Allostery and Folding of the N-terminal Receiver Domain of Protein NtrC

Article pubs.acs.org/JPCB

Allostery and Folding of the N‑terminal Receiver Domain of Protein NtrC Swarnendu Tripathi† and John J. Portman*,‡ †

Department of Physics, University of Houston, Houston, Texas 77204, United States Department of Physics, Kent State University, Kent, Ohio 44242, United States

‡

S Supporting Information *

ABSTRACT: The N-terminal receiver domain of protein NtrC (NtrCr) exhibits allosteric transitions between the inactive (unphosphorylated) and active (phosphorylated) state on the microsecond time scale. Using a coarse-grained variational model with coupled energy basins, we illustrate that significant loss of conformational flexibility is the key determinant of the inactive (I) → active (A) state transition mechanism of NtrCr. In particular, our results reveal that the rearrangements of the native contacts involving the regulatory helix-α4 and the flexible β3-α3 loop upon activation play a crucial role in the activation mechanism. Interestingly, we find that the β3-α3 loop exhibits a gradual decrease in flexibility throughout the activation transition, while helixα4, in contrast, becomes more rigid abruptly near the free energy barrier separating the two states. To gain further insight into role these flexible regions play in the transition mechanism, we consider folding of NtrCr to both states using a similar model. Our calculated folding routes suggest that helix-α4 becomes structured later when folding to the I state compared to folding of the A state, a result consistent with it is relative conformational flexibility in the two states. Finally, we find a good qualitative agreement between our predicted I → A transition mechanism and the measured backbone dynamics from nuclear magnetic resonance experiments.

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INTRODUCTION Protein dynamics are essential to their ability to perform adaptive and highly specific functions.1 Allosteric transitions, for example, provide a general mechanism for an effector ligand to modulate the conformation and dynamics of a distant regulated site for signal transduction and regulation. Indeed, the crystal structure of proteins with bound ligands (the closed form) is often distinct from the ligand free structure (the open form). The classic Monod−Wyman−Changeux (MWC) model of allostery,2 developed to explain cooperativity in hemoglobin, emphasizes that the conformational change is a concerted motion between two pre-existing distinct states, and upon ligand binding, the dominant population shifts from the open form to the closed one. This “population-shift” mechanism3−5 is distinguished from the “induced-fit” scenario developed in the Koshland−Némethy−Filmer (KNF) model6 in which the ligand binds first to the open state before making a transition to the closed state. Recent theoretical studies suggest that whether induced-fit or population-shift dominates the binding of a particular ligand depends its interaction strength and range7 or the relative rate of the conformational change.8 The particular binding kinetics notwithstanding, a folded protein’s inherent flexibility enables dynamic exploration of distinct conformational substates in the protein’s energy landscape essential to protein function.9,10 The part of the energy landscape relevant to conformational transitions and ligand binding are low energy states of primarily folded conformations (see Figure 1). This “functional energy land© 2013 American Chemical Society

scape” is complex and is likely sensitive to frustration associated with the detailed interactions and the particular sequence identity of the protein.11−13 Frustration may give rise to a diversity of transition mechanisms including “cracking”14 (local unfolding and refolding).15 The conformational dynamics on the functional landscape may be sensitive to minor changes of the topology of the conformational states16 as well as sequence mutations. Protein folding, on the other hand is controlled by a kinetic bottleneck higher up in the folding funnel. The folding mechanism is protected by principle of minimal f rustration and the self-averaging properties of the many paths leading to the folded state.17−19 This accounts for the success of topologybased folding models predicting the folding mechanism of small two state folding proteins: folding is determined by topology.20−27 Nonetheless, “topological frustration”28 may cause “backtracking”29 or local unfolding due to incorrect ordering of two subsets of native contacts competing with each other along the folding routes.30−33 For allosteric proteins, with at least two important metastable folded conformations, it is reasonable to anticipate folding in a multifunnel can be relatively unfrustrated if the conformational states are similar enough.15 Special Issue: Peter G. Wolynes Festschrift Received: March 31, 2013 Revised: August 20, 2013 Published: August 20, 2013 13182

dx.doi.org/10.1021/jp403181p | J. Phys. Chem. B 2013, 117, 13182−13193

The Journal of Physical Chemistry B

Article

Figure 1. Folding funnel for an allosteric protein. This figure is simplified by depicting a single order parameter for folding, a reasonable assumption higher up the folding funnel as long as the allosteric conformations are similar enough. Allosteric transtions between the inactive and active states (indicated by the small box) occur lower down the funnel where dynamics are more sensitive to frustration. The value of the folding order parameter at which the energy basins to the allosteric states meet and couple depends on the topology of the allosteric states.

Figure 2. The inactive (I) and active (A) conformations of NtrCr. (a) The I [protein data bank (PDB) ID code 1ntr] and the A (BeF3−activated, PDB ID code 1krw) conformations of NtrCr are shown by representing the secondary structure with different colors. (b) Cartoon of the secondary structure of NtrCr, where the α-helices and β-sheets are represented by rectangles and arrows respectively, along with the residue number. (c) Deviations between the two native state structures of NtrCr (the I and the A states) measured directly from the corresponding PDBs, where |ΔrNi |=|rNi I − rNi A|. Here, {rNi I} and {rNi A} denote the Cα coordinates of the I and A conformations of NtrC, respectively. a = 3.8 Å is defined as the distance between adjacent monomers in the variational model. Molecular images produced with the program VMD.36

