proteins STRUCTURE O FUNCTION O BIOINFORMATICS
Molecular dynamics study on folding and allostery in RfaH Liqin Xiong and Zhenxing Liu* Department of Physics, Beijing Normal University, Beijing, 100875, China
ABSTRACT Upon being released from the N-terminal domain (NTD), the C-terminal domain (CTD) switches from a-helix conformation to b-barrel conformation, which converts RfaH from a transcription factor into an activator of translation. The afib conformational change may be viewed as allosteric transition. We use molecular dynamics simulations of coarse-grained off-lattice model to study the thermal folding of NTD, CTD, RfaH and the allosteric transition in CTD. The melting temperatures from the specific heat profiles indicate that the b-barrel conformation is much more stable than the a-helix conformation. Two helices in a-helix conformation have similar thermodynamic stabilities and the melting temperatures for b sheets show slight dispersion. Under the interaction with NTD, CTD is greatly stabilized and the cooperativity for thermal folding is also significantly improved. The afib allosteric transition can be approximately described by a two-state model and three parallel pathways are identified. The transition state ensemble, quantified by a Tanford b-like parameter, resembles the ahelix and b-barrel conformations almost to the same extent. Proteins 2015; 83:1582–1592. C 2015 Wiley Periodicals, Inc. V
Key words: SOP-sidechain model; thermal folding; melting temperature; allostery; transition state ensemble.
INTRODUCTION Allostery happens in all dynamic proteins1,2 and is essentially important to protein functions3,4 and to disease and drug discovery.5,6 Sequence-based7–9 or structure-based10,11 methods have been proposed to investigate the allosteric wiring diagram. Theoretical and simulation works were conducted to study the allosteric transition pathways.12–21 Among these studies, the involved conformational changes are either at small scales, for example, loop structure change in DHFR12,13,22,23 or at medium scales, such as helix reorientation in calmodulin’s N-terminal domain (NTD),14,15,24,25 domain displacements in adenylate kinase16–18,26,27 or at large scales, such as subunit movements in GroEL19,28–30 and in hemoglobin.20,21,31 In contrast to the previously studied allostery, where the secondary, tertiary and quaternary structures are only displaced by certain distances or angles and no significant structure unfolding is involved, RfaH’s CTD completely switches from a-helix to b-barrel structure, the magnitude of this conformational change is unprecedented.32 It is of great interest to study this most extreme structural transition example known to date.
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RfaH is a two-domain antitermination factor(CTD and NTD) and whether its CTD is in a-helix or b-barrel structure determines its very different functions.32–34 When CTD adopts a-helix conformation, RfaH acts as a transcription regulator as CTD is packed tightly against NTD, masking the RNAP interaction surface. It is proposed that binding of RfaH to operon polarity site of the nontemplate DNA strand triggers the CTD release from NTD35,36 and CTD spontaneously switches to b-barrel conformation, similar to RfaH’s paralog, the general transcription factor NusG.37 When in b-barrel conformation, RfaH’s CTD stimulates translation through
Abbreviations: CTD, C-terminal domain; FENE, finite extensible nonlinear elastic potential; MSM, Markov State Model; NTD, N-terminal domain; PDB, Protein Data Bank; REMD, replica-exchange molecular dynamics; RMSD, root mean square deviation; SOP, self-organized polymer; TS, transition state; TSE, transition state ensemble Grant sponsor: National Natural Science Foundation of China; Grant number: 11104015; Grant sponsor: Fundamental Research Funds for the Central Universities; Grant number: 2012LYB08. *Correspondence to: Zhenxing Liu, Department of Physics, Beijing Normal University, Beijing 100875, China. E-mail:[email protected] Received 9 February 2015; Revised 18 May 2015; Accepted 22 May 2015 Published online 29 May 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/prot.24839
C 2015 WILEY PERIODICALS, INC. V
Folding and Allostery in RfaH
recruitment of the S10 component of the ribosome to an mRNA that lacks ribosome binding site. Thus, switch from a-helix structure to b-barrel structure converts RfaH from a transcription factor into an activator of translation. The folding of RfaH has been studied by both experiments and theoretical approaches.32,38–40 Urea-denatured RfaH spontaneously refolds into its native structure where CTD is in a-helix structure and forms a tight interface with NTD.38 However, separately expressed CTD folds into b-barrel conformation.32 Targeted molecular dynamics and Markov state model (MSM) were used to study the mechanism of this conformational transition and parallel transition pathways are demonstrated.40 Despite these studies, in this article we will address the following questions: (a)Which conformation is more stable for CTD, a-helix or b-barrel conformation? b-barrel conformation seems to be the preferred conformation for CTD since for NusG protein family all other known CTD adopts b-barrel structure,41 we expect b-barrel conformation is more stable than a-helix conformation; (b)Is CTD stabilized by the interaction with NTD in the RfaH? (c) What are the nature of the kinetics and the pathways associated with a ! b transition? (d) What are the characteristics of the transition state ensemble (TSE) in the transition? We use molecular dynamics simulations of coarse-grained off-lattice model42,43 to address these questions.
