2.1.1 Chemical shift ambiguity

NOE-assignment programs start from a list of peaks (compiled from all the NMR spectra) and a list of chemical shifts, each of which corresponds to a particular atom (or group of atoms) in the protein. It is common for the chemical shifts of many nuclei to be degenerate within the limits of the NOESY linewidth and the measurement precision. Indeed, it can be shown, using a sphere model to represent a biomolecule (Güntert, Reference Güntert2003) that the number of peaks assignable to a unique pair of protons decreases exponentially with the size of the protein, while the average initial ambiguity for a 3D ¹³C-resolved NOESY spectrum is typically of the order of 10–20.

An expert spectroscopist will use one's trained intuition to discard incorrect assignments and artefacts, and will exploit preliminary structures once they become available. In this context, computer programs must find ways of transalating human reasoning into systematic procedures. And while it is relatively trivial to cyclically incorporate knowledge from (correct) intermediate 3D structures, more intricate techniques must be employed to reduce the assignment ambiguity at the very start of the structure-determination process.

2.1.2 Initial ranking of assignments

The simplest way of ranking the assignment possibilities of an individual peak is to compare how close the chemical shift coordinates match those of the peak. However, it is easy to overinterpret this ranking, since unaccounted-for effects from misaligned spectra, slight referencing offsets and variations in experimental conditions can lead to significant changes (actual or reported) in the resonance frequencies.

2.1.3 Network anchoring

Network anchoring (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002b) measures how well a particular assignment is supported by the list of all other potential assignments compiled across all available spectra. Correct assignments form a self-consistent set and will score highly, whereas wrong assignments act incoherently in the network and do not support each other.

In CANDID (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002b), the network anchoring score is calculated by finding all the atoms connected to both interacting protons either through another candidate assignment or via the covalent polypeptide structure. The procedure is cyclic in that individual scores depend on all the others; by that means, connections through highly supported assignments are more influential.

A somewhat more formal expression of network anchoring is implemented in the BACUS algorithm, in which Bayes’ theorem is used to convert the network support into assignment probabilities (Grishaev & Llinás, Reference Grishaev and Llinás2004; Lemak et al. Reference Lemak, Steren, Arrowsmith and Llinás2008). The BACUS approach is original in that network anchoring is used without chemical shift assignment. Rather, the covalent information necessary to understand the mutual network support is extracted directly from additional assignment-type experiments (TOCSY, COSY, etc.) and database statistics.

The value of network anchoring has been demonstrated qualitatively – for ARIA (Bardiaux et al. Reference Bardiaux, Bernard, Rieping, Habeck, Malliavin and Nilges2009) and CANDID (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002b) – and quantitatively, whereby for two test cases BACUS was able to reduce the initial chemical shift ambiguity by at least a factor of six.

2.1.4 Bayesian statistics

As an alternative to network anchoring, a Bayesian approach has been proposed to select the most probable assignment using information from a database of know structures (Gronwald et al. Reference Gronwald, Moussa, Elsner, Jung, Ganslmeier, Trenner, Kremer, Neidig and Kalbitzer2002; Hung & Samudrala, Reference Hung and Samudrala2006).

In the context of NOE assignment, Bayes’ theorem gives the probability of each putative assignment as a function of its prior probability and corrected for the overall reliability of the peak. More precisely,

(2)

where P(A|B) is the probability of the candidate contact given the observation of the current peak and conversely for P(B|A), whereas P(B) is the prior probability of the peak. P(A) finally is the prior probability of the contact, calculated as follows.

Different classes are constructed depending on the amino-acid type, the residue separation and the secondary structure. The latter only in the ProtInfo approach (Hung & Samudrala, Reference Hung and Samudrala2006), where the prior probability for each class is then the proportion of such contacts in the database liable to interact via an NOE. KNOWNOE (Gronwald et al. Reference Gronwald, Moussa, Elsner, Jung, Ganslmeier, Trenner, Kremer, Neidig and Kalbitzer2002) on the other hand measures the distribution of distances from the database for each contact type and converts these to volume distributions. These are then used for each putative assignment in an attempt to identify a unique solution: one that has a high-enough probability to account for peak intensity in its entirety. While it is clear that such approaches are effective at ranking short-range above medium- and long-range assignments, the primary objective of ambiguity reduction is to select amongst several long-distance assignments. In this respect, the prior probabilities are not sufficiently discriminatory and no clear criterion for accepting or rejecting assignments emerges.

2.1.5 Ambiguous restraints

A key feature of an NOE-assignment protocol is its ability to deal with peaks with several assignment possibilities. Indeed, it is often the case – especially for larger proteins – that even the best filtering is unable to completely resolve all the ambiguities. The application of early algorithms (Güntert et al. Reference Güntert, Mumenthaler and Wüthrich1991, Reference Güntert, Berndt and Wüthrich1993; Mumenthaler & Braun, Reference Mumenthaler and Braun1995; Mumenthaler et al. Reference Mumenthaler, Güntert, Braun and Wüthrich1997; Duggan et al. Reference Duggan, Legge, Dyson and Wright2001) was thereby limited to cases where the number of unambiguous signals was sufficient to obtain an initial fold.

To overcome this obstacle, Michael Nilges (Nilges, Reference Nilges1993, Reference Nilges1995) proposed treating ambiguous peaks as an overlap of signals from all the n possible assignments (which, in fact, is almost never the case, but we shall see that this does not matter) and to set the constraint on the summed volume rather than on one of the individual components.

(3)

where V_A is the total (ambiguous) peak volume and V_k is the volume associated with a particular assignment. In terms of distances, this becomes

(4)

As illustrated in Fig. 5, because the intensity of the signal is inversely related to separation, ambiguous restraints are always laxer than those corresponding to the native structure. This means that the information is somewhat blurred out but more importantly, it guarantees that ambiguous constraints never distort a structure as long as the correct assignment is present. In fact, the concerted action of many ambiguous restraints during the molecular dynamics (MD) calculation forces each one to converge towards the correct unambiguous assignment. However, it is clear that this action becomes less and less effective as the average ambiguity increases. It is therefore vital that incorrect assignments be weeded out as much as possible prior to the constraints being set.

Fig. 5.

Illustration of the principle of ambiguous restraints for the case of two-fold assignment ambiguity. (a) The peak is unambiguously assigned to the correct candidate constraint. (b) The peak is unambiguously assigned to the wrong restraint, distorting the structure. (c) The peak volume is assumed to originate from both candidate contacts. An ambiguous restraint is applied such that the summed contribution from both assignments equals the experimental volume. Since constraints are applied as upper-distance limits, the correct structure is always fulfilled as long as the correct assignment is included.

Fig. 6.

Histogram plot of the number of citations from PDB depositions for NOE assignment programs as of 27 August 2010. Citations from internal depositions are represented in black whereas those from external use of the program are shown in grey. In this context, we define internal depositions as those for which one or more of the developers appear as a structure author, or which originate from the same structural genomics project in which the program was developed. Exact search strings can be found in the Appendix, Table A2.

Fig. 7.

