Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints

Diego del Alamo; Kevin L. Jagessar; Jens Meiler; Hassane S. Mchaourab

doi:10.1371/journal.pcbi.1009107

Abstract

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å C_α RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.

Author summary

Proteins transition between different conformations during function. Double Electron-Electron Resonance (DEER) spectroscopy enables the direct observation of structural rearrangements that underpin these transitions. Typically, histograms of distances between spin labels, called distance distributions, are measured under different conditions. Structural rearrangements that underlie conformational transitions are manifested by changes in the averages and widths of the distance distributions. To transform these distance distributions into restraints for modeling alternate protein conformations, we developed an algorithm in the modeling suite Rosetta for direct analysis of DEER primary data that yield the optimum ensemble of spin label positions in space, referred to as rotamers, that account for the data. We benchmarked the effectiveness of this algorithm using experimental data collected in two proteins, the model system T4 Lysozyme and the multidrug transporter PfMATE in an outward-facing conformation. We then used optimized spin label rotamers to model the inward-facing conformation of PfMATE from the starting outward-facing conformation. Our results demonstrate substantial improvements in both precision and accuracy among the resulting models. Further improvement of this strategy will enable modeling of protein conformational changes involving complex modes of movements.

Citation: del Alamo D, Jagessar KL, Meiler J, Mchaourab HS (2021) Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints. PLoS Comput Biol 17(6): e1009107. https://doi.org/10.1371/journal.pcbi.1009107

Editor: Turkan Haliloglu, Bogazici University, TURKEY

Received: February 28, 2021; Accepted: May 24, 2021; Published: June 16, 2021

Copyright: © 2021 del Alamo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files. The RosettaDEER multilateration algorithm is included with the Rosetta software suite.

Funding: This research was supported by the National Institutes of Health (NIH, www.nih.gov; HSM: GM077659; JM: GM080403 and GM073151) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, www.dfg.de; JM: SFB1423, project number 421152132, subproject A07 and Z04). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

This is a PLOS Computational Biology Methods paper.

Introduction

Distance measurements between pairs of spin labels by Double Electron-Electron Resonance (DEER) spectroscopy have been utilized extensively to investigate the structures and dynamics of proteins[1–4] and the assembly of protein-protein complexes[5–8]. At the fundamental level, DEER measures magnetic dipolar coupling to infer the distributions of distances between two or more spin labels[9,10]. A two-step process typically interprets these distances as spatial restraints describing the protein backbone structure. First, the echo-decay time traces are transformed into distributions consisting of distance components characterized by a mean and width[11–15]. Second, these distributions are compared to those predicted using one of several strategies, ranging from generic rotamer libraries[16–18], explicitly modeled pseudoatoms[1,19,20], or explicitly modeled spin label side chains[21–27]. However, these strategies tend to overestimate the dynamics of flexible probes such as the commonly used methanethiosulfonate spin label (MTSSL). Therefore, the predicted distributions are broad relative to the experimental ones[18,20,28–31], which hinders DEER-based evaluation of protein structures or complexes as well as mapping of protein conformational changes. The latter can be obscured entirely if modeled distribution widths exceed distance changes observed between spin labels[1]. Another layer of complications in modeling of conformational changes arises if the ensemble of spin label rotamers is allowed to reconfigure, hence providing a low energy pathway to account for changes in distance distributions that originate from backbone movements. Collectively, these caveats limit the accuracy and precision of molecular models generated from DEER restraints.

Several algorithms have recently been developed to refine ensembles of spin label rotamers by employing multilateration[16,32–36]. Multilateration refers to the determination of an object’s position in three-dimensional space given its distance from a constellation of points; common applications include the positioning of electronic devices using the Global Positioning System and of earthquake epicenters using time-of-arrival data[37]. To utilize this approach to position spin label rotamers requires both a high-resolution starting structure and a set of DEER distance data consistent with that structure. However, a unique challenge in this endeavor is that spin labels are flexible relative to the protein backbone. As a result, the ensembles characterizing their positions must be refined simultaneously for all spin labels in a given protein model.

Molecular dynamics simulations have been used to determine a set of optimized rotamers from explicitly modeled spin labels restrained by experimental distance distributions[14,21,38,39]. Alternatively, rotamer libraries have been precomputed and reweighed using either Monte Carlo[32,35], singular value decomposition[34], or nonlinear least-squares minimization[33]. The positions of these labels can, in turn, be used to more precisely locate paramagnetic ligands or metal ions[35,36,40,41], as well as make small-scale refinements to protein structures[16,42]. To our knowledge, however, none of these methods have demonstrated that these optimized rotamers can lead to improvements in modeling conformational changes.

Furthermore, these methods generally do not address unique factors confounding multilateration of spin labels. First, the width of a distribution reflects disorder in the solid state as a result of backbone and spin label side chain dynamics at room temperature. Existing multilateration methods generally ignore the former, by assuming the distribution is explained entirely by spin label dynamics[16,35], or both, by extracting the peak distance from the distribution and discarding the width[42]. Second, relying on distance distributions rather than time domain data propagates assumptions intrinsic to the method used for the transformation of the latter[10,14]. Depending on the noise level of the experimental measurements, this step can distort true components or introduce ghost components to the distribution. Finally, although DEER distributions are often reported with confidence bands to reflect the uncertainty inherent to this transformation[14,15,43], they are generally taken at face value when used for rotamer multilateration. This incorrectly implies that experimental uncertainty is uniformly distributed across the dataset and can lead to rotamers that over- or underfit the DEER distributions. Collectively, these obstacles prevent the positioning of spin label ensembles in three-dimensional space and complicate the confidence with which such ensembles can be used for subsequent modeling purposes.

To address these issues, we developed and implemented, as part of the RosettaDEER module[20], an algorithm that combines rotamer multilateration[33,35,41] for pairs sharing common spin labeling sites with direct analysis of DEER time traces. The algorithm calculates a weighted distribution of “pseudo-rotamers”, or inflexible coarse-grained side chains, capable of recapitulating large experimental datasets collected using DEER. Importantly, this algorithm goes beyond comparable methods by refining these ensembles using raw data in the time domain, rather than distance distributions calculated a priori, thus avoiding the loss of information that can occur as result of data transformation. Using experimental data collected in the model system T4 Lysozyme and the multidrug transporter PfMATE, we demonstrate that this algorithm is able to fit time domain data as effectively as widely-used DEER data analysis programs. Integrated with Rosetta, these rotamers ensembles yield substantial improvements in both accuracy and precision of modeling the outward-to-inward isomerization of the multidrug transporter PfMATE, thus reinforcing the notion that coupling analysis of primary data with rotamer optimization is a superior approach for restrained modeling of protein conformational states.

Results and discussion

Overview of the multilateration algorithm

The algorithm capitalizes on the concept of pseudo-rotamers, which are simplified representations of the spin label designed to maximize computational efficiency[20]. A pseudo-rotamer models the spin label side chain as a centroid atom representing the nitroxide ring and its unpaired electron, yielding predicted distance distributions that are comparable to full-atom depictions. Unlike explicit depictions of the spin label used in all-atom simulations, ensembles of pseudo-rotamers do not interact with one another; as a result, the dynamics of spin labels close in space are fully independent. However, in principle, any rotamer library can be used for the multilateration strategy described here[17,18,22,26,27,30].

The transformation of DEER data to distance distributions is an ill-posed mathematical problem necessitating the use of either regularization[15,44,45], parametric modeling[13–15], neural networks[46], or other methods[11,43,47,48]. Because these methods have intrinsic approximations which could interfere with rotamer ensemble determination, we elected to fit the raw experimental data directly using an iterative simulated annealing strategy that 1) measures all pairwise distances between pseudo-rotamers, 2) converts each distance distribution into a DEER decay, and 3) calculates the intermolecular dipolar coupling contribution by nonlinear least-squares minimization. Different levels of noise between DEER traces linked by multilateration were normalized using estimates obtained from each signal’s corresponding imaginary component[21]. The algorithm prioritized the generation of parsimonious ensembles by minimizing the total number of pseudo-rotamers with nonzero weights using the Akaike Information Criterion-corrected (AICc)[49,50]. This metric, which allows for regularization in rotamer space rather than the distance domain, was guided by the heuristic that the flash-freezing process sharpens the distribution of rotamers that contribute to the DEER signal[51,52]. Finally, to account for backbone heterogeneity and the expectation of smoothness in the distance domain, simulated distributions were broadened by a magnitude corresponding to the residues’ intrinsic flexibility, as reported by their respective crystallographic B-factor values[53,54].

Data analysis benchmark

We benchmarked this method using experimental DEER data collected in two model proteins, T4 Lysozyme[31,55] (PDB: 2LZM) and the MATE multidrug transporter PfMATE[56–58] in its outward-facing conformation (PDB: 6GWH). The extracellular and intracellular spin label pairs of PfMATE were treated independently since they did not share residues in common. These three DEER datasets consisted of 65 restraints between 47 residues; a subset of the restraints in T4 Lysozyme is shown in Fig 1A. We note that unlike the benchmarks used in other multilateration methods, these restraints were highly interconnected; half of the residues were spin labeled in three or more DEER pairs, and in the most extreme case, two residues in T4 Lysozyme were spin labeled across seven pairs (S1 Fig). For each of the three datasets, the RosettaDEER multilateration algorithm was executed for 1000 replicas, with each replica yielding refined pseudo-rotamer ensembles at every spin labeled site.

Download:

Fig 1.

