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Phosphorylation is one of the most commonly used signaling mechanisms in biology. However, the molecular transition pathways between inactive and active states are poorly understood. Here we quantitatively characterize the free-energy landscape of activation of the signaling protein Nitrogen regulatory protein C (NtrC) by connecting functional protein dynamics of phosphorylation-dependent activation to protein folding. We show that only a rarely populated, pre-existing active conformation is capable of being phosphorylated. Atomistic details of a pathway for the complex conformational transition, inferred from molecular dynamics simulations (Lei et al., 2009) is experimentally tested here by NMR dynamics experiments. We found that the loss of native stabilizing contacts during activation is compensated by non-native transient atomic interactions during the transition. The results demonstrate the power of combining computation with experimental corroboration to unravel atomistic details of native-state protein energy landscapes by expanding the energy landscape from the ground states to transition landscapes.
Proceeding from the original description of an energy landscape for a folded protein based on classical experiments on myoglobin by Frauenfelder and coworkers (Austin et al., 1975; Frauenfelder et al., 1991), this concept has been applied to protein folding expanding the conformational space from the native to the unfolded states (Dill and Chan, 1997; Dobson, 1998; Vendruscolo and Dobson, 2005; Wolynes, 2005). While the energy landscape idea is widely accepted for folding, it has only recently been embraced for protein function within the native state. Specifically, the existence of discrete conformational substates and resulting shifts of populations by binding of ligands, originally proposed for multi-subunit proteins (Monod et al., 1965) are likely to be a general paradigm for protein function (Boehr et al., 2006a; Boehr et al., 2006b; Henzler-Wildman and Kern, 2007; Kumar et al., 2000; Li et al., 2008; Mulder et al., 2001; Tsai et al., 2009)Lau and Roux, 2007; Ravindranathan et al., 2005; Yang et al., 2009).
This concept was proposed for the single-domain signaling domain of nitrogen regulatory protein C (NtrCr) where NMR analysis described a population-shift between an inactive and active substate by phosphorylation or activating mutations (Volkman et al., 2001). NtrC, a transcriptional activator, belongs to the family of “two-component systems”, the prototypical switch proteins in bacterial signaling (Stock and Guhaniyogi, 2006; Stock et al., 2000). The inactive to active conformational switch of the N-terminal domain (NtrCr) resulting from phosphorylation of D54 involves an extensive change in structure (Fig. 1A) (Kern et al., 1999). Activation through a shift in a pre-existing equilibrium between the inactive and active conformation rather than an induced fit mechanism has been proposed to be a more general mechanism for two-component signaling (Silversmith and Bourret, 1999; Stock and Guhaniyogi, 2006; Volkman et al., 2001) or even kinases in general (Buck and Rosen, 2001; Huse and Kuriyan, 2002).
The key subsequent questions are: How is the population shift achieved? How can a protein interconvert among folded substates but avoid unfolding at the same time? What are the molecular pathways for conformational transitions? Here we address these questions by connecting the energetics of functional protein dynamics within the native state to protein folding (Fig. 1). Through experimental corroboration of computational prediction (Lei et al., 2009), we infer a molecular pathway for the conformational transition in this signaling protein involving transient hydrogen bonds that stabilize the transition state.
To determine whether the population shift in NtrCr occurs through an inactive state destabilization, an active state stabilization, or a combination of the two (Fig. 1C), we measured the microscopic rate constants of the forward and reverse reaction (kIA, kAI, Fig. 1B) of the structural transition for nonphosphorylated inactive wild-type, partially active mutants D86N and D86N/A89T, and phospho-mimicking BeF3- bound (Hastings et al., 2003), fully active NtrCr. If mutation or phosphorylation yields a stabilization of the active state, the rate of active to inactive transition would decrease; conversely, a destabilization of the inactive state would result in an increase in the rate of inactive to active transition.
The rate constants were determined using NMR 15N backbone amide CPMG (Carr-Purcell-Meiboom-Gill) relaxation dispersion experiments (Palmer et al., 2001), providing dynamic information for each residue. For residues undergoing micro- to millisecond dynamics, the effective transverse relaxation rate, R2eff, is increased by an amount Rex in addition to the intrinsic relaxation rate (R20):
(in the limit of fast exchange, kex Δω).