METHODS SOP-sidechain model
The simulations were carried out using a coarsegrained model in which the previously introduced selforganized polymer (SOP) representation44 was augmented to include side chains (SCs).45,46 In the resulting SOP-SC model, which accurately accounts for packing effects, each residue is represented by two interaction centers, one that is located at the Ca position and the other is at the center of mass of the side chain. In the SOP-SC model the native state stabilization is achieved by accounting for backbone-backbone (bb), side chain-side chain (ss), and backbone-sidechain(bs) interactions. The energy (viewed as an effective free energy obtained by integrating over solvent (water) degrees of freedom) of a conformation, which describes the intrapeptide interactions, is EP ðfri gÞ ¼ VFENE 1VLJNAT 1V NEI 1VLJNN :
bb bs VFENE ¼ VFENE 1VFENE
¼2
N 21 X i¼1
2
N X k i¼1
2
ðri;i11 k 2 Ro log 12 2
Ro2 log 12
ðri;i
2 o bb 2ri;i11 bb Þ Ro2
o bs 2ri;i bs Þ Ro2
2
!
!
(2)
:
The non-bonded interaction, VLJNAT in Eq. (1), which accounts for the stability of the folded structures, is taken to be VLJNAT ¼ VLJbb NAT 1VLJss NAT 1VLJbs NAT " o 12 o 6 # N 23 X N X ri;j bb ri;j bb Dbb ¼ ebb 22 ij r r i;j bb i;j bb i¼1 j¼i13 " 12 o 6 # o N 23 X N X ri;j ri;j ss ss Dssij 1 ess jeij 20:7j 22 r r i;j ss i;j ss i¼1 j¼i13 " o 12 o 6 # N X ri;j bs ri;j bs Dbs 1 ebs 22 ij : ri;j bs ri;j bs i¼1;j¼1 ji2jj3
(3) If the distance between two noncovalently linked beads, rij ðji2jj 3Þ in the Protein Data Bank (PDB) structure is within a cutoff distance Rc, a native contact is formed and correspondingly Dij 5 1; if rij > Rc ; Dij ¼ 0. The strengths of non-bonded interactions ebb, ess, ebs are assumed to be uniform. The Betancourt–Thirumalai (BT)47 statistical potential matrix with elements ij, is used to explicitly treat the dependence of ss interactions on the side-chain type. We used repulsive interactions to account for excluded volume effects between neighboring beads with strength el. The ranges of repulsion are rbb ; ri;j ss ; rj bs for bb, ss and bs interactions respectively. The form of VNEI is bb ss bs V NEI ¼ VNEI 1VNEI 1VNEI 6 N 22 X rbb ¼ el ri;i12 bb i¼1 N 21 22 X ri;i11 ss 6 NX ri;i12 ss 6 1 el 1 el ri;i11 ss ri;i12 ss i¼1 i¼1 6 N X rj bs 1 el : ri;j bs i¼1;j¼1
(4)
0 and , ; < Qb34 >; < Qb45 > to dissect the order of events. The time-dependent changes of , [Fig. 3(C)] shows that the two helices almost finish unfolding within the time window for switching the conformational force ð33:600ls 33:617lsÞ. By fitting the relaxation kinetics to single or double exponentials, hQb12 i ¼ 0:706 12e 2t=97:7ls , hQb23 i ¼ 0:13010:699 ð12 2t=73:7l 0:37e 2t=1:1ls 20:63e2t=71:5ls Þ; hQb34 i ¼ 0:826 12e sÞ, hQb45 i ¼ 0:718 12e 2t=112:8ls [Fig. 3(D)], we think that b23 forms first, subsequently b34 folds, followed by the formations of b12 and b45. By integrating Figure 3(C,D), we conclude that the two helices rapidly unfold to random coil-like structure with a small portion of residual structures and then b sheets are gradually acquisited. By analyzing the 100 trajectories, we find that the transition happens through three parallel pathways (Fig. 4). In the dominant pathway [Fig. 4(A,B)], which accounts for 63% of the trajectories, the b-sheet formation sequence is b23, b34, b12, b45, which is the same as the picture exhibited in the ensemble average over all the trajectories [Fig. 3(D)]. In the second pathway [Fig. 4(C,D)], through which 23% of the trajectories fold, the b sheets b23, b12, b45, b34 form one after another. In the third pathway [Fig. 4(E,F)], representing 14% of the trajectories, transition occurs through the successive formations of b34, b23,b12, b45.