A) Distribution of pseudo-rotamers, shown as spheres, at four representative residues in T4 Lysozyme prior to (top, gold) and following (bottom, teal) refinement by multilateration. A flow chart detailing the iterative steps of pseudo-rotamer refinement using RosettaDEER is shown between the two T4L structures. B) Five representative DEER traces in T4 Lysozyme used for multilateration, alongside simulated DEER traces prior to (yellow) and following (teal) refinement. Insets: Simulated DEER distributions following pseudo-rotamer refinement alongside reference distributions with 95% confidence bands (calculated using GLADDvu and shown in grey). C) Goodness-of-fit evaluated from the RMSD between simulated and experimental DEER traces comparing RosettaDEER to other analysis programs.

https://doi.org/10.1371/journal.pcbi.1009107.g001

We compared the resulting fits to those obtained using GLADDvu[14], DeerAnalysis[44], and DeerNet[46], which are programs that analyze DEER data using Gaussian mixture models, Tikhonov regularization, and feed-forward neural networks, respectively. Although other analysis methods are available, we believe these represent a sufficiently diverse range of analytical approaches for the purposes of comparison. We found that the optimum rotamer ensembles, selected by the AICc, could recapitulate the experimental DEER traces as effectively as each of these programs (Figs 1B, 1C and S2–S5 and S1–S3 Appendices). The mean squared errors obtained by the best fit were not statistically different from those obtained by any of these three methods, or from the noise estimated from the imaginary component (Student’s paired one-tailed t-test with Bonferroni correction). However, unlike the latter methods, the interconnectedness of the spin label pairs allowed our algorithm to couple pseudo-rotamer parametrization to the analysis of DEER data in the time domain.

Distance distribution benchmark

We anticipated that the analysis of DEER data by multilateration would yield distance distributions similar to those obtained using traditional methods. Consistent with this expectation, distributions between refined pseudo-rotamers in both T4L and PfMATE showed remarkable agreement with those obtained using the three methods mentioned above (see Figs 1B insets for examples and S3–S5 Figs for all distributions). For example, the average values of these distributions were within 0.5 Å of those obtained using GLADDvu for 60 of the 65 restraints (Fig 2A). Additionally, the widths of 52 of these restraints were within 0.5 Å of those obtained using GLADDvu. Discrepancies occurred for broad distributions or long distances (because the information content in the time domain is not as well-defined) or components less than 15 Å (because these distances minimally contribute to the DEER signal). Additionally, we uncovered differences when comparing the widths of these distributions to those obtained using DeerAnalysis, likely resulting from small “ghost” side peaks frequently observed in regularization. Discrepancies were also observed when comparing these distributions to those obtained using DeerNet, which yielded widths clustered between 2.5 and 4.5 Å (S6 Fig).

Download:

Fig 2.

Evaluation of average distances (A) and distribution widths (B) between pseudo-rotamers prior to (top) and following (bottom) refinement by multilateration. T4 lysozyme distributions omitted from multilateration are shown in light green. C and D) Boxplots showing the difference between values obtained using GLADDvu and values simulated between pseudo-rotamer ensembles prior to and following refinement.

https://doi.org/10.1371/journal.pcbi.1009107.g002

Finally, the uncertainty of these distributions was calculated from the five pseudo-rotamer ensembles with the lowest AICc values. The resulting confidence bands, which capture 95% of the variation in the distance distributions, are qualitatively comparable to those obtained using GLADDvu, DeerAnalysis, and DeerNet (S7 Fig).

To further validate the algorithm, we simulated distance distributions for six T4L spin label pairs which were excluded from the multilateration dataset. We observed that the median error between the average distance values fell by 50% (Fig 2; full distributions shown in S8 Fig) using the refined rotamers. By contrast, the standard deviations did not significantly sharpen, and their values are similar to those observed prior to refinement. Notably, the uncertainty of these distributions is greater than those of the distributions included in the training set.

Modeling of PfMATE’s conformational changes using refined pseudo-rotamers

While the results above demonstrate the robustness of the multilateration algorithm in identifying optimal spin label pseudo-rotamer ensembles, the central question is whether these provide superior restraint quality for modeling conformational changes. To address this question, we modeled the isomerization of PfMATE between outward- and inward-facing conformations[56,57] (OF and IF, shown in Figs 3A and 3B, respectively), both of which were determined by x-ray crystallography. The two conformations differ primarily in the relative orientations of the N- and C-terminal domains resulting from changes in the backbone dihedral angles of transmembrane helix 7 (TM7). Of direct relevance to the question addressed here, distance distributions between pairs of spin labels measured at pH 7.5 and pH 4.0 were shown to be consistent with the OF and IF conformations, respectively[58].

Download:

Fig 3. Modeling the outward-to-inward conformational change in the multidrug transporter PfMATE.

(A) Outward-facing and (B) inward-facing crystal structures of PfMATE. N- and C-terminal domains are shown in purple and green, respectively, and TM7 is shown in red. (C) RMSD values of the ten best-scoring models for each of four sets of restraints relative to the inward-facing conformation using either pseudo-rotamers refined by multilateration (teal) or unrefined pseudo-rotamers available by default (yellow).

https://doi.org/10.1371/journal.pcbi.1009107.g003

We generated several thousand models, using Rosetta[59] without DEER restraints, by perturbing TM7 and found that none of the built-in membrane protein scoring functions[60–63] could identify the inward-facing state by score alone (S9 Fig and S4 Appendix) even if it was included in the initial model set. Thus, from a Monte Carlo modeling perspective, the OF-to-IF conformational transition can be sampled, but not necessarily identified, without experimental data.

To test the notion that DEER restraints interpreted with the refined pseudo-rotamers can drive convergence of Rosetta modeling, we identified spin label pairs where the EPR lineshape showed minimal changes upon a pH shift from 7.5 to 4.0 (see ref. [58] for all data), supporting the approximation that the spin label rotamer ensembles are invariant and thus were not allowed to reconfigure during Rosetta modeling. From these pairs, 40 sets of restraints were generated, each of which consisted of one to ten spin label pairs (S1 Table). Using scoring functions to assess the agreement with the DEER restraints (see Materials and Methods), the OF-to-IF conformational transition was modeled by perturbing the dihedral angles of TM7. DEER distributions were simulated using either the pseudo-rotamers ensembles refined by multilateration or the unrefined ensembles available to RosettaDEER by default. Agreement with the experimental distributions was evaluated by the overlap between the experimental and simulated distance distributions. Similarity to the inward-facing crystal structure was quantified by the root mean squared deviation (RMSD) of the alpha carbons excluding TMs 1 and 7.

We observed a striking contrast between the effectiveness of the refined and unrefined ensembles (Fig 3C and S4 Appendix). The default rotamer library did not effectively improve the average RMSD of the ten lowest-scoring models beyond 2.0–3.5 Å. By contrast, the use of multilaterated pseudo-rotamers converged upon inward-facing models with a 1.5–2.5 Å C_α RMSD using restraints obtained from the same spin label pairs.

Alongside these improvements in accuracy, the sharper range of RMSD values among these models suggested that multilateration improved model precision. Distributions of representative distances across the intracellular and extracellular sides of the top ten models (Figs 4A and 4B) revealed that, when using the default pseudo-rotamers, a majority of these models failed to close the extracellular cavity and were far less inward-open than the crystal structure (Fig 4C), even when ten restraints were used. By contrast, the best-scoring models obtained using refined pseudo-rotamers deviated less drastically from the crystal structure. Nonetheless, these models were virtually all less inward-open than the crystal structure, consistent with shorter-than-expected experimental DEER measurements on the intracellular side at pH 4.0[58] (Fig 4D).

Download:

Fig 4. Models of PfMATE obtained using multilaterated rotamers more closely resemble the inward-facing crystal structure than those obtained using default rotamers.

Deviation between C_α-C_α distances observed between representative pairs of residues on the A) extracellular and B) intracellular sides of the crystal structure (PDB: 6FHZ) and the corresponding distances predicted from each of the best-scoring models. (C and D) Best-scoring inward-facing models of PfMATE obtained using ten restraints either with pseudo-rotamers available by default (left) or with those refined by multilateration (right). Inward-facing crystal structure shown in black. Ribbon thickness corresponds to the C_α root mean squared fluctuation among the top ten models. Bottom: The best-scoring models obtained using default rotamers (left) were less inward-open than those obtained using multilaterated rotamers (right).

https://doi.org/10.1371/journal.pcbi.1009107.g004

Concluding remarks

Our results highlight a general strategy to substantially improve the quality of models obtained from EPR restraints. We envision that the main application of this strategy is to model alternate conformational states starting from an experimental structure and a set of interconnected DEER data. By implementing this algorithm in Rosetta, we hope to encourage its use for a wide variety of modeling applications, such as protein-protein docking and de novo folding. Moreover, further development of this approach, as well as extensive use of multilateration in the design of spin label pairs, will open the door to modeling proteins where conformational changes are defined by more complex modes of motion.

Materials and methods

Overview of the model-based approach

The objective of the RosettaDEER multilateration algorithm is to fit a set of DEER data by weighting the nitroxide pseudo-rotamers available to each spin-labeled residue in a protein structural model. Each replicate of the algorithm independently generates a unique set of pseudo-rotamer ensembles for each spin-labeled residue. For clarity throughout this text, we will refer to these outputs as "coordinate models", to differentiate them from the starting structural models. The space accessible to the unpaired electron of each residue’s spin label is divided into fifty discrete pseudo-rotamers, which are shown as small spheres in Fig 1A. RosettaDEER then identifies and removes pseudo-rotamers that clash with the protein backbone. Each residue’s ensemble of pseudo-rotamers represents a probability density function of the space accessible to the unpaired electron of that residue’s spin label. As a result, following refinement using this algorithm, the weights of a coordinate model’s pseudo-rotamers for any given residue are tightly coupled to those of other residues.