The large-scale structural change of the N-terminal receiver domain of nitrogen regulatory protein C (NtrCr) upon activation is a good model system that illustrates how allostery plays a key role in protein function. NtrC is a member of the response regulator protein family that contains a CheY-like receiver domain NtrCr. These small β/α-repeat structure proteins typically contain approximately 125 residues with a β5/α5 fold. The structure of NtrCr is shown in Figure 2a. Phosphorylation (activation) of Asp54 (at the C-terminal end of β3) induces large structural rearrangements in the potential switch region α3-β4-α4-β5 (the “3445” face) and the β3-α3 loop of the NtrCr that transmits the signal to the C-terminal DNA-binding domain.34,35 This is also evident from the calculated structural difference of the native state inactive (I)NtrCr and active (A)-NtrCr conformations in Figure 2c, which shows significant deviations in the β3-α3 loop and in most of the part of 3445 face upon activation. NMR relaxation37 as well as all-atom molecular dynamics (MD) simulations38 have recognized the population-shift mechanism due to phosphorylation (activation) takes advantage of the high flexibility in helix-α4 in the I-NtrCr. NMR relaxation experiments have revealed a strong correlation between phosphorylation driven activation of NtrCr and its microsecond time-scale backbone dynamics,37 which is evident from dynamical exchange between the I-state and A-state conformations. The NMR study also suggests that both conformations of NtrCr are populated at room temperature, with the population of the A-state being considerably smaller than that of the I-state in the unphosphorylated form, while after phosphorylation, the A form dominates.37 Therefore, to understand the molecular basis of the activation mechanism of NtrCr, it is important to explore how the conformational transition occurs. The inactive-state to active-state (I → A) conformational transition of protein NtrCr has been studied recently through both all-atom and coarse-grained protein models. 39−44 Two outcomes from these studies need clarification. One is the disagreement in the description of the key mechanism of phosphorylation induced conformational

change of NtrCr, and the other is possibility of cracking of the regulatory helix-α4. In this paper, we explore the mechanism of I → A conformational change of NtrCr, as well the folding to both the I-NtrCr and A-NtrCr structures to address these issues. Our study aims to elucidate the role of conformational flexibility of NtrCr along the I→A transition route. Although energetic frustration can potentially influence the transition mechanism of allosteric proteins, in this paper we follow other studies45−55 and focus on the topological frustration arising from the coupling of two distinct energy basins. We use a topology based, coarse grained analytical approach inspired from a variational model of protein folding56−58 to investigate the allosteric transition mechanism of NtrCr. Following ref 47, two single energy basins, defined by the native contacts of each metastable state, are coupled together through an interpolation formula based on the total energy of a conformation. Our result suggest that allostery in NtrCr is driven primarily by its loss in flexibility upon activation. In particular, the predicted transition mechanism between the inactive and active states of NtrCr involves the loss of local flexibility of the β3−α3 loop and the helix-α4 upon activation. Significant rearrangements in the contacts mainly account for this loss. That is, gains in free energy due to entropic loss in these region are partially offset by stabilizing nonlocal interactions that form as the protein reorganizes its secondary structure elements from the inactive to active conformations. The part of the free energy landscape controlling conformational transitions between folded states is 13183



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with respect to H0. The free energy can be written as F[{C}] = E[{C}] − TS[{C}], where

distinct from the kinetic bottleneck that controls folding to the native basin surrounding the metastable states. Still, we find that the topologies of the metastable conformations, which influences their distinct conformational properties such as local flexibility near the native ensemble, have distinct signatures in the folding mechanism determined higher up in the funnel.

E[{C}] =

■

S[{C}] =

ij

ij ∈ [ij]

3 3 log det G − 2 2 2a

∑ si ·Γ(ch) ij · sj + ij

3 2

∑ CiGii (4)

where G is the matrix of polymeric correlations Gij = ⟨(ri − si)· (rj − sj)⟩0, and si = ⟨ri⟩0 is the average position of the ith monomer. The values of the parameters {Ci} along a folding route are determined by the critical points in the variational free energy surface, F[{C}]. We search for local minima and saddlepoints by numerically solving ∂CiF[{C}] = 0. Transition state ensembles are identified as the saddle points of F[{C}] that connect two local minima by a steepest descent path in the variational parameters. A folding route is a series of minimumsaddlepoint-minimum which connect the globule and native minima of F[{C}]. Characterizing Partially Folded Ensembles. The magnitude of the conformational fluctuations of each residue defines a set of natural local order parameters that describe the structure of partially folded ensembles. The mean square fluctuations of each residue (related to the temperature factors of X-ray crystallography) are calculated as Bi [{C}] = ⟨δ r i2⟩0

(5)

with δri = r − ⟨ri⟩0. The magnitude of individual temperature factors reflects the degree of conformational freedom of each residue in an ensemble: relatively unstructured residues are delocalized (and have large Bi) while structured residues are more localized (and have small Bi). The structural ordering of each residue of protein along a folding route can be characterized by the evolution of the temperature factors as they decrease inhomogeneously from large values corresponding to the unfolded globule state. The structural similarity of each residue to the native conformation can also be characterized by the native density,

(1)

I(A)

(3)

is the energy due to native contacts, and S[{C}] is the polymeric entropy loss due to the localization of each residue around mean positions {⟨ri⟩0}:

where T is the temperature and kB is Boltzmann’s constant. The first term in eq 1, which represents the protein backbone as a weakly collapsed, uniformly stiff homopolymer,63 harmonically enforces chain connectivity with mean bond length a = 3.8 Å and mean valence angle cos θ = 0.8.57 The second term is an external field in which the N variational parameters, {Ci}, control the magnitude of the fluctuations about the native Cα positions {rNi I(A)} of the residues in the I (A) state of NtrCr. The reference Hamiltonian is used to probe the free energy surface of partially folded ensemble structures corresponding to the Hamiltonian