Transition state ensemble (TSE) centered along the transition
Using RMSD as a surrogate reaction coordinate, we assume the transition state (TS) is reached for the first time at tTS when jRMSD=aðtTS Þ2 RMSD=bðtTS Þj < ¼ 0:2A˚ . This criterion puts the TS equidistant to ahelix and b-barrel structures as far as RMSD is concerned. Although most transitions happen between 50 ls 200 ls, some transitions happen even around 300 ls and 500 ls [Fig. 5(A)]. The very broad distribution of transition time, P(tTS), also reflects the heterogeneity observed in the transition dynamics [Fig. 3(A)]. To quantify the position of TSE along the transition, we computed a Tanford b-like parameter q‡,19 using q‡ ¼
D‡ 2minðRMSD=bÞ ; maxðRMSD=bÞ2minðRMSD=bÞ
(13)
where D‡ ¼ ðRMSD=aðtTS Þ 1 RMSD=bðtTS ÞÞ=2, maxð RMSD=bÞ ¼ 24:2A˚ and minðRMSD=bÞ ¼ 1:1A˚ are the maximum and minimum values of RMSD=b, respectively. Thus, q‡ is in fact the normalized D‡ . If q‡ is close to 0(1), the most probable TS is similar to b-barrel(ato‡ 0.65 [Fig. helix) conformation. q‡ ranges from 0.35 ‡2 i2 ¼ 0:012, 5(B)] and the small fluctuation, r2 ¼ hq hqi2hq ‡ i2 shows that the TSE in CTD is conformationally restricted. Its fluctuation is significantly smaller than that for DHFR13 albeit with an extraordinarily large magnitude of conformational change. The peak position of the distribution, Pðq‡ Þ, is surprisingly at 0.5 and the average value of q‡ is also 0.5, which implies that the TSE resembles the a-helix and b-barrel conformations almost to the same extent. Therefore, the position of TSE is approximately centered along the a ! b transition as far as both RMSD and q‡ are concerned. PROTEINS
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Figure 3 (A)Time dependence of RMSD/a(solid lines) and RMSD/b(dashed lines) of several individual trajectories. The inset gives an example of one trajectory(blue lines) that has multiple crossings through the transition region. (B) Ensemble average of hRMSD=ai(black diamonds) and hRMSD=bi(red circles) over 100 trajectories. The solid line is exponential fit to hRMSD=bi relaxation kinetics. (C)Time dependence of hQa4 i(black line), hQa5 i(red line) and hQa45 i(blue line). (D)Time dependence of hQb12 i(black diamonds), hQb23 i(red circles), hQb34 i(blue stars), hQb45 i(dark cyan triangles). The solid lines are corresponding exponential fits to hQbij i relaxation kinetics. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
In experiment, U-values are used to describe the structure of the TS, specifically, the similarity of each residue in TSE with respect to that in the native state. Here, we compute the U-value for residue i with respect to a-helical CTD as: Uai ¼ hNNai i, where Ni is the number of native coni tacts formed between residue i and other residues in the a TS, Ni is the number of native contacts formed between residue i and other residues in a-helical CTD. This definition, that is, the ensemble average of the fraction of native contacts formed in TSE, is in fact equivalent to that used by Cho et al.57 and Uai are shown in Figure 5(C). Likewise, we compute Ubi ¼ h Nbi i[Fig. 5(D)]. Comparing Fig-
dominant TS (found in 79% of the transition trajectories), b23 and b34 are packed orthogonally as in the native state [structures in Fig. 5(B), Left]. The member of the other group of TSE (21%) has well-formed b12 and b23 [conformations of Fig. 5(B), Right]. The common features of the TSE is that the central b23 is well structured. Although simulations predict a single domi ‡ nant TS structure, diversity (assessed by P q or contact formation) in the TSE structures, which is hard to glean from experiments, points to the inherent plasticity of the TSE.