In this study we focus our attention on coordinate models with high parsimony. For example, coordinate models capable of recapitulating DEER traces using only one pseudo-rotamer per residue are prioritized over those with two or more. However, if the DEER trace indicates a broad and multimodal distribution, additional pseudo-rotamers may be necessary to improve the goodness-of-fit. The total number would ideally be no greater than the minimum required to fit the data, and multiple combinations of pseudo-rotamers may be equally consistent with the data. We identified parsimonious coordinate models using the Akaike Information Criterion-corrected (AICc)[49,50,64]: (1)

This metric balances two competing objectives of 1) fitting the experimental data as well as possible and 2) simplifying the model as much as possible. The leftmost term, goodness-of-fit, is expressed as the maximum likelihood estimate of the coordinate model with parameters θ given the experimental DEER data D and is described below. The middle and rightmost term express the complexity of the model, with the variable K corresponding to the total number of parameters in the coordinate model and n_total corresponding to the total number of time points in the experimental DEER data. K includes the number of pseudo-rotamers with nonzero weights, as well as the number of parameters required to fit the intramolecular DEER data in the time domain. The rightmost term, which converges to zero as the data-to-parameter ratio increases, serves as further regularization in modeling cases where less experimental data is available (in this case corresponding to the number of time points in all DEER traces). Overall, the AICc quantifies the expectation that few spin label rotamers contribute to the distance distribution.

Detailed description of the multilateration algorithm

The multilateration algorithm is implemented in Rosetta[59] as part of the RosettaDEER package and can be run using RosettaScripts[65]. It uses an iterative simulated annealing approach and is therefore non-deterministic. As a result, it obtains diverse sets of solutions when executed multiple times. However, there is no guarantee that the global minimum solution is obtained using this algorithm.

The positions of the pseudo-rotamers are kept fixed in space throughout the duration of the algorithm, e.g., they are reweighted, rather than moved. Initial positions are obtained from the nitroxide bond midpoints of each rotamer in the Rosetta MTSSL rotamer library following clash evaluation[22]. At the start of the algorithm, one of these pseudo-rotamers is randomly chosen for each residue and has its weight set to 1; the rest have weights set to zero.

The algorithm then proceeds as follows:

The weight of a randomly chosen pseudorotamer is modified by a randomly chosen number. Initially this value ranges uniformly from -0.1 to 0.1.
The weight change is applied, and the resulting sum-of-squared residuals is calculated as discussed below.
Any move that decreases the sum-of-squared residuals is accepted, while any move that increases it is accepted with the following probability (with iter being the current iteration):

(2)

The Boltzmann temperature k_BT starts at 1.5 and asymptotically approaches zero with each iteration as the algorithm proceeds. A total of 2500 trials per round are performed per DEER trace in the dataset. However, each round is aborted if 500 consecutive trials fail to sample an improvement.
At the end of each round, the temperature k_BT is raised to 1.5. If no improvements were sampled, the magnitude of the weight changes made to coordinates is reduced by a factor of . Once this magnitude reaches 10⁻⁴, the algorithm is concluded.

For PfMATE, we used a non-three-dimensional background model to fit the intermolecular contribution of the experimental signal. This required a modification to the algorithm in which the first round of optimization was performed using a three-dimensional background. The first time k_BT was reset to 1.5, this restriction was removed. Otherwise, the dimensionality of the intermolecular background coupling was found to immediately drop to a value of 2, trapping the solution in a local minimum.

Simulation of DEER distance distributions

To simulate distance distributions between two spin-labeled residues u and v, pairwise distances were measured between all coordinates belonging to each residue. To account for backbone heterogeneity, each of these measurements were then broadened by a value equal to the pairwise root mean square fluctuation (RMSF) as inferred from the crystallographic isotropic B-factor of the residues’ C_α atoms: (3) (4)

The result is equivalent to the convolution of the original distribution with a Gaussian distribution with a width of RMSF_uv. Regions of proteins with higher B-factors, such as loops, have previously been found to exhibit a greater degree of backbone flexibility in solution[53,66,67]. Failure to account for backbone flexibility could potentially overstate the intrinsic dynamics of the spin label and decrease the precision of the models generated using the pseudo-rotamers obtained this way. We did not normalize the experimental B-factors to account for differences in experimental crystallographic resolution, since such differences may reflect variations in the backbone disorder of different proteins.

Evaluating coordinate models obtained from raw DEER traces

In all examples discussed in this manuscript, the data D comprises N decay traces (V_exp), e.g., D = {V_exp,1, V_exp,2,…, V_exp,N}, with the ith decay trace consisting of n_i time points for a total of n_total experimental time points among all experimental traces. In this case, the likelihood of the model was evaluated by the noise-normalized sum-of-squared residuals to the experimental data: (5)

Here σ_i is the standard deviation of the noise corresponding to the ith decay trace, V_exp,i(t_i) refers to the experimental data at the i_tth time point of decay trace i, and refers to the value of the simulated data in decay trace i at time point i_t given the model parameters θ. The values of σ_i were calculated from the imaginary component of each DEER trace. Normalizing the data to the noise was necessary to satisfy the assumption that the sum of squared residuals is independently and identically distributed. Forgoing this correction led to overfitting of noisier DEER traces and underfitting of less noisy traces.

Simulation of DEER traces occurred in three steps. First, the distance distributions were obtained from the model coordinates as described above. Second, the intramolecular form factor was calculated for each time point : (6)

Here, g is the electron g-factor, μ₀ is the vacuum permeability constant, μ_B is the Bohr magneton, is the i_tth time point in microseconds, r is the bin distance in nanometers, and x is the angle between the bulk magnetic field and the interspin vector.

In the third step, the modulation depth, background slope, and dimensionality (in the case of PfMATE) were determined using nonlinear least-squares minimization. This background was modeled as follows: (7)

The parameter d refers to the dimensionality of background coupling and was constrained to a value of 3.0 for T4 Lysozyme and to between 2.0 and 3.5 for PfMATE. In the latter case, we generally obtained values ranging from 2.0 to 2.5. These parameters were determined using an initial search as previously described and were fine-tuned throughout the duration of the algorithm using the Levenberg-Marquardt algorithm.

Determination of distance distributions

We used GLADDvu[14] and DeerAnalysis2019b[44] to fit the data and obtain distance distributions. Each DEER trace was truncated by 500 ns to avoid fitting artifacts. Sum-of-Gaussian distributions were obtained with GLADDvu using the interior point method. The distribution with the lowest Bayesian Information Criterion was selected. Distributions were also obtained using Tikhonov regularization with an L-curve criterion with default settings, as well as the generic DeerNet neural network ensemble, using DeerAnalysis2019b[46]. Confidence bands and/or error margins were obtained using the delta method for GLADDvu, the Validation tool for Tikhonov regularization, and built-in ensemble statistics for DeerNet.

Application to T4 Lysozyme and PfMATE

The algorithm as described above was applied to T4 Lysozyme[55] (PDB: 2LZM) and outward-facing PfMATE structure[56] (PDB: 6GWH). For PfMATE, the data were further separated into the extracellular restraints and the intracellular restraints. The algorithm was executed one thousand times for each of these three datasets. Each of the one thousand coordinate models were scored using the AICc (Eq 1).

Modeling the OF-to-IF conformational change of PfMATE

Modeling the outward-to-inward conformational change of PfMATE was achieved using a Monte Carlo fragment insertion approach implemented in RosettaScripts. This protocol randomly changes the backbone dihedral angles of certain residues chosen at random to match those of a similar stretch of residues found in protein structures deposited in the PDB. Only residues 1–50 and 241–268 were perturbed. Peptide fragments were obtained from a July 2011 version of the PDB using the Robetta web server[68] with homologous protein structures removed. The fragment insertion protocol was executed 1000 times in RosettaScripts[65] using the score3 scoring function and was repeated for 5000 cycles. The Boltzmann temperature was set to 1.0. The following scoring function was then used to quantify the similarity between the experimental and simulated DEER distributions: (8)

If the event that an experimental and simulated distribution did not overlap, the inner term resolves to ln(0). Under these circumstances, this value was automatically set to -87.0, which is equivalent to the natural logarithm of the lowest non-negative value that can be described by a single-precision floating point number.

Supporting information

S1 Fig. Number of DEER restraints per spin-labeled residue across T4 Lysozyme and PfMATE.

https://doi.org/10.1371/journal.pcbi.1009107.s001

(TIFF)

S2 Fig. All DEER traces determined by multilateration are shown in red. Experimental DEER traces are shown in black.

https://doi.org/10.1371/journal.pcbi.1009107.s002

(TIFF)

S3 Fig. All DEER distance distributions determined by multilateration are shown in black.

DEER distributions calculated using GladdVU are shown in green, with the shaded regions indicating 95% confidence intervals. Distance values shorter than 15 Å (indicated by the dashed line) were not used to simulate DEER traces.

https://doi.org/10.1371/journal.pcbi.1009107.s003

(TIFF)

S4 Fig. All DEER distance distributions determined by multilateration are shown in black.

DEER distributions calculated using DeerAnalysis are shown in blue, with the shaded regions obtained using the validation tool.

https://doi.org/10.1371/journal.pcbi.1009107.s004

(TIFF)

S5 Fig. All DEER distance distributions determined by multilateration are shown in black.

DEER distributions calculated using DeerNet are shown in pink, with the shaded regions obtained using ensemble statistics.

https://doi.org/10.1371/journal.pcbi.1009107.s005

(TIFF)

S6 Fig. Comparison of average and standard deviation values obtained when fitting DEER data collected in pfMATE and T4 Lysozyme to values obtained using DeerAnalysis and DeerNet.