Histograms representing the number of citations from PDB depositions for peak picking algorithms as of 27 August 2010. Citations from internal depositions are represented in black, whereas those from external use of the program are shown in grey. In this context, we define internal depositions as those for which one or more of the developers appear as a structure author, or which originate from the same structural genomics project in which the program was developed. Exact search strings can be found in the Appendix, Table A3.

Fig. 8.

Histogram plot of the number of citations from PDB depositions for selected chemical shift assignment programs as of 27 August 2010. Only those programs are listed for which at least one citation was found. Citations from internal depositions are represented in black, whereas those from external use of the program are shown in grey. In this context, we define internal depositions as those for which one or more of the developers appear as a structure author, or which originate from the same structural genomics project in which the program was developed. Note that (Bermejo & Llinás, Reference Bermejo and Llinás2010) count 31 depositions for ABACUS. Exact search strings can be found in the Appendix, Table A1.

Fig. 9.

Histogram plot of the number of citations – as of 7 September 2010 – from PDB depositions for torsion angle-prediction software. Exact search strings can be found in the Appendix, Table A6.

2.1.6 Using intermediate structures: violation analysis

Once a preliminary structural model has been built, this can be used to re-evaluate the experimental data and filter assignments based on their agreement with the intermediate fold. Not only does this significantly reduce the initial chemical shift-based assignment ambiguity but it also identifies artefacts as the peaks with no structure-supported assignment. The difficulty, however, lies in identifying true violations from those caused by insufficient convergence or distortions caused by other artefacts. Violation analysis is therefore a double-edged sword; on the one hand, it ensures that the algorithms converge, but it makes it extremely hard to recover the native fold if this has not already been obtained after the first cycle. The algorithms are therefore heavily reliant on efficient, ab initio analysis of the experimental data.

As described above, ambiguous restraints are a means to let the MD algorithm decide which of the potential assignments should take precedent. Partial NOE assignment (Nilges & O'Donoghue, Reference Nilges and O'Donoghue1998; Linge et al. Reference Linge, O'Donoghue and Nilges2001; Kuszewski et al. Reference Kuszewski, Schwieters, Garrett, Byrd, Tjandra and Clore2004) aims at retrieving this information from the intermediate structures and may be used to supplement or replace (Kuszewski et al. Reference Kuszewski, Schwieters, Garrett, Byrd, Tjandra and Clore2004) violation analysis in reducing the assignment ambiguity.

For a given peak, the relative volume contributions from the list of candidate assignments are calculated according to the separation of the corresponding atoms in the latest structure. Usually, a cycle-dependent cut-off is imposed whereby initially, only very small contributions (long distances) are discarded with the selection criterion becoming more stringent after each cycle.

2.1.7 Eliminating artefacts

Experimental NMR spectra contain a substantial number of artefacts. As described above, intra-peak ambiguous restraints never distort a structure as long as the correct assignment is included. Artefacts clearly violate this rule and will lead to distortions. The risk being that these are carried through when intermediate structures are used to reassign the spectra. When working with unrefined peak lists, it is therefore critical to minimise the effect of artefacts even before the first structure is calculated.

Constraint combination (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002b) involves the implementation of inter-peak ambiguous restraints, which ensures a significant reduction in the number of artefacts. In the first stage, long-distance peaks are ranked according to their network anchoring and split into four categories from the most reliable quarter to the least. For each set of four peaks, one from each category, the most reliable is paired once with each of the three others, while the two middle-ranking peaks are combined to form the fourth ambiguous constraint. Thereby, a combined constraint will only distort the structure if both peaks are artefacts. The extent to which artefacts are suppressed depends on the initial proportion thereof and how well the network anchoring score reflects the true error probability of the peaks. For instance, the analysis of Herrmann et al. (Reference Herrmann, Güntert and Wüthrich2002b) shows that for a set of 1000 peaks of which 100 are artefacts and for which the top-ranked quarter is, respectively, twice and three times more reliable than the middle two and bottom-ranked quarters, only seven artefacts remain after constraint combination.

2.1.8 Distance calibration

In NMR protein structure determination, the peak volumes (or intensities) measured experimentally are converted to distance constraints under the two-spin approximation. As mentioned above, this simplification is rather drastic for proteins. In addition, it is actually quite difficult to accurately measure a peak volume in the presence of many overlapping lines. However, several factors contribute to the robustness of this approach. To begin with, because of the inverse power of six relationships, the NOE method is not sensitive to errors in the volume assessment. Furthermore, the distance constraints need not be precise as long as there are many and as long as conservative estimates (upper-distance limits) are taken. The remaining task is then to determine C, the spectrum-dependent constant, for which several methods have been proposed.

CANDID applies a continuous calibration whereby initially, peaks assigned to covalent contacts (for which the polypeptide structure imposes a maximal spatial separation such that an NOE is always expected) are used to calculate the calibration constant. In later cycles, the calibration constant is set such that no more than a given percentage (15 then 10%) of constraints violate the intermediate structure. AutoStructure (Moseley & Montelione, Reference Moseley and Montelione1999; Huang et al. Reference Huang, Tejero, Powers and Montelione2006) on the other hand, classes peaks according to their relative intensities before deriving upper-distance limits for each class.

A more precise interpretation of the information contained in the peak volumes may be achieved by back-calculating the experimental spectrum using the intermediate structure. Bardiaux et al. (Reference Bardiaux, Bernard, Rieping, Habeck, Malliavin and Nilges2009) have shown that the relaxation matrix (Ernst et al. Reference Ernst, Bodenhausen and Wokaun1987) approach employed in ARIA (Linge et al. Reference Linge, Habeck, Rieping and Nilges2004) effectively corrects for spin diffusion effects and results in tighter error bounds for the distance restraints. Understandably though, this more intricate approach is hungrier for computer resources.

2.1.9 Recent developments

The NOE-assignment programs mentioned above (see also Table 1 and Fig. 6), released roughly 10 years ago, are still in active development. A clear objective of the field in general is to make such tools more accessible to non-specialists. In this perspective, most programs now come complete with graphical user interfaces (GUIs). In fact, though the interpretation of the results is still the domain of experts, it reflects well on the maturity of the field that a virtual novice can set up and run a calculation in a matter of minutes.

To mention but a few examples, KUJIRA (Kobayashi et al. Reference Kobayashi, Iwahara, Koshiba, Tomizawa, Tochio, Güntert, Kigawa and Yokoyama2007) was developed as part of the RIKEN structural proteomics project (Yokoyama et al. Reference Yokoyama, Hirota, Kigawa, Yabuki, Shirouzu, Terada, Ito, Matsuo, Kuroda, Nishimura, Kyogoku, Miki, Masui and Kuramitsu2000a) to provide a graphical front end for CANDID with CYANA (Güntert, Reference Güntert2004) and to facilitate data management and analysis in the context of high-throughput structure calculations. Similarly, CANDID as part of UNIO and also ARIA now provide a number of graphical reports at the end of a structure calculation to facilitate the evaluation of the result. In addition, ARIA automatically performs energy refinement and reports on the quality of the structure obtained using several validation tools (see Section 2.2), as does AutoStructure with the recall, precision and F-measure (RPF) score (Huang et al. Reference Huang, Powers and Montelione2005). Finally, the software package AUREMOL (Gronwald & Kalbitzer, Reference Gronwald and Kalbitzer2004) associates KNOWNOE with graphical tools for NMR data processing and analysis.