Ni
ure 5(C,D), we find that Ubi are mostly larger than Uai except for a few U-values of the residues near the two terminals. Thus, TSE is more similar to b-barrel structure than to a-helical structure in terms of U-value analysis. We classified the TSE structures into two groups according to their similarity to the native state. In the
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DISCUSSIONS To characterize the large-scale conformational change of CTD in RfaH, there are several issues which should be addressed, including the stability change, the kinetic
Folding and Allostery in RfaH
Figure 4 Three parallel pathways and corresponding structural features in allosteric transition. Representative trajectories for three pathways are given in the left column and average (black lines), (red lines), (blue lines), (dark cyan lines) over the trajectories belonging to the same pathway are shown in right column. (A,B) For the dominant pathway. (C,D) For the second pathway. (E,F) For the third pathway. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
processes and TSE. Facing with these aspects, our results are compared with the previous simulations by Gc et al.39 and by Li et al.40 The stability change
To study the stability change during the allosteric transition, we use molecular dynamics simulations of coarsegrained off-lattice model to obtain the melting temperatures of a-helical and b-barrel structures, which proves that a-helical form is indeed less stable than b-barrel structure. In Ref. 40, Li et al. reached the same
conclusion based on the unfolding times extracted from three implicit solvent all-atom MD trajectories. In fact, many more MD trajectories need to be generated in their simulations to extract the unfolding information because of the stochastic nature of the allosteric transitions. In Ref. 39 by GC et al. the stability change of CTD was also analyzed using the free-energy landscape. Since their study is based on implicit solvent REMD in atomistic details, the convergence would be worse than our coarsegrained model, which is indicated by the fact that in their simulations the a to b transition does not happen very frequently (only once in their selected replica) and PROTEINS
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Figure 5 Features of TSE. (A) Distribution of transition times P(tTS). (B) Distribution of Tanford b-like parameter q‡ ; Pðq‡ Þ. Superposition of a few structures of the dominant TSE cluster (Left) shows formation of b23 and b34. The other cluster(Right) has well-formed b12 and b23. (C) U-values with respect to a-helical structure, Uai . (D) U-values with respect to b-barrel structure, Ubi . [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
the conversion from b-barrel back to a-helical form is not observed. The kinetic processes
The kinetic processes of allosteric transition are generally described by the variation of the secondary structure elements and their interactions. From our simulated 100 transition trajectories which are hundreds of microseconds, we find that structural formation takes place clearly through multiple pathways. During the formation of the b-barrel structure, statistically, b23 forms first, subsequently b34 folds, followed by the formations of b12 and b45. The ensemble average of RMSD/b over 100 trajectories varies in a single exponential manner, which indicates the transition is cooperative, and the predicted transition timescale is about 129 ls.
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To investigate this dramatically large scale transition, Li et al. in Ref. 40 constructed MSM using both biased and unbiased implicit solvent all-atom MD simulations. Their biased MD simulations, including targeted MD simulations and high-temperature MD simulations performed at 370K, are used to identify the metastable states. Their unbiased MD simulations at 300K range from 150 ns to 1 ls, which is below the typical timescale of microseconds to milliseconds for large scale protein conformational changes, therefore they build MSM to determine the full ensemble of transition pathways. In the transition pathway determined by Li et al. b23 forms first, followed by the formation of b12, and finally b45 forms. Comparing their b-sheet formation sequence (b23, b12, b45) and ours (b23, b34, b12, b45), we identify b34 forms before b12 and therefore a fuller picture is provided. Their predicted transition timescale is
Folding and Allostery in RfaH
approximately 0.1s, which is much longer than the typical timescale of microseconds to milliseconds and is also in contrast to our predicted transition timescale 129 ls. These above differences between Ref. 40 and our study probably originate from different models and force fields and can only be tested experimentally. GC et al. in Ref. 39 also study the transition pathway using one replica of the implicit solvent REMD in atomistic details. The b-sheet formation sequence they proposed is b12, b23, b34, b45, which is very different from the results of Li et al.40 and ours. It is well known that the kinetics information is lost in REMD because of frequent exchanges of temperatures. Accordingly, the transition pathway and folding sequence in b-barrel structure is extracted from only a single replica of REMD. TSE
In our work, we study TSE of the a to b transition, which has not been investigated elsewhere. Using RMSD as a surrogate reaction coordinate, we locate TSE. The position of TSE along the transition is quantified by a Tanford b-like parameter q‡. We find that the position of TSE is approximately centered along the transition as far as both RMSD and q‡ are concerned. CONCLUSIONS We simulated the thermal folding of CTD, NTD, RfaH and the allosteric transition from a-helix to b-barrel conformation for CTD. Through these studies, we address the questions raised in the INTRODUCTION section: (a) For CTD, b-barrel structure is much more stable than a-helix structure as inferred from equilibrium simulation. Specifically speaking, melting temperature for bbarrel conformation is 103K higher than a-helix conformation. (b)The interaction between CTD and NTD not only greatly stabilizes CTD by increasing its melting temperature(Tm, from 263K to 329K) but also improves its cooperativity significantly (Xc, from 100 to 482). However, NTD has the same stabilities even under the interaction with CTD and its folding cooperativity is compromised. (c)The a ! b transition approximately follows two-state kinetics and happens via three parallel pathways. In each pathway, the secondary structures form in different sequences. (d) The transition region is broad and the TSE resembles the a-helix and b-barrel structures almost to the same extent (hq‡ i 0:5). Therefore, the position of TSE is approximately centered along the a ! b transition in terms of both RMSD and q‡ . REFERENCES 1. Tsai CJ, del Sol A, Nussinov R. Allostery: absence of a change in shape does not imply that allostery is not at play. J Mol Biol 2008; 378:1–11.