∑ ri·Γ(ch) ∑ ij · rj +

εij⟨uij⟩0 57

METHODS Structural Models of NtrCr. NMR structures of the active (A) and inactive (I) forms of NtrCr are used to model the transition. Following ref 40, we use the PDB ID code 1ntr59 to model the inactive state (I-NtrCr), and the berrylofluoride activated protein (BeF3−-NtrCr, PDB ID code 1krw60) to model the active state (A-NtrCr). We note that the phosphorylated form of the protein (P-NtrCr), PDB ID code 1dc8, is an alternative choice for the active state. These two activated protein structures are similar, with a backbone rootmean-square deviation (RMSD) of 0.57 Å between PDB ID codes 1dc8 and 1krw.60 Before calculations, the structures of the A/I NtrCr pair are aligned over the residues 4−9, 14−53, and 108−121 as suggested in ref 37, using the program SuperPose.61 Variational Model of Folding. The model of protein folding described briefly here is presented in more detail in ref 57. While a quasi-harmonic description of atomic fluctuations have well-known limitations,62 in this analytic coarse-grained model, we assume that partially folded ensembles of structures can be characterized by their Gaussian fluctuations. In this model, a protein conformation is represented by the N position vectors of the Cα polypeptide backbone, {ri}. Partially ordered ensembles of protein configurations are described by a reference Hamiltonian, 3 3 N H0/kBT = 2 ∑ ri·Γ(ch) C [r − r i I(A)]2 ij · rj + 2 ∑ i i 2a ij 2a i

3 H= 2 2a

∑ ij ∈ [ij]I(A)

ρi [{C}]I(A) =

⎤ ⎡ 3 N exp⎢ − 2 α N(ri − r i I(A))2 ⎥ ⎦ ⎣ 2a

0

(6)

where α = 0.5 defines the width of a Gaussian window centered on the native conformation {rNi I(A)} of the I (A) state of NtrCr. It is convenient to normalize the native density N

εiju(ri − rj) (2)

Here, u(ri − rj) is the pair potential with an attractive minimum at an approximately 6 Å, and εij is the strength of a fully formed contact between residues i and j given by Miyazawa−Jernigan interaction parameters.64 The sum in eq 2 is restricted to a set of contacts [ij]I(A) determined by pairs of residues in the proximity of the native structure of the I (A) state. (See ref 57 for details and parameters of the pair interactions.) The probability for an ensemble of a configurations specified by the set of variational parameters {C} at temperature T is given by the variational free energy F[{C}] = −kBT log Z0 + ⟨H − H0⟩0, where Z0 is the partition function associated with the reference Hamiltonian, and ⟨...⟩0 represents an average taken

ρi I(A) =

ρi I(A) − ρiGI(A) ρi NI(A) − ρiGI(A)

(7)

where the superscripts GI(A) and NI(A) represent the native density evaluated at the variational parameters describing the globule and native states of the I(A)-NtrCr, respectively. The native density serves as local order parameters describing the native similarity of each residue of an ensemble specified by the variational constraints, {C}. Progress along the folding route can be represented by the global order parameter QI(A) = I(A) (∑iρ̅I(A) = 0 and QI(A) = 1 represent the i )/N, where Q 13184



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finding saddle points with respect to 2N variational parameters {Ci,αi}, simplifies to minimizing the free energy, F[{C},α0] with respect to N variational parameters, {Ci} for a given α0. The temperature T for the inactive → active transition is taken as T = 0.7 Tf, where Tf is the folding temperature of the INtrCr given by, kBTf/εMJ ∼ 2.15 and εMJ is the basic energy unit of the Miyazawa−Jernigan scaled contacts.64 Besides the energy offset and coupling parameter of the energy interpolation formula, the other parameters of this model in this study are same as given in ref 65. Appropriate values for E0 and Δ are determined by the behavior of the single basin energies E I [{C},α 0] and EA[{C},α0]. The single basin free energy is found by minimizing the corresponding variational free energy F[{C},α0] with respect to the variational parameters {Ci} for each set of interpolated reference structures parametrized by α0. The dashed and the dotted curves in Figure 3a show the single

unfolded (globule) state and the folded (native) state, respectively. Variational Model of Conformational Transitions. To model conformational transitions between two known metastable conformations, we use a coarse-grained reference Hamiltonian similar to eq 1 H0/kBT = Hchain /kBT +

3 2a 2

∑ Ci[ri − r iN(αi)]2 i

(8)

where the harmonic constraints {Ci} control the magnitude of fluctuations of each residue about the interpolated native state conformation of NtrCr r iN(αi) = αi r iNI + (1 − αi)r iNA

(9)

Here, we have introduced another set of N variational parameters, {αi} (0 ≤ αi ≤ 1), that specify the backbone positions of the Cα atoms as an interpolation between the I and A state conformations of NtrCr, {rNi I} and {rNi A}, respectively. The variational free energy F[{C},{α}] = E[{C},{α}] − TS[{C},{α}], now depends on both sets of variational parameters. The form of the entropy S[{C},{α}] of a conformational ensemble specified by {C} and {α} is similar to the expression in the folding model (eq 4), except now the mean position for each residue is a linear interpolation between the average position relative to the native I- and A-state conformations.65 The energy of the system E[{C},{α}] is composed of two single-basin energies EI[{C},{α}] and EA[{C},{α}] defined by the native contacts found in the Iand A-state of the protein, respectively. The energy within each basin is derived from two-body interactions given in eq 3 between native contacts [ij]I ([ij]A) in the single basin of the I (A) state. Following ref 47, the two basins are coupled through the expression E[{C}, {α}] = −

EI[{C}, {α}] + E A [{C}, {α}] + E 0 2

⎛ EI[{C}, {α}] − E A [{C}, {α}] − E 0 ⎞2 ⎜ ⎟ + Δ2 2 ⎝ ⎠

(10) Figure 3. Energy and free energy profiles for conformational transition of NtrCr. The single basin energies EI and EA are for the I (dashed curve) and A (dotted curve) states, respectively in (a). The solid curve E is the energy path of the I (α0 = 1) → A (α0 = 0) state transition in (a). The free energy profile of the I (α0 = 1) → A (α0 = 0) state transition of NtrCr is shown in (b).

