In order to verify whether protein sequence modification has a significant effect on protein structure, we used protein structure prediction to characterize the structure of the proteins that were modified in this project since we are not in a position to directly analyze their protein structure using nuclear magnetic resonance (NMR), X-ray crystal diffraction (X-ray), and Cryo-EM.
2A sequence is a component that enables cis-transposition of eukaryotic exogenous genes, but the “skip” function of the cis-transposition is at the translation level, so 2A sequence leaves a short peptide at the C-terminus of the upstream cis-transposon protein. To verify whether this residual peptide affects the structure and function of the protein, we need to model the structure of the target protein and the protein with 2A attached to it (T2A), and determine whether the structure of the protein is affected by using RMSD.
Furthermore, in the design of our project, we ligated the nuclear localization sequence (NLS) before the sequences of Csy4 and yeGFP, respectively, so that the Csy4 protein and yeGFP green fluorescent protein could be transported into the nucleus. And in the design of PA synthesis, in order to purify ABA 8'-hydroxylase, we plan to express ABA 8'-hydroxylase with 6xHis tag. Therefore, we need to predict the structure of the modified protein to help us understand if the modification of Csy4, yeGFP and ABA 8'-hydroxylase will affect its structure.
Related Work
Protein structure prediction is a mapping from the amino acid sequence of a protein to the three-dimensional structure. It is highly important in medicine and biotechnology although it is not as accurate as the structure from the experiments. It is observed that similar sequences often adopt similar protein structures, which form the foundation of homology modeling.
As the most popular type of protein structure simulation method, we constructed homology modeling based on servers and softwares including SWISS-MODEL (Waterhouse et al., 2018) and Modeller (Webb B et al., 2014).
However, we found that the method sometimes failed to obtain structural features that did not have a template part in the amino acid sequence, which led to poorer results of the obtained models, when we used SWISS-MODEL to predict the structure of proteins. We, therefore, simultaneously used a server called I-TASSER (Yang J et al., 2014), a powerful structure prediction tool based on fold recognition. And through combining and comparing the two predictions, we obtained more credible results.
Fold recognition is another method of protein modeling. It differs from the homology modeling method of structure prediction as it is used for proteins which do not have their homologous protein structures deposited in PDB, whereas homology modeling is used for those proteins which do. From its definition, we know that it solves our problem quite well, because sometimes we can not find any fair template for our proteins.
2A peptides in yeGFP-2A-DsRed and DsRed-2A-yeGFP
We constructed the NLSyeGFP-2A-DsRed expression system to deeply investigate its feasibility at the level of translation by experimentally expressing eukaryotic polysomes dependent on 2A peptides. Unexpectedly, however, the experimental results showed red and green fluorescence both in the nucleus and cytoplasm. To assist in illustrating this phenomenon, we predicted the protein structure during the expression of NLSyeGFP-2A-DsRed.
Table 1. SWISS-MODEL prediction results evaluation. From the score, the above protein models can be used.
Name
Coverage
GMQE
QMEAN Z-score
yeGFP-2A-DsRed
88%
0.71
-1.47
DsRed-2A-yeGFP
85%
0.67
-1.56
Table 2. Evaluation of I-TASSER prediction results. From the score, the above protein models can be used.
Name
C-score
yeGFP-2A-DsRed
-1.37
DsRed-2A-yeGFP
-1.11
Table 3. Structure alignment results by using PyMol align. The above results show the comparison of the protein models using SWISS-MODEL and I-TASSER for the same protein. The results show that the protein models predicted by the two methods are relatively similar.
Name
RMSD
yeGFP-2A-DsRed
0.306 (317 to 317 atoms)
DsRed-2A-yeGFP
0.453 (334 to 334 atoms)
Fig 1. a. yeGFP-2A-DsRed. b. DsRed-2A-yeGFP.
Green is the yeGFP part of the SWISS-MODEL prediction structure. red is the DsRed part of the SWISS-MODEL prediction structure. white is 2A peptides part of the SWISS-MODEL prediction structure.
By analyzing the predicted results of the yeGFP-2A-DsRed fusion protein, we have the unexpected benefit that we find that 2A peptides in the fusion protein causes extremely significant changes in the structure of the downstream protein. As shown, the upstream protein yeGFP was slightly influenced, whereas the barrel structure of the downstream protein DsRed was disrupted. However, since the active center of DsRed is not affected, it remains colorable.