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Molecular dynamics study on folding and allostery in RfaH Liqin Xiong and Zhenxing Liu* Department of Physics, Beijing Normal University, Beijing, 100875, China
ABSTRACT Upon being released from the N-terminal domain (NTD), the C-terminal domain (CTD) switches from a-helix conformation to b-barrel conformation, which converts RfaH from a transcription factor into an activator of translation. The afib conformational change may be viewed as allosteric transition. We use molecular dynamics simulations of coarse-grained off-lattice model to study the thermal folding of NTD, CTD, RfaH and the allosteric transition in CTD. The melting temperatures from the specific heat profiles indicate that the b-barrel conformation is much more stable than the a-helix conformation. Two helices in a-helix conformation have similar thermodynamic stabilities and the melting temperatures for b sheets show slight dispersion. Under the interaction with NTD, CTD is greatly stabilized and the cooperativity for thermal folding is also significantly improved. The afib allosteric transition can be approximately described by a two-state model and three parallel pathways are identified. The transition state ensemble, quantified by a Tanford b-like parameter, resembles the ahelix and b-barrel conformations almost to the same extent. Proteins 2015; 83:1582–1592. C 2015 Wiley Periodicals, Inc. V
Key words: SOP-sidechain model; thermal folding; melting temperature; allostery; transition state ensemble.
INTRODUCTION Allostery happens in all dynamic proteins1,2 and is essentially important to protein functions3,4 and to disease and drug discovery.5,6 Sequence-based7–9 or structure-based10,11 methods have been proposed to investigate the allosteric wiring diagram. Theoretical and simulation works were conducted to study the allosteric transition pathways.12–21 Among these studies, the involved conformational changes are either at small scales, for example, loop structure change in DHFR12,13,22,23 or at medium scales, such as helix reorientation in calmodulin’s N-terminal domain (NTD),14,15,24,25 domain displacements in adenylate kinase16–18,26,27 or at large scales, such as subunit movements in GroEL19,28–30 and in hemoglobin.20,21,31 In contrast to the previously studied allostery, where the secondary, tertiary and quaternary structures are only displaced by certain distances or angles and no significant structure unfolding is involved, RfaH’s CTD completely switches from a-helix to b-barrel structure, the magnitude of this conformational change is unprecedented.32 It is of great interest to study this most extreme structural transition example known to date.
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RfaH is a two-domain antitermination factor(CTD and NTD) and whether its CTD is in a-helix or b-barrel structure determines its very different functions.32–34 When CTD adopts a-helix conformation, RfaH acts as a transcription regulator as CTD is packed tightly against NTD, masking the RNAP interaction surface. It is proposed that binding of RfaH to operon polarity site of the nontemplate DNA strand triggers the CTD release from NTD35,36 and CTD spontaneously switches to b-barrel conformation, similar to RfaH’s paralog, the general transcription factor NusG.37 When in b-barrel conformation, RfaH’s CTD stimulates translation through
Abbreviations: CTD, C-terminal domain; FENE, finite extensible nonlinear elastic potential; MSM, Markov State Model; NTD, N-terminal domain; PDB, Protein Data Bank; REMD, replica-exchange molecular dynamics; RMSD, root mean square deviation; SOP, self-organized polymer; TS, transition state; TSE, transition state ensemble Grant sponsor: National Natural Science Foundation of China; Grant number: 11104015; Grant sponsor: Fundamental Research Funds for the Central Universities; Grant number: 2012LYB08. *Correspondence to: Zhenxing Liu, Department of Physics, Beijing Normal University, Beijing 100875, China. E-mail:[email protected] Received 9 February 2015; Revised 18 May 2015; Accepted 22 May 2015 Published online 29 May 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/prot.24839
C 2015 WILEY PERIODICALS, INC. V
Folding and Allostery in RfaH
recruitment of the S10 component of the ribosome to an mRNA that lacks ribosome binding site. Thus, switch from a-helix structure to b-barrel structure converts RfaH from a transcription factor into an activator of translation. The folding of RfaH has been studied by both experiments and theoretical approaches.32,38–40 Urea-denatured RfaH spontaneously refolds into its native structure where CTD is in a-helix structure and forms a tight interface with NTD.38 However, separately expressed CTD folds into b-barrel conformation.32 Targeted molecular dynamics and Markov state model (MSM) were used to study the mechanism of this conformational transition and parallel transition pathways are demonstrated.40 Despite these studies, in this article we will address the following questions: (a)Which conformation is more stable for CTD, a-helix or b-barrel conformation? b-barrel conformation seems to be the preferred conformation for CTD since for NusG protein family all other known CTD adopts b-barrel structure,41 we expect b-barrel conformation is more stable than a-helix conformation; (b)Is CTD stabilized by the interaction with NTD in the RfaH? (c) What are the nature of the kinetics and the pathways associated with a ! b transition? (d) What are the characteristics of the transition state ensemble (TSE) in the transition? We use molecular dynamics simulations of coarse-grained off-lattice model42,43 to address these questions.