Long-distance fitting artifacts were removed from fits obtained using DeerAnalysis. These fits appeared to overstate the standard deviation values relative to GLADDvu, whereas those obtained using DeerNet appeared to be biased toward certain width values.

https://doi.org/10.1371/journal.pcbi.1009107.s006

(TIFF)

S7 Fig. Shaded regions depict 95% confidence intervals, and line represents the mean distribution.

Ensembles were selected using the AICc.

https://doi.org/10.1371/journal.pcbi.1009107.s007

(TIFF)

S8 Fig. Comparison of DEER distance distributions used to validate pseudo-rotamers obtained using the RosettaDEER multilateration algorithm.

Distributions obtained using GLADDvu and RosettaDEER are shown in green and grey, respectively. Confidence bands for RosettaDEER depict the five best sets of pseudo-rotamers.

https://doi.org/10.1371/journal.pcbi.1009107.s008

(TIFF)

S9 Fig. Rosetta energy functions for membrane proteins cannot identify the inward-facing conformation of PfMATE.

In all three cases, the lowest-energy models are fully occluded from both sides of the membrane. RMSD is measured from the inward-facing crystal structure (PDB: 6FHZ); the first 50 residues were omitted.

https://doi.org/10.1371/journal.pcbi.1009107.s009

(TIFF)

S1 Table. List of restraints used for scoring intermediate PfMATE models.

https://doi.org/10.1371/journal.pcbi.1009107.s010

(DOCX)

S1 Appendix. Summary of experimental DEER measurements collected in T4 Lysozyme and PfMATE.

https://doi.org/10.1371/journal.pcbi.1009107.s011

(XLSX)

S2 Appendix. Coordinates of top five ensembles of pseudo-rotamers in T4 Lysozyme.

https://doi.org/10.1371/journal.pcbi.1009107.s012

(TXT)

S3 Appendix. Coordinates of top five ensembles of pseudo-rotamers in PfMATE.

https://doi.org/10.1371/journal.pcbi.1009107.s013

(TXT)

S4 Appendix. Scores of intermediate PfMATE models.

https://doi.org/10.1371/journal.pcbi.1009107.s014

(CSV)

S5 Appendix. Supplemental methods.

https://doi.org/10.1371/journal.pcbi.1009107.s015

(DOCX)

Acknowledgments

We thank Dr. Derek P. Claxton and Dr. Richard A. Stein for critical reading of the manuscript, and Dr. Eric Hustedt for both fruitful discussions regarding the AICc and model-based fitting as well as critical reading of the manuscript.

