Prediction of indirect interactions in proteins
- Peteris Prusis^{1, 2},
- Staffan Uhlén^{1, 3},
- Ramona Petrovska^{1},
- Maris Lapinsh^{1} and
- Jarl ES Wikberg^{1}Email author
https://doi.org/10.1186/1471-2105-7-167
© Prusis et al; licensee BioMed Central Ltd. 2006
Received: 09 December 2005
Accepted: 22 March 2006
Published: 22 March 2006
Abstract
Background
Both direct and indirect interactions determine molecular recognition of ligands by proteins. Indirect interactions can be defined as effects on recognition controlled from distant sites in the proteins, e.g. by changes in protein conformation and mobility, whereas direct interactions occur in close proximity of the protein's amino acids and the ligand. Molecular recognition is traditionally studied using three-dimensional methods, but with such techniques it is difficult to predict the effects caused by mutational changes of amino acids located far away from the ligand-binding site. We recently developed an approach, proteochemometrics, to the study of molecular recognition that models the chemical effects involved in the recognition of ligands by proteins using statistical sampling and mathematical modelling.
Results
A proteochemometric model was built, based on a statistically designed protein library's (melanocortin receptors') interaction with three peptides and used to predict which amino acids and sequence fragments that are involved in direct and indirect ligand interactions. The model predictions were confirmed by directed mutagenesis. The predicted presumed direct interactions were in good agreement with previous three-dimensional studies of ligand recognition. However, in addition the model could also correctly predict the location of indirect effects on ligand recognition arising from distant sites in the receptors, something that three-dimensional modelling could not afford.
Conclusion
We demonstrate experimentally that proteochemometric modelling can be used with high accuracy to predict the site of origin of direct and indirect effects on ligand recognitions by proteins.
Background
The processes of life depend on intermolecular recognition. Molecular recognition by proteins is a complex process that is determined not only by direct interactions of a protein with the interacting molecule, but also by indirect effects arising at distant sites in the proteins. Using three-dimensional (3D) structure approaches it is not straightforward to analyze long distance effects on, for example, protein conformation, mobility, and stability. Recently, a new approach using statistical analysis of protein and ligand interaction space, proteochemometrics, was developed [1, 2]. It was used to model protein-peptide interactions and interactions of proteins with organic compounds [1, 3–7]. Here we show its utility in predicting indirect effects in proteins.
Proteochemometrics originates from chemometrics, the mathematical methods used to analyze chemical data. Proteochemometrics aims to describe the interactions between a series of macromolecules (such as proteins) and a series of ligands. Proteochemometric models are thereby created. These models are useful for predicting the affinities of new proteins for their ligands if the new molecules fall within the description space of the protein-ligand pairs of the training data set. A proteochemometric experiment is typically described by three descriptor blocks; the ligand descriptor (D^{ L }), protein descriptor (D^{ P }), and ligand-protein cross-term (D^{ LP }) blocks. A vector of numbers, called the ligand descriptors (D^{ L }), characterizes each ligand L. Similarly, each protein P has its protein descriptors (D^{ P }). If we use a linear method of regression, the negative logarithm of ligand L's affinity (pK_{ LP }) for the protein P is expressed by:
$p{K}_{LP}=\overline{pK}+{\displaystyle \sum _{i}^{N}{C}_{i}}{D}_{i}^{L}+{\displaystyle \sum _{j}^{M}{C}_{j}}{D}_{j}^{P}+{\displaystyle \sum _{i}^{N}{\displaystyle \sum _{j}^{M}{C}_{ij}}}{D}_{ij}^{LP}\text{}Eq.\text{}1$
where $\overline{pK}$ is the average affinity, C_{ i }, C_{ j }, and C_{ ij }are the regression coefficients for ligand descriptors, protein descriptors, and ligand-protein cross-terms, respectively, and N and M are the number of descriptors for ligands and proteins, respectively.
