp23 was also found to suppress protein aggregation dependent on to its C-terminal tail, showing that it has chaperone activity independent of PfHsp90 [61]. In a separate study to screen cancer inhibitors, the anticancer compound gedunin was identified as a specific inhibitor of p23 [101]. Gedunin binds p23 and abrogates interaction with Hsp90, resulting in cancer cell death. Although gedunin was previously shown to inhibit the chaperone function of Hsp90, the precise inhibitory mechanism is unclear, as gedunin does not bind to the N-terminus or the C-terminus of Hsp90 as most Hsp90specific inhibitors do (e.g., ansamycin antibiotics, radicicol, and novobiocin) [102,103]. In addition, gedunin shows antimalarial activity, which may or may not be related to its ability to modulate the interaction of Pfp23 and Hsp90 [104]. The presence of two Pfp23 isoforms with putative functional differences is interesting, and suggests that the mechanism of stabilization of PfHsp90 late stage complexes differs from that of the human Hsp90 complex.

#### **8. PfAha1 (Activator of Hsp90 ATPase/PF3D7\_0306200)**

The Aha1 co-chaperone binds to the MD and stimulates Hsp90 ATPase activity, promoting client protein activation (Figure 1) [105]. PfAha1 was found using split ubiquitin assays [63] (Table 1). Employing GST pull-down assays, PfAha1 binds PfHsp90 in a manner dependent on MgCl2 and ATP [63]. PfAha1 competes with Pfp23 to interact with PfHsp90 under similar conditions [57]. In contrast to the Pfp23–PfHsp90 interaction, where Pfp23 has an inhibitory effect on the ATPase activity of PfHsp90, PfAha1 stimulates the ATPase activity of PfHsp90 [63], consistent with the function of the human homolog [105]. It was observed by computational modelling that residue N108 in PfAha1 is critical for interaction with PfHsp90, and the mutation of N108 to alanine leads to reduced stimulation of the AT-Pase activity of PfHsp90 [63]. The PfAha1–PfHsp90 interaction is likely polar in nature, as it is disrupted by high salt concentration. PfAha1 most likely plays a role in the maturation of PfHsp90 client proteins [57]. Furthermore, the presence of PfAha1 suggests that, despite the higher basal ATPase activity of PfHsp90 compared to hHsp90, client release from late stage chaperone complexes is still regulated by ATPase stimulation.

#### **9. PfPP5 (Protein Phosphatase 5/PF3D7\_1355500)**

PP5 is a TPR-containing co-chaperone that regulates the Hsp90 chaperone cycle through the dephosphorylation of Hsp90 or co-chaperones, such as Cdc37 [106]. Degenerate deoxyoligonucleotide primers were used to identify the protein phosphatase protein in *P. falciparum* for the first time [107] (Table 1). Sequence analysis reveals that PfPP5 has a N-terminal TPR domain followed by a Ser/Thr phosphatase sequence at the C-terminal domain. The PfPP5 Ser/Thr domain is essential for phosphatase activity, and the TPR domain of the protein can act as a negative regulator of phosphatase activity. The N-terminal PfPP5 TPR domain is a potential anti-malaria target for the design of selective inhibitors [107]. This is because PfPP5 possesses an unusually long TPR domain with four TPR motifs, as opposed to the three usually observed in homologs of other species, including human. Using a PfPP5 antibody, both PfPP5 and PfHsp90 were co-immunoprecipitated, which implies that PfPP5 may be part of the Hsp90 chaperone complexes, as observed in mammals [64,65]. PP5 and Aha1 are important in many cellular processes in neurodegenerative diseases in association with Hsp90; therefore, it is important to study this co-chaperone in *P. falciparum* to understand its precise mechanism [108].