References

1. Kazmier K, Sharma S, Quick M, Islam SM, Roux B, Weinstein H, et al. Conformational dynamics of ligand-dependent alternating access in LeuT. Nat Struct Mol Biol. 2014;21: 472–479. pmid:24747939
- View Article
- PubMed/NCBI
- Google Scholar
2. Collauto A, Deberg HA, Kaufmann R, Zagotta WN, Stoll S, Goldfarb D. Rates and equilibrium constants of the ligand-induced conformational transition of an HCN ion channel protein domain determined by DEER spectroscopy. Phys Chem Chem Phys. 2017;19: 15324–15334. pmid:28569901
- View Article
- PubMed/NCBI
- Google Scholar
3. Evans EGBB Morgan JLWW, DiMaio F Zagotta WN, Stoll S. Allosteric conformational change of a cyclic nucleotide-gated ion channel revealed by DEER spectroscopy. Proc Natl Acad Sci U S A. 2020;117: 10839–10847. pmid:32358188
- View Article
- PubMed/NCBI
- Google Scholar
4. Mishra S, Verhalen B, Stein RA, Wen PC, Tajkhorshid E, Mchaourab HS. Conformational dynamics of the nucleotide binding domains and the power stroke of a heterodimeric ABC transporter. Elife. 2014;3: e02740. pmid:24837547
- View Article
- PubMed/NCBI
- Google Scholar
5. Kim S, Brandon S, Zhou Z, Cobb CE, Edwards SJ, Moth CW, et al. Determination of structural models of the complex between the cytoplasmic domain of erythrocyte band 3 and ankyrin-R repeats 13–24. J Biol Chem. 2011;286: 20746–20757. pmid:21493712
- View Article
- PubMed/NCBI
- Google Scholar
6. Bhatnagar J, Freed JH, Crane BR. Rigid Body Refinement of Protein Complexes with Long-Range Distance Restraints from Pulsed Dipolar ESR. Methods Enzymol. 2007;423: 117–133. pmid:17609128
- View Article
- PubMed/NCBI
- Google Scholar
7. Tessmer MH, Anderson DM, Pickrum AM, Riegert MO, Moretti R, Meiler J, et al. Identification of a ubiquitin-binding interface using Rosetta and DEER. Proc Natl Acad Sci. 2018; 201716861. pmid:29295930
- View Article
- PubMed/NCBI
- Google Scholar
8. Lim S, Roseman G, Peshenko I, Manchala G, Cudia D, Dizhoor AM, et al. Retinal guanylyl cyclase activating protein 1 forms a functional dimer. PLoS One. 2018;13. pmid:29513743
- View Article
- PubMed/NCBI
- Google Scholar
9. McHaourab HS, Steed PR, Kazmier K. Toward the fourth dimension of membrane protein structure: Insight into dynamics from spin-labeling EPR spectroscopy. Structure. 2011;19: 1549–1561. pmid:22078555
- View Article
- PubMed/NCBI
- Google Scholar
10. Jeschke G. DEER Distance Measurements on Proteins. Annu Rev Phys Chem. 2012;63: 419–46. pmid:22404592
- View Article
- PubMed/NCBI
- Google Scholar
11. Pannier M, Veit S, Godt A, Jeschke G, Spiess H. Dead-Time Free Measurement of Dipole-Dipole Interactions between Electron Spins. J Magn Reson. 2000;18: 463–470. pmid:10648151
- View Article
- PubMed/NCBI
- Google Scholar
12. Jeschke G, Panek G, Godt A, Bender A, Paulsen H. Applied Magnetic Resonance Data Analysis Procedures for Pulse ELDOR Measurements of Broad Distance Distributions. Appl Magn Reson. 2004. Available: http://www.mpip-mainz.mpg.de/-jeschke/distance.html.
- View Article
- Google Scholar
13. Stein RA, Beth AH, Hustedt EJ. A straightforward approach to the analysis of double electron-electron resonance data. 1st ed. Methods in Enzymology. Elsevier Inc.; 2015. https://doi.org/10.1016/bs.mie.2015.07.031 pmid:26478498
14. Hustedt EJ, Martinelli F, Stein RA, Faraldo-Gomez J, Mchaourab HS. Confidence Analysis of DEER Data and its Structural Interpretation with Ensemble-Biased Metadynamics. Biophys J. 2018; 1–17. pmid:30197182
- View Article
- PubMed/NCBI
- Google Scholar
15. Fábregas Ibáñez L, Jeschke G, Stoll S. DeerLab: A comprehensive toolbox for analyzing dipolar EPR spectroscopy data. Magn Reson. 2020;1: 209–224.
- View Article
- Google Scholar
16. Reichel K, Stelzl LS, Koefinger J, Hummer G. Precision DEER Distances from Spin-Label Ensemble Refinement. J Phys Chem Lett. 2018; acs.jpclett.8b02439. pmid:30212206
- View Article
- PubMed/NCBI
- Google Scholar
17. Polyhach Y, Bordignon E, Jeschke G. Rotamer libraries of spin labelled cysteines for protein studies. Phys Chem Chem Phys. 2011;13: 2356–2366. pmid:21116569
- View Article
- PubMed/NCBI
- Google Scholar
18. Hagelueken G, Ward R, Naismith JH, Schiemann O. MtsslWizard: In Silico Spin-Labeling and Generation of Distance Distributions in PyMOL. Appl Magn Reson. 2012;42: 377–391. pmid:22448103
- View Article
- PubMed/NCBI
- Google Scholar
19. Raghuraman H, Islam SM, Mukherjee S, Roux B, Perozo E. Dynamics transitions at the outer vestibule of the KcsA potassium channel during gating. Proc Natl Acad Sci U S A. 2014;111: 1831–1836. pmid:24429344
- View Article
- PubMed/NCBI
- Google Scholar
20. del Alamo D, Tessmer MH, Stein RA, Feix JB, Mchaourab HS, Meiler J. Rapid Simulation of Unprocessed DEER Decay Data for Protein Fold Prediction. Biophys J. 2019. pmid:31892409
- View Article
- PubMed/NCBI
- Google Scholar
21. Marinelli F, Fiorin G. Structural Characterization of Biomolecules through Atomistic Simulations Guided by DEER Measurements. Structure. 2019;27: 1–12. pmid:30605659
- View Article
- PubMed/NCBI
- Google Scholar
22. Alexander NS, Stein RA, Koteiche HA, Kaufmann KW, Mchaourab HS, Meiler J. RosettaEPR: Rotamer Library for Spin Label Structure and Dynamics. PLoS One. 2013;8. pmid:24039810
- View Article
- PubMed/NCBI
- Google Scholar
23. Dastvan R, Brouwer EM, Schuetz D, Mirus O, Schleiff E, Prisner TF. Relative Orientation of POTRA Domains from Cyanobacterial Omp85 Studied by Pulsed EPR Spectroscopy. Biophys J. 2016;110: 2195–2206. pmid:27224485
- View Article
- PubMed/NCBI
- Google Scholar
24. Sale K, Song L, Liu YS, Perozo E, Fajer P. Explicit treatment of spin labels in modeling of distance constraints from dipolar EPR and DEER. J Am Chem Soc. 2005;127: 9334–9335. pmid:15984837
- View Article
- PubMed/NCBI
- Google Scholar
25. Krug U, Alexander NS, Stein RA, Keim A, McHaourab HS, Sträter N, et al. Characterization of the Domain Orientations of E. coli 5′-Nucleotidase by Fitting an Ensemble of Conformers to DEER Distance Distributions. Structure. 2016;24: 43–56. pmid:26724996
- View Article
- PubMed/NCBI
- Google Scholar
26. Spicher S, Abdullin D, Grimme S, Schiemann O. Modeling of spin-spin distance distributions for nitroxide labeled biomacromolecules. Phys Chem Chem Phys. 2020;22: 24282–24290. pmid:33107523
- View Article
- PubMed/NCBI
- Google Scholar
27. Fajer P, Fajer M, Zawrotny M, Yang W. Full Atom Simulations of Spin Label Conformations. 1st ed. Methods in Enzymology. Elsevier Inc.; 2015. https://doi.org/10.1016/bs.mie.2015.07.030
28. Jeschke G. Conformational dynamics and distribution of nitroxide spin labels. Prog Nucl Magn Reson Spectrosc. 2013;72: 42–60. pmid:23731861
- View Article
- PubMed/NCBI
- Google Scholar
29. Klose D, Klare JP, Grohmann D, Kay CWM, Werner F, Steinhoff HJ. Simulation vs. reality: A comparison of in silico distance predictions with DEER and FRET measurements. PLoS One. 2012;7. pmid:22761805
- View Article
- PubMed/NCBI
- Google Scholar
30. Hatmal MM, Li Y, Hegde BG, Hegde PB, Jao CC, Langen R, et al. Computer modeling of nitroxide spin labels on proteins. Biopolymers. 2012;97: 35–44. pmid:21792846
- View Article
- PubMed/NCBI
- Google Scholar
31. Islam SM, Stein RA, McHaourab HS, Roux B. Structural refinement from restrained-ensemble simulations based on EPR/DEER data: Application to T4 lysozyme. J Phys Chem B. 2013;117: 4740–4754. pmid:23510103
- View Article
- PubMed/NCBI
- Google Scholar
32. Hays JM, Cafiso DS, Kasson PM. Hybrid Refinement of Heterogeneous Conformational Ensembles Using Spectroscopic Data. J Phys Chem Lett. 2019;10: 3410–3414. pmid:31181934
- View Article
- PubMed/NCBI
- Google Scholar
33. Jeschke G. MMM: A toolbox for integrative structure modeling. Protein Sci. 2018;27: 76–85. pmid:28799219
- View Article
- PubMed/NCBI
- Google Scholar
34. Hagelueken G, Abdullin D, Ward R, Schiemann O. MtsslSuite: In silico spin labelling, trilateration and distance-constrained rigid body docking in PyMOL. Mol Phys. 2013;111: 2757–2766. pmid:24954955
- View Article
- PubMed/NCBI
- Google Scholar
35. Gaffney BJ, Bradshaw MD, Frausto SD, Wu F, Freed JH, Borbat P. Locating a lipid at the portal to the lipoxygenase active site. Biophys J. 2012;103: 2134–2144. pmid:23200047
- View Article
- PubMed/NCBI
- Google Scholar
36. Abdullin D, Florin N, Hagelueken G, Schiemann O. EPR-based approach for the localization of paramagnetic metal Ions in biomolecules. Angew Chemie—Int Ed. 2015;54: 1827–1831. pmid:25522037
- View Article
- PubMed/NCBI
- Google Scholar
37. Fang BT. Trilateration and extension to Global Positioning System navigation. J Guid Control Dyn. 1986;9: 715–717.
- View Article
- Google Scholar
38. Marinelli F, Faraldo-Gómez JD. Ensemble-Biased Metadynamics: A Molecular Simulation Method to Sample Experimental Distributions. Biophys J. 2015;108: 2779–2782. pmid:26083917
- View Article
- PubMed/NCBI
- Google Scholar
39. Roux B, Islam SM. Restrained-ensemble molecular dynamics simulations based on distance histograms from double electron-electron resonance spectroscopy. J Phys Chem B. 2013;117: 4733–4739. pmid:23510121
- View Article
- PubMed/NCBI
- Google Scholar
40. Yang Z, Kurpiewski MR, Ji M, Townsend JE, Mehta P. ESR spectroscopy identifies inhibitory Cu sites in a DNA-modifying enzyme to reveal determinants of catalytic specificity. 2012; 3–10. pmid:22493217
- View Article
- PubMed/NCBI
- Google Scholar
41. Abdullin D, Schiemann O. Localization of Metal Ions in Biomolecules by means of Pulsed Dipolar EPR Spectroscopy. Dalt Trans. 2021. pmid:33416053
- View Article
- PubMed/NCBI
- Google Scholar
42. Wingler LM, Elgeti M, Hilger D, Latorraca NR, Lerch MT, Staus DP, et al. Angiotensin Analogs with Divergent Bias Stabilize Distinct Receptor Conformations. Cell. 2019; 1–11. pmid:30639099
- View Article
- PubMed/NCBI
- Google Scholar
43. Edwards TH, Stoll S. A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy. J Magn Reson. 2016;270: 87–97. pmid:27414762
- View Article
- PubMed/NCBI
- Google Scholar
44. Jeschke G, Chechik V, Ionita P, Godt A, Zimmermann H, Banham J, et al. DeerAnalysis2006—a comprehensive software package for analyzing pulsed ELDOR data. Appl Magn Reson. 2006;30: 473–498.
- View Article
- Google Scholar
45. Chiang Y-W, Borbat PP, Freed JH. Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR. J Magn Reson. 2005;177: 184–196. pmid:16137901
- View Article
- PubMed/NCBI
- Google Scholar
46. Worswick SG, Spencer JA, Jeschke G, Kuprov I. Deep neural network processing of DEER data. Sci Adv. 2018;4: eaat5218. pmid:30151430
- View Article
- PubMed/NCBI
- Google Scholar
47. Srivastava M, Freed JH. Singular Value Decomposition Method To Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance: II. Estimating Uncertainty. J Phys Chem A. 2019;123: 359–370. pmid:30525624
- View Article
- PubMed/NCBI
- Google Scholar
48. Srivastava M, Freed JH. Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance. J Phys Chem A. 2017;22: 5648–5655. pmid:29099190
- View Article
- PubMed/NCBI
- Google Scholar
49. Akaike H. Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory. 1973. pp. 267–281.
- View Article
- Google Scholar
50. Sugiura N. Further analysts of the data by akaike’ s information criterion and the finite corrections. Commun Stat—Theory Methods. 1978;7: 13–26.
- View Article
- Google Scholar
51. Georgieva ER, Roy AS, Grigoryants VM, Borbat PP, Earle KA, Scholes CP, et al. Effect of freezing conditions on distances and their distributions derived from Double Electron Electron Resonance (DEER): A study of doubly-spin-labeled T4 lysozyme. J Magn Reson. 2012;216: 69–77. pmid:22341208
- View Article
- PubMed/NCBI
- Google Scholar
52. Banham JE, Jeschke G, Timmel CR. Evidence from EPR that nitroxide spin labels attached to human hemoglobin alter their conformation upon freezing. Mol Phys. 2007;105: 2041–2047.
- View Article
- Google Scholar
53. Yang LW, Eyal E, Chennubhotla C, Jee JG, Gronenborn AM, Bahar I. Insights into Equilibrium Dynamics of Proteins from Comparison of NMR and X-Ray Data with Computational Predictions. Structure. 2007;15: 741–749. pmid:17562320
- View Article
- PubMed/NCBI
- Google Scholar
54. Sun Z, Liu Q, Qu G, Feng Y, Reetz MT. Utility of B-Factors in Protein Science: Interpreting Rigidity, Flexibility, and Internal Motion and Engineering Thermostability. Chem Rev. 2019. pmid:30698416
- View Article
- PubMed/NCBI
- Google Scholar
55. Weaver LH, Matthews BW. Structure of Bacteriophage T4 Lysozyme Refined at 1.7 A Resolution. J Mol Biol. 1987; 193–189. pmid:3586019
- View Article
- PubMed/NCBI
- Google Scholar
56. Zakrzewska S, Mehdipour AR, Malviya VN, Nonaka T, Koepke J, Muenke C, et al. Inward-facing conformation of a multidrug resistance MATE family transporter. Proc Natl Acad Sci U S A. 2019;116: 12275–12284. pmid:31160466
- View Article
- PubMed/NCBI
- Google Scholar
57. Tanaka Y, Hipolito CJ, Maturana AD, Ito K, Kuroda T, Higuchi T, et al. Structural basis for the drug extrusion mechanism by a MATE multidrug transporter. Nature. 2013;496: 247–251. pmid:23535598
- View Article
- PubMed/NCBI
- Google Scholar
58. Jagessar KL, Claxton DP, Stein RA, Mchaourab HS. Sequence and Structural Determinants of Ligand-Dependent Alternating Access of a MATE Transporter. Proc Natl Acad Sci U S A. 2020;117: 4732–4740. pmid:32075917
- View Article
- PubMed/NCBI
- Google Scholar
59. Leaver-fay A, Tyka M, Lewis SM, Lange F, Thompson J, Jacak R, et al. ROSETTA 3: An Object-Oriented Software Suite for the Simulation and Design of Macromolecules. 2011;487: 545–574.
- View Article
- Google Scholar
60. Alford RF, Fleming PJ, Fleming KG, Gray JJ. Protein structure prediction and design in a biologically realistic implicit membrane. Biophys J. 2020. pmid:32224301
- View Article
- PubMed/NCBI
- Google Scholar
61. Alford RF, Koehler Leman J, Weitzner BD, Duran AM, Tilley DC, Elazar A, et al. An Integrated Framework Advancing Membrane Protein Modeling and Design. PLoS Comput Biol. 2015;11: 1–23. pmid:26325167
- View Article
- PubMed/NCBI
- Google Scholar
62. Yarov-Yarovoy V, Schonbrun J, Baker D. Multipass membrane protein structure prediction using Rosetta. Proteins. 2006;62: 1010–1025. pmid:16372357
- View Article
- PubMed/NCBI
- Google Scholar
63. Weinstein JY, Elazar A, Fleishman SJ. A lipophilicity-based energy function for membrane-protein modelling and design. PLoS Comput Biol. 2019;15. pmid:31461441
- View Article
- PubMed/NCBI
- Google Scholar
64. Burnham K, Anderson DR. Model Selection and Multimodel Inference. 2002.
- View Article
- Google Scholar
65. Fleishman SJ, Leaver-Fay A, Corn JE, Strauch EM, Khare SD, Koga N, et al. Rosettascripts: A scripting language interface to the Rosetta Macromolecular modeling suite. PLoS One. 2011;6. pmid:21731610
- View Article
- PubMed/NCBI
- Google Scholar
66. Powers R, Clore GM, Garrett DS, Gronenborn AM. Relationships between the Precision of High-Resolution Protein NMR Structures, Solution-Order Parameters, and Crystallographic B Factors. J Magn Reson. 1993;101: 325–327. Available: http://digitalcommons.unl.edu/chemistrypowershttp://digitalcommons.unl.edu/chemistrypowers/20
- View Article
- Google Scholar
67. Billeter M, Vendrell J, Wider G, Avils FX, Coll C’ M, Guasch B’c A, et al. Comparison of the NMR solution structure with the X-ray crystal structure of the activation domain from procarboxypeptidase B. J Biomol NMR. 1992. pmid:1422143
- View Article
- PubMed/NCBI
- Google Scholar
68. Kim DE, Chivian D, Baker D. Protein structure prediction and analysis using the Robetta server. Nucleic Acids Res. 2004;32: 526–531. pmid:15215442
- View Article
- PubMed/NCBI
- Google Scholar