2.1.10 Structure calculation and energy refinement

Being virtually unachievable manually or interactively, the building of atomic-resolution structure models was the first task to be successfully automated and indeed, this particular problem has been considered solved for the past 10 years or so. There is not much to add therefore to Peter Güntert's comprehensive review (Güntert, Reference Güntert1998) and the main programs (DYANA (Güntert et al. Reference Güntert, Mumenthaler and Wüthrich1997), CNS (Brunger et al. Reference Brunger, Adams, Clore, Delano, Gros, Grosse-Kunstleve, Jiang, Kuszewski, Nilges, Pannu, Read, Rice, Simonson and Warren1998), X-PLOR (Brunger, Reference Brunger1992; Schwieters et al. Reference Schwieters, Kuszewski, Tjandra and Clore2003)) have not changed significantly since then. Briefly though, in CYANA for example, the structure is obtained starting from an initially random fold by restrained MD simulations using a hybrid energy function that incorporates physical interactions and experimental constraints. For reasons of efficiency, the physical component in the target function is over-simplified, and therefore the final round of structure calculation should be followed by refinement using a physically realistic potential in explicit solvent (Güntert, Reference Güntert1998; Spronk et al. Reference Spronk, Nabuurs, Krieger, Vriend and Vuister2004; Nabuurs et al. Reference Nabuurs, Nederveen, Vranken, Doreleijers, Bonvin, Vuister, Vriend and Spronk2004a; Nederveen et al. Reference Nederveen, Doreleijers, Vranken, Miller, Spronk, Nabuurs, Güntert, Livny, Markley, Nilges, Ulrich, Kaptein and Bonvin2005). This is usually performed using force fields adapted from standard MD packages (Linge & Nilges, Reference Linge and Nilges1999; Koradi et al. Reference Koradi, Billeter and Güntert2000; Linge et al. Reference Linge, Williams, Spronk, Bonvin and Nilges2003; Case et al. Reference Case, Cheatham, Darden, Gohlke, Luo, Merz, Onufriev, Simmerling, Wang and Woods2005; Christen et al. Reference Christen, Hunenberger, Bakowies, Baron, Burgi, Geerke, Heinz, Kastenholz, Krautler, Oostenbrink, Peter, Trzesniak and Van Gunsteren2005; Phillips et al. Reference Phillips, Braun, Wang, Gumbart, Tajkhorshid, Villa, Chipot, Skeel, Kale and Schulten2005; Schwieters et al. Reference Schwieters, Kuszewski and Clore2006) but an alternative approach has recently been proposed, based on Rosetta structure prediction (Qian et al. Reference Qian, Raman, Das, Bradley, Mccoy, Read and Baker2007; Das & Baker, Reference Das and Baker2008; Ramelot et al. Reference Ramelot, Raman, Kuzin, Xiao, Ma, Acton, Hunt, Montelione, Baker and Kennedy2009). Protocols for energy refinement are constantly being updated and this improves structures past, present and future. A couple of recent studies have indeed demonstrated the value of amending prior depositions using the latest software (Nabuurs et al. Reference Nabuurs, Nederveen, Vranken, Doreleijers, Bonvin, Vuister, Vriend and Spronk2004a; Nederveen et al. Reference Nederveen, Doreleijers, Vranken, Miller, Spronk, Nabuurs, Güntert, Livny, Markley, Nilges, Ulrich, Kaptein and Bonvin2005): an excellent reason – if another were needed – to upload experimental restraints as well as the structure!

2.3.1 Generalities

Automated chemical shift assignment is usually performed in four stages with the aim first, to group resonances into spin systems; second, to determine the amino-acid type of each spin system; third, to create fragments from collections of spin systems that match sequentially; fourth, to associate the said fragments with a particular position in the amino-acid sequence. Usually at this stage, only the backbone and Cβ atoms are assigned (in the context of chemical shift assignment, the Cβ atoms are generally treated with the backbone atoms, rather than the side chain. In the following therefore, we use ‘backbone assignment’ to mean ‘backbone and Cβ assignment’) and indeed, the assignment of the side-chain atoms has proved even more problematic to complete automatically. A (smaller) number of algorithms have nonetheless been developed that include the side-chain atoms in the initial spin systems (stage one) (Bartels et al. Reference Bartels, Billeter, Güntert and Wüthrich1996, Reference Bartels, Güntert, Billeter and Wüthrich1997; Moseley & Montelione, Reference Moseley and Montelione1999; Baran et al. Reference Baran, Huang, Moseley and Montelione2004; Gronwald & Kalbitzer, Reference Gronwald and Kalbitzer2004). Alternatively, the two problems may be treated entirely separately with an algorithm dedicated to the side chains being applied (Fiorito et al. Reference Fiorito, Herrmann, Damberger and Wüthrich2008) once the backbone assignment has been completed.

The defining feature of most programs is their approach to mapping fragments onto the primary sequence (stage four), which involves finding the optimal combination amongst myriad possibilities. Most programs can thereby be classified accordingly as exhaustive search, best-first, Monte-Carlo or genetic algorithms.

2.3.2 AutoAssign

The best-first approach employed in AutoAssign (Zimmerman et al. Reference Zimmerman, Kulikowski, Huang, Feng, Tashiro, Shimotakahara, Chien, Powers and Montelione1997; Moseley et al. Reference Moseley, Monleon and Montelione2001) is perhaps the simplest to understand conceptually, if only because its description is jargon-free and does not require the assignment problem to be recast in terms of a more general theory. AutoAssign performs backbone assignment starting from a set of peak lists (five to eight) from traditional assignment experiments and information on amino-acid-specific chemical shift distributions extracted from the Biological Magnetic Resonance Bank (BMRB) (Doreleijers et al. Reference Doreleijers, Nederveen, Vranken, Lin, Bonvin, Kaptein, Markley and Ulrich2005). Following the approach outlined above, resonances from different spectra are aligned and grouped into dipeptide spin systems (stage one). At this stage, three classes are defined – distinct, overlapped and incomplete – for the spin systems depending on the ambiguity and/or completeness in terms of constituent resonances. The three subsequent steps are applied initially to the distinct class before exploiting the results to interpret and assign the overlapped and then incomplete spin systems. First, the amino-acid-type probabilities are determined for each dipeptide group (stage two) by comparing experimental chemical shifts with BMRB statistics. Then, spin systems are linked using a best-first approach. For each dipeptide, candidate neighbours are ranked according to the number of common resonances that match, and then according to the closeness of the match; the highest-ranking candidate is chosen and removed from subsequent consideration. Finally, the fragments of varying length are mapped to a unique position on the amino-acid sequence.

2.3.3 MATCH

In MATCH, the problem of sequence-specific backbone assignment is expressed in terms of the evolution of a set of individuals. The initial population is a set of sequence-specific resonance assignments (the individuals), each one built from fragments assembled from one or several APSY (Hiller et al. Reference Hiller, Fiorito, Wüthrich and Wider2005) spectra and arranged in a random sequence. In MATCH, a spin system consists of up to 18 frequencies (6 intra- and 12 inter-residue) linking two or three residues. The consolidation of resonances into spin systems is facilitated greatly by the numerous correlations already apparent in the high-dimensional APSY peak lists.