For a fuller description, we predicted the structure of the fusion protein DsRed-2A-yeGFP. The results show that the upstream protein DsRed is slightly influenced, while the barrel structure of the downstream protein yeGFP is disrupted. This is consistent with our conclusion that 2A peptides in the fusion protein causes significant structural changes in the downstream protein.
The above indicates that we can supplement DsRed-2A-yeGFP expression experiments to verify our speculation.
2A in BcABA1-2A-BcABA4 and BcABA3-2A-BcABA2
Table 4. SWISS-MODEL prediction results evaluation. QMEAN Z-score of BcABA1, BcABA2, and BcABA3 are all poor, indicating that these three protein models are less reliable. the prediction results of BcABA4 have good scores and can be used.
Name
Coverage
GMQE
QMEAN Z-score
BcABA1
88%
0.50
-5.07
BcABA2
87%
0.49
-5.59
BcABA3
21%
0.05
-6.44
BcABA4
92%
0.69
-2.55
Table 5. Evaluation of I-TASSER prediction results. From the score, all the above protein models can be used. However, the scores of BcABA3 and BcABA3-2A were lower.
Name
C-score
BcABA1
-0.22
BcABA1-2A
-0.69
BcABA2
-0.44
BcABA3
-2.62
BcABA3-2A
-2.65
BcABA4
0.43
BcABA1-2A-BcABA4
-2.17
BcABA3-2A-BcABA2
-0.62
Table 6. Results of structural comparisons by using PyMol align. The last 5 columns show a comparison of partial structures in a protein and a fusion protein.
Name
RMSD
BcABA1 to BcABA1-2A
0.384 (392 to 392 atoms)
BcABA3 to BcABA3-2A
16.106 (425 to 425 atoms)
BcABA1-2A-BcABA4 to BcABA1
4.876 (356 to 356 atoms)
BcABA1-2A-BcABA4 to BcABA4
15.407 (264 to 264 atoms)
BcABA1-2A-BcABA4 to BcABA4_s
14.072 (245 to 245 atoms)
BcABA3-2A-BcABA2 to BcABA3
17.774 (440 to 440 atoms)
BcABA3-2A-BcABA2 to BcABA2
28.447 (527 to 527 atoms)
We tried to use SWISS-MODEL to obtain structural information for BcABA1-4, but as shown in the table, we obtained a very low quality model for BcABA1-3, where the predicted structure of BcABA3 contains only a very small fraction of amino acid residues. Therefore, we will use other approaches to predict the structure of several proteins.
Through a prior literature survey, we learned that in a translational level eukaryotic polycistronic expression system constructed using 2A sequences, broken 2A sequences attach to the N-terminus of the upstream protein. From previous modeling results, we constructed two gene pathways for the BcABA expression system, which BcABA1 and BcABA3 are located upstream of the gene pathways. To understand whether 2A attached to the N terminus of the upstream protein would affect the structures of BcABA1 and BcABA3, we predicted the structures of BcABA1, BcABA3, and BcABA1-2A and BcABA3-2A using the I-TASSER server.
Fig 2. Comparison of BcABA1 and BcABA1-2A. Blue is the I-TASSER predicted structure of BcABA1, cyan is the I-TASSER predicted structure of BcABA1-2A, and red is 2A peptides after break.
By comparing the predicted protein structures of BcABA1 and BcABA1-2A, we found minor differences. Although the information provided by I-TASSER is not perfect because of the presence of an unnatural α-helix at the C-terminus that sticks out to the outer side of the protein (due to the fact that there is still room for optimization of the I-TASSER algorithm), useful information can still be gleaned from it. The N-terminal 2A sequence of BcABA1 may not affect its catalytic activity because the predicted structure of the BcABA1 has almost no change.
Fig 3. Comparison of BcABA3 and BcABA3-2A. Yello is the I-TASSER predicted structure of BcABA3, white is the I-TASSER predicted structure of BcABA3-2A, and red is the post-break 2A sequence.
Unfortunately. After we compared the predicted protein structures of BcABA3 and BcABA3-2A, we found that the N-terminal 2A sequence had a more significant effect on BcABA3. The comparison showed that 2A peptides of BcABA3 significantly altered the structure of BcABA3 (a curved plane formed by numerous α-helices) in the I-TASSER predictions due to the formation of an α-helix at its N-terminal end, which caused the large difference between the predicted protein structures of BcABA3 and BcABA3-2A. It is most likely that this significant structural change affects the enzymatic activity of BcABA3, resulting in a reduction in yield.
