We model a protein as a chain of evenly spaced C_α atoms placed on a lattice (Chomilier et al., 2004). We define a lattice unit (lu) to be 1.7 Å. Hence, C_α atoms are connected by vectors of the form (2,1,0), these vectors are 5^1/2 lu in length which corresponds to 3.8 Å—the mean distance between adjacent C_α atoms. This results in 24 immediate neighbor positions for each point in the lattice. This represents the intersection of a 4 × 4 × 4 segmented cube with a sphere of radius 3.8 Å (5 ^1/2 lu).

The model does not take into account the presence of side chains; therefore, the required separation is modeled with the 3.8 Å minimum distance requirement. Based on chain geometry, we limit the angle between some C_αs at positions i and i + 2 by requiring the distance between them to range from 4.1 to 7.2 Å (or from 6^1/2 to 18^1/2 lu). This corresponds to angles from 66° to 143°, which is closer to the real angles in alpha and beta conformations. This is illustrated in Figure 24.3, where a residue i is fixed at [0, 0, 0] and all 24 possible positions for residue i + 1 are represented as black vectors. There is a choice of 23 possible vectors for residue i + 2. For the sake of clarity, only one position [0, 1, 2] (the green and red vectors) is shown. Red vectors are those that violate the distance (angle) restriction.

To initiate the simulations, 100 different starting models within this lattice are used. Figures 24.3 and 24.4 display a sample of five and all models, respectively, as a comprehensive plot. These models were computed randomly offline for chains of 1100 residues. For the initial models, our only requirement is that they have some level of noncompactness (Papandreou et al., 2004). Starting from the first residue, located at position [0, 0, 0], the first n positions in the seed model will be used for an input model with n residues—any additional residues in the random sequence will be discarded.

3.2 SMIR

The MIR method was first developed in 2004 (Chomilier et al., 2004; Papandreou et al., 2004), and MIR 1.0 was first made available online as a function of the Ressource Parisienne en Bioinformatique Structurale (RPBS) server in 2005 (Alland et al., 2005). The present SMIR server exploits MIR2.2 implemented with Fortran for server-side simulation and a SMIR JavaScript front end for interactive analysis. The input to the MIR algorithm is a FASTA file containing a sequence using standard amino acids. The input file is either provided by the user or automatically retrieved from RCSB via a Protein Data Bank (PDB) ID. The output consists of a table associated with each residue: AA letter, NCN, MIRs, and LIRs. NCN is an integer while MIR and LIR are Boolean flags.

Server-side computation time is quadratic on the length of the sequence and may be modeled by 6.062E − 5x² − 0.0138x + 0.843 hours, where x is the number of residues, on an Intel Core 2 Duo E6600 computer. The results are stored in a MySQL 5.1 database running on Ubuntu 13.04 LTS. The new SMIR smoothing method is implemented in JavaScript with D3 (Bostock et al., 2011) and has been primarily tested in Google Chrome 33. Firefox 18 and Safari 6 have also been tested. Microsoft Internet Explorer is not currently supported. It has been found that the computation time for SMIR, once MIR results are available, is negligible on Intel Core 2 Duo–based computers. A browser-based implementation allows users to retrieve this new analysis for any existing protein without the need to resubmit the entry to our submission server.

3.3 Submitting a protein

The SMIR interface illustrated in Figure 24.5 supports the submission of a PDB ID, a list of PDB IDs, or a FASTA file. In the latter case, the user will also enter a four-letter alphanumeric code to identify the submission and later retrieve the results. The submission of an e-mail address is optional. Should one be submitted, it will be used only for the purpose of informing the user of the availability of the results in the database with a reminder of the code. After submission, the server returns a SMIR status window (see Figure 24.6). Here, the window displays the status for five proteins of PDB codes: 1AMM, 1DX5, 1I5I, 1QUC, and 1ZAC. At the top of the status windows are listed the PDB IDs that have already been analyzed by MIR. Each PDB (e.g., 1AMM, 1DX5, or 1I5I) is listed with a bullet. If a protein has more than one chain, each available chain will be listed on that PDB’s line and enclosed in parentheses [e.g., 1DX5(A), 1DX5(I), etc.]. The middle part of the window lists invalid retrieval PDB codes (e.g., 1QUC). The last part consists of the proteins that will be submitted to the server (e.g., 1ZAC). In this case, the PDB IDs will be added to the server queue for processing. Each protein submitted to the server is displayed in the status window with the retrieval link to access the data once the execution is completed. If an e-mail address was entered on the previous screen, a notification with a link will be sent upon completion. The proteins listed at the top of the SMIR status window are immediately viewable with a 2D graph (see Figure 24.7). If a PDB ID is not in the list of available proteins, it will be automatically submitted for analysis. Once the user’s protein is ready to be analyzed, the server downloads the information associated with that PDB ID from the PDB and runs MIR. After execution, the user may use the retrieval link or return to MIR query mode and enter that PDB ID to access the SMIR results. Additionally, the information that was generated for the new PDB ID is now available to other researchers for further use.