Starting with the longest fragments but otherwise randomly, these are removed from the buffer to the best-matching available position on the current individual. This procedure is repeated until a heterogeneous population is obtained, the size of which is determined automatically according to the ambiguity of the input data.

The evolutionary cycle proceeds through the independent mutation of each individual. Randomly, a fragment is chosen along with a new position where a swap is performed if at least one extremity of the candidate fragment fits with its neighbour. Furthermore, an assignment is made if the sequence-specific score – the chemical shift matching score between the experimental and predicted values, evaluated for the fragment at its new location, is above a given threshold. Conversely, if no compatible location is found after a given number of attempts, the process is re-initialised for a different candidate. However, those fragments that have already been assigned are locked in their positions.

This local optimisation is followed by an evaluation of assignments across the whole population. Temporary assignments are associated with a particular individual, whereas a permanent assignment is defined if a given temporary assignment is found in more than a predetermined fraction of the population.

Each cycle is punctuated by selective breeding whereby the genetic information from the fittest individuals forms a gene pool from which descendants are constructed. Specifically: in the first stage, the parent individuals are ranked according to their sequence-specific scores. This evaluates how well each fragment fits at its current position and the overall quality of the assignment. A buffer is then created using fragments from the highest-ranked individuals. As for the initial genesis, descendant individuals are constructed fragment by fragment from the gene pool, only now, the position of the fragments is inherited from the previous cycle.

The optimisation ends once all the individuals in the population are identical. The resulting assignment is then stored in a buffer of elite individuals and the whole procedure is repeated a predetermined number of times. An assignment is considered correct if it appears in more than 50% of the final elite population.

2.3.4 MARS

The emphasis so far has been placed on chemical shift assignment for de-novo NMR protein structure determination. In many cases, however, for instance when protein dynamics are of interest, a structural model already exists. The MARS procedure is original in that it can be augmented with a structural model and RDCs (Jung & Zweckstetter, Reference Jung and Zweckstetter2004a, Reference Jung and Zweckstetterb). Starting with the more conventional ‘chemical shift-only’ approach – which also forms the core of the ‘structure & RDC’ method – MARS relies on chemical shift and secondary structure prediction along with cumulative exhaustive searches to arrive at the correct assignment.

More precisely, a pseudo-energy is calculated for assigning a spin system to a particular position, based on how well the experimental chemical shifts match those expected from the primary structure. In MARS, the relevance of the comparison is enhanced by predicting the secondary structure of the protein using the program PSIRED (McGuffin et al. Reference Mcguffin, Bryson and Jones2000) and then using this information along with corrections for neighbouring residues to refine the chemical shift statistics from the BMRB. It should be noted that MARS requires spin systems rather than peak lists as input; i.e. stage one must be performed externally (manually or otherwise).

The MARS algorithm is constructed around an exhaustive search procedure initiated by allocating to all spin systems a random position in the amino-acid sequence. A spin-system is selected randomly and a forward search is performed along the sequence until all possible five fragments (fragments of five spin systems) have been constructed. The procedure for establishing sequential connectivities is tolerant for missing or imprecise data in that a putative link is only rejected if both common resonances are present and are in disagreement above a certain threshold. In contrast to best-first approaches (e.g. AutoAssign described above), candidate fragments are not ranked according to the quality of sequential match and all possibilities are considered at each stage of the exhaustive search. Each fragment is then placed at every possible position in the amino-acid list, the pseudo energy is calculated and a ranking is established. The lowest-energy five-fragment with its associated position identifies the best position for the optimal five-fragment starting from the initially selected spin system. Now, starting from the last residue of the highest-ranked fragment, the procedure is repeated in reverse. If again, the same five-fragment comes out on top associated with the same position, the initial spin system is relocated. This back and forth search is repeated until all spin systems have been used once as the root residue before re-initialising the cycle with four, three and two fragments. However, moving previously assigned spin systems comes with an extra energy cost. This ensures that correctly assigned residues are not repeatedly (and incorrectly) shifted around.

At this stage, a comparison is made between the fragment-derived assignments and the lowest pseudo-energy position for each spin system, analysed individually. Assignments are only conserved if they are found repeatedly in multiple runs. Indeed, the MARS procedure involves performing both assignment schemes 100 times during which Gaussian noise is added to the predicted shifts according to an empirically devised strategy. Assignments that are conserved in the first 20 pairs are kept fixed for subsequent rounds, then similarly for consistent assignments in the next 30, then again for the next 20 and the final 30. At each stage, the variance of the noise is reduced such that the most reliable assignments constrain the search for more uncertain attributions.

When RDCs and a structural model are provided, MARS proceeds in the same way except for an extra term in the pseudo energy that evaluates the match between RDCs measured experimentally and those back calculated from the structure. Since RDCs are very sensitive to small structural changes – that can occur for example due to dynamics, the RDC matching weighs less than the chemical shift. In addition, the alignment tensor is initially calculated using one of four possible methods and then the estimate is refined gradually as more assignments are made using singular value decomposition (SVD).

2.3.5 ABACUS

ABACUS (Lemak et al. Reference Lemak, Steren, Arrowsmith and Llinás2008) performs backbone and side-chain assignment using a traditional set of assignment experiments, minus those for establishing sequential connectivities. Indeed, in ABACUS, this information is extracted directly from the NOE spectra used subsequently for the structure calculation.

To begin with, NOEs are assigned to specific fragments using BACUS (Grishaev & Llinás, Reference Grishaev and Llinás2004; Lemak et al. Reference Lemak, Steren, Arrowsmith and Llinás2008) and the relative proximities of the later are determined from the resulting distance information according to the CLOUDS procedure (Grishaev & Llinás, Reference Grishaev and Llinás2002a).

ABACUS employs a multi-canonical MC algorithm (Berg & Neuhaus, Reference Berg and Neuhaus1991; Berg & Celik, Reference Berg and Celik1992) to find the minimum energy in the assignment space. The pseudo energy of the system has two components, the first of which accounts for the matching between the chemical shifts of the current fragment and those for the amino acid type at the candidate position, while the second evaluates whether the current fragment is close enough to its putative neighbour to form a sequential link. Thereby, the closer the two fragments are in the clouds (constructed in the previous cycle), the greater the number of NOEs connecting the pair (assigned by BACUS) and the higher the chemical shift similarity at the candidate position, the lower the energy.

During each MC run, fragment swaps are performed randomly and accepted if they lower the energy, or if they do not, with a probability

(5)

where E is the total energy of the system. Following a multi-canonical approach, the weight function S(E) is updated after each MC cycle such that

(6)

where H_i(E) is the energy histogram from MC run i. In addition, an absolute energy limit is imposed, which is reduced after each cycle; the idea in both cases being to push the sampling of assignment space towards low-energy regions.

2.4.1 AUTOPSY

AUTOPSY (Koradi et al. Reference Koradi, Billeter, Engeli, Güntert and Wüthrich1998) is a stand-alone method for automatic peak picking in the sense that it does not use any additional information to that which is contained in the spectrum. The main features of the program are an algorithm for local noise estimation, the segmentation of the spectrum into more-manageable chunks, the use of spectrum-specific peak templates and the exploitation of the intrinsic symmetry of magnetisation transfers.