[ref1] 1. Kazmier K, Sharma S, Quick M, Islam SM, Roux B, Weinstein H, et al. Conformational dynamics of ligand-dependent alternating access in LeuT. Nat Struct Mol Biol. 2014;21: 472–479. pmid:24747939
View Article
PubMed/NCBI
Google Scholar

[2] View Article

[3] PubMed/NCBI

[4] Google Scholar

[ref2] 2. Collauto A, Deberg HA, Kaufmann R, Zagotta WN, Stoll S, Goldfarb D. Rates and equilibrium constants of the ligand-induced conformational transition of an HCN ion channel protein domain determined by DEER spectroscopy. Phys Chem Chem Phys. 2017;19: 15324–15334. pmid:28569901
View Article
PubMed/NCBI
Google Scholar

[6] View Article

[7] PubMed/NCBI

[8] Google Scholar

[ref3] 3. Evans EGBB Morgan JLWW, DiMaio F Zagotta WN, Stoll S. Allosteric conformational change of a cyclic nucleotide-gated ion channel revealed by DEER spectroscopy. Proc Natl Acad Sci U S A. 2020;117: 10839–10847. pmid:32358188
View Article
PubMed/NCBI
Google Scholar

[10] View Article

[11] PubMed/NCBI

[12] Google Scholar

[ref4] 4. Mishra S, Verhalen B, Stein RA, Wen PC, Tajkhorshid E, Mchaourab HS. Conformational dynamics of the nucleotide binding domains and the power stroke of a heterodimeric ABC transporter. Elife. 2014;3: e02740. pmid:24837547
View Article
PubMed/NCBI
Google Scholar

[14] View Article

[15] PubMed/NCBI

[16] Google Scholar

[ref5] 5. Kim S, Brandon S, Zhou Z, Cobb CE, Edwards SJ, Moth CW, et al. Determination of structural models of the complex between the cytoplasmic domain of erythrocyte band 3 and ankyrin-R repeats 13–24. J Biol Chem. 2011;286: 20746–20757. pmid:21493712
View Article
PubMed/NCBI
Google Scholar

[18] View Article

[19] PubMed/NCBI

[20] Google Scholar

[ref6] 6. Bhatnagar J, Freed JH, Crane BR. Rigid Body Refinement of Protein Complexes with Long-Range Distance Restraints from Pulsed Dipolar ESR. Methods Enzymol. 2007;423: 117–133. pmid:17609128
View Article
PubMed/NCBI
Google Scholar

[22] View Article

[23] PubMed/NCBI

[24] Google Scholar

[ref7] 7. Tessmer MH, Anderson DM, Pickrum AM, Riegert MO, Moretti R, Meiler J, et al. Identification of a ubiquitin-binding interface using Rosetta and DEER. Proc Natl Acad Sci. 2018; 201716861. pmid:29295930
View Article
PubMed/NCBI
Google Scholar

[26] View Article

[27] PubMed/NCBI

[28] Google Scholar

[ref8] 8. Lim S, Roseman G, Peshenko I, Manchala G, Cudia D, Dizhoor AM, et al. Retinal guanylyl cyclase activating protein 1 forms a functional dimer. PLoS One. 2018;13. pmid:29513743
View Article
PubMed/NCBI
Google Scholar

[30] View Article

[31] PubMed/NCBI

[32] Google Scholar

[ref9] 9. McHaourab HS, Steed PR, Kazmier K. Toward the fourth dimension of membrane protein structure: Insight into dynamics from spin-labeling EPR spectroscopy. Structure. 2011;19: 1549–1561. pmid:22078555
View Article
PubMed/NCBI
Google Scholar

[34] View Article

[35] PubMed/NCBI

[36] Google Scholar

[ref10] 10. Jeschke G. DEER Distance Measurements on Proteins. Annu Rev Phys Chem. 2012;63: 419–46. pmid:22404592
View Article
PubMed/NCBI
Google Scholar

[38] View Article

[39] PubMed/NCBI

[40] Google Scholar

[ref11] 11. Pannier M, Veit S, Godt A, Jeschke G, Spiess H. Dead-Time Free Measurement of Dipole-Dipole Interactions between Electron Spins. J Magn Reson. 2000;18: 463–470. pmid:10648151
View Article
PubMed/NCBI
Google Scholar

[42] View Article

[43] PubMed/NCBI

[44] Google Scholar

[ref12] 12. Jeschke G, Panek G, Godt A, Bender A, Paulsen H. Applied Magnetic Resonance Data Analysis Procedures for Pulse ELDOR Measurements of Broad Distance Distributions. Appl Magn Reson. 2004. Available: http://www.mpip-mainz.mpg.de/-jeschke/distance.html.
View Article
Google Scholar

[46] View Article

[47] Google Scholar

[ref13] 13. Stein RA, Beth AH, Hustedt EJ. A straightforward approach to the analysis of double electron-electron resonance data. 1st ed. Methods in Enzymology. Elsevier Inc.; 2015. https://doi.org/10.1016/bs.mie.2015.07.031 pmid:26478498

[ref14] 14. Hustedt EJ, Martinelli F, Stein RA, Faraldo-Gomez J, Mchaourab HS. Confidence Analysis of DEER Data and its Structural Interpretation with Ensemble-Biased Metadynamics. Biophys J. 2018; 1–17. pmid:30197182
View Article
PubMed/NCBI
Google Scholar

[50] View Article

[51] PubMed/NCBI

[52] Google Scholar

[ref15] 15. Fábregas Ibáñez L, Jeschke G, Stoll S. DeerLab: A comprehensive toolbox for analyzing dipolar EPR spectroscopy data. Magn Reson. 2020;1: 209–224.
View Article
Google Scholar

[54] View Article

[55] Google Scholar

[ref16] 16. Reichel K, Stelzl LS, Koefinger J, Hummer G. Precision DEER Distances from Spin-Label Ensemble Refinement. J Phys Chem Lett. 2018; acs.jpclett.8b02439. pmid:30212206
View Article
PubMed/NCBI
Google Scholar

[57] View Article

[58] PubMed/NCBI

[59] Google Scholar

[ref17] 17. Polyhach Y, Bordignon E, Jeschke G. Rotamer libraries of spin labelled cysteines for protein studies. Phys Chem Chem Phys. 2011;13: 2356–2366. pmid:21116569
View Article
PubMed/NCBI
Google Scholar

[61] View Article

[62] PubMed/NCBI

[63] Google Scholar

[ref18] 18. Hagelueken G, Ward R, Naismith JH, Schiemann O. MtsslWizard: In Silico Spin-Labeling and Generation of Distance Distributions in PyMOL. Appl Magn Reson. 2012;42: 377–391. pmid:22448103
View Article
PubMed/NCBI
Google Scholar

[65] View Article

[66] PubMed/NCBI

[67] Google Scholar

[ref19] 19. Raghuraman H, Islam SM, Mukherjee S, Roux B, Perozo E. Dynamics transitions at the outer vestibule of the KcsA potassium channel during gating. Proc Natl Acad Sci U S A. 2014;111: 1831–1836. pmid:24429344
View Article
PubMed/NCBI
Google Scholar