It has been reported in the literature that the efficiency of 2A-mediated protein breakage is usually difficult to reach 100%, so we need to focus on the structure of the fusion proteins caused by 2A sequences unable to break to infer their effect on the final yield. Therefore, we predicted the structures of two fusion proteins, BcABA3-2A-BcABA2 and BcABA1-2A-BcABA4, to observe the effect of 2A sequences on upstream and downstream protein structures. Since the complete structures of the two fusion proteins were not obtained using SWISS-MODEL, we predicted them using the I-TASSER server.
Fig4. a. BcABA1-2A-BcABA4 and BcABA1, BcABA4. b. BcABA3-2A-BcABA2 and BcABA3, BcABA2.
Green is the BcABA1 portion of the I-TASSER prediction structure for BcABA1-2A-BcABA4. hotpink is the BcABA4 portion of the I-TASSER prediction structure for BcABA1-2A-BcABA4. white is the I-TASSER prediction structure for BcABA1-2A-BcABA4. Blue is the I-TASSER prediction structure of BcABA1. Orange is the I-TASSER prediction structure of BcABA4.
Yello is the BcABA3 part of the I-TASSER prediction structure for BcABA3-2A-BcABA2.Magenta is the BcABA2 part of the I-TASSER prediction structure for BcABA3-2A-BcABA2.White is the I-TASSER prediction structure for BcABA3-2A-BcABA2 Green is the I-TASSER prediction structure of BcABA3. red is the I-TASSER prediction structure of BcABA2.
By comparing protein structures, we found that although 2A peptides in the fusion protein affects the upstream sequence, it changes the structure of the downstream protein extremely much more significantly. In the fusion proteins BcABA1-2A-BcABA4, the RMSD value for the predicted structural difference between the upstream and BcABA1 is 4.876, which is much smaller than the effect that 2A peptides causes for the downstream protein proteins, both with the I-TASSER prediction (RMSD value of 15.407) and with the SWISS-MODEL prediction (RMSD value of 14.072) compared to the fusion protein BcABA3-2A-BcABA2. Similarly, in the fusion proteins BcABA3-2A-BcABA2, although 2A peptides caused a large structural change in the upstream protein (RMSD value of 17.774, even though 2A peptides also greatly changed the structure of BcABA3 even if not in the fusion protein), its effect on the structure of the downstream protein was even more significant (RMSD value of 28.447). Therefore, when 2A peptides fails to break the structure of the fusion protein formed, it almost always greatly affects the activity of the downstream protein and the final yield.
Analysis of BcABA3 active sites in three formation
As BcABA3, constructed as BcABA3-T2A-BcABA2 formation, is a rate-limiting enzyme in our gene circuit, it’s important to analyze the influence of 2A polypeptide on the kinetic characteristic of BcABA3 additionally.
We first compare BcABA3 with BcABA3-EGRGSLLTCGDVEENPGP. The most possible active sites of these two polypeptide were predicted by Discovery studio 2016 and MOE.
Fig 5. Active sites(showed in red) of BcABA3 and BcABA3- EGRGSLLTCGDVEENPGP
Fig 6. Interaction of FPP and two active sites. A:Model of FPP B: BcABA3. C: BcABA3- EGRGSLLTCGDVEENPGP
Interestingly, the active site of BcABA3-EGRGSLLTCGDVEENPGP moves inner, which could cause a dramatically change of enzymatic reaction. So we apply molecule dock to analyze the interaction of FPP with these two enzymes.
The interaction of FPP with BcABA3 is classic in many enzymes react with FPP: Lys358 donor a proton to O in the junction of PP and carbon skeleton, and there are also interactions on other Oxygen atom. What’s more, the exposure(showed as bule cloud in 2D diagram) is satisfying for reaction.
But for BcABA3-EGRGSLLTCGDVEENPGP, the influence of enzyme to FPP is poor, means that the function of BcABA3 drops.
Fig 7. The secondary predicted active site of BcABA3- EGRGSLLTCGDVEENPGP and its interaction model. A:the secondary predicted active site; B: the molecule docking result. some amino acids participate in this active site are the remain of 2A.
Meanwhile, we also noticed that there is another active site with high possibility in BcABA3-EGRGSLLTCGDVEENPGP, and it may act to catalyze FPP. Interestingly, some amino acids participate in this active site are the remain of 2A.