In yeast, Ppt1 (PP5 homologue) is demonstrated to specifically dephosphorylate Hsp82 [109]. The deletion of Ppt1 in yeast leads to the hyperphosphorylation of Hsp90 and the reduced efficiency of the Hsp90 chaperone system in activating client proteins (e.g., glucocorticoid receptors, v-Src, and Ste11). In addition, PP5/Ppt1 was also found to dephosphorylate another co-chaperone Cdc37 at the phosphorylated S13 residue, and modulate its activity in recruiting protein kinase clients to Hsp90 [106]. Hence, PP5/Ppt1 was proposed as a positive modulator for the activation of Hsp90 client proteins. In the case of *P. falciparum*, although PfPP5 interacts with PfHsp90 [107], it remains unclear whether PfPP5 exerts its phosphatase activity on PfHsp90. However, the presence of the PfPP5 phosphatase implies that the PfHsp90 complex undergoes phosphorylation by *P. falciparum* kinases.

#### **10. PfCBP (Calcyclin-Binding Protein/PF3D7\_0933200) and PfCns1 (Cyclophilin Seven Suppressor 1/PF3D7\_1108900)**

The calcyclin-binding protein (CBP), suppressor of G2 allele of Skp1 (Sgt1), cyclophilin seven suppressor 1 (Cns1), and tetratricopeptide repeat domain 4 (TTC4) all share significant sequence similarity, contain TPR domains, and are co-chaperones of Hsp90 [110–112]. While related, these co-chaperones each bind differently to Hsp90, and target selective sets of client proteins [57,60,66]. For example, Sgt1 associates with the N-terminus of Hsp90, and specifically recruits leucine-rich-repeat proteins [112]. Bioinformatics analyses applying protein domain homology, identified several putative PfHsp90 co-chaperones related to Sgt1/CBP and TTC4/Cns1, namely, PfCBP and PfCns1, respectively [94] (Table 1). However, further investigation is needed to confirm if these co-chaperones directly interact with PfHsp90 and modulate its chaperone function.

#### **11. Cdc37 (Cell Division Cycle 37) Homolog Potentially Missing in** *P. falciparum*

Cdc37 is involved in the recruitment of nascent or unstable kinases to Hsp90 for folding into their active conformation [113,114], and is known to be important for the activation of a diverse group of protein kinases (e.g., Cdk1, Cdk4, Akt, v-Src, Raf, and CK2) [115,116]. Indeed, as many as 65% of the kinases in yeast are reported to require Cdc37 for activation and stabilization [117]. In human cells, 60% of kinases interact with Hsp90, and the recognition of these kinases is mediated by Cdc37 [118]. As many of the kinases have essential signal transduction roles that regulate growth and development, Cdc37 is, thus, recognized as an important component of the Hsp90 chaperone machinery. In addition, Hsp90 chaperone activity itself is integrated with cellular proliferation by phosphorylation. It is, therefore, noteworthy that a Cdc37 homolog has not been found in *P. falciparum* (Table 1). This could mean that other *P. falciparum* co-chaperones are able to functionally compensate for the lack of Cdc37, especially since critical kinases known to associate with Cdc37, such as Cdk1 (PfPK5; MAL13P1·279), Akt (PfPKB; PFL2250c), and CK2 (PfCK2; PF11\_0096), are found in *P. falciparum* [94]. The Cdc37 ortholog may be divergent from that of humans and, hence, has not been identified based on sequence identity. Alternatively, *P. falciparum* kinases may have differing chaperone requirements, meaning they can enter the cycle in the absence of Cdc37, or are less reliant on Hsp90 for function.

#### **12. Conclusions**

This review suggests that the Hsp90 chaperone, and its associated co-chaperone complexes in *P. falciparum,* are broadly conserved in comparison to other organisms. PfHsp90 displays biochemical differences to hHsp90, which may be targeted for selective inhibition. Importantly, Hsp90 does not function alone, and appropriate proteostasis requires that the chaperone be fine-tuned by co-chaperones. The core co-chaperones regulating client entry, ATPase activity, and Hsp90 conformational regulation at the early, intermediate, and late stages of the chaperone cycle are broadly conserved in *P. falciparum*. However, there are two notable differences that may indicate important areas for future study and evaluation of therapeutic potential.