Ligand-protein cross-terms are usually defined by a new vector that is formed by multiplying each ligand descriptor with each receptor descriptor of particular ligand-receptor pairs. Hence,
${D}_{ij}^{LP}={D}_{i}^{L}{D}_{j}^{P}\text{}Eq.\text{}2$
and then
$p{K}_{LP}=\overline{pK}+{\displaystyle \sum _{i}^{N}{C}_{i}}{D}_{i}^{L}+{\displaystyle \sum _{j}^{M}{C}_{j}}{D}_{j}^{P}+{\displaystyle \sum _{i}^{N}{D}_{i}^{L}}\left[{\displaystyle \sum _{j}^{M}{C}_{ij}{D}_{j}^{P}}\right]\text{}Eq.\text{3}$
By using Eq. 3, the selectivity, S_{ LAB }, between protein A and protein B for some particular ligand L can be expressed as:
${S}_{LAB}=p{K}_{LA}-p{K}_{LB}={\displaystyle \sum _{j}^{M}{C}_{j}}\left({D}_{j}^{A}-{D}_{j}^{B}\right)+{\displaystyle \sum _{i}^{N}{D}_{i}^{L}}\left[{\displaystyle \sum _{j}^{M}{C}_{ij}}\left({D}_{j}^{A}-{D}_{j}^{B}\right)\right]\text{}Eq.\text{}4$
If a region U of a protein is described by the set of descriptors, V, then the contribution to the selectivity, ${S}_{LAB}^{U}$, by U between proteins A and B for ligand L is obtained by:
${S}_{LAB}^{U}={\displaystyle \sum _{j\in V}^{K}{C}_{j}}\left({D}_{j}^{A}-{D}_{j}^{B}\right)+{\displaystyle \sum _{i}^{N}{D}_{i}^{L}}\left[{\displaystyle \sum _{j\in V}^{K}{C}_{ij}}\left({D}_{j}^{A}-{D}_{j}^{B}\right)\right]\text{}Eq.\text{5}$
Accordingly, we can localize regions in a protein that afford selectivity (i.e., functionality difference between protein pairs) for a particular ligand by applying Eq. 5. A region can be a subsequence, a 3D molecular interaction field, a single amino acid, or even a physicochemical property of an individual amino acid, and is only restricted by the way the descriptors are assigned to the proteins [1–7]. Since Eq. 5 places no restriction how far in space a ligand is located from a region in a protein, proteochemometrics is useful to predict indirect interactions in proteins.
Results
Design and testing of multiple chimeric melanocortin receptor library
Affinities of multiple chimeric melanocortin receptors. Affinities (pK ± standard deviation, SD) of multiple chimeric melanocortin receptors for α-MSH, NDP-MSH and [^{125}I]-NDP-MSH determined by radioligand binding.
N^{ o } | Name | Set | Parts | pK | ||||
---|---|---|---|---|---|---|---|---|
A | B | C | ^{125}I-NDP-MSH | NDP-MSH | α-MSH | |||
1 | MC_{1} | wt. | MC_{1} | MC_{1} | MC_{1} | 9.96^{a} | 10.34^{a} | 9.68^{a} |
2 | MC_{3} | wt. | MC_{3} | MC_{3} | MC_{3} | 9.40^{a} | 9.31^{a} | 7.27^{a} |