[69] View Article

[70] PubMed/NCBI

[71] Google Scholar

[ref20] 20. del Alamo D, Tessmer MH, Stein RA, Feix JB, Mchaourab HS, Meiler J. Rapid Simulation of Unprocessed DEER Decay Data for Protein Fold Prediction. Biophys J. 2019. pmid:31892409
View Article
PubMed/NCBI
Google Scholar

[73] View Article

[74] PubMed/NCBI

[75] Google Scholar

[ref21] 21. Marinelli F, Fiorin G. Structural Characterization of Biomolecules through Atomistic Simulations Guided by DEER Measurements. Structure. 2019;27: 1–12. pmid:30605659
View Article
PubMed/NCBI
Google Scholar

[77] View Article

[78] PubMed/NCBI

[79] Google Scholar

[ref22] 22. Alexander NS, Stein RA, Koteiche HA, Kaufmann KW, Mchaourab HS, Meiler J. RosettaEPR: Rotamer Library for Spin Label Structure and Dynamics. PLoS One. 2013;8. pmid:24039810
View Article
PubMed/NCBI
Google Scholar

[81] View Article

[82] PubMed/NCBI

[83] Google Scholar

[ref23] 23. Dastvan R, Brouwer EM, Schuetz D, Mirus O, Schleiff E, Prisner TF. Relative Orientation of POTRA Domains from Cyanobacterial Omp85 Studied by Pulsed EPR Spectroscopy. Biophys J. 2016;110: 2195–2206. pmid:27224485
View Article
PubMed/NCBI
Google Scholar

[85] View Article

[86] PubMed/NCBI

[87] Google Scholar

[ref24] 24. Sale K, Song L, Liu YS, Perozo E, Fajer P. Explicit treatment of spin labels in modeling of distance constraints from dipolar EPR and DEER. J Am Chem Soc. 2005;127: 9334–9335. pmid:15984837
View Article
PubMed/NCBI
Google Scholar

[89] View Article

[90] PubMed/NCBI

[91] Google Scholar

[ref25] 25. Krug U, Alexander NS, Stein RA, Keim A, McHaourab HS, Sträter N, et al. Characterization of the Domain Orientations of E. coli 5′-Nucleotidase by Fitting an Ensemble of Conformers to DEER Distance Distributions. Structure. 2016;24: 43–56. pmid:26724996
View Article
PubMed/NCBI
Google Scholar

[93] View Article

[94] PubMed/NCBI

[95] Google Scholar

[ref26] 26. Spicher S, Abdullin D, Grimme S, Schiemann O. Modeling of spin-spin distance distributions for nitroxide labeled biomacromolecules. Phys Chem Chem Phys. 2020;22: 24282–24290. pmid:33107523
View Article
PubMed/NCBI
Google Scholar

[97] View Article

[98] PubMed/NCBI

[99] Google Scholar

[ref27] 27. Fajer P, Fajer M, Zawrotny M, Yang W. Full Atom Simulations of Spin Label Conformations. 1st ed. Methods in Enzymology. Elsevier Inc.; 2015. https://doi.org/10.1016/bs.mie.2015.07.030

[ref28] 28. Jeschke G. Conformational dynamics and distribution of nitroxide spin labels. Prog Nucl Magn Reson Spectrosc. 2013;72: 42–60. pmid:23731861
View Article
PubMed/NCBI
Google Scholar

[102] View Article

[103] PubMed/NCBI

[104] Google Scholar

[ref29] 29. Klose D, Klare JP, Grohmann D, Kay CWM, Werner F, Steinhoff HJ. Simulation vs. reality: A comparison of in silico distance predictions with DEER and FRET measurements. PLoS One. 2012;7. pmid:22761805
View Article
PubMed/NCBI
Google Scholar

[106] View Article

[107] PubMed/NCBI

[108] Google Scholar

[ref30] 30. Hatmal MM, Li Y, Hegde BG, Hegde PB, Jao CC, Langen R, et al. Computer modeling of nitroxide spin labels on proteins. Biopolymers. 2012;97: 35–44. pmid:21792846
View Article
PubMed/NCBI
Google Scholar

[110] View Article

[111] PubMed/NCBI

[112] Google Scholar

[ref31] 31. Islam SM, Stein RA, McHaourab HS, Roux B. Structural refinement from restrained-ensemble simulations based on EPR/DEER data: Application to T4 lysozyme. J Phys Chem B. 2013;117: 4740–4754. pmid:23510103
View Article
PubMed/NCBI
Google Scholar

[114] View Article

[115] PubMed/NCBI

[116] Google Scholar

[ref32] 32. Hays JM, Cafiso DS, Kasson PM. Hybrid Refinement of Heterogeneous Conformational Ensembles Using Spectroscopic Data. J Phys Chem Lett. 2019;10: 3410–3414. pmid:31181934
View Article
PubMed/NCBI
Google Scholar

[118] View Article

[119] PubMed/NCBI

[120] Google Scholar

[ref33] 33. Jeschke G. MMM: A toolbox for integrative structure modeling. Protein Sci. 2018;27: 76–85. pmid:28799219
View Article
PubMed/NCBI
Google Scholar

[122] View Article

[123] PubMed/NCBI

[124] Google Scholar

[ref34] 34. Hagelueken G, Abdullin D, Ward R, Schiemann O. MtsslSuite: In silico spin labelling, trilateration and distance-constrained rigid body docking in PyMOL. Mol Phys. 2013;111: 2757–2766. pmid:24954955
View Article
PubMed/NCBI
Google Scholar

[126] View Article

[127] PubMed/NCBI

[128] Google Scholar

[ref35] 35. Gaffney BJ, Bradshaw MD, Frausto SD, Wu F, Freed JH, Borbat P. Locating a lipid at the portal to the lipoxygenase active site. Biophys J. 2012;103: 2134–2144. pmid:23200047
View Article
PubMed/NCBI
Google Scholar

[130] View Article

[131] PubMed/NCBI

[132] Google Scholar

[ref36] 36. Abdullin D, Florin N, Hagelueken G, Schiemann O. EPR-based approach for the localization of paramagnetic metal Ions in biomolecules. Angew Chemie—Int Ed. 2015;54: 1827–1831. pmid:25522037
View Article
PubMed/NCBI
Google Scholar

[134] View Article

[135] PubMed/NCBI

[136] Google Scholar

[ref37] 37. Fang BT. Trilateration and extension to Global Positioning System navigation. J Guid Control Dyn. 1986;9: 715–717.
View Article
Google Scholar

[138] View Article

[139] Google Scholar

[ref38] 38. Marinelli F, Faraldo-Gómez JD. Ensemble-Biased Metadynamics: A Molecular Simulation Method to Sample Experimental Distributions. Biophys J. 2015;108: 2779–2782. pmid:26083917
View Article
PubMed/NCBI
Google Scholar

[141] View Article

[142] PubMed/NCBI

[143] Google Scholar

[ref39] 39. Roux B, Islam SM. Restrained-ensemble molecular dynamics simulations based on distance histograms from double electron-electron resonance spectroscopy. J Phys Chem B. 2013;117: 4733–4739. pmid:23510121
View Article
PubMed/NCBI
Google Scholar

[145] View Article

[146] PubMed/NCBI

[147] Google Scholar

[ref40] 40. Yang Z, Kurpiewski MR, Ji M, Townsend JE, Mehta P. ESR spectroscopy identifies inhibitory Cu sites in a DNA-modifying enzyme to reveal determinants of catalytic specificity. 2012; 3–10. pmid:22493217
View Article
PubMed/NCBI
Google Scholar

[149] View Article

[150] PubMed/NCBI

[151] Google Scholar

[ref41] 41. Abdullin D, Schiemann O. Localization of Metal Ions in Biomolecules by means of Pulsed Dipolar EPR Spectroscopy. Dalt Trans. 2021. pmid:33416053
View Article
PubMed/NCBI
Google Scholar

[153] View Article

[154] PubMed/NCBI

[155] Google Scholar

[ref42] 42. Wingler LM, Elgeti M, Hilger D, Latorraca NR, Lerch MT, Staus DP, et al. Angiotensin Analogs with Divergent Bias Stabilize Distinct Receptor Conformations. Cell. 2019; 1–11. pmid:30639099
View Article
PubMed/NCBI
Google Scholar

[157] View Article

[158] PubMed/NCBI

[159] Google Scholar

[ref43] 43. Edwards TH, Stoll S. A Bayesian approach to quantifying uncertainty from experimental noise in DEER spectroscopy. J Magn Reson. 2016;270: 87–97. pmid:27414762
View Article
PubMed/NCBI
Google Scholar

[161] View Article

[162] PubMed/NCBI

[163] Google Scholar

[ref44] 44. Jeschke G, Chechik V, Ionita P, Godt A, Zimmermann H, Banham J, et al. DeerAnalysis2006—a comprehensive software package for analyzing pulsed ELDOR data. Appl Magn Reson. 2006;30: 473–498.
View Article
Google Scholar

[165] View Article

[166] Google Scholar

[ref45] 45. Chiang Y-W, Borbat PP, Freed JH. Maximum entropy: a complement to Tikhonov regularization for determination of pair distance distributions by pulsed ESR. J Magn Reson. 2005;177: 184–196. pmid:16137901
View Article
PubMed/NCBI
Google Scholar

[168] View Article

[169] PubMed/NCBI

[170] Google Scholar

[ref46] 46. Worswick SG, Spencer JA, Jeschke G, Kuprov I. Deep neural network processing of DEER data. Sci Adv. 2018;4: eaat5218. pmid:30151430
View Article
PubMed/NCBI
Google Scholar