This formula depends on two parameters: an energy offset parameter, E0, that adjusts the relative stability of the two basins, and the coupling constant, Δ, that controls the interpolation of the energy when EI[{C},{α}] and EA[{C}, {α}] are comparable. Note, the coupling of the two basins is controlled by the values of the total single basin energies. This coupling is similar in spirit to other recently developed coarsegrained models to study protein conformational change, which either combines the two single-energy basins globally46−48,50−52,54,55 or switches between local individual native contacts.45,49,53 In previous studies on the open/closed transition of the calmodulin domains, we used an alternative coupling of the basins based on the energy of individual contacts.16,65,66 Both ways of coupling the two energy basins give qualitatively similar results for calmodulin (unpublished results). Analysis of the free energy surface, F[{C},{α}] = E[{C},{α}] − TS[{C},{α}] follows the program developed to study folding. The mechanism controlling the kinetics of the transitions is determined by the structural ensemble along the transition route defined by critical points of the free energy. As in previous studies,16,65,66 we restrict the interpolation parameters {αi} to be same for all the residues, αi = α0 to simplify the analysis.67 With this modification, the numerical problem of

basin energies EI and EA, respectively, as the reference structure rNi (α0) is interpolated between the two states according to eq 9. The single basin energies increase as the reference structure is distorted away from its local minimum, with EI < EA near the inactive state (α0 = 1) and EA < EI near the active state (α0 = 0). The single basin energies are comparable at an intermediate interpolated structure determined by the relative stability of the basins. With the offset energy set to E0/kBT = 5.96, the intersection of the two energy curves occurs at α0 ∼ 0.5. The energy for the I → A conformational transition shown as the solid curve in Figure 3a is obtained by combining the two energies EI and EA through eq 10, with the coupling constant Δ = 6. The coupling parameter was adjusted by increasing Δ in eq 10 from 0 in small steps until the two energy basins are connected smoothly47 and this happens at α0 ∼ 0.5 [Figure 3a]. Note that, the coupling constant Δ lowers the energy barrier for the I → A transition relative to the intersection of the single 13185



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basin energy EI and EA. Figure 3b shows the free energy F[{C},α0] = E[{C},α0] − TS[{C},α0] of the I → A conformational change of the NtrCr and the transition state is determined from the peak of the F[{C},α0] at α0 = 0.5. The energy offset is adjusted to E0/kBT = 5.96, so that the I-state is more populated than the A-state [see Figure 3b], in qualitative agreement with the experiment.34 Conformational Flexibility. Structural order in the coupled basin model is characterized with similar measures to those introduced to describe folding. Differences in main-chain flexibility during the allosteric transition is monitored by the mean square fluctuations Bi[{C},α0] of each Cα of the polypeptide chain.

used in the current study for the A-state of NtrCr or due to the limitation in our current model. We note that parts of some loops have similar flexibility in both the I- and A-state. For example, the two ends of the β3−α3 loop, which remain relatively rigid, while some residues of the α2−β3 loop close to helix-α2 remain flexible during the conformational change. To more clearly illustrate how the flexibility evolves throughout the transition, we consider the mean square fluctuations relative to the fluctuations in the inactive state, Bri (α0) = Bi(α0)/BIi (α0 = 1). Here, Bi(α0) is the fluctuations of residues calculated along the transition route parametrized by α0 and BIi (α0 = 1) is the fluctuations of the I-NtrCr. The relative temperature factors highlight changes in the conformational flexibility of each residue of NtrCr with respect to the I-state along the transition route. Residues for which Bri (α0) < 1 as α0 decreases become more rigid during the I → A conformational transition, while residues for which Bri (α0) > 1 become more flexible. As shown in Figure 4b, the flexibility of the residues for β3−α3 loop, helix-α4 and α4−β5 loop decreases sharply at α0 = 0.5 (near the transition state). These regions are highlighted by the dotted curves in Figure 4. On the other hand, the β4−α4 loop remains flexible throughout the transition. Figure 4b also shows that the mobile part (in the C-terminal end) of β5-sheet increases its flexibility slightly during the transition. These observations are consistent with NMR observations reporting that β4−α4 loop and β5-sheet have persistent motions in both the I and A states.34,60 Although many regions of the protein NtrCr exhibit some changes in flexibility during the I → A transition in our study, we will restrict our attention mainly to the β3−α3 loop and helix-α4 because these particular segments have the most prominent changes in structure and flexibility. Inactive to Active State Transition Mechanism. In order to explore the transition mechanism for the I → A conformation of NtrCr in more detail, we plot the fluctuations Bi(α0) for selected residues of the β3−α3 loop and helix-α4 segments in Figure 5. The specific residues in the β3-α3 loop were chosen based on their significant decrease in flexibility upon activation, whereas the residues from α4 were selected arbitrarily because the entire helix is highly flexible in the inactive state. [Bi(α0) for the rest of the residues from α4 are shown in the Supporting Information, Figure S1.] As seen in Figure 5a, the flexibility of residues 57−59 in the N-terminal part of the β3−α3 loop decreases gradually. By contrast, the flexibility of the other residues (60−62) in the C-terminal part of the loop decreases abruptly near the transition state (α0 ∼ 0.5−0.55). The residues in helix-α4 also lose their flexibility abruptly as shown in Figure 5b. Some residues in α4 exhibit nonmonotonic changes in the flexibility at α0 ∼ 0.6. Similarly, the residue Gly62 of β3-α3 loop shown in Figure 5(a) increases its conformational flexibility transiently along the transition route. In a previous study of the conformational change of the domains of calmodulin (CaM),16,66 we identified nonmonotonic changes in flexibility near the transition state as cracking,14 or local unfolding and refolding along the transition route. In NtrCr, however, the relative magnitude of the transient increase in flexibility of NtrCr along the I → A transition route is comparatively much smaller than predicted for the CaM domain. Consideration of the contact maps of I and A conformations of NtrCr shown in Figure 6 helps rationalize the predicted transition mechanism of NtrCr. Comparison of the contact maps of each state reveals that the β3−α3 loop and helix-α4 have many additional contacts in the activated state. Individual