Invariably, due to noise bands, water lines, artefacts, etc., the noise in NMR spectra is not evenly spread. The first stage of the AUTOPSY program involves calculating the average noise level for each 1D slice of the spectrum. The spectrum is then simplified by setting the intensity of pixels to zero if their value is below the local threshold. Next, the spectrum is split into connected regions using a flood-filling algorithm (Foley, Reference Foley1996). This ensures that even the most bulky multidimensional NMR spectra are treated efficiently. A set of reference line shapes is created by comparing the selections of well-resolved peaks from different regions. These templates are then used to resolve regions of strong overlap. Thereby, a peak – or rather a peak component – is accepted as a signal if a corresponding model can be found within the reference set. In addition, the presence of a symmetric peak, mirrored with respect to the spectrum diagonal is taken as an indication of the validity of a particular candidate.

2.4.2 ATNOS

The algorithm ATNOS was developed initially for combined NOE signal identification and protein structure calculation (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002b). It has subsequently been adapted for side-chain chemical shift assignment in combination with ASCAN (Fiorito et al. Reference Fiorito, Herrmann, Damberger and Wüthrich2008) and is used in APSY for the identification of projection peaks (Hiller et al. Reference Hiller, Fiorito, Wüthrich and Wider2005). ATNOS is designed to interface cyclically with assignment algorithms such that the selection criteria – and therefore the resulting peak lists – evolve as new assignments or more accurate structures become available. Updating the peak lists in this way ensures that the likelihood of an artefact being fed repeatedly to the assignment algorithm is much lower than if the peak picking were performed once only, as is common when signal identification is performed manually.

NOE assignment and structure calculation programs require essentially artefact-free peak lists. Indeed, it has been shown that when trading between accuracy and completeness, the former is much more valuable (Güntert, Reference Güntert2003; Jee & Güntert, Reference Jee and Güntert2003). To this end, ATNOS applies a series of increasingly stringent criteria for candidate resonances. Notably, and in contrast with other approaches, ATNOS makes extensive use of the information contained in the chemical shift assignments.

As a first step, all peaks whose intensities are no more than three times the AUTOPSY-calculated local noise level are removed. The covalent polypeptide structure imposes upper-distance limits on inter-nuclear distances. In ATNOS, these are calculated analytically for all proton pairs separated by fewer than two torsion angles. Correlations are expected for distances less than 5·5 Å. Candidate peaks whose coordinates match those for one of the predicted covalent signals form a reference set from which stricter area and intensity thresholds are defined.

The remaining peaks are divided into three classes: the reference or covalent set, peaks which are close to the diagonal and the rest. If no structural model is available, the ‘diagonal’ set is ignored. Peaks in the covalent set are accepted so long as they do not appear in a noise band, defined as an area in which the local noise level is more than three times the spectrum average. The remaining peaks must satisfy three additional criteria. First, the candidate peak must be well removed from others in the vicinity; if an area of noise does not separate it from its neighbours then the candidate peak must either be the most intense of the local group or be detached by a sufficiently deep intensity valley. Second, the candidate peak must have a symmetric double. Third, the candidate peak should be aligned with at least two peaks from the same plane (i.e. well anchored in the network of signals) and its coordinates should match at least one combination from the list of assigned atoms. If on the other hand, a preliminary structure is available, the grid of predicted signals is extended to all atoms within 5·5 Å and all peaks appearing close to an intersection are accepted. Those that do not satisfy this criterion are analysed as described above.

For ASCAN side-chain assignment, since the objective is to discover hitherto unknown assignments, rather than only accepting peaks at grid intersections where the nD coordinates are prescribed by the n interacting atoms, whole lines are considered as valid locations for peaks whereby the n−1 previously assigned chemical shifts provide the anchor points.

2.4.3 Noise reduction

Low signal-to-noise ratios are a clear obstacle to automated routines. A number of recently published methods aim at removing (some or most of) the noise in order to facilitate peak picking and render the process more robust.

The MICE (Serban, Reference Serban2007) protocol involves de-noising spectra using wavelet reconstruction (Daubechies, Reference Daubechies1992; Donoho & Johnstone, Reference Donoho and Johnstone1994, Reference Donoho and Johnstone1995; Mallat, Reference Mallat1999). Local maxima are then accepted above a certain threshold that is set relative to the average noise level in the spectrum. All line shapes are assumed to be Lorentzian and the average line width calculated from well-resolved peaks is then used to fit crowded regions.

Dancea & Gunther (Reference Dancea and Gunther2005) have investigated the effect of different de-noising algorithms on a 3D ¹⁵N-NOESY spectrum. The optimal schemes were then applied for the automated structure calculation of the polysulfide-sulfur transferase (Sud) protein (a homodimer with 2×137 residues), by which automatically picked peaks were fed into ARIA. Perhaps unsurprisingly, the more the noise level is reduced, the more spectral fine structure is lost. Consequently, two different de-noising schemes were employed during the structure calculation process. The most aggressive scheme was used to obtain a preliminary fold during five ARIA cycles and a spectrum that retained more weak features was analysed for four additional iterations. The final four cycles exploited a peak list extracted from the original spectrum. In contrast to the ATNOS protocol described above, each spectrum was analysed once only and no structure-based filters were used.

Within this framework, local maxima are accepted if they satisfy three criteria. First, they must be more intense than the local noise level (calculated as in AUTOPSY). Second, they must be supported by at least one different non-diagonal peak that is assignable to the same two residues (cf. network anchoring). And third, they must be supported by a symmetric double the other side of the diagonal.

An alternative approach has been proposed with PICKY, to remove noise using SVD (Alipanahi et al. Reference Alipanahi, Gao, Karakoc, Donaldson and Li2009b). Simple selection rules are then applied whereby the remaining noise is assumed to be evenly spread across the spectrum and maxima are accepted based on a minimum signal-to-noise threshold. Any additional spectra available are analysed in parallel such that depending on the type of experiment, signals originating from common atoms support each other.

2.4.4 Using new experiments

With many types of recently developed experiments, such as those based on reduced dimensionality or projections from higher-order dimensions (Malmodin & Billeter, Reference Malmodin and Billeter2005; Gryk et al. Reference Gryk, Vyas and Maciejewski2010), signals appear in standard patterns that can be analysed systematically in order to obtain peak lists. MUNIN (Korzhneva et al. Reference Korzhneva, Ibraghimov, Billeter and Orekhov2001; Orekhov et al. Reference Orekhov, Ibraghimov and Billeter2001) exploits the multi-dimensional decomposition (MDD) spectrum reconstruction procedure through which multi-dimensional (3D or higher) spectra are reconstructed from a set of model peaks. Peak positions are thereby obtained as a by-product, as it were, of the MDD process. APSY (Hiller et al. Reference Hiller, Fiorito, Wüthrich and Wider2005) experiments share the similarity with HIFI (Eghbalnia et al. Reference Eghbalnia, Bahrami, Tonelli, Hallenga and Markley2005a) that peak positions are extracted directly from projected spectra without reconstructing the multi-dimensional parent. In APSY, a simple peak picker is included to analyse 2D projections such that all maxima are accepted as long as they satisfy the local threshold criterion described above. Then, GAPRO repeatedly selects n−1 of the peak lists and back calculates peak positions in the n-dimensional spectrum. The resulting triangulation of individual peaks is highly redundant and therefore extremely precise. Similarly, although artefacts are picked in individual projections, these do not correlate during the GAPRO reconstruction, whereas signals do. Such approaches should prove particularly useful for providing peak lists for chemical shift assignments, for which high dimensionality is particularly valuable at tracing out sequential connectivities, as demonstrated for instance in the association of APSY with the MATCH algorithm for backbone assignment (Volk et al. Reference Volk, Herrmann and Wüthrich2008).