METHODS SOP-sidechain model
The simulations were carried out using a coarsegrained model in which the previously introduced selforganized polymer (SOP) representation44 was augmented to include side chains (SCs).45,46 In the resulting SOP-SC model, which accurately accounts for packing effects, each residue is represented by two interaction centers, one that is located at the Ca position and the other is at the center of mass of the side chain. In the SOP-SC model the native state stabilization is achieved by accounting for backbone-backbone (bb), side chain-side chain (ss), and backbone-sidechain(bs) interactions. The energy (viewed as an effective free energy obtained by integrating over solvent (water) degrees of freedom) of a conformation, which describes the intrapeptide interactions, is EP ðfri gÞ ¼ VFENE 1VLJNAT 1V NEI 1VLJNN :
bb bs VFENE ¼ VFENE 1VFENE
¼2
N 21 X i¼1
2
N X k i¼1
2
ðri;i11 k 2 Ro log 12 2
Ro2 log 12
ðri;i
2 o bb 2ri;i11 bb Þ Ro2
o bs 2ri;i bs Þ Ro2
2
!
!
(2)
:
The non-bonded interaction, VLJNAT in Eq. (1), which accounts for the stability of the folded structures, is taken to be VLJNAT ¼ VLJbb NAT 1VLJss NAT 1VLJbs NAT " o 12 o 6 # N 23 X N X ri;j bb ri;j bb Dbb ¼ ebb 22 ij r r i;j bb i;j bb i¼1 j¼i13 " 12 o 6 # o N 23 X N X ri;j ri;j ss ss Dssij 1 ess jeij 20:7j 22 r r i;j ss i;j ss i¼1 j¼i13 " o 12 o 6 # N X ri;j bs ri;j bs Dbs 1 ebs 22 ij : ri;j bs ri;j bs i¼1;j¼1 ji2jj3
(3) If the distance between two noncovalently linked beads, rij ðji2jj 3Þ in the Protein Data Bank (PDB) structure is within a cutoff distance Rc, a native contact is formed and correspondingly Dij 5 1; if rij > Rc ; Dij ¼ 0. The strengths of non-bonded interactions ebb, ess, ebs are assumed to be uniform. The Betancourt–Thirumalai (BT)47 statistical potential matrix with elements ij, is used to explicitly treat the dependence of ss interactions on the side-chain type. We used repulsive interactions to account for excluded volume effects between neighboring beads with strength el. The ranges of repulsion are rbb ; ri;j ss ; rj bs for bb, ss and bs interactions respectively. The form of VNEI is bb ss bs V NEI ¼ VNEI 1VNEI 1VNEI 6 N 22 X rbb ¼ el ri;i12 bb i¼1 N 21 22 X ri;i11 ss 6 NX ri;i12 ss 6 1 el 1 el ri;i11 ss ri;i12 ss i¼1 i¼1 6 N X rj bs 1 el : ri;j bs i¼1;j¼1
(4)
0 and , ; < Qb34 >; < Qb45 > to dissect the order of events. The time-dependent changes of , [Fig. 3(C)] shows that the two helices almost finish unfolding within the time window for switching the conformational force ð33:600ls 33:617lsÞ. By fitting the relaxation kinetics to single or double exponentials, hQb12 i ¼ 0:706 12e 2t=97:7ls , hQb23 i ¼ 0:13010:699 ð12 2t=73:7l 0:37e 2t=1:1ls 20:63e2t=71:5ls Þ; hQb34 i ¼ 0:826 12e sÞ, hQb45 i ¼ 0:718 12e 2t=112:8ls [Fig. 3(D)], we think that b23 forms first, subsequently b34 folds, followed by the formations of b12 and b45. By integrating Figure 3(C,D), we conclude that the two helices rapidly unfold to random coil-like structure with a small portion of residual structures and then b sheets are gradually acquisited. By analyzing the 100 trajectories, we find that the transition happens through three parallel pathways (Fig. 4). In the dominant pathway [Fig. 4(A,B)], which accounts for 63% of the trajectories, the b-sheet formation sequence is b23, b34, b12, b45, which is the same as the picture exhibited in the ensemble average over all the trajectories [Fig. 3(D)]. In the second pathway [Fig. 4(C,D)], through which 23% of the trajectories fold, the b sheets b23, b12, b45, b34 form one after another. In the third pathway [Fig. 4(E,F)], representing 14% of the trajectories, transition occurs through the successive formations of b34, b23,b12, b45.