3 | MC_{4} | wt. | MC_{4} | MC_{4} | MC_{4} | 8.64^{a} | 8.73^{a} | 5.69^{a} |
4 | MC_{5} | wt. | MC_{5} | MC_{5} | MC_{5} | 8.54^{a} | 8.58^{a} | 5.30^{a} |
5 | F134 | F | MC_{1} | MC_{3} | MC_{4} | 8.58 ± 0.17 | 10.37 ± 0.01 | 7.70 ± 0.14 |
6 | F153 | F | MC_{1} | MC_{5} | MC_{3} | 8.88 ± 0.16 | 10.38 ± 0.12 | 7.80 ± 0.56 |
7 | F354 | F | MC_{3} | MC_{5} | MC_{4} | 8.80 ± 0.16 | 8.66 ± 0.48 | 5.72 ± 0.65 |
8 | F413 | F | MC_{4} | MC_{1} | MC_{3} | 8.62 ± 0.16 | 8.64 ± 0.16 | 6.21 ± 0.42 |
9 | F435 | F | MC_{4} | MC_{3} | MC_{5} | 8.96 ± 0.08 | 8.81 ± 0.14 | 6.39 ± 0.40 |
10 | F451 | F | MC_{4} | MC_{5} | MC_{1} | 9.06 ± 0.31 | 8.54 ± 0.26 | 6.33 ± 0.43 |
11 | F514 | F | MC_{5} | MC_{1} | MC_{4} | 9.19 ± 0.21 | 8.45 ± 0.11 | 5.11 ± 0.14 |
12 | F531 | F | MC_{5} | MC_{3} | MC_{1} | 8.67 ± 0.48 | 10.85 ± 0.28 | 5.33 ± 0.08 |
13 | F543 | F | MC_{5} | MC_{4} | MC_{3} | 9.24 ± 0.25 | 9.51 ± 0.50 | 6.39 ± 0.50 |
14 | S134 | S | MC_{1} | MC_{3} | MC_{4} | 9.30 ± 0.26 | 9.98 ± 0.16 | 9.02 ± 0.22 |
15 | S354 | S | MC_{3} | MC_{5} | MC_{4} | 8.81 ± 0.18 | 8.62 ± 0.37 | 4.88 ± 0.25 |
16 | S451 | S | MC_{4} | MC_{5} | MC_{1} | 9.06 ± 0.31 | 9.35 ± 0.36 | 6.10 ± 0.16 |
17 | S514 | S | MC_{5} | MC_{1} | MC_{4} | 9.19 ± 0.21 | 10.04 ± 0.31 | 7.31 ± 0.38 |
18 | S531 | S | MC_{5} | MC_{3} | MC_{1} | 8.96 ± 0.35 | 9.18 ± 0.65 | 7.57 ± 0.19 |
Proteochemometrics modelling
Performance of proteochemometric models. Performance of proteochemometric models derived using wild-type and multiple chimeric receptors interacting with melanocortins, α-MSH, NDP-MSH and [^{125}]-NDP-MSH. Shown are results from the model based on binary receptor descriptors (A) and the model based on physicochemical description of amino acids of the transmembrane regions presumed to face in a direction opposite to the membrane (B) (see Methods for further details).
Model | R^{2} | RMSE (log(M)) | Q^{2} | iR^{2} | iQ^{2} | eQ^{2} |
---|---|---|---|---|---|---|
A | 0.91 | 0.45 | 0.83 | 0.49 | -0.21 | 0.84 |
B | 0.91 | 0.46 | 0.82 | 0.46 | -0.25 | 0.85 |
Prediction of ligand recognition
Selectivity recognition map predicted from binary model. Selectivity recognition map for wild-type MC receptor pairs for α-MSH computed from the binary proteochemometric model. The contribution to the selectivity S^{ u }, log(M), for indicated segments S1–S5, was computed from the model using Eq. 5. Total selectivity represents the entire differences in affinity between receptor pairs computed from the model (see Eq. 4).