The variation of Rex with an applied radio-frequency field (νCPMG) permits the CPMG dispersion experiment to quantitatively determine kinetics (exchange rate constant, kex = kIA+kAI), thermodynamics (populations pI and pA) and structure (chemical shift of exchanging species, Δω=ωA- ωI) for a two-state exchange process (Loria et al., 1999; Palmer et al., 2001), even for highly skewed populations (Mulder et al., 2001).
While non-phosphorylated and partially activating mutant forms of NtrCr revealed kex -values faster than 10,000 s-1 (Fig. 2A, B, C), the phospho-mimicking species reduced the rate constant of interconversion by an order of magnitude (Fig. 2D). From these experiments two qualitative inferences can be drawn. First, for all NtrCr forms, conformational changes are localized in the previously identified conformational switch region (Kern et al., 1999; Volkman et al., 2001); all such residues can be fit with a single exchange rate constant suggesting the measured motions correspond to a collective structural transition between the inactive and active substates. Second, considering that these mutations or phosphorylation shift the equilibrium towards the active substate, an increased exchange rate constant in the mutant forms relative to nonphosphorylated wild-type suggests a population shift by destabilization of the inactive substate whereas the decrease in exchange rate constant for phosphorylated NtrCr implies a strong stabilization of the active substate upon phosphorylation.
For a quantitative analysis of the energy landscape, the microscopic forward (kIA) and reverse (kAI) rate constants of the structural transition were determined. These rate constants are linked to the equilibrium constant (Keq=pA/pI=kr/kf), which is directly embedded in the population-weighted average resonance position (ωobs= pI·ωI + pA·ωA) for residues undergoing exchange. Consequently, if ωI and ωA are known, the equilibrium constant for each form can be directly extracted from its resonance position (Fig. 2E). However, the NMR resonance positions of wild-type and BeF3- activated NtrCr are not equivalent to the fully inactive and active substates as both forms exhibit conformational exchange (Fig. 2A, D). A combined fitting of relaxation dispersion and chemical shift data provided a molecular ruler of the equilibrium for all functional NtrCr forms and allowed extraction of kIA and kAI (Fig. 2E). The results strongly suggest that mutation mainly acts through destabilizing the inactive substate whereas BeF3- activation was found to drive the equilibrium almost fully towards the active substate solely by stabilizing the active form as evidenced by an identical kIA rate constant between inactive and active NtrCr (Fig. 5A).
Although these kinetic results indicate an energy landscape in which these NtrCr forms share the same transition state (Fig. 5A), a scenario in which the entire energy landscape is shifted along the energy axis for the mutant and/or BeF3- activated form relative to wild-type is theoretically possible. This would mean that the mutations and/or BeF3- activation would affect both the ground states and the transitions state. To address this issue, we depict the reaction coordinate describing the conformational transition within the folded state as energetically connected to a second reaction coordinate describing the folding/unfolding transition (Fig. 1C, Fig. 5A, B).
Unfolding kinetics for all NtrCr forms were measured by stopped-flow fluorescence at different GdmHCl concentrations, and the rate constant of unfolding under native conditions was determined by linear extrapolation to 0 M GdmHCl (Fig. 3A) (Fersht, 1999). The unfolding rate constants were found to be about eight orders of magnitude slower than those of the transition within the native state (Fig. 2, ,3A).3A). Consequently, for connecting these two energy landscapes through the measured energies, the free energy of the folded form can be treated as a population-weighted average of the inactive and active substates (Fig. 1C, ,5A).5A). Remarkably, the differences of the activation free energy of unfolding measured for wild-type, partially active mutants and phosphorylated NtrCr quantitatively agree with the corresponding changes in free energy extracted from the inactive/active substate kinetics (Fig. 3B). Through a quantitative analysis of two distinct reaction coordinates within the energy landscapes, we were able to validate the energetics underlying the population-shift mechanism (Fig. 5A, B). We want to highlight the quantitative agreement of the free energy difference for BeF3-activated NtrCr relative to inactive wild-type extracted from the inactive/active transition (Fig. 5A) with the one determined from the unfolding kinetics of P-NtrCr (Fig. 5B). This result validates BeF3- as a faithful phospho-mimic not only in structural terms (Hastings et al., 2003; Kern et al., 1999), but even in respect to the energy landscape of inactive/active interconversion.
The question of the effect of mutations on the ground- or transition-states has been extensively studied for protein folding, also known as Φ-value analysis (Fersht, 1999; Weikl and Dill, 2007) including the application of NMR relaxation dispersion experiments (Neudecker et al., 2007). There, changes in the energy landscape through mutations are depicted using the unfolded state as an energetic reference point. For NtrCr, the refolding rate contants of all forms are the same; however the unfolded state as reference point is no longer an assumption but rather a result derived from the connection of the folding landscape to the inactive/active conformational landscape through the measured energies (Fig. 5A, B).