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RESULTS Change in Conformational Flexibility. The change in conformational flexibility of NtrCr, is characterized by the mean square fluctuations, Bi(α0), for each residue evaluated at different values of the interpolation parameter α0 along the I → A transition route. Overall, the protein NtrCr becomes significantly more rigid upon activation, as shown in Figure 4a.

Figure 4. Conformational flexibility of NtrCr along the I → A transition route. Mean square fluctuations Bi(α0) vs residue index for selected values of the interpolation parameter α0 are shown in (a). Ratio of mean square fluctuations, Bri (α0) = Bi(α0)/BIi , (b) where Bi(α0) is calculated for different α0 and BIi is fluctuations of the I state at α0 = 1. The dotted curves in (a) and (b) enclose the regions from β4−α4 loop, helix-α4, α4−β5 loop and β3−α3 loop of NtrCr.

In particular, loops β3−α3, β4−α4, and α4−β5, and helix-α4 are highly flexible in the I-state. This observation is consistent with NMR measurements34 that showed these loops fluctuate freely in the I-state and become more restricted in the A-state conformation. Our calculation suggests that the middle part of β5 remains rigid during the I → A transition, a result in apparent conflict with the NMR results suggesting that β5 is relatively more flexible in the I state.34 Additionally, Figure 2c shows that structural deviation in the middle part of the β5 (near residue 101) between the I and A states is not significant compared to the β3−α3 loop and helix-α4. Interestingly, comparison of the I and A state NtrCr structures (Figure 2a) indicates that part of β5 near the β5−α5 loop has significant tilt. This kind of movement cannot be captured using our current model due to the limitations of linearly interpolating between the two native structures of NtrCr . Therefore, this discrepancy could arise either because of the different structures 13186



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These additional contacts arise from a substantial axial rotation (corresponding to half a turn) and register shift of α4 by about two residues from the N to C terminus (observed from the changes in chemical shifts of Cα carbons from NMR experiments of NtrCr upon phosphorylation34). These additional contacts account for the significant increase in rigidity of helix-α4 in the activated state. Lastly, we note there are substantial rearrangements in the contacts between the β3−α3 loop and helix-α4 (see Figure 6). Additional contacts are also formed between the C-terminal part of the β3−α3 loop (residue indices 60−63) and from the N-terminal half of α4 (residues indices 85−90) upon activation (see Supporting Table S3). This is interesting because Figure 5a,b shows that these particular residues exhibit relatively sharp changes in conformational flexibility during the I → A state transition. This is especially true for the residues in helix-α4. Strain Energy Analysis of the Inactive State. To further investigate the role that the flexibility of helix-α4 plays in the transition mechanism, we consider the local strain that develops in NtrCr as the structure is deformed from the inactive conformation. Following ref 68, we use the elastic network model69−71 to estimate the strain during the I → A structural transition72

Figure 5. Mean square fluctuations of selected residues of NtrCr along the conformational transition route. (a) Plot of fluctuations Bi(α0) vs interpolation parameter α0 of residues from β3−α3 loop for inactive (I) → active (A) transition. (b) Similar plot of Bi(α0) vs α0 of residues from helix-α4.

εi(α0)I → A =

kI 4

(|r iN, j(α0)| − |r iN, jI|)2

∑ I

j ∈ [ij]

(11)

Here, the sum is taken over all residues in contact with the ith residue in I-NtrCr, |ri,jN(α0)| = |rNi (α0) − rNj (α0)| is the distance between the Cα positions of the ith and jth residue in the interpolated structure (eq 9), and |rNi,j I| = |rNi I − rNj I|, is the corresponding distance for the ith and jth residue in the inactive state. The spring constant kI, which determines the overall rigidity of the molecule, is assigned to unity for all the residues of I-NtrCr for simplicity. For structural deformation of the inactive NtrCr, the Cα position vectors are interpolated by varying the parameter α0 in a small step of 0.01, linearly from the I (α0 = 1) → A (α0 = 0) state conformation (see eq 9). The strain energy distribution of each residue εi(α0)I→A is plotted in Figure 7. There are many regions in NtrCr that are under relatively high strain during the I → A structural change, including residues from β1, the α1−β2 loop, part of the α2−β3

Figure 6. Contact maps (sequence networks) of the I and A conformations of NtrCr. The contacts represented in squares are for the I state, and the contacts in triangles are for the A state. The set of contacts inside the solid circles are for the β3α3 loop and helix-α4. The contacts between the β3α3 loop and helix-α4 are shown inside the dotted circles. Note that for α4 and the β3α3 loop and between β3α3−α4 there are more contacts in the A state than the I state.

contacts involving these secondary structures are given in the Supporting Information. Several residues of the β3−α3 loop make additional contacts during the transition (see Supporting Table S1). In particular, Pro58, which has a gradual decrease in flexibility during the I → A transition, gains all of its contacts upon activation. By contrast, residue Met57, which has relatively constant flexibility during the transition, only has contacts that are common in both structures. The active state also has six more contacts between residues with sequence indices i → i + 4 within helix-α4 (see Supporting Table S2.).