The graphical representation illustrated in Figure 24.7 is composed of three areas: legend for the MIR interface (top left), 2D display graph (top right), and data download (bottom). On recent browsers, such as Chrome 24, the data can be downloaded with a comma-separated values (CVS) file. They can alternately be copied and pasted from a text box. The MIR analysis for protein 1amm(A), shown in Figure 24.8, displays MIR residues in blue as a 2D graph. Dark blue vertical bars indicate which residues are MIRs, while dark red bars indicate LIRs (note that no LIR was shown in Figure 24.8). All the bars plot the NCN count at a position on the vertical axis. When browsing on the graph with the mouse, a black pop-up information box displays the amino acid name, its exact position in the protein (with respect to the FASTA file the protein is associated with), the number of NCNs, and the MIR status. The orange regions in the background indicate TEFs (Chomilier et al., 2004), which overlap on slightly darker orange areas. The SMIR method is activated with a check box. When SMIR is selected, the 2D graph will show dynamically how MIR predictions (see the top left of Figure 24.8) are replaced by SMIR predictions (see the bottom right of Figure 24.8). When in smooth mode (i.e., when SMIR is selected), the dark blue and dark red bars indicate SMIRS and SLIRS (smoothed LIR, which are minima in the NCN curves) respectively. Note that two SMIRS are shown for protein 1amm(A) in Figure 24.8.

3.4 Use case and discussion

John Orban’s group has demonstrated how a single point mutation could have a transformative impact on the protein fold (He et al., 2005, 2012; Alexander et al., 2007, 2009). They first considered two short domains G_A and G_B with low sequence similarity (because their sequence identity is 16%, we will use the notations GA16 and GB16, respectively, for G_A and G_B in the rest of this discussion). The two wild types (WTs) GA16 and GB16 were not entered in PDB, but their sequences shown in Table 24.1 were published by He and colleagues in 2005. They engineered two proteins, 2LHC (also referred to as GA98) and 2LHD (also referred to as GB98), of length 56, with 98% sequence identity. Their sequences only differ by one residue on position 45, as displayed in Table 24.2. Although these two sequences show very high sequence identity, the structures display significantly different structures. 2LHC contains three alpha helices, while 2LHD contains four beta sheets and one alpha helix, as illustrated in Figure 24.9. A single mutation at the 45th residue (leucine toward tyrosine) changes dramatically the folded conformation.

We conducted a SMIR analysis on the 14 proteins presented, including the 2 WTs, 10 intermediate engineered proteins, and 2LHC and 2LHD. The SMIRs and SLIRs collected are displayed in Table 24.3 and illustrated in Figure 24.10. The SMIR method is sensitive to structure conservation, which relies more on the concept of a protein seen as a micelle, with a hydrophobic core and an outer shell, mainly hydrophilic. Structure conservation when transferred into sequence space, can be approached as conservation of a class of amino acids. Usually, two classes are proposed, called H and P classes in the literature. Class H is the class of hydrophobic (FILMVYW) amino acids. The reasons for the transformation from one fold to another has been the object of much conjecture, for instance in the so-called Paracelsus challenge in the 1990s. Following this idea, John Orban and colleagues proposed to keep the initial fold of a set of two proteins, each one being mutated with the purpose of increasing the sequence identity with the partner. In execution, they used two domains of 56 amino acids each, from the Streptococus celle surface G. In a series of papers, starting from the WT pair at 16% identity, they progressively increased identity up to one single mutation, but with two folds—namely, three helices on one hand (called G_A) and a four-stranded sheet plus one helix on the other (called G_B).