The experiments described above reveal that the functional transitions in NtrCr occur rapidly while the energy barrier for unfolding is much larger. This situation is of course a general requirement for signaling and many other cellular protein functions. The immediate question that emerges is how a protein can rapidly interconvert among folded substates but avoid unfolding at the same time even though many native stabilizing contacts need to be broken during the transition? The answer is embedded in the actual molecular pathways of the conformational transitions. While the structures of the inactive and active substates could be experimentally determined since they represent minima in the energy landscape, structures along the transition pathway cannot be directly monitored in an experiment since they are not significantly populated. However, computational methods can in principle provide high-resolution information of these transition pathways. The challenge lies in current computational sampling times, which are too short relative to the typical microsecond to second conformational transitions in proteins. A variety of pathway methods have been developed to ameliorate this problem for which we cite only a few representative examples (Anthony et al., 2007; Bolhuis, 2008; Christen and van Gunsteren, 2008; Dellago and Bolhuis, 2007; Elber, 2005; Henzler-Wildman and Kern, 2007; Lei et al., 2009; Maragliano et al., 2006; Pan et al., 2008; Rogal and Bolhuis, 2008; Schlitter et al., 1994; Schutkowski et al., 1994; van der Vaart, 2006; Vendruscolo and Dobson, 2005; Yang et al., 2009), for more examples see references therein).
For NtrCr, transition pathways have been proposed using either coarse-grained models (Latzer et al., 2008; Pan et al., 2008; Vanden-Eijnden and Venturoli, 2009) or all atom simulations suggesting motions in the β3-α3 loop to be crucial for the transition (Hu and Wang, 2006; Khalili and Wales, 2008). Using all atom targeted molecular dynamics simulations (TMD) in explicit water, we predicted a different transition pathway between the active and inactive substates (Lei et al., 2009). TMD is a widely used biased molecular simulation method that generates conformational transition pathways through pulling the protein from a starting structure to an end structure via an RMSD (root mean square deviation) constraint to the end state (Banavali and Roux, 2005; Isralewitz et al., 2001; Karplus et al., 2005; Ma and Karplus, 1997; Schlitter et al., 1994; van der Vaart, 2006). Briefly, the conformational switch in NtrCr can be described by few major stages including a tilt, rotation, and register shift accompanied with a loss and gain of one half helical turn on opposite ends of helix 4 (Fig. 1A). Helix 4 is stable during the whole transition. The details of the computational analysis and the predicted pathway has been described (Lei et al., 2009).
The complex nature of this structural rearrangement (Fig. 1A) calls for either a pathway with partial unfolding (Latzer et al., 2008) or concerted conformational changes over a large area of the protein (Lei et al., 2009). Using simple native structure-based quadratic potentials, Latzer et al. estimated a barrier height for the activation transition of 54 kcal/mol (Latzer et al., 2008). From this result, they concluded that “protein cracking motions are involved”; i.e., that local unfolding in helix 4 is an essential part of the transition. This high barrier is in contrast to our experimentally determined barrier of only 6 kcal/mol for the activation (Gardino and Kern, 2007) (Fig. 2, ,55).
Biases and simplifications made in all computational algorithms, including our own simulations using biasing potentials (Lei et al., 2009) require stringent experimental testing. We therefore first measured the stability and rate of unfolding on a per residue basis using NMR (Fig. 3). While our fluorescence unfolding experiments determined a 109-fold difference in rate constants between the conformational switch and global unfolding (Fig. 3, ,5),5), these experiments do not rule out a transition pathway between the inactive and active conformation through partial unfolding of helix 4 particularly because the fluorescence markers Trp7 and Trp17 are not located in the conformational switch region. Notably, helix 4 was found to have the same stability as the remainder of the protein (Fig. 3C-E) and the NMR stability data agree with the fluorescence data (Fig. 3E, S5). Moreover, the rate constant of unfolding of residues in helix 4 is at least five orders of magnitude slower (Fig. 3C) than the conformational switch within the native state. We note that the performed stopped-flow fluorescence and NMR unfolding experiments were not intended to unravel the detailed pathway of unfolding, a question extensively studied for many proteins in the last decades, but rather aimed to energetically evaluate the native-state energy landscape including the predicted activation pathway. The NMR unfolding results rule out a pathway with partial unfolding (Latzer et al., 2008) and are qualitatively consistent with the computed pathway comprised of multi-step concerted rearrangements (Lei et al., 2009).