Figure 7. Residue strain energy distribution for linearly interpolated NtrCr structures. Strain energy of the I-NtrCr vs residue index during the deformation from the I → A state conformation for different values of the interpolation parameter α0, (a). Residue strain energy distribution at an intermediate stage, α0 = 0.35, (b). Strain energy of helix-α4 is enclosed inside the dotted curves in (a) and (b). 13187



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loop, and helix-α5. Although, residues in the β3−α3 loop and helix-α4 have significant changes in flexibility upon activation, these segments are under much lower strain compared to other residues of the protein. We also note that the magnitude of the strain for NtrCr is much lower than the strain calculated for the CaM domains using the same approach.66 Since cracking relieves regions of high local strain during a conformational transition, the relatively low values of strain calculated for NtrCr may explain why local unfolding and refolding is not significant in the predicted transition route of NtrCr . Comparison with NMR Experiments. Volkman et al.37 have measured the correlation between backbone dynamics parameters and conformational switching mechanism of NtrCr upon activation from NMR relaxation experiments. The exchange parameter Rex from these experiments indicates motions that occur on the microsecond to millisecond time scale and reflect a large difference in chemical shift between the exchanging species.37 The data reproduced in Figure 8a shows large exchange rates for the β3−α3 loop and the switch region 3445 face (α3−β4−α4−β5 segment).

= BIi (α0 = 1) − BAi (α0 = 0). Here, α0 = 1 and α0 = 0 represent the I- and A-states of NtrCr, respectively. Residues with ΔBi > 0 are more conformationally restricted in the activate state than in the inactive state, whereas residues with ΔBi < 0 have more conformational freedom in the active state than the inactive state. Energetic contributions to changes in the local environment can be calculated from the energy of each residue due to contacts in the A-state (using eq 3) EiA [{C}, α0] =

∑

εijuij

j ∈ [ij]A A

(12) r

where [ij] is the native contacts of the A-NtrC . We consider change in energy within the active basin between inactive and active conformations, ΔEAi = EAi (α0 = 1) − EAi (α0 = 0). The magnitude of ΔEAi reflects the energetic stabilization of the ith residue within the active basin. Plots of ΔBi and ΔEAi for each residue are shown in Figure 8b,c. Aside from the ends of the protein, large values of ΔBi occur primarily for residues from the β3−α3 loop and the segment α4−β5 as shown in Figure 8b. Not surprisingly, residues in the β3−α3 loop and the α4−β5 segment have significant energy stabilization that accompanies the large entropy loss upon activation, as shown in Figure 8c. Residues within these regions of the protein have large exchange rates as shown in Figure 8a. The flexibility is relatively constant, however, for some of the residues with large exchange rates, such as in α3 and β4, as well as other residues with smaller exchange rates. Many of these residues, such those in α3 and β4 with large Rex as well as residues in β3, α1 and β1 with smaller Rex have significant energetic changes. Taken together, the energetic and entropic signatures from the model qualitatively agree with the exchange rates from NMR. Relative Stability and the Transition Mechanism. Results for additional calculations that explore the sensitivity of the transition mechanism on the relative stability between the active and inactive states of NtrCr are given in the Supporting Information. As shown in Figure S2 and Figure S6 of the Supporting Information, adjusting the offset energy in eq 10 to the values E0/kBT = 3.97 and 7.95 allows us to compare the transition mechanism when the transition state shifts toward the inactive conformation (α0 = 0.6) and toward the active conformation (α0 = 0.4), respectively. The qualitative description of the predicted evolution of conformational flexibility upon activation (Supporting Figure S3−S5) as well as the key mechanism of the transition (Supporting Figure S7− S9) are largely robust with respect to changes in stability. Nevertheless, the model predicts that the flexibility of some residues are more sensitive to the relative stability than others, particularly near the transition state. Larger quantitative differences in flexibility are seen for residues Met57, Asp61, and Gly62 from the β3−α3 loop (Figure 5a and Supporting Figures S4a and S8a), and residues Ser85 to Asp88 and Glu95 from helix-α4 (Figure 5b and Supporting Figures S1, S4b, and S8b). For most of these residues, greater flexibility is observed as the transition state moves toward the active state (from α0 = 0.6 to 0.4). However, there are exceptions, such as residues Met57 and Gln95 for which the flexibility decreases near the transition state. These predictions could be tested through mutagenesis experiments in the β3-α3 loop and/or helix-α4. Folding Mechanism of NtrCr. In this section, we compare predicted folding routes to each of the metastable states to see if the corresponding folding mechanisms anticipate the conformationally distinct properties of the two states such as

Figure 8. Comparison of the experimentally measured backbone conformational dynamics of NtrCr from NMR with parameters calculated from the variational model. (a) Exchange parameter Rex vs residue index from NMR relaxation study.37 The blue dots indicate Rex data for residues with larger than a threshold in the NMR experiments.37 (b) Difference in the mean square fluctuations ΔBi between the I and A conformations of each residue. (c) Difference in the energy per residue ΔEAi of the A conformation for two end values of the interpolation parameter α0.