Segment | Contribution to selectivity S^{ u }, (log(M)) | |||||
---|---|---|---|---|---|---|
MC_{1}/MC_{3} | MC_{1}/MC_{4} | MC_{1}/MC_{5} | MC_{3}/MC_{4} | MC_{3}/MC_{5} | MC_{4}/MC_{5} | |
S1 | 1.14 | 1.07 | 1.04 | -0.07 | -0.09 | -0.02 |
S2 | 0.39 | 0.91 | 1.15 | 0.52 | 0.77 | 0.24 |
S3 | -0.15 | 0.33 | 0.44 | 0.49 | 0.60 | 0.11 |
S4 | -0.07 | 0.54 | 0.62 | 0.61 | 0.69 | 0.08 |
S5 | 0.10 | 0.29 | 0.46 | 0.19 | 0.36 | 0.17 |
Total selectivity | 1.40253 | 3.1389 | 3.71986 | 1.73638 | 2.31735 | 0.58095 |
Predicted amino acid selectivity recognition map. Amino acid selectivity recognition map for MC receptors for α-MSH computed from the proteochemometric model based on the physicochemical description of amino acids of the transmembrane regions presumed to facing in the direction opposite to the membrane. The contributions to selectivity S^{ u }, log(M), of the indicated amino acid positions were computed from the model using Eq. 5. Total selectivity represents the entire difference in affinity between receptor pairs computed from the model (see Eq. 4). TM, transmembrane regions; SG, segments.
Amino Acids | TM | SG | Contribution to selectivity S^{ u }, (log(M)) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
MC_{1} | MC_{3} | MC_{4} | MC_{5} | MC_{1}/MC_{3} | MC_{1}/MC_{4} | MC_{1}/MC_{5} | MC_{3}/MC_{4} | MC_{3}/MC_{5} | MC_{4}/MC_{5} | ||
Glu37 | Gln74 | Gln43 | Asp35 | 1 | S1 | 0.23 | 0.23 | 0.18 | 0.00 | -0.05 | -0.05 |
Val38 | Val75 | Leu44 | Met36 | 1 | S1 | 0.00 | 0.11 | 0.12 | 0.11 | 0.12 | 0.00 |
Ser41 | Lys78 | Ser47 | Ala39 | 1 | S1 | 0.04 | 0.00 | 0.05 | -0.04 | 0.01 | 0.05 |
Asp42 | Pro79 | Pro48 | Val40 | 1 | S1 | 0.21 | 0.21 | 0.21 | 0.00 | 0.00 | 0.00 |
Val60 | Ile97 | Ile66 | Ile58 | 1 | S1 | 0.48 | 0.48 | 0.48 | 0.00 | 0.00 | 0.00 |
Ile63 | Val100 | Ile69 | Ile61 | 1 | S1 | 0.07 | 0.00 | 0.00 | -0.07 | -0.07 | 0.00 |
Ile77 | Leu114 | Ile83 | Val75 | 2 | S2 | -0.11 | 0.00 | 0.07 | 0.11 | 0.18 | 0.07 |
Ser83 | Ala120 | Ala89 | Ala81 | 2 | S2 | 0.14 | 0.14 | 0.14 | 0.00 | 0.00 | 0.00 |
Asn91 | Asn128 | Asn97 | Ser89 | 2 | S2 | 0.00 | 0.00 | 0.14 | 0.00 | 0.14 | 0.14 |
Val92 | Ala129 | Gly98 | Ala90 | 2 | S2 | 0.03 | 0.10 | 0.03 | 0.07 | 0.00 | -0.07 |
Ala96 | Ile133 | Ile102 | Ile94 | 2 | S2 | 0.14 | 0.14 | 0.14 | 0.00 | 0.00 | 0.00 |
Leu99 | Ala136 | Thr105 | Tyr97 | 2 | S2 | -0.01 | 0.05 | 0.06 | 0.06 | 0.07 | 0.01 |
Gln114 | Gln151 | Val119 | Arg112 | 3 | S2 | 0.00 | 0.08 | 0.11 | 0.08 | 0.11 | 0.03 |
Leu116 | Met153 | Ile121 | Ile114 | 3 | S2 | -0.16 | 0.01 | 0.01 | 0.17 | 0.17 | 0.00 |