We then thought to directly experimentally test the computationally predicted transition pathway (Lei et al., 2009) by identifying several atomic interactions that might stabilize this pathway. We particularly sought energetically correlated events in the TMD trajectories. Breakage of two backbone hydrogen bonds at the C-terminal end of helix 4, resulting in a loss of half of a helical turn, seems to be energetically compensated by formation of a few transient hydrogen bonds including hydrogen bonds between the side chains of S85 and D86 at the top of helix 4 and between the side chains of Q96 and Y101 connecting the bottom of helix 4 and strand 5 (Fig. 4A, (Lei et al., 2009)). These non-native hydrogen bonds are present only during the transition but not in the active or inactive state. Finally two new main chain hydrogen bonds are formed between H84 and S85 adding a half helical turn to complete the helical register shift and thereby the transition to the inactive state (Fig. 4A).
To test the validity of this network of correlated motions during the transition, we disrupted these transient hydrogen bonds by mutagenesis (Fig. 4). Strikingly, replacing S85 with an aspartate resulted in a decrease in the rate constant of inactive/active interconversion from about 14,000 s-1 for wild-type to about 3,000 s-1 for this S85D mutant (Fig. 4C). Moreover, a mutation that restores the hydrogen bond donor capacity at position 85 (S85N) restores the fast interconversion rate of wild-type (Fig. 4D). The decrease in rate in S85D is not due to the introduction of a charge, since S85G produces the same slow rate as S85D (Fig. 4E). Importantly, the spectra of S85D, S85G and S85N are almost identical to the wild-type spectrum (Fig. S 6). This indicates that both the structures and the relative population of the inactive and active states are not altered. This result is further buttressed by 20 ns MD simulations of both mutant forms in the inactive and active states (Fig. S7). Furthermore, TMD simulations for both mutant forms reveal the same transitions stages as the TMD simulation on the wild-type protein, however, without the transient non-native hydrogen bonds between S85 and D86.
We infer that the transient hydrogen bond between S85 and D86 lowers the activation barrier of the slowest step in the overall conformational transition by about 1 kcal/mol. Finally, the identical unfolding rates for wild-type and S85D complete the quantitative description of the energy landscapes by identifying this hydrogen bond as affecting only the free energy of the transition state (Fig. 5 and Fig. S6).
The concept that non-native hydrogen bonds reduce the barrier for this complex conformational transition is buttressed by additional experiments that disrupt the hydrogen bond between Q96 and Y101. Both Y101F and Q96N mutations significantly decrease the interconversion rate constant (Fig 4F, G). The reduction of the interconversion rate constant by shortening the side-chain of the hydrogen bond acceptor (Q96N mutation) reveals that in addition to the presence of the hydrogen bond acceptor/donor pair, a quite specific distance between them is required.
Removal of both transient hydrogen bonds do not further decrease the interconversion rate constant (Fig. 4H) suggesting that they influence the free energy of the system at slightly different parts of the transition pathway. These experimental results further demonstrate the complex multidimensional nature of the transition energy landscape. We note that the described experiments do not allow characterization of the entire complex pathway, however, they provide critical information about structural configurations that are not only along the pathway but also influencing the energy of the transition states. Thus they serve as key starting points for further extensive unbiased computational exploration of the multidimensional energy landscape, which is beyond our current scope and in fact beyond current methodology. We feel that direct experimental testing of computational predictions, which is done in this work, is the strongest validation of simulations.
The concept of preexisting equilibria within the folded state and their roles in biological function such as enzyme catalysis, signaling and ligand binding has become widely accepted (Monod et al., 1965) (Boehr et al., 2006a; Boehr et al., 2006b; Frauenfelder et al., 1991; Henzler-Wildman and Kern, 2007; Henzler-Wildman et al., 2007; Kumar et al., 2000; Li et al., 2008; Silversmith and Bourret, 1999; Stock and Guhaniyogi, 2006; Volkman et al., 2001) (Lau and Roux, 2007; Ravindranathan et al., 2005; Yang et al., 2009). We now show that rare excursions to the active conformation are essential for activating this signaling protein, since the data suggest that only the higher-energy active conformation can be phosphorylated. This is supported structurally by the solvent-inaccessibility of D54, the site of phosphorylation, in the inactive conformation. While our earlier work indicated that activation is mediated via a shift in preexisting populations, we have now characterized the underlying molecular mechanism. Such a selective binding to a lowly populated conformation, that is usually “hidden” to traditional structural methods, may be a general mechanism for other kinases (Buck and Rosen, 2001; Huse and Kuriyan, 2002) or even more general for ligand binding (Henzler-Wildman and Kern, 2007; Li et al., 2008).