Transition state ensemble (TSE) centered along the transition
Using RMSD as a surrogate reaction coordinate, we assume the transition state (TS) is reached for the first time at tTS when jRMSD=aðtTS Þ2 RMSD=bðtTS Þj < ¼ 0:2A˚ . This criterion puts the TS equidistant to ahelix and b-barrel structures as far as RMSD is concerned. Although most transitions happen between 50 ls 200 ls, some transitions happen even around 300 ls and 500 ls [Fig. 5(A)]. The very broad distribution of transition time, P(tTS), also reflects the heterogeneity observed in the transition dynamics [Fig. 3(A)]. To quantify the position of TSE along the transition, we computed a Tanford b-like parameter q‡,19 using q‡ ¼
D‡ 2minðRMSD=bÞ ; maxðRMSD=bÞ2minðRMSD=bÞ
(13)
where D‡ ¼ ðRMSD=aðtTS Þ 1 RMSD=bðtTS ÞÞ=2, maxð RMSD=bÞ ¼ 24:2A˚ and minðRMSD=bÞ ¼ 1:1A˚ are the maximum and minimum values of RMSD=b, respectively. Thus, q‡ is in fact the normalized D‡ . If q‡ is close to 0(1), the most probable TS is similar to b-barrel(ato‡ 0.65 [Fig. helix) conformation. q‡ ranges from 0.35 ‡2 i2 ¼ 0:012, 5(B)] and the small fluctuation, r2 ¼ hq hqi2hq ‡ i2 shows that the TSE in CTD is conformationally restricted. Its fluctuation is significantly smaller than that for DHFR13 albeit with an extraordinarily large magnitude of conformational change. The peak position of the distribution, Pðq‡ Þ, is surprisingly at 0.5 and the average value of q‡ is also 0.5, which implies that the TSE resembles the a-helix and b-barrel conformations almost to the same extent. Therefore, the position of TSE is approximately centered along the a ! b transition as far as both RMSD and q‡ are concerned. PROTEINS
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Figure 3 (A)Time dependence of RMSD/a(solid lines) and RMSD/b(dashed lines) of several individual trajectories. The inset gives an example of one trajectory(blue lines) that has multiple crossings through the transition region. (B) Ensemble average of hRMSD=ai(black diamonds) and hRMSD=bi(red circles) over 100 trajectories. The solid line is exponential fit to hRMSD=bi relaxation kinetics. (C)Time dependence of hQa4 i(black line), hQa5 i(red line) and hQa45 i(blue line). (D)Time dependence of hQb12 i(black diamonds), hQb23 i(red circles), hQb34 i(blue stars), hQb45 i(dark cyan triangles). The solid lines are corresponding exponential fits to hQbij i relaxation kinetics. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
In experiment, U-values are used to describe the structure of the TS, specifically, the similarity of each residue in TSE with respect to that in the native state. Here, we compute the U-value for residue i with respect to a-helical CTD as: Uai ¼ hNNai i, where Ni is the number of native coni tacts formed between residue i and other residues in the a TS, Ni is the number of native contacts formed between residue i and other residues in a-helical CTD. This definition, that is, the ensemble average of the fraction of native contacts formed in TSE, is in fact equivalent to that used by Cho et al.57 and Uai are shown in Figure 5(C). Likewise, we compute Ubi ¼ h Nbi i[Fig. 5(D)]. Comparing Fig-
dominant TS (found in 79% of the transition trajectories), b23 and b34 are packed orthogonally as in the native state [structures in Fig. 5(B), Left]. The member of the other group of TSE (21%) has well-formed b12 and b23 [conformations of Fig. 5(B), Right]. The common features of the TSE is that the central b23 is well structured. Although simulations predict a single domi ‡ nant TS structure, diversity (assessed by P q or contact formation) in the TSE structures, which is hard to glean from experiments, points to the inherent plasticity of the TSE.