Figure 24.10 shows the smoothed NCN on the pairs of mutated proteins, starting from the WT, until the two sequences at 98% identity (i.e., different by a single mutation). If one looks at the left column of the figure, with the fold with three helices, some peaks appear in the NCN distribution, but one peak remains at the same location all over the proteins: the one at 30–31. Since some structures are available, such as 1ZXG for the protein GA59, one can see that positions 30–31 are in the middle of the second helix. The second observation that one can make on the set of proteins from the mixed fold (right column of Figure 24.10) is that most of the peaks are displaced when the number of mutations increases, at the exception of the one around 30–31, which remains a maximum in the NCN distribution throughout the set of proteins. Analysis of the structure with the PDB code 1ZXH, corresponding to the sequence GB59 in Figure 24.10, shows that positions 30–31 are also in the middle of the sole helix of this fold. Therefore, we may hypothesize that these positions are crucial for the formation of a helix, independent of the rest of the structure. It is not arbitrary if position 30 is occupied by a hydrophobic residue, F, in both WTs. Moreover, if one looks thoroughly at this position all along the sequences of either the A or the B fold (shown in Figure 24.10), there is either F or I at this position, and it is known to belong to the core of the GA protein (He et al., 2012). One must also remember that these lab proteins are rather unstable, as noticed by the authors.

For a possible understanding of the SMIR prediction in the context of this set of experiments, one may somehow consider a degenerate alphabet. We used the most common one in the field of lattice simulation of folding by two classes of amino acids: FILMVYW as the hydrophobic group (Callebaut et al. 1997), named H, and the rest denoted as P. It is noticeable that the profiles of smoothed NCN are sensitive to point mutation. Considering the A fold scenario, increasing the number of mutations in order to look like the B fold, one starts with a landscape of three main and clear peaks, roughly centered on the three alpha helices. So long as mutations are performed, a new peak appears at both terminal ends, although it is much clearer at the N terminus. This is the bulk of the discussion proposed by John Orban’s group in successive papers. There is an equilibrium between the two folds, at least when one single mutation separates the two proteins, and the two ends play a critical role. If the folding nucleates around position 30, producing the presence of a helix under the local interactions, the rest of the fold will depend on long-range interactions. In the case of a Leu at position 45, as is the case for GA98, this will favor the formation of a helix because Leu propensity is highest for helices. In addition, this is the most frequent residue predicted as a MIR. This second helix formation will guide the rest of the fold toward the alpha type. Otherwise, if there is a Tyr, the small difference in propensity to form helices and to be involved in numerous side chain interactions, is sufficient to drive the folding toward a beta fold. MIR simulation on its own is insufficient to provide a complete and correct prediction; nevertheless, it can help in obtaining a better understanding of the steps followed by the proteins along their folding pathways.

As a particular case of interpreting the SMIR results for generations of similar sequences, consider A91–A95. The main effect in A95 compared to A91 occurs at the place of the mutation, 50: the peak disappears, enhancing the 45 peak. In A95, position 30 is mutated, which is a peak in the smoothed NCN. The mutation is I30F. The frequencies of Ile and Phe as MIR (Acuña et al., 2014) are similar; thus, they should not significantly modify the number of local interactions. According to Alexander et al., the core of A95 contains 9 AA, with 5 hydrophobic interacting residues located at 16, 20, 30, 33, and 49. If we assume that we have a low resolution, it means that we have three interacting clusters: 20, 30, and 45. It is also indicated that the three positions 20, 30, and 45 can either produce a core and therefore an alpha class (with LIL at these positions) or a sheet with AFY. One can assume that the two leucines, which have a higher propensity for helices, drive the pathway. We predict these peaks, although we have an extra one at the N terminus. Looking at the structure (PDB 2KDL) for A95, we see that I6 is very close in distance from V39 (6.1 Å), even if it is in a loop. This is noted by Alexander et al. since both ends are loops in the A form and strands in the B form.