Second, we shed light into possible mechanisms of how proteins can efficiently change conformations that require complicated realignment of multiple atomic contacts while avoiding unfolding. The marriage between experiment and computation has provided a glimpse into molecular pathways of interconversion, thereby expanding the energy landscape from the ground states to “transition landscapes”. The signaling protein NtrCr has apparently solved the problem of stability in the face of loss of native stabilizing contacts during activation through fine tuned concerted motions. This results in a roughly “isoenergetic” transition involving non-native transient atomic interactions that are used to “hold on” to the free energy until the final new native contacts of the active state are built, thereby circumventing the risk of unwanted unfolding during the transition. Our results on NtrCr illustrate sophisticated “designer” principles in proteins through the multifaceted use of specific atoms guaranteeing not only one stable folded structure, but also efficient interconversion among functionally essential ensembles of structures. We acknowledge that the list of transient atomic interactions identified and experimentally tested here for NtrCr is by far not complete, however, the concept of non-native interactions lowering the energy barrier may help to improve the current limited success in design of protein function, such as enzyme catalysis, drug binding and protein/protein interactions.
Unlabeled and uniformly 15N-labeled NtrCr wild-type, mutant forms, phosphorylated and BeF3- activated NtrCr was prepared as previously described (Hastings et al., 2003; Volkman et al., 2001). All NMR samples were 0.75mM NtrCr in 50 mM NaP buffer, pH 6.75 with 10% D20.
TROSY 15N CPMG relaxation dispersion experiments (Loria et al., 1999; Mulder et al., 2001; Palmer et al., 2001; Tollinger et al., 2001) were acquired on a Varian Inova 600 and a Bruker Avance 800 spectrometer equipped with a cryoprobe at 298K with constant time T2 delays between 60 and 70 ms which roughly yielded 55% of residual signal intensity, and CPMG field strengths between 28 and 1000 Hz. The data were fit as described (Henzler-Wildman et al., 2007). The method to determine the exchange-free transverse relaxation time (R20, νCPMG→∞) and its usage in the global fits of the relaxation dispersion data are described (Gardino and Kern, 2007). 15N R1 values were measured using standard experiments (Farrow et al., 1994). R1H values were measured using a TROSY-based R1HzNz pulse sequence (L.E. Kay, personal communication) employing a reburp pulse to selectively invert the amide region. Data was processed using NMRPipe (Delaglio et al., 1995). Intensities were fit to a mono-exponential decay curve, and uncertainties were measured from duplicate points and an estimate of signal-to-noise (2% of R2eff).
Final active state populations (pA) for each functional form of NtrCr were determined through the following equation:
where δexp is the experimental chemical shift value in the indirect dimension (15N) taken from a 2D 1H-15N correlated HSQC NMR spectrum, δI,calc is the calculated endpoint representing the fully inactive chemical shift value, and δΔω,calc is the calculated difference in chemical shift between the inactive (δI,calc) and active (δA,calc) state endpoints. While δexp can be directly read out from the HSQC spectra (Fig. 2E), δI,calc and δA,calc are not known since the chemical shifts of both wild-type and BeF3- activated forms do not represented the true endpoints. The difference in chemical shift between wild-type and BeF3- activated NtrCr however provided a lower limit of Δω. Only extremely skewed populations of BeF3- NtrCr (pA≥0.994) yielded chemical shift differences (Δω) on a per residue basis that were large enough to fit the experimentally observed displacements. Incorporation of CPMG dispersion of wild-type, BeF3- activated, D86N and D86NA89T NtrCr together with the corresponding chemical shift changes (Fig. 2E), which also emulated their respective activities (Volkman et al., 2001), then allowed us to estimate the relative populations of active and inactive states for each NtrCr form (see supplemental data, table S1). A good correlation was found between the experimentally observed amide backbone chemical shift position for D88 and other residues with the calculated populations computed for the wild-type and mutant forms of NtrCr. In addition, Δω values fitted from the CPMG dispersion showed good agreement among different NtrCr forms for residues that are not locally perturbed in chemical shift due to the proximity of either BeF3- or mutation (see supplemental data, table S1). For the BeF3- activated form and the transition-state mutant forms (S85D and Y101F), global fitting of the CPMG data collected at 600 MHz and 800 MHz was possible because the exchange in these proteins is in the time regime in which Rex can be sufficiently suppressed with the imparted νCPMG field strength. Global fitting data from two external magnetic field strengths further confirmed the exchange rate constants and populations (Fig. S1).