Ni
ure 5(C,D), we find that Ubi are mostly larger than Uai except for a few U-values of the residues near the two terminals. Thus, TSE is more similar to b-barrel structure than to a-helical structure in terms of U-value analysis. We classified the TSE structures into two groups according to their similarity to the native state. In the
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DISCUSSIONS To characterize the large-scale conformational change of CTD in RfaH, there are several issues which should be addressed, including the stability change, the kinetic
Folding and Allostery in RfaH
Figure 4 Three parallel pathways and corresponding structural features in allosteric transition. Representative trajectories for three pathways are given in the left column and average (black lines), (red lines), (blue lines), (dark cyan lines) over the trajectories belonging to the same pathway are shown in right column. (A,B) For the dominant pathway. (C,D) For the second pathway. (E,F) For the third pathway. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
processes and TSE. Facing with these aspects, our results are compared with the previous simulations by Gc et al.39 and by Li et al.40 The stability change
To study the stability change during the allosteric transition, we use molecular dynamics simulations of coarsegrained off-lattice model to obtain the melting temperatures of a-helical and b-barrel structures, which proves that a-helical form is indeed less stable than b-barrel structure. In Ref. 40, Li et al. reached the same
conclusion based on the unfolding times extracted from three implicit solvent all-atom MD trajectories. In fact, many more MD trajectories need to be generated in their simulations to extract the unfolding information because of the stochastic nature of the allosteric transitions. In Ref. 39 by GC et al. the stability change of CTD was also analyzed using the free-energy landscape. Since their study is based on implicit solvent REMD in atomistic details, the convergence would be worse than our coarsegrained model, which is indicated by the fact that in their simulations the a to b transition does not happen very frequently (only once in their selected replica) and PROTEINS
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Figure 5 Features of TSE. (A) Distribution of transition times P(tTS). (B) Distribution of Tanford b-like parameter q‡ ; Pðq‡ Þ. Superposition of a few structures of the dominant TSE cluster (Left) shows formation of b23 and b34. The other cluster(Right) has well-formed b12 and b23. (C) U-values with respect to a-helical structure, Uai . (D) U-values with respect to b-barrel structure, Ubi . [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
the conversion from b-barrel back to a-helical form is not observed. The kinetic processes
The kinetic processes of allosteric transition are generally described by the variation of the secondary structure elements and their interactions. From our simulated 100 transition trajectories which are hundreds of microseconds, we find that structural formation takes place clearly through multiple pathways. During the formation of the b-barrel structure, statistically, b23 forms first, subsequently b34 folds, followed by the formations of b12 and b45. The ensemble average of RMSD/b over 100 trajectories varies in a single exponential manner, which indicates the transition is cooperative, and the predicted transition timescale is about 129 ls.
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To investigate this dramatically large scale transition, Li et al. in Ref. 40 constructed MSM using both biased and unbiased implicit solvent all-atom MD simulations. Their biased MD simulations, including targeted MD simulations and high-temperature MD simulations performed at 370K, are used to identify the metastable states. Their unbiased MD simulations at 300K range from 150 ns to 1 ls, which is below the typical timescale of microseconds to milliseconds for large scale protein conformational changes, therefore they build MSM to determine the full ensemble of transition pathways. In the transition pathway determined by Li et al. b23 forms first, followed by the formation of b12, and finally b45 forms. Comparing their b-sheet formation sequence (b23, b12, b45) and ours (b23, b34, b12, b45), we identify b34 forms before b12 and therefore a fuller picture is provided. Their predicted transition timescale is
Folding and Allostery in RfaH
approximately 0.1s, which is much longer than the typical timescale of microseconds to milliseconds and is also in contrast to our predicted transition timescale 129 ls. These above differences between Ref. 40 and our study probably originate from different models and force fields and can only be tested experimentally. GC et al. in Ref. 39 also study the transition pathway using one replica of the implicit solvent REMD in atomistic details. The b-sheet formation sequence they proposed is b12, b23, b34, b45, which is very different from the results of Li et al.40 and ours. It is well known that the kinetics information is lost in REMD because of frequent exchanges of temperatures. Accordingly, the transition pathway and folding sequence in b-barrel structure is extracted from only a single replica of REMD. TSE
In our work, we study TSE of the a to b transition, which has not been investigated elsewhere. Using RMSD as a surrogate reaction coordinate, we locate TSE. The position of TSE along the transition is quantified by a Tanford b-like parameter q‡. We find that the position of TSE is approximately centered along the transition as far as both RMSD and q‡ are concerned. CONCLUSIONS We simulated the thermal folding of CTD, NTD, RfaH and the allosteric transition from a-helix to b-barrel conformation for CTD. Through these studies, we address the questions raised in the INTRODUCTION section: (a) For CTD, b-barrel structure is much more stable than a-helix structure as inferred from equilibrium simulation. Specifically speaking, melting temperature for bbarrel conformation is 103K higher than a-helix conformation. (b)The interaction between CTD and NTD not only greatly stabilizes CTD by increasing its melting temperature(Tm, from 263K to 329K) but also improves its cooperativity significantly (Xc, from 100 to 482). However, NTD has the same stabilities even under the interaction with CTD and its folding cooperativity is compromised. (c)The a ! b transition approximately follows two-state kinetics and happens via three parallel pathways. In each pathway, the secondary structures form in different sequences. (d) The transition region is broad and the TSE resembles the a-helix and b-barrel structures almost to the same extent (hq‡ i 0:5). Therefore, the position of TSE is approximately centered along the a ! b transition in terms of both RMSD and q‡ . REFERENCES 1. Tsai CJ, del Sol A, Nussinov R. Allostery: absence of a change in shape does not imply that allostery is not at play. J Mol Biol 2008; 378:1–11.
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