ARG450 make a great difference to the second P of pyrophosphate group. The influence of amino acid to the second P could lead some change into the first P indirectly, this may make reaction proceed normally in some degree.
In our system, BcABA3 could also form a fusion protein, BcABA3-T2A-BcABA2. As above-mentioned, 2A peptides in the fusion protein causes significant structural changes in the downstream protein, while has little influence in upstream protein.
Fig 8. BcABA3 active site of BcABA3-T2A-BcABA2 and its interaction model. A: BcABA3 active site(red) and T2A linker(yellow),B: interaction model.
To explore the influence of 2A, we applied our method to BcABA3-T2A-BcABA2 fusion protein.
In this form, there are also an active site for BcABA3 to catalyze FPP. Both P are influenced, and this is beneficial to the process of dephosphorylation.
In short, all three formation of BcABA3 were considered, and we found all of them have the potential to catalyze FPP, which is the critical step of the synthesis of ABA.
The effect of protein tagging on protein structure
Table 7. SWISS-MODEL prediction results evaluation. QMEAN Z-score of Csy4 was poor, indicating that this protein prediction model has low confidence. The prediction results for the remaining proteins have good scores and can be used.
Name
Coverage
GMQE
QMEAN Z-score
NLS-Csy4
95%
0.97
-2.18
Csy4
100%
0.99
-6.19
NLS-yeGFP
96%
0.99
0.42
yeGFP
100%
0.99
0.40
ABA-8'-hydroxylase
92%
0.69
-1.27
ABA-8'-hydroxylase-6xHis
91%
0.68
-1.25
Table 8. Evaluation of I-TASSER prediction results. From the score, the above protein models can be used.
Name
C-score
NLS-Csy4
0.33
NLS-yeGFP
0.82
ABA-8'-hydroxylase-6xHis
0.28
1. NLS-Csy4
Due to the low reliability of the SWISS-MODEL predictions of Csy4, we decided not to use this modeling structure. In the meantime, we find the X-ray diffraction structure of Csy4 for subsequent analysis.
Table 9. Structure comparison results by using PyMol align. "_x" indicates the protein structure obtained by X-ray diffraction, "_s" indicates the protein structure predicted by SWISS-MODEL, and "_i" indicates the protein structure predicted by I -TASSER predicted protein structures. Analysis of the data suggests that the differences in the structure of the two proteins compared in each group are small.
Name
RMSD
Csy4_x to NLS-Csy4_i
0.447 (131 to 131 atoms)
Csy4_x to NLS-Csy4_s
1.428 (142 to 142 atoms)
NLS-Csy4_s to NLS-Csy4_i
1.561 (145 to 145 atoms)
Fig 9. Comparison of the predicted structure of I-TASSER of NLS-Csy4 (Blue) and the X-ray diffraction structure of Csy4 (Yello). Red is the NLS sequence. Green is the possible active center.
The position of the NLS tag in the I-TASSER results for NLS-Csy4 is free from the main body of the Csy4 structure, suggesting that the NLS sequence may not significantly affect the active center and main structure of Csy4.The possible active center in the X-ray diffraction structure of Csy4 (predicted by the ligand binding site analysis of I-TASSER) is distributed precisely at the substrate binding site . This confirms the plausibility of the activity centers predicted by I-TASSER.
By aligning the X-ray diffraction structure of Csy4 by PyMol with the SWISS-MODEL, I-TASSER predictions of NLS-Csy4, we find that the predicted active center in the predicted protein structure coincides with the real ligand binding site. Therefore, we conclude that the active center of Csy4 is not significantly altered after the introduction of the NLS sequence.
In fact, the NLS sequence did not bring significant changes to the structure of Csy4 because its location far from the possible active centers. In conclusion, we can conclude that the addition of the NLS sequence does not negatively affect the structure and catalytic activity of Csy4.
2. NLS-yeGFP
Table 10. Structure comparison between I-TASSER prediction of NLS- yeGFP and SWISS-MODEL prediction. "_s" indicates the protein structure obtained by SWISS-MODEL prediction and "_i" indicates the protein structure obtained by I-TASSER prediction. The data indicate that the three protein structures are very similar.
Name
RMSD
yeGFP_s to NLS-yeGFP_s
0.272 (209 to 209 atoms)
yeGFP_s to NLS-yeGFP_i
0.283 (214 to 214 atoms)
NLS-yeGFP_s to NLS-yeGFP_i
0.281 (207 to 207 atoms)
Fig 10. Comparison of the predicted structure of I-TASSER of NLS-yeGFP (Cyan) with the predicted structure of SWISS-MODEL of yeGFP (Green). Red is NLS sequence.