It is difficult to estimate exchange rates from our model directly. Nevertheless, since Rex is proportional to the difference in the chemical shift between the two metastable states, it is interesting to compare Rex qualitatively with local structural changes predicted from our model. The origin or the chemical shift of individual residue has entropic and energetic contributions. Accordingly, we characterize differences in entropy and energy, as well as structural similarity to the two metastable states to identify the changes in the local structural environment of each residue. The entropic differences between the inactive and active state is reflected in the corresponding change in local flexibility, ΔBi 13188



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local flexibility. We study the folding to the inactive and active state at their respective folding temperatures. Here, we describe the structural organization of the protein along the folding route by the local order parameter ρ̅i (eq 6) and the global order parameter Q. (Another way to characterize the structure of the protein along the folding route is through the temperature factors evaluated at the critical points; these results are shown in Supporting Figure S10.) The free energy profile and structure along the folding route to the inactive state are shown in Figure 9a,c. The free energy

The predicted folding route of the NtrCr to the active conformation at its folding temperature Tf is quite different (shown in Figure 9b,d). Folding to the A-NtrCr structure initiates with the C-terminal half of the protein before its Nterminal half. The early folding of the β3-α3 segment and β4 corresponds to a transition barrier of ∼11kBT (Figure 9b), somewhat higher than the first barrier to the inactive structure. Notably, α4 folds much earlier in the folding route to A- NtrCr at QA ∼ 0.3. This striking difference likely reflects an increase in the stability of this helix upon activation. The rest of the route shown in Figure 9(b) consists of the helices α5 and α2 folding at QA = 0.5 and 0.6, respectively, followed by the ordering of the β1-α1-β2 segment at the end. These results are in harmony with the theoretical study by Itoh and Sasai,44 who predicted that the C-terminal half of NtrCr becomes ordered first in the dominant folding pathway to A-NtrCr. The flexibility of the key structural elements in the conformational transition of NtrCr β3−α3 loop and α4, has kinetic signatures in the predicted folding mechanism. Namely, when these elements are more flexible in the folded structure, they fold later along the folding route. The difference is particularly striking for α4, which orders late in the folding to the inactive state. This means that α4 is relatively unstable in the inactive conformation, being among the first segments to unfold.

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DISCUSSION NMR relaxation experiments indicate that both β3−α3 as well as the regulatory helix α4 of NtrCr exhibits large scale conformational dynamics.34,37 The functional dynamics of these structural elements play a prominent role of the transition mechanism of NtrCr predicted by the present model. Focusing first on the nature of the folded metastable states, the variational model predicts that the β3−α3 loop and the α4 helix are more conformationally restricted in the inactive state than the active state in agreement with NMR measurements,37 as well as targeted MD simulations38 and elastic network model41 of NtrCr . A natural way to describe the transition mechanism from the variational model is in terms of the evolution of conformational flexibility throughout the transition. We find that the key mechanism of allostery in NtrCr is controlled by the large change in conformational flexibility of both the β3−α3 loop and the helix-α4. The large decrease in conformational flexibility is driven by additional contacts involving these two particular structural segments formed in the active conformation. Interestingly, the β3−α3 loop and α4 helix lose flexibility during the transition in distinct ways; the β3−α3 loop exhibits a gradual decrease in flexibility, whereas the change in flexibility of the α4 helix is abrupt near the transition state. This abrupt change in flexibility of α4 is likely accompanied by the addition of four main chain hydrogen bonds formed cooperatively near the transition state. Our results also suggest that the residues from the central part of the β3−α3 loop, in conjunction with helix-α4, play an important role in the conformational change of NtrCr. We believe our prediction of the key mechanism could be tested in the future, for example, through mutagenesis experiments in the β3-α3 loop and/or helix-α4. The detailed transition mechanism for NtrCr has been studied recently by several groups through MD simulations. These all atom simulations describe transition mechanisms with more molecular detail than can be obtained with the analytic coarse-grained variational model. Interestingly, the results from

Figure 9. Folding mechanism of the I- and A-NtrCr. (a) folding route is characterized locally by the normalized native density ρ̅Ii and the global order parameter QI, where I denotes the inactive state. (b) folding route characterization of the A state by the normalized native density ρ̅Ai and the global order parameter QA. The degree of structural localization of each residue (ρ̅Ii ) is reflected in the colors, linearly scaled between 0 (blue) for G (globule) and 1 (red) for N (native) states. Free energy profiles along the folding route vs global order parameter for I-NtrCr is shown in (c) and that for A-NtrCr is shown in (d).

profile has two free energy barriers and an intermediate along the folding route. Folding of the segments α2−β3 and α3−β4 occur early in the folding, resulting in a barrier of ∼9kBT at QI = 0.2. Folding of the β3−α3 loop also starts early at QI = 0.2 but it gains structure gradually probably due to its high flexibility in the native conformation. The second barrier of ∼9.5kBT occurs at QI = 0.6 where the protein is folded except α1 and the β3−α3 loop are partially ordered, and α4−β5 is still unfolded. The last region to fold is the α4−β5 segment at QI = 0.8, probably due to its high flexibility of this segment in the native state (see Figure 4a). Overall, these results agree qualitatively with other folding studies of the NtrCr protein which showed that the N-terminal half (β1−α1−β2−α2−β3 element of the secondary structure) of the NtrCr folds earlier than its Cterminal half (α3−β4−α4−β5−α5 element of the secondary structure).44,73 Similar folding routes have been reported for the folding studies of other β/α-repeat proteins, as well.73 13189