2.4.5 Integration

A number of proposals have also been made to interface peak picking of traditional experiments directly with chemical shift assignment algorithms. ATNOS/ASCAN for instance performs automated side-chain resonance assignment directly from NOESY or TOCSY spectra (Fiorito et al. Reference Fiorito, Herrmann, Damberger and Wüthrich2008). For backbone assignment, AUTOPSY has been interfaced directly with GARANT (Bartels et al. Reference Bartels, Güntert, Billeter and Wüthrich1997; Malmodin et al. Reference Malmodin, Papavoine and Billeter2003). Once the chemical shift assignment is complete, ATNOS/CANDID (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002a) is well established as a robust algorithm for constraint gathering directly from NOE spectra and a similar approach has been proposed by Dancea and Gunther with ARIA in the context of wavelet de-noised NOE spectra (Dancea & Gunther, Reference Dancea and Gunther2005).

Integration of the stages outlined in this section is a key objective in the ongoing quest for higher throughput and objectivity. At this stage, it seems that the mashups described above strike the optimal balance between efficiency and accuracy, and between time spent on data acquisition and analysis (see below). Indeed, a major obstacle for fully integrative approaches – in this context, those that read spectra and output a structure – is the cumulative propagation of errors.

The principle of fully automated NMR protein structure determination was first proven with the FLYA algorithm (Lopez-Mendez & Güntert, Reference Lopez-Mendez and Güntert2006); for three 12–16 kDa proteins the FLYA approach performed to a similar standard as traditional step-by-step automation. FLYA interleaves a series of well-established programs: peaks are picked automatically using NMRView (Johnson & Blevins, Reference Johnson and Blevins1994) or AUTOPSY; GARANT performs the chemical shift assignment while the overall process is controlled through the CYANA (Güntert, Reference Güntert2004) suite for NOE assignment and structure calculation; finally, energy minimisation is performed using OPALp (Koradi et al. Reference Koradi, Billeter and Güntert2000) with the AMBER (Case et al. Reference Case, Cheatham, Darden, Gohlke, Luo, Merz, Onufriev, Simmerling, Wang and Woods2005) force field.

Similarly, the FAPSY (Shin & Lee, Reference Shin and Lee2008) approach associates AutoAssign (Zimmerman et al. Reference Zimmerman, Kulikowski, Huang, Feng, Tashiro, Shimotakahara, Chien, Powers and Montelione1997; Moseley et al. Reference Moseley, Monleon and Montelione2001) for chemical shift assignment with TALOS (Cornilescu et al. Reference Cornilescu, Delaglio and Bax1999) and CYANA for constraint gathering and structure calculation. Applied to two proteins of 90 and 111 residues, the FAPSY protocol calculated structures that deviated from the reference by 3·2 and 3·0 Å, respectively.

There is a clear disadvantage with these methods, however, – if high-throughput is a concern – in terms of the number of spectra required and hence the experimental expenditure. In the original FLYA implementation, for instance, 16 spectra were used. Subsequent implementations of the FLYA algorithm for SAIL-labelled proteins (Kainosho et al. Reference Kainosho, Torizawa, Iwashita, Terauchi, Ono and Güntert2006) suggest that peak picking is the limiting step in the procedure; with this task being performed interactively, nine spectra were sufficient to calculate the N- and C-terminus of calmodulin and five for ubiquitin (Takeda et al. Reference Takeda, Chang, Ikeya, Güntert, Chang, Hsu, Huang and Kainosho2008; Ikeya et al. Reference Ikeya, Takeda, Yoshida, Terauchi, Jee, Kainosho and Güntert2009).

UNIO attempts to alleviate problems of cumulative errors by promoting user-intervention at the completion of each step. UNIO is composed of the assignment modules MATCH (Volk et al. Reference Volk, Herrmann and Wüthrich2008) and ATNOS/ASCAN (Fiorito et al. Reference Fiorito, Herrmann, Damberger and Wüthrich2008), respectively for the backbone and side-chain atoms, along with ATNOS/CANDID (Herrmann et al. Reference Herrmann, Güntert and Wüthrich2002a) for NOE constraint gathering and structure calculation (with CYANA, CNS or X-PLOR). The standard input requirements are three APSY (Hiller et al. Reference Hiller, Fiorito, Wüthrich and Wider2005) and three NOE spectra although the assignment process with MATCH has already been demonstrated with a single 6D APSY spectrum (Volk et al. Reference Volk, Herrmann and Wüthrich2008). As part of the JCSG's proteins structure venture, the UNIO protocol has led to the deposition of 19 structures (67–198 residues) in the past two years.

3.1.1 Torsion angle constraints

The programs for torsion angle constraints TALOS (Cornilescu et al. Reference Cornilescu, Delaglio and Bax1999), TALOS+ (Shen et al. Reference Shen, Delaglio, Cornilescu and Bax2009a), PREDITOR (Berjanskii et al. Reference Berjanskii, Neal and Wishart2006) and DANGLE (Cheung et al. Reference Cheung, Maguire, Stevens and Broadhurst2010) match sections of a target protein to those from a structural database based on their sequence and chemical shift similarity. The underlying idea is that a particular chemical shift pattern is indicative of a specific set of torsion angles. Thereby, if such a pattern from a query fragment can be matched to one in a database, so the corresponding torsion angles must also agree.

The overall strategy for each program being essentially identical, differences reside only in its implementation. A similarity score is calculated for each position in the amino-acid sequence, measuring the level of agreement between the chemical shifts of the query triplet (quintuplet in the case of DANGLE) and fragments of the same length from the database. A residue difference correction is applied, which separates primary and secondary structural influences on the chemical shifts. A parallel search is conducted based solely on sequence homology, which exploits the structural information intrinsic to the amino-acid sequence. The best results are then combined and the prediction is output along with a confidence rating or error estimate. TALOS+ and DANGLE also classify results based on favoured regions in Ramachandran plots (Ramachandran et al. Reference Ramachandran, Ramakrishnan and Sasisekharan1963).

To a first approximation, the larger the database, the more likely one is to find a match for a particular fragment and the more reliable are the predictions (Shen et al. Reference Shen, Delaglio, Cornilescu and Bax2009a). However, great care must be taken in constructing these databases such that the referencing for all chemical shifts is consistent. TALOS+ uses the 200-protein database constructed and calibrated as part of the SPARTA chemical shift prediction project (Shen & Bax, Reference Shen and Bax2007). A subset of this database (186 structures) forms the basis of the DANGLE approach for which Cheung et al. (Reference Cheung, Maguire, Stevens and Broadhurst2010) have investigated the effect of systematic miss-referencing in the query protein. For PREDITOR, the reference-correction module ensures consistency between experimental shifts and those in the associated database of 141 proteins.