Ile120 | Phe157 | Ile125 | Phe118 | 3 | S2 | -0.03 | 0.00 | -0.03 | 0.03 | 0.00 | -0.03 |
Thr124 | Ile161 | Ile129 | Ile122 | 3 | S2 | 0.14 | 0.14 | 0.14 | 0.00 | 0.00 | 0.00 |
Met128 | Leu165 | Leu133 | Val126 | 3 | S2 | 0.09 | 0.09 | 0.11 | 0.00 | 0.02 | 0.02 |
Leu129 | Val166 | Leu134 | Val127 | 3 | S2 | -0.03 | 0.00 | -0.03 | 0.03 | 0.00 | -0.03 |
Leu132 | Ile169 | Ile137 | Met130 | 3 | S2 | 0.01 | 0.01 | 0.15 | 0.00 | 0.14 | 0.14 |
Gly136 | Leu173 | Leu141 | Leu134 | 3 | S2 | 0.14 | 0.14 | 0.14 | 0.00 | 0.00 | 0.00 |
Ala171 | Cys208 | Ala176 | Phe169 | 4 | S3 | -0.09 | 0.00 | 0.04 | 0.09 | 0.13 | 0.04 |
Ser172 | Cys209 | Cys177 | Cys170 | 4 | S3 | 0.12 | 0.12 | 0.12 | 0.00 | 0.00 | 0.00 |
Phe175 | Cys212 | Ser180 | Cys173 | 4 | S3 | 0.02 | 0.11 | 0.02 | 0.09 | 0.00 | -0.09 |
Ser176 | Gly213 | Gly181 | Gly174 | 4 | S3 | 0.12 | 0.12 | 0.12 | 0.00 | 0.00 | 0.00 |
Asp184 | Glu221 | Asp189 | Glu182 | 5 | S3 | -0.07 | 0.00 | -0.07 | 0.07 | 0.00 | -0.07 |
Ala187 | Met224 | Ala192 | Tyr185 | 5 | S3 | -0.08 | 0.00 | -0.03 | 0.08 | 0.05 | -0.03 |
Phe195 | Met232 | Met200 | Met193 | 5 | S3 | 0.12 | 0.12 | 0.12 | 0.00 | 0.00 | 0.00 |
Leu200 | Met237 | Leu205 | Leu198 | 5 | S3 | -0.26 | 0.00 | 0.00 | 0.26 | 0.26 | 0.00 |
Met203 | Met240 | Met208 | Leu201 | 5 | S3 | 0.00 | 0.00 | 0.16 | 0.00 | 0.16 | 0.16 |
Leu243 | Ile281 | Leu247 | Val240 | 6 | S4 | -0.07 | 0.00 | 0.63 | 0.07 | 0.70 | 0.63 |
Leu247 | Leu285 | Ile251 | Leu244 | 6 | S4 | 0.00 | 0.57 | 0.00 | 0.57 | 0.00 | -0.57 |
Ile264 | Ile302 | Tyr268 | Met261 | 6 | S5 | 0.00 | 0.13 | 0.12 | 0.13 | 0.12 | 0.00 |
Val265 | Ile303 | Ile269 | Leu262 | 6 | S5 | 0.02 | 0.02 | 0.11 | 0.00 | 0.09 | 0.09 |
Ala285 | Val323 | Ile289 | Ile282 | 7 | S5 | 0.02 | 0.06 | 0.06 | 0.05 | 0.05 | 0.00 |
Ile288 | Met326 | Met292 | Met285 | 7 | S5 | 0.04 | 0.04 | 0.04 | 0.00 | 0.00 | 0.00 |
Ala291 | Ser329 | Ser295 | Ser288 | 7 | S5 | 0.04 | 0.04 | 0.04 | 0.00 | 0.00 | 0.00 |
Ile292 | Val330 | Ile296 | Val289 | 7 | S5 | -0.01 | 0.00 | -0.01 | 0.01 | 0.00 | -0.01 |
Total selectivity | - | 1.30 | 3.26 | 3.70 | 1.96 | 2.40 | 0.44 |
Verification of predictions using mutagenesis
Experimentally determined pK values of α-MSH for MC_{4} receptor mutants. Shown is the average pK ± SD determined in radioligand binding competition using [^{125}I]NDP-MSH as radioligand. (The numbers of independent replicates are in brackets). The significance, p, is calculated using nonparametric Wilcoxon Rank Sum test [29] (see Methods for details), when compared with the wild-type MC_{4} receptor.