Unfolding kinetics were measured at 298K by stopped-flow fluorescence or discontinuously for P-NtrCr by mixing protein stock solution with GdmCl in a 1:1 ratio to a final concentration of ≥ 3.2M denaturant and 5μM protein. The sample was excited at 281nm and emission measured using a 320nm long-pass filter. Sequential stopped-flow was used to measure the rate constants of folding in order to overcome the slow phase due to cis/trans prolyl isomerization (Fig. S2). 250μM NtrCr was mixed 1:1 with denaturant to a final concentration ≥ 3.2M for 10 sec followed by a 1:1 mixing with buffer yielding a final denaturant concentration between 1.6-2.0M and a 62.5μM final protein concentration. An average of 10 (unfolding) and 30 (folding) scans were best fit to single exponentials.
Unfolding of wild-type NtrCr by NMR at 298K was measured by 15N-HSQC's at various GdmCl concentrations and the decrease in the peak intensities of the folded form, corrected for the effect of ionic strength on the peak intensity, were fit to a sigmoidal curve to determine the stability of each residue (Fig. S3-5).
For visualization of the experimentally determined kinetic and thermodynamic values in form of an energy landscape, changes in free energies were calculated from the ratio of the rate constants. The differences in free energies between the inactive and active substate for wild-type were calculated according to ΔG = -RTln(kIA/kAI). Changes of the free energies of mutant forms and BeF3- activated NtrCr relative to wild-type were then determined from the changes in the microscopic rate constants of the interconversion process (kIA, kAI) using the following equation according to standard transition state theory assuming an identical pre-exponential factor for the wild-type and mutant forms: ΔΔG‡,IACPMG= -RTln(kIA,wild-type/kIA,mutant, BeF3-) and ΔΔG‡,AICPMG = -RTln(kAI,wild-type/kAI,mutant,BeF3-) where R is the universal gas constant.
We then set the population weighted average of the free energy of wild-type to zero. Changes in the free energies of the native state of the mutant forms relative to wild-type could then be determined by comparing the population averaged free energies (ΔΔGCPMG).
The energy landscape derived from these calculations was quantitatively verified by determining the changes in unfolding rate constants that consequently reflect the changes in the free energies of the folded states. The same equations were used to determine the differences in the free energies of unfolding: ΔΔG‡unfolding = -RTln(kuwild-type/kumutant,BeF3-). We note that the absolute values of ΔG‡ IA and ΔG‡unfolding depend on the pre-exponential factor for which we used a value described in the literature for protein folding (106 s-1) (Kubelka et al., 2004). However, for the important comparison of energy changes between different forms of NtrCr (ΔΔG), it is reasonable to assume very similar pre-exponential factors among the NtrCr forms for each separate process, in which case they are canceling out as assumed in the equation above. The strong agreement of the ΔΔG values determined from the inactive/active transition within the folded state and the ΔΔG values determined from unfolding validates this assumption.
MD and TMD simulations were performed in explicit solvent, with TIP3P water molecules (Price, 2004), using the simulation program CHARMM (Brooks et al., 1983) version c31b1 with the all atom force field C22 (MacKerell, 1998) and the CMAP correction for the protein backbone dynamics (MacKerrell et al., 2004) as described in (Lei et al., 2009).
We thank Dr. Martin Karplus for a fruitful collaboration and helpful discussions in the computational studies that led to the predicted pathway, Dr. Chunyu Wang at Columbia University for providing us with a pulse sequence to measure Rex in large proteins and for helpful discussions, Dr. Lewis E. Kay at the University of Toronto for the R1HzNz pulse sequence, and Dr. Jack Skalicky at the NHMFL at Florida with support from NSF for NMR time. This work was supported by the Howard Hughes Medical Institute, NIH grants to D.K. (GM62117 and GM67963), a DOE grant to D.K (DE-FG02-05ER15699) and by instrumentation grants by the NSF and the Keck foundation to D.K.