In terms of output, the TALOSs and DANGLE predict the backbone φ/ψ angles only, whereas PREDITOR also includes estimates of the side chain χ₁ and ω angles, thanks to a sequence homology analysis. Note in this context, the recent release of the PROMEGA software (Shen & Bax, Reference Shen and Bax2010), which employs a TALOS-like approach to predict Xaa-Pro peptide bond conformations (pre-proline ω angles).

In terms of performance, Cheung et al. (Reference Cheung, Maguire, Stevens and Broadhurst2010) report similar prediction accuracy – ca. 70–80% within 30° – for all methods with their DANGLE algorithm providing more realistic error estimates. David Wishart has recently sought an objective ranking by running each program for the same set of 33 proteins. PREDITOR made accurate (φ and ψ within 30°) predictions for approximately 10% more residues than DANGLE or TALOS (94% vs. ~85%).

The backbone restraints obtained using these programs are approximate and local. It is therefore not possible to reconstruct the full protein fold using these constraints alone and indeed, in situations where a dense network of NOE restraints is available, the information gained from torsion angles adds little to the precision. However, in situations where inter-atomic distances are harder to come by – for large proteins for example, or for solid-state NMR – these approaches come to the fore. To bypass NOE-type experiments completely though, different recipes are required of which angle predictions are nonetheless one of their main ingredients.

3.1.2 From structures to chemical shifts

The fundamentals of chemical shift prediction from structure are not within the scope of this review. Moreover, a thorough description of this topic has newly been published (Wishart, Reference Wishart2010). For the sake of protein structure determination, the reverse problem of predicting chemical shifts from existing structures is not a concern per se. However, they do allow much larger X-ray databases to be translated. This expansion of protein fold space turns out to be critical for the accuracy of algorithms for (full) structure calculation based (primarily) on chemical shift data (see the following section). Briefly therefore, programs for chemical shift prediction (we have censured 10, namely 4DSPOT (Lehtivarjo et al. Reference Lehtivarjo, Hassinen, Korhonen, Perakyla and Laatikainen2009), CamShift (Kohlhoff et al. Reference Kohlhoff, Robustelli, Cavalli, Salvatella and Vendruscolo2009), PROSHIFT (Meiler, Reference Meiler2003), PRSI (Wang, Reference Wang2004), SHIFTCALC (Iwadate et al. Reference Iwadate, Asakura and Williamson1999), SHIFTS (Xu & Case, Reference Xu and Case2001), SPARTA (Shen & Bax, Reference Shen and Bax2007), and SHIFTX/SHIFTX2 (Neal et al. Reference Neal, Nip, Zhang and Wishart2003; Wishart, Reference Wishart2010)) construct nucleus-specific contour maps that translate torsion angles into chemical shifts. In general, these structure-shift tables are assembled from a set of high-resolution X-ray structures for which chemical shifts are also available. These relationships are generally supplemented by semi-classical or quantum-mechanical calculations of physico-chemical effects (e.g. solvent exposure, peptide anisotropy, motional averaging, pH, temperature, etc.). Corrections for protein dynamics can also be made (Lehtivarjo et al. Reference Lehtivarjo, Hassinen, Korhonen, Perakyla and Laatikainen2009) and some programs make direct use of sequence homology (Meiler, Reference Meiler2003; Shen & Bax, Reference Shen and Bax2007). Thereafter, variations mainly concern the size and content of the reference database, the number and nature (which nuclei) of the predictions for each residue and of course, the implementation of the prediction algorithm.

As for torsion angles, David Wishart has measured the correlation between experimental chemical shifts and those predicted by the algorithms SHIFTX, SHIFTX2, CamShift, Shifts and ProShifts for a set of 61 high-resolution X-ray structures (Wishart, Reference Wishart2010). In terms of the different nuclei, Cβ predictions score highest on average (correlation coefficient ~0·99) and HN lowest (~0·69). In terms of the different programs, the correlation coefficients obtained with SHIFTX predictions are the highest on average (~0·95), and lowest with SHIFTS (~0·79).

3.1.3 From chemical shifts to structures

A structure defines a single chemical shift pattern, no unique solution exists to the reverse problem as many different global conformations can satisfy specific local arrangements. The recent development of accurate chemical shift prediction algorithms (see the preceding section) points towards an iterative solution to the problem whereby candidate structures can be ranked according to their chemical shift agreement with the query protein. To this date three methods, namely CHESHIRE (Cavalli et al. Reference Cavalli, Salvatella, Dobson and Vendruscolo2007), CS-Rosetta (Shen et al. Reference Shen, Lange, Delaglio, Rossi, Aramini, Liu, Eletsky, Wu, Singarapu, Lemak, Ignatchenko, Arrowsmith, Szyperski, Montelione, Baker and Bax2008b) and CS23D (Wishart et al. Reference Wishart, Arndt, Berjanskii, Tang, Zhou and Lin2008) have been published although a general pathway to low-resolution structures was first published by Gong et al. (Reference Gong, Shen and Rose2007) and already in 2001, the structure of ubiquitin was computed using chemical shift data exclusively (Wishart & Case, Reference Wishart and Case2001). The idea moreover of supplementing Rosetta structure prediction with experimental data dates from the turn of the century (Bowers et al. Reference Bowers, Strauss and Baker2000).

Chemical shifts are again used to scan a database of solved structures but compared to the programs for torsion angle prediction, alternative approaches are implemented for the subsequent reconstruction of the 3D fold. CS-Rosetta simply uses the fragments as a restricted (but much more relevant) database for a standard Rosetta (Das & Baker, Reference Das and Baker2008) calculation; CHESHIRE uses molecular fragment replacement based on Monte-Carlo substitution of candidate fragments; CS23D meanwhile assembles fragments based on simple matching criteria. Chemical shift matching along with a standard energy functional then guides the refinement of the coarse-grain CHESHIRE and CS23D models. Specific details of these protocols may be found in the following.

Exploiting previously solved structures

3.2.2 Non-database methods

Since the theoretical link between NMR observable and structure is well-established in the case of RDCs, the tantalising prospect exists of accessing novel folds by calculating structures directly from the experimental values, thereby waiving the database homology requirement.

3.2.3 Combined chemical shift assignment and structure determination

On the other hand, the recording of RDCs as an alternative to chemical shift assignment is an alluring prospect. Note that the methods described so far in this section all require chemical shift assignment. As mentioned above, this process is notoriously labour-intensive and uncongenial to traditional automatic approaches.

3.3.1 CS-DP-Rosetta

We have seen that NMR peak picking is hard to perform automatically and that NOE-assignment algorithms are extremely sensitive to artefacts. In the course of most NMR protein structure calculations therefore, a lot of time is spent manually refining peak lists. One option to expedite this process is simply to avoid it. However, methods such as CS-Rosetta are only effective for small proteins. As a compromise therefore between efficiency and robustness, Raman et al. propose to filter CS-Rosetta models against NOE peak lists, thereby achieving the range of traditional NOE-assignment algorithms but with raw (or ‘minimally edited’) peak lists (Raman et al. Reference Raman, Huang, Mao, Rossi, Aramini, Liu, Montelione and Baker2010a).