The first is the presence of two p23 orthologs in *P. falciparum*. While both of these isoforms function similar to p23 in the Hsp90 complex, there are differences in client protein specificity and ATPase inhibition. The requirement of both isoforms for parasite viability, and their individual importance in the PfHsp90 chaperone cycle, have not yet been determined. Since one of the functions of p23 is to inhibit Hsp90 ATPase activity, it may be speculated that the two isoforms arose because of the higher basal ATPase activity of PfHsp90. Given that Pfp23A inhibits the PfHsp90 ATPase activity more than Pfp23B, and that the folding and activation of different clients may require different cycle timing, the two p23 isoforms may have evolved to assist different client protein groups (i.e., the higher ATPase activity of PfHsp90 may allow for more inhibitory steps in the chaperone cycle). A detailed analysis of the co-chaperone functions of these p23 isoforms in vitro and

in the parasite would be useful in determining if mechanistic differences do exist, and if they have therapeutic potential.

The second notable difference is the apparent absence of a Cdc37 ortholog in *P. falciparum*. However, since Cdc37 orthologs were identified in other obligate intracellular protozoan parasites (e.g., *Theileria annulata* and *Cryptosporidium parvum*) [119], deeper scrutiny of the *P. falciparum* genome is required. Cdc37 is regarded as one of the most important therapeutic Hsp90 co-chaperones, because of its role in regulating kinase entry into Hsp90 complexes. Kinases are considered important therapeutic targets in both cancer (focusing on human kinases) and malaria, and kinase inhibitors form one of the largest classes of approved drugs. The *P. falciparum* kinome was recently updated, confirming that its kinome is considerably smaller (98 members compared to 497 members in the human kinome) and divergent (38% unique; 46% potentially unique; and 16% human homologs) from that of humans [120]. Therefore, the apparent lack of a Cdc37 ortholog, or the presence of a yet to be identified divergent Cdc37 ortholog or functional equivalent, is likely to reflect differences in the folding requirements of the *P. falciparum* kinome by the Cdc37–PfHsp90 co-chaperone–chaperone machinery. Furthermore, the co-evolution of PfHsp90 and the kinome could have resulted in reduced dependency on a canonical Cdc37 for kinase activation. Indeed, there is evidence that Hsp90 may be able to activate kinases in the absence of Cdc37 [121,122]. Importantly, no study has demonstrated that *P. falciparum* kinases require PfHsp90 in a mechanism analogous to their yeast and human orthologs. Given the importance of kinases to drug discovery, and the fact that many *P. falciparum* kinases are being evaluated as drug targets, it would be interesting to identify a bona fide PfHsp90 kinase client. This could easily be done using available Hsp90 inhibitors in malaria parasite cell lines expressing GFP-tagged kinases. Validation of at least one PfHsp90 kinase client would subsequently support efforts to determine whether or not Cdc37 exists in the malaria parasite. This would be interesting not only from a fundamental perspective, but also in terms of identifying a selective therapeutic target for simultaneous inhibition of multiple kinases.

Taken together, both the conservation and differences in the co-chaperone complexes of PfHsp90 suggest that, as in non-communicable diseases [34], targeting Hsp90–co-chaperone interactions is an exciting new area of research that can both extend our understanding of proteostasis, and identify novel approaches for inhibition.

**Author Contributions:** Conceptualization, T.D. and G.L.B.; Figure 1, A.L.E.; bioinformatics analyses and Figure 2, H.S.; writing—original draft preparation, T.D.; writing—review and editing, T.D., A.L.E., H.S. and G.L.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** G.L.B. acknowledges the financial support of Higher Colleges of Technology, UAE (Interdisciplinary Research Grant, IRG), and Rhodes University, South Africa (Rated Researcher Grant). Research activities in the laboratory of A.L.E are supported by a Newton Advanced Fellowship from the Academy of Medical Sciences (UK), and grants from the Resilient Futures Challenge-Led Initiative from the Royal Society (UK) (Grant No CHL\R1\180142), the South African Research Chairs Initiative of the Department of Science and Technology (DST), and the NRF (Grant No 98566), Rhodes University and the Grand Challenges Africa Drug Discovery Programme (which is a partnership between The African Academy of Sciences [AAS], the Bill and Melinda Gates Foundation, Medicines for Malaria Venture [MMV], and the University of Cape Town Drug Discovery and Development Centre [H3D]) (Grant No GCA/DD/rnd3/043).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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