Comparison of the SWISS-MODEL predicted structure of yeGFP, the SWISS-MODEL predicted structure of NLS-yeGFP, and the NLS-yeGFPI-TASSER predicted structure of NLS-yeGFP shows that the main body structures of the three structures overlap almost completely, and the three predicted structures are highly similar. This indicates that the addition of the NLS sequence to the N-terminal of yeGFP did not affect the main structure of yeGFP.
In addition, I-TASSER predictions showed that the NLS sequence is not located in the main structure of NLS-yeGFP, but is free from the main body of the NLS-yeGFP structure and points to an irregularly structured peptide segment on the outside of the protein. This further suggests that the introduced NLS sequence does not significantly alter the main structure of NLS-yeGFP.
3. ABA 8'-hydroxylase-6xHis
Table 11. Structure comparison results between I-TASSER and SWISS-MODEL predictions of ABA 8'-hydroxylase-6xHis. "_s" indicates the protein structure predicted by SWISS-MODEL and "_i" indicates the protein structure predicted by I-TASSER.
Name
RMSD
ABA-8'-hydroxylase_s to ABA-8'-hydroxylase-6xHis_s
0.000 (316 to 316 atoms)
ABA-8'-hydroxylase_s to ABA-8'-hydroxylase-6xHis_i
1.119 (371 to 371 atoms)
ABA-8'-hydroxylase-6xHis_s to ABA-8'-hydroxylase-6xHis_i
1.115 (370 to 370 atoms)
Fig 11. Comparison of the predicted structure of I-TASSER of ABA-8'-hydroxylase-6xHis (Green) and the predicted structure of SWISS-MODEL of ABA-8'-hydroxylase (Magenta). yello is the 6xHis label. orange is the ABA-8'- The predicted structure of I-TASSER of hydroxylase-6xHis has an extrapolated α-helix. red as a possible active center.
Comparing the structure of the SWISS-MODEL prediction of ABA 8'-hydroxylase and the SWISS-MODEL prediction of ABA 8'-hydroxylase-6xHis, we were surprised to find that they almost completely overlapped in the common region (RMSD of 0.000). The comparison between the SWISS-MODEL predicted structure of ABA 8'-hydroxylase and the I-TASSER predicted structure of ABA 8'-hydroxylase-6xHis was also better, and the two structures were also more similar, except for an outwardly extending α-helix at one place in the I-TASSER predicted structure. This indicates that the introduction of the 6xHis Tag at the C-terminus of ABA 8'-hydroxylase does not affect the main structure of the protein when using homology modeling to predict the protein structure.
As mentioned earlier, there is a noteworthy outwardly extended α-helix in the I-TASSER predicted structure, which is apparently not a stable and natural structure in natural proteins. This may be due to the fact that the I-TASSER server we used is still flawed in its protein structure prediction algorithm, resulting in an irrational structure in our ABA 8'-hydroxylase-6xHis prediction results. However, this does not affect our ability to derive some useful information from it. We used PyMol to align the three protein prediction structures, and the possible active centers of ABA 8'-hydroxylase overlap in position and are structurally similar in the three protein predictions. Also, from the I-TASSER predictions, we can see that the 6xHis Tag is located away from the active center region and outside the main protein structure. Therefore, 6xHis Tag does not negatively affect the structure of ABA8'hydroxylase and its activity.
Discussion
By predicting the structure of the BcABA1-4 series of proteins, we realized that in translational-level eukaryotic multicistronic expression systems constructed using 2A sequences, the broken 2A sequence will always be attached as a short peptide to the C-terminus of its upstream protein. Because of the length of 2A peptides, it inevitably affects the structure of proteins such as BcABA3, which is a thorny issue for us.
Although previous enzyme kinetic modeling results have identified BcABA3 as a key rate-limiting enzyme that should be placed upstream of 2A peptides, the above findings indicate that this does not appear to be a viable solution. However, placing this rate-limiting enzyme downstream of 2A peptides is equally problematic, as the experimental results of yeGFP-2A-DsRed indicate that 2A peptides does not break as efficiently as we expected. And it often dramatically alters the structure of the downstream protein, thus affecting its properties, when 2A peptides fails to break.