The thousand or so lowest-energy CS-Rosetta models out of an initial set of 50 000 are filtered against the NOE peak lists using the RPF software (Huang et al. Reference Huang, Powers and Montelione2005). This evaluates how well a structure explains the experimental peak pattern. The top 20 conformers (energy+DP score) are then extensively refined according to the Rosetta ‘rebuild and refine’ protocol (Qian et al. Reference Qian, Raman, Das, Bradley, Mccoy, Read and Baker2007; Ramelot et al. Reference Ramelot, Raman, Kuzin, Xiao, Ma, Acton, Hunt, Montelione, Baker and Kennedy2009). When refined peak lists are available, an alternative strategy, ‘AssignNOE-Rosetta’ is to use a traditional NOE-assignment algorithm to produce a preliminary structure subsequently refined using Rosetta.

The CS-DP-Rosetta protocol was tested on six proteins, ranging in length from 97 to 145 amino acids. Three of these calculations were performed blind (i.e., without knowledge of the reference structure). Only in one case, surprisingly for the smallest protein, was the RMSD bias to the reference structure greater than 3·0 Å (Raman et al. Reference Raman, Huang, Mao, Rossi, Aramini, Liu, Montelione and Baker2010a). Moreover, AssignNOE-Rosetta performed systematically better than CYANA or AutoStructure with refined peak lists: for a set of five proteins (100–160 amino acids) the RMSD biases for the structured regions were in the range 1·0–1·4 Å as compared to 1·3–2·5 Å for the reference calculations (Raman et al. Reference Raman, Huang, Mao, Rossi, Aramini, Liu, Montelione and Baker2010a).

One would need to weigh up the extra computational cost incurred through the use of Rosetta (each CS-Rosetta model takes ~5–10 CPU minutes to build (Shen et al. Reference Shen, Lange, Delaglio, Rossi, Aramini, Liu, Eletsky, Wu, Singarapu, Lemak, Ignatchenko, Arrowsmith, Szyperski, Montelione, Baker and Bax2008b)) and the time-cost of manual peak-list refinement. Or perhaps a more relevant comparison could have been made with the ATNOS/CANDID protocol for (unsupervised) automatic peak picking and NOE assignment. Nonetheless, these results suggest that CS-DP-Rosetta is a viable alternative to the traditional NOE algorithms for medium-sized proteins.

3.3.2 CS-RDC-(NOE)-Rosetta

A different strategy has been proposed for larger proteins. Fig. 2 shows that for proteins longer than 200 residues solution NMR in general, and automated algorithms in particular are not a popular choice. Raman et al. seek to address this problem by supplying Rosetta with backbone chemical shifts and sparse NOEs (Raman et al. Reference Raman, Lange, Rossi, Tyka, Wang, Aramini, Liu, Ramelot, Eletsky, Szyperski, Kennedy, Prestegard, Montelione and Baker2010b). The authors argue that by exclusively using experimental constraints from the protein backbone, this approach should be more conducive to solving larger targets for which deuteration significantly reduces the density of the NOE network.

CS-Rosetta is robust up to approximately 100 residues. Adding RDC restraints to guide the conformational search towards low-energy regions (Rohl & Baker, Reference Rohl and Baker2002) helps CS-RDC-Rosetta to consistently solve structures up to a length of 120 amino acids (Raman et al. Reference Raman, Lange, Rossi, Tyka, Wang, Aramini, Liu, Ramelot, Eletsky, Szyperski, Kennedy, Prestegard, Montelione and Baker2010b). To push the size limit even further, backbone amide NOEs (HN–HN) were included at the ‘rebuild and refine’ stage (Raman et al. Reference Raman, Lange, Rossi, Tyka, Wang, Aramini, Liu, Ramelot, Eletsky, Szyperski, Kennedy, Prestegard, Montelione and Baker2010b). This CS-RDC-NOE-Rosetta protocol was tested for 15 proteins (122–266 residues) such that 13 structures were obtained that had converged for more than half of the sequence. Of these, ten had an RMSD bias to the reference structure of less than 3·5 Å (Raman et al. Reference Raman, Lange, Rossi, Tyka, Wang, Aramini, Liu, Ramelot, Eletsky, Szyperski, Kennedy, Prestegard, Montelione and Baker2010b).

This approach is advantageous since no experimental information is required for the side-chain atoms as these are added automatically during the refinement stage. Rosetta is not in the business of proving free lunches however: according to this study, the calculation of a 200 amino-acid protein takes in the order of 82 000 CPU hours. In terms of range and robustness moreover, it is not clear that CS-RDC-NOE-Rosetta actually constitutes an improvement on pre-existing methods.

3.4.1 CLOUDS

Indeed, these always encode the spatial arrangement of protons in terms of correlated frequencies, whether the latter have been attributed to specific atoms or not. The pioneering work on this subject dates from the early 90 s (Malliavin et al. Reference Malliavin, Rouh, Delsuc and Lallemand1992) but so far, these ideas have only been pursued by a couple of research groups (Atkinson & Saudek, Reference Atkinson and Saudek1997, Reference Atkinson and Saudek2002; Grishaev & Llinás, Reference Grishaev and Llinás2002a, Reference Grishaev and Llinásb). Of the algorithms proposed, CLOUDS is the only one to have been successful starting from experimental data. For two small proteins (60 & 83 residues), the CLOUDS approach yielded backbone structures with less than 1·5 Å RMSD from the reference (Grishaev & Llinás, Reference Grishaev and Llinás2002a).

Parallels may be drawn between CLOUDS and X-ray methods for protein structure determination, in that NOESY spectra are used to create a spatial distribution (of protons here, rather than electrons) into which a model structure is then fit. Upper- and lower-distance constraints are extracted from the NOE spectra by relaxation matrix analysis. An MD simulation is then performed with electrostatic repulsions to assemble 1000 proton clouds. The candidates that deviate most from the mean are then discarded and the resulting family of clouds defines a sleeve into which the covalent structure is folded. Sequential connectivities are established through the clouds based on the likelihood of H^N–H^N, H^α–H^N and H^α–H^α contacts obtained from a Bayesian interpretation of database values. A similar approach is used to attach the side chains. Finally, the fully assembled protein is squeezed into shape using MD constrained by the proton density.

A variation on the CLOUDS protocol has recently been proposed (Bermejo & Llinás, Reference Bermejo and Llinás2008). SC-CLOUDS is designed to work with selectively labelled perdeuterated proteins and uses Rosetta to assemble the final structure. Rosetta is required because the distance constraints are too sparse to collapse the proton clouds down to a single structure. SC-CLOUDS borrows this approach – roughly speaking: to use Rosetta instead of assigned chemical shifts – from the work of Jens Meiler and David Baker (Meiler & Baker, Reference Meiler and Baker2003), and we have seen that ITAS employs a similar strategy. We refer the interested reader to the comparison of these three methods in (Bermejo & Llinás, Reference Bermejo and Llinás2010).