Name | pK_{i} (log(nM)) ± SD (Repeats) | p |
---|---|---|
MC_{4} | 5.73 ± 0.32 (22) | - |
Q43E/P48D | 6.19 ± 0.14 (11) | 1.3E-4 |
I66V | 5.98 ± 0.26 (12) | 9.8E-3 |
A89S | 5.69 ± 0.14 (14) | 6.4E-1 |
I102A | 5.56 ± 0.30 (12) | 1.8E-1 |
I129T | 6.02 ± 0.15 (11) | 4.1E-3 |
A135S | 6.00 ± 0.15 (10) | 1.0E-2 |
L141G | 6.08 ± 0.15 (9) | 3.0E-3 |
I251L | 5.71 ± 0.36 (10) | 7.0E-1 |
Y268I | 5.88 ± 0.20 (14) | 3.8E-2 |
Q43E/P48D/I66V | 6.30 ± 0.17 (11) | 1.5E-5 |
I66V/L141G | 6.03 ± 0.20 (11) | 4.6E-3 |
I129T/A135S | 6.47 ± 0.51 (10) | 2.3E-5 |
L141G/Y268I | 6.01 ± 0.27 (12) | 9.8E-3 |
Q43E/P48D/I66V/I129T/A135S | 6.52 ± 0.17 (11) | 1.4E-7 |
Q43E/P48D/I66V/I129T/A135S/L141G/Y286I | 6.49 ± 0.31 (9) | 1.8E-5 |
N240G/M241L/I245V | 6.10 ± 0.10 (5) | 1.1E-2 |
V253I/V255F/V256L | 6.19 ± 0.16 (5) | 4.3E-3 |
IL3 | 6.72 ± 0.14 (5) | 1.7E-5 |
S4 | 6.98 ± 0.17 (5) | 1.7E-5 |
However, three of the ten positions (A89S, I102A and I251L) did not show the predicted increase in affinity (see Fig. 2, Table 5). The failure of the A89S and I102A mutations to increase the affinity of the MC_{4} receptor can be explained by the presence of several amino acid positions in the protein library that show the same or similar variability (i.e., they co-vary). For example, positions A89 and A135 (numbered according to the MC_{4} receptor) both reside in the same segment and are serines in the MC_{1} receptor and alanines in the MC_{3}, MC_{4}, and MC_{5} receptors. Such co-varying sequence positions gain equal importance in a proteochemometric model, even when some of them are not responsible for the explained activity. In the present library, mutations A89S, I102A, I129T, A135S, and L141G represent co-varying amino acid positions. The failure of the A89S and I102A mutations to cause the predicted increase in affinity may thus be explained on the basis of co-variance, where the actual effect is caused by mutations I129T, A135S, and L141G. In fact, the sum of the experimentally determined affinity increase by mutations A89S, I102A, I129T, A135S, and L141G (pKi = 0.69) closely agrees with that predicted from the model (S^{ U } = 0.56).
Discussion
Mapping molecular recognition with proteochemometrics obtains different information than 3D-structure-based methods. The latter generally reveal where one particular ligand touches one particular receptor in one of many bound states. Proteochemometrics, by contrast, reveals regions of biomacromolecules that influence the selectivity of their ligand binding, and it has the capacity to predict effects arising from distant sites in a protein. The information obtained is only partially overlapping and, therefore, the approaches complement each other. The information gained in proteochemometrics relates to protein function and has direct utility for changing the function of a protein in a desired direction by mutation, in a priori protein engineering, or by altering the structure of a chemical entity and improving its interaction with binding sites, in a priori drug design [2].