In fact, the intractable dilemmas by using 2A sequences suggests that our idea is untrustworthy, which is trying to construct eukaryotic multicistronic expression systems at the translational level. So we turned our attention to the RNA level, which is full of infinite possibilities, and tried to implement eukaryotic multicistronic expression systems by cutting mRNAs.
Furthermore, by analyzing and comparing the structures of the original proteins Csy4, yeGFP, and ABA 8'-hydroxylase with our modified structural prediction models of NLS-Csy4, NLS-yeGFP, and ABA 8'-hydroxylase-6xHis, we reach the consistent conclusion that we are satisfied that the three proteins' tiny modifications will not significantly affect its structure or function.
The above protein structure prediction conclusions provide theoretical guidance for our project design and experimental advancement.
Methods
1. Homologous modeling
Homology modeling is a computational method that enables the creation of a 3D model of a protein from its amino acid sequence (target sequence). A successful model requires at least one experimentally determined protein 3D structure (called a "template"), and the amino acid sequence of the protein should have significant similarity with the target sequence (sequence identity greater than 30%). Using the template as the basis of the pedestal, the target sequence is modeled, the steps are: the selection of the template, the target and the template of the coupling, model building, evaluation, the cycle is repeated until a satisfactory model is obtained. Tools based on the homology modeling approach are SWISS-MODEL, Modeller, etc.
Homology modeling of proteins was performed using SWISS-MODEL. The important parameters to evaluate the quality of the SWISS-MODEL model are Coverage, GMQE, and QMEAN Z-score. Coverage indicates the template coverage, when the template coverage is more than 60%, the homology modeling is generally accurate, when the template coverage is less than 30%, the prediction is unreliable. Model Quality Estimates) is a quality estimate that combines the attributes of the target-template alignment and the template search method. The resulting GMQE score is expressed as a number between 0 and 1, reflecting the expected accuracy of the model constructed using that alignment and template, as well as the coverage of the target, with higher numbers indicating higher reliability. The QMEAN Z-score, which represents the model's QMEAN Whether the scores are comparable to what would be expected for a similarly sized experimental structure, QMEAN Z-scores around 0 indicate good agreement between the model structure and a similarly-sized experimental structure, while scores of -4.0 or less indicate a lower quality model match.
2. Fold recognition (threading)
"Fold" is a widely used concept in protein research in recent years, it is a protein structure level between the secondary and tertiary structure, it describes the way of mixing and combining the secondary structural elements. The number of protein folds is limited, and there are only 1393 topologies for different folds, which means that almost all structures can fall within these 1393 topologies. Unlike the homology modeling approach to protein structure prediction, protein structure prediction based on fold identification yields the lowest matching energy fold combinations from a finite number of protein fold entries.
We use the I-TASSER online site developed by the Zhang Yang group at the University of Michigan for protein structure prediction. By using I-TASSER we can predict the secondary structure, the higher structure, the solvent-accessible surface area, the ligand with which the protein is likely to bind, and the binding site of that ligand. The important parameters for evaluating the quality of the I-TASSER model are C-score, TM-score, and RMSD. c-score represents the confidence level and is usually in the range $[-5, 2]$, with a higher c-score indicating higher confidence in the model. tm-score represents the coefficient of similarity between two structures, $>0.5$ indicating that the model has the correct structure Topology, plausible, $<0.17$ indicates that the model is a follow-on model and is not plausible.RMSD, on the other hand, represents the deviation of the distance between the two structures, and lower indicates a higher similarity of the protein structural components.
3. Structural comparison
We used PyMol-align to compare protein structures before and after micro-modification.
RMSD, root-mean-square deviation, is a quantitative measure of structural differences and is measured in angstroms. The root-mean-square deviation of an atomic position is a measure of the average distance between the atoms (usually skeletal atoms) of a superimposed protein. In studies of globular protein conformation, the similarity of the three-dimensional structure is usually characterized by calculating the RMSD between the C α atomic coordinates after the rigid body has been superimposed.
$$RMSD = \sqrt{\frac{1}{N} \sum_{i=1}^N \delta^2_i}$$
where $\delta_i$ is the distance between atom $i$ and the reference atom. The calculations are usually done for only the skeleton heavy atoms $C$, $N$, $O$, and $C \alpha$ or sometimes only the $C \alpha$ atom. Typically, the RMSD is used as a quantitative measure of the similarity between two or more protein structures, usually the lower the better.
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