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NtrCr. They argue that the combinatorial number transition routes results in a large change in entropy that lowers the free energy barrier of the transition state ensemble. The calculated barrier height from their study was found to be in the range of ∼5−10 kBT.80 Finally, we note that the use of different NMR structures of NtrCr may account for some of the inconsistencies reported in the literature.74 In particular, large fluctuations and local unfolding of helix-α4 may be due to the poorly resolved regions of the protein structure in some of the earlier studies.39,42 In the present study, a BeF−3 -activated structure is used as the active state NtrCr (A-NtrCr). Although the NMR structures of phosphorylated NtrCr (P-NtrCr) are available,34 it has been found that the lifetime of the P-NtrCr state was short, and some key features in the NMR data were not well-defined. The main structural difference between the BeF−3 -NtrCr and P-NtrCr is observed in the position of helix-α3. In the BeF3−-NtrCr structure, α3 seems closer to the position adopted in the INtrCr.60

different simulations apparently do not agree on the key mechanistic features of the inactive/active (I/A) transition of NtrCr.74 Hu and Wang,38 using a targeted MD method, reported on the specific role of the flexible β3−α3 in addition to the regulatory helix-α4 in the activation mechanism of NtrCr. Khalili and Wales40 described a transition mechanism involving several steps consisting of the movement of α4 followed by the movement of α2 and then a concerted flip of the β3−α3 loop. In another recent simulation study using targeted MD pathways and quasi-harmonic analysis, Lei et al.43 identified several steps along the conformational change pathway of NtrCr, suggesting a transition mechanism in which α4 tilts followed by rotation of α4 and then a flip of the α4−β5 loop. From this study it is concluded that helix-α4 plays the primary role in the transition with several other secondary structural rearrangements.43 Different reports have also appeared in the literature concerning the structural integrity of the helix-α4 during the transition and the magnitude of the theoretically predicted free energy barrier separating the active and inactive states. These questions are related to cracking, a mechanism that can lower an otherwise high free energy barrier. Using a mixture of elastic networks models of the I and A conformations of NtrCr, Lätzer et al.39 suggested that the functionally important helix-α4 partially unfolds and refolds during the transition in order to lower an unreasonably high calculated barrier of ∼90 kBT. Subsequently, Pan et al.75 found an optimized transition path using a string method76 for a coupled Cα elastic network model similar to Lätzer et al. The resulting barrier was also very high, approximately 50 kBT, though lower than reported in ref 39. Later, Vanden−Eijneden and Venturoli77 obtained a lower I/A conformational transition barrier of ∼15 kBT for NtrCr without invoking cracking for a model similar to ref 75. This is much closer to the experimentally determined barrier height of ∼10 kBT.78 Damjanovic et al.42 employed a self-guided Langevin dynamics to find a transition pathway in which helix-α4 partially unfolds. Kern and co-workers43 argued that the unfolding of α4 in this study may be a consequence of using an unrefined NMR structures that did not have the full complement of hydrogen bonds. The simulations reported in ref 43 suggested that transient non-native hydrogen bonds, instead of local unfolding of α4, lower the free energy barrier of this transition. Additional unfolding experiments revealed that α4 unfolds cooperatively with the protein NtrCr; a result, Kern and co-workers argue, that shows helix-α4 remains intact during the conformational transition.79 The transition route calculated from the variational model in the present paper does not show significant sign of helix α4 unfolding during the transition. Furthermore, deformations away from the inactive state resulted in small amount of local strain in α4. On the other hand, for the folding route to INtrCr predicted in this paper, helix-α4 folds very late. This is not only consistent with the high flexibility of the α4 helix in the inactive state, but also suggests that it would be one of the first regions to become unstructured in the unfolding of INtrCr . Even without local unfolding or non-native interactions, the predicted free energy barrier from our I → A transition is found to be lower (ΔF†/kBT ∼ 2.7) than the estimated barrier based on NMR relaxation experiments [∼6 kcal/mol (∼10 kBT)].78 One reason for the small value of activation barrier from our simple model is the relatively large entropic contribution to the transition state ensemble. Recently, Itoh and Sasai80 extended the structure based folding model of Muñoz and Eaton81 to predict the allosteric transition route in

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CONCLUSION In this paper, we present a coarse-grained variational model for the allosteric transition mechanism of the protein NtrCr upon activation. The multiple-basin energy model presented in ref 47 provides a convenient way to couple the two energy basins and control the stability of the two metastable native states. Our model predicts that the allosteric transition of NtrCr is governed by its loss of conformational flexibility upon activation without any local unfolding along the transition route. Specifically, we find that the regulatory helix-α4 and the β3−α3 loop becomes significantly more rigid upon activation, in good qualitative agreement with NMR relaxation experiments.34 The loss of local flexibility is not the complete description of the transition; including the energetic stabilization that accompanies entropic losses in the active conformation provides a more complete picture of the transition consistent with the NMR exchange rates of individual residues. Furthermore, our study illustrates that protein folding and allostery are related through a dynamic energy landscape,10,82−84 where the conformational fluctuations play a key role. We find the folding mechanism to each metastable state is very different when folding to the other state is prevented. When this source of topological frustration is eliminated, the α4 helix is predicted to order much later when folding to the inactive state, a result consistent with its high flexibility in the inactive state. The present model includes the topological frustration due to competing metastable conformations, but neglects energetic frustration due to non-native contacts. Several theoretical studies have shown that frustration due to non-native interactions can have significant influences on folding cooperativity,85,86 protein stability87 and ligand binding sites in allosteric proteins.13 It will be interesting to incorporate nonnative interactions into this model of conformational transitions in the future. We note that coarse-grained topology based models have natural limitations in describing allosteric transition at high resolution. Allosteric transitions of some proteins may be sensitive to the detailed shape of the minima that control conformational dynamics. Allostery in the absence of a conformational change is a situation where topology-based models might be inappropriate (however, even here the relevant dynamics of the single folded basin may indeed be 13190



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modeled through topology based models). Nonetheless, in our current study, this is not directly relevant for NtrCr, which does exhibit a conformational change upon phosphorylation.

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ASSOCIATED CONTENT

S Supporting Information *

Nine figures and three tables are included in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (330) 672 - 9518. Fax: (330) 672 - 2959. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by a grant from the National Science Foundation (MCB-0951039). REFERENCES

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Allostery and Folding of the N-terminal Receiver Domain of Protein NtrC

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