Conclusion
In the present work we have presented a theoretical basis for the use of proteochemometrics to assess direct and indirect interactions in proteins, and we verified its utility to this end experimentally. We have also outlined a general strategy to afford cost effective mapping of molecular recognition using proteochemometrics and indicate important differences of proteochemometric mapping of ligand recognitions compared to traditional three-dimensional approaches. We propose that proteochemometrics can be used as a complement to classical 3D based methods to the study of ligand recognition, or even as the prime choice, in particular when three-dimensional protein structures are not available. Moreover, since proteochemometrics can be used to map both direct and indirect interactions, it may find a more general use in e.g. protein engineering and mapping protein function.
Methods
Receptor clones and multichimeric receptors
The coding sequences of the MC_{1} and MC_{5} receptors were cloned earlier [13, 14]. The coding sequences of the MC_{3} and MC_{4} receptor were gifts of Dr. Ira Gantz [15, 16]. Multichimeric MC_{1,3–5} receptors were constructed so that each receptor was divided into three regions, with each region being replaced with a corresponding region from one of the four wild-type MC_{1,3–5} receptors. Swapping all segments from the four receptors would have created a library with an extensive number of combinations, but this would have been impractical. We applied a statistical molecular design, which combines statistical approaches to maximize information gained from a minimal number of experiments. We used a D-optimal design, which could approximate all combinations of the melanocortin receptor regions making up 16 receptors, of which 4 were wild-type and 12 were multiple chimeric receptors. The multiple chimeric receptors were constructed in two sets, the F- and S-sets. The divisions were made at the end of the third and fifth transmembrane segments for the F-set (9 receptors of the 12 designed could be obtained), and at the beginning of the second and middle of the sixth transmembrane segments for the S-set (5 receptors were thus obtained, completing the library according to the design). Thus, the library came to include a total of 18 receptors: 14 that were multiple chimeric (in five segments) and four wild-type MC_{1,3–5} receptors. We have previously reported a full account of the construction of this receptor library [7]. Moreover, full accounts of the theory and applicability of statistical molecular design have also been reported previously [8–10].
Site-directed mutagenesis
Selected individual amino acids in the MC_{4} receptor were exchanged for the corresponding amino acids of the MC_{1} receptor, using mutation-inducing primers and PCR [17]. Eight single mutants (I66V, A89S, I102A, I129T, A135S, L141G, I251L, and Y268I), a double mutant (Q43E/P48D), and two triple mutants (N240G/M241L/I245V, V253I/V255F/V256L), were created. Some of these mutants were then used as templates for constructing mutants with multiple mutations, yielding I66V/L141G, I129T/A135S, L141G/Y268I, Q43E/P48D/I66V, Q43E/P48D/I66V/I129T/A135S, and Q43E/P48D/I66V/I129T/A135S/L141G/Y268I. We also manufactured two chimeric receptors in which subsequences of the MC_{4} receptor were replaced by the corresponding subsequences of the MC_{1} receptor. First we constructed a receptor ("S4 chimeric receptor") in which the entire S4 segment in the MC4 receptor was replaced with that from the MC_{1} receptor. Another receptor ("IL3 chimeric receptor") comprised the MC_{4} receptor with intracellular loop 3 replaced with the corresponding loop of the MC_{1} receptor.
Peptides and radioligand
Peptide ligands α-MSH (Ac-SYSMGHFRWGKPV-NH_{2}) and NDP-MSH ([Tyr^{2}, Nle^{4}, D-Phe^{7}]-α-MSH) were synthesized using standard solid phase peptide synthesis and purified by HPLC; their correct molecular weights were verified by mass spectrometry. [^{125}I]-NDP-MSH ([^{125}I-Tyr^{2}, Nle^{4}, D-Phe^{7}]-α-MSH) was prepared in radiochemically pure form by custom iodination at EuroDiagnostica AB, Sweden.