[172] View Article

[173] PubMed/NCBI

[174] Google Scholar

[ref47] 47. Srivastava M, Freed JH. Singular Value Decomposition Method To Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance: II. Estimating Uncertainty. J Phys Chem A. 2019;123: 359–370. pmid:30525624
View Article
PubMed/NCBI
Google Scholar

[176] View Article

[177] PubMed/NCBI

[178] Google Scholar

[ref48] 48. Srivastava M, Freed JH. Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance. J Phys Chem A. 2017;22: 5648–5655. pmid:29099190
View Article
PubMed/NCBI
Google Scholar

[180] View Article

[181] PubMed/NCBI

[182] Google Scholar

[ref49] 49. Akaike H. Information theory and an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory. 1973. pp. 267–281.
View Article
Google Scholar

[184] View Article

[185] Google Scholar

[ref50] 50. Sugiura N. Further analysts of the data by akaike’ s information criterion and the finite corrections. Commun Stat—Theory Methods. 1978;7: 13–26.
View Article
Google Scholar

[187] View Article

[188] Google Scholar

[ref51] 51. Georgieva ER, Roy AS, Grigoryants VM, Borbat PP, Earle KA, Scholes CP, et al. Effect of freezing conditions on distances and their distributions derived from Double Electron Electron Resonance (DEER): A study of doubly-spin-labeled T4 lysozyme. J Magn Reson. 2012;216: 69–77. pmid:22341208
View Article
PubMed/NCBI
Google Scholar

[190] View Article

[191] PubMed/NCBI

[192] Google Scholar

[ref52] 52. Banham JE, Jeschke G, Timmel CR. Evidence from EPR that nitroxide spin labels attached to human hemoglobin alter their conformation upon freezing. Mol Phys. 2007;105: 2041–2047.
View Article
Google Scholar

[194] View Article

[195] Google Scholar

[ref53] 53. Yang LW, Eyal E, Chennubhotla C, Jee JG, Gronenborn AM, Bahar I. Insights into Equilibrium Dynamics of Proteins from Comparison of NMR and X-Ray Data with Computational Predictions. Structure. 2007;15: 741–749. pmid:17562320
View Article
PubMed/NCBI
Google Scholar

[197] View Article

[198] PubMed/NCBI

[199] Google Scholar

[ref54] 54. Sun Z, Liu Q, Qu G, Feng Y, Reetz MT. Utility of B-Factors in Protein Science: Interpreting Rigidity, Flexibility, and Internal Motion and Engineering Thermostability. Chem Rev. 2019. pmid:30698416
View Article
PubMed/NCBI
Google Scholar

[201] View Article

[202] PubMed/NCBI

[203] Google Scholar

[ref55] 55. Weaver LH, Matthews BW. Structure of Bacteriophage T4 Lysozyme Refined at 1.7 A Resolution. J Mol Biol. 1987; 193–189. pmid:3586019
View Article
PubMed/NCBI
Google Scholar

[205] View Article

[206] PubMed/NCBI

[207] Google Scholar

[ref56] 56. Zakrzewska S, Mehdipour AR, Malviya VN, Nonaka T, Koepke J, Muenke C, et al. Inward-facing conformation of a multidrug resistance MATE family transporter. Proc Natl Acad Sci U S A. 2019;116: 12275–12284. pmid:31160466
View Article
PubMed/NCBI
Google Scholar

[209] View Article

[210] PubMed/NCBI

[211] Google Scholar

[ref57] 57. Tanaka Y, Hipolito CJ, Maturana AD, Ito K, Kuroda T, Higuchi T, et al. Structural basis for the drug extrusion mechanism by a MATE multidrug transporter. Nature. 2013;496: 247–251. pmid:23535598
View Article
PubMed/NCBI
Google Scholar

[213] View Article

[214] PubMed/NCBI

[215] Google Scholar

[ref58] 58. Jagessar KL, Claxton DP, Stein RA, Mchaourab HS. Sequence and Structural Determinants of Ligand-Dependent Alternating Access of a MATE Transporter. Proc Natl Acad Sci U S A. 2020;117: 4732–4740. pmid:32075917
View Article
PubMed/NCBI
Google Scholar

[217] View Article

[218] PubMed/NCBI

[219] Google Scholar

[ref59] 59. Leaver-fay A, Tyka M, Lewis SM, Lange F, Thompson J, Jacak R, et al. ROSETTA 3: An Object-Oriented Software Suite for the Simulation and Design of Macromolecules. 2011;487: 545–574.
View Article
Google Scholar

[221] View Article

[222] Google Scholar

[ref60] 60. Alford RF, Fleming PJ, Fleming KG, Gray JJ. Protein structure prediction and design in a biologically realistic implicit membrane. Biophys J. 2020. pmid:32224301
View Article
PubMed/NCBI
Google Scholar

[224] View Article

[225] PubMed/NCBI

[226] Google Scholar

[ref61] 61. Alford RF, Koehler Leman J, Weitzner BD, Duran AM, Tilley DC, Elazar A, et al. An Integrated Framework Advancing Membrane Protein Modeling and Design. PLoS Comput Biol. 2015;11: 1–23. pmid:26325167
View Article
PubMed/NCBI
Google Scholar

[228] View Article

[229] PubMed/NCBI

[230] Google Scholar

[ref62] 62. Yarov-Yarovoy V, Schonbrun J, Baker D. Multipass membrane protein structure prediction using Rosetta. Proteins. 2006;62: 1010–1025. pmid:16372357
View Article
PubMed/NCBI
Google Scholar

[232] View Article

[233] PubMed/NCBI

[234] Google Scholar

[ref63] 63. Weinstein JY, Elazar A, Fleishman SJ. A lipophilicity-based energy function for membrane-protein modelling and design. PLoS Comput Biol. 2019;15. pmid:31461441
View Article
PubMed/NCBI
Google Scholar

[236] View Article

[237] PubMed/NCBI

[238] Google Scholar

[ref64] 64. Burnham K, Anderson DR. Model Selection and Multimodel Inference. 2002.
View Article
Google Scholar

[240] View Article

[241] Google Scholar

[ref65] 65. Fleishman SJ, Leaver-Fay A, Corn JE, Strauch EM, Khare SD, Koga N, et al. Rosettascripts: A scripting language interface to the Rosetta Macromolecular modeling suite. PLoS One. 2011;6. pmid:21731610
View Article
PubMed/NCBI
Google Scholar

[243] View Article

[244] PubMed/NCBI

[245] Google Scholar

[ref66] 66. Powers R, Clore GM, Garrett DS, Gronenborn AM. Relationships between the Precision of High-Resolution Protein NMR Structures, Solution-Order Parameters, and Crystallographic B Factors. J Magn Reson. 1993;101: 325–327. Available: http://digitalcommons.unl.edu/chemistrypowershttp://digitalcommons.unl.edu/chemistrypowers/20
View Article
Google Scholar

[247] View Article

[248] Google Scholar

[ref67] 67. Billeter M, Vendrell J, Wider G, Avils FX, Coll C’ M, Guasch B’c A, et al. Comparison of the NMR solution structure with the X-ray crystal structure of the activation domain from procarboxypeptidase B. J Biomol NMR. 1992. pmid:1422143
View Article
PubMed/NCBI
Google Scholar

[250] View Article

[251] PubMed/NCBI

[252] Google Scholar

[ref68] 68. Kim DE, Chivian D, Baker D. Protein structure prediction and analysis using the Robetta server. Nucleic Acids Res. 2004;32: 526–531. pmid:15215442
View Article
PubMed/NCBI
Google Scholar

[254] View Article

[255] PubMed/NCBI

[256] Google Scholar

Figures

Abstract

Author summary

Introduction

Results and discussion

Overview of the multilateration algorithm

Data analysis benchmark

Distance distribution benchmark

Modeling of PfMATE’s conformational changes using refined pseudo-rotamers

Concluding remarks

Materials and methods

Overview of the model-based approach

Detailed description of the multilateration algorithm

Simulation of DEER distance distributions

Evaluating coordinate models obtained from raw DEER traces

Determination of distance distributions

Application to T4 Lysozyme and PfMATE

Modeling the OF-to-IF conformational change of PfMATE

Supporting information

S1 Fig. Number of DEER restraints per spin-labeled residue across T4 Lysozyme and PfMATE.

S2 Fig. All DEER traces determined by multilateration are shown in red. Experimental DEER traces are shown in black.

S3 Fig. All DEER distance distributions determined by multilateration are shown in black.

S4 Fig. All DEER distance distributions determined by multilateration are shown in black.

S5 Fig. All DEER distance distributions determined by multilateration are shown in black.

S6 Fig. Comparison of average and standard deviation values obtained when fitting DEER data collected in pfMATE and T4 Lysozyme to values obtained using DeerAnalysis and DeerNet.

S7 Fig. Shaded regions depict 95% confidence intervals, and line represents the mean distribution.

S8 Fig. Comparison of DEER distance distributions used to validate pseudo-rotamers obtained using the RosettaDEER multilateration algorithm.

S9 Fig. Rosetta energy functions for membrane proteins cannot identify the inward-facing conformation of PfMATE.

S1 Table. List of restraints used for scoring intermediate PfMATE models.

S1 Appendix. Summary of experimental DEER measurements collected in T4 Lysozyme and PfMATE.

S2 Appendix. Coordinates of top five ensembles of pseudo-rotamers in T4 Lysozyme.

S3 Appendix. Coordinates of top five ensembles of pseudo-rotamers in PfMATE.

S4 Appendix. Scores of intermediate PfMATE models.

S5 Appendix. Supplemental methods.

Acknowledgments

References