Receptor expression and radioligand binding
COS-1 cells were grown in Dulbecco's modified Eagle's medium with 10% fetal calf serum. Eighty-percent confluent cultures were transfected in 100-mm dishes with the DNA constructs (10 μg DNA per dish, mixed with liposomes, as described [18]. Twelve to sixteen hours after transfection, the serum-free medium was replaced with growth medium and the cells were cultivated for approximately 48 hours, then scraped off, centrifuged, and used for radioligand binding. Dissociation constants (K_{d}) for [^{125}I]-NDP-MSH were estimated for all the receptors by radioligand binding saturation as described [7, 18]. Inhibition constants (K_{i}) for α-MSH and NDP-MSH were then estimated in competition with [^{125}I]-NDP-MSH using established procedures [7, 18]. Obtained pK values (i.e., the negative logarithms of the K_{i} and K_{d} values) are listed in Tables 1 and 5.
Numerical descriptions of receptors for proteochemometric modelling
Two types of descriptions were used for the receptors, namely a binary description and a description based on physicochemical descriptions of amino acids. For the binary description, four binary numbers described each region, with each number corresponding to one receptor subtype. Each of these descriptors was assigned a value of +1 if the region was taken from descriptors' corresponding receptor subtype, otherwise it was assigned the number -1 [7].
The receptor descriptions based on physicochemical descriptions of amino acids at 38 selected sequence positions was used as described [7]. These positions were selected from a three-dimensional model of the transmembrane regions of the MC_{1} receptor.
Using the crystal structure coordinates of rhodopsin as a template [12], the model was derived by replacing the side chains with the corresponding side chains of the MC_{1} receptor, using the alignments of the GPCRDB database [19] and the SCWRL program [20]. Only amino acids pointing in the direction opposite the lipid bilayer were considered. This led to a considerable reduction in the number of co-varying sequence positions considered in the proteochemometric modelling, albeit with the obvious risk of excluding important positions. The selected positions are listed in Table 4.
Each position was coded by using five principal components derived from 26 physicochemical properties of amino acids, so called z-scales [21]. These z-scales represent hydrophobicity, steric properties, polarizability (z1–z3), polarity, and electronic effects (z4, z5). The data for the 38 × 5 = 190 descriptors obtained were compressed by applying principal component analysis (PCA) [22] to each of the five segments of the receptor library, which yielded in total 15 descriptors, with three descriptors for each segment. Prior to PCA, the z-scale descriptors had been scaled to unit variance [23]. Principal component analysis was performed using the Simca-P program [23].
Numerical description of peptides for proteochemometric modelling
Description of peptides for proteochemometric modelling. The general sequence of the peptides used herein was: Ac-Ser-Pos2-Ser-Pos4-Gly-His-Pos7-Arg-Trp-Gly-Lys-Pro-Val-NH_{2}. Amino acids in Pos2, Pos4, Pos7, and the corresponding description, were as shown.
Peptides | Sequence position | Descriptors | ||||
---|---|---|---|---|---|---|
Pos2 | Pos4 | Pos7 | Y | F | Y*F | |
α-MSH | Tyr | Met | Phe | -1 | -1 | 1 |
NDP-MSH | Tyr | Nle | D-Phe | -1 | 1 | -1 |
^{125}I-NDP-MSH | ^{125}I-Tyr | Nle | D-Phe | 1 | 1 | 1 |
Numerical description of binding experiments and proteochemometric modelling
In each binding experiment, the receptor-peptide combination was described using the above receptor and peptide descriptors, and by computing receptor-ligand cross-terms using Eq. 2, each cross-term being calculated as the product of one peptide and one receptor descriptor. Prior to calculating cross-terms, all descriptors were mean-centred and scaled to unit variance [23]. In order to account for differences in the number and mutual correlation of each descriptor type, the peptide descriptors, receptor descriptors, and cross-terms, block scaling was applied. All descriptors and cross-terms were mean centred and scaled to unit variance prior to block scaling [23]. Descriptors were finally correlated to the pK values using partial least squares projection to latent structures (PLS) regression [22]. PLS modelling was done using Simca-P [23].
Validation of modelling
The goodness-of-fit was estimated by the correlation coefficient R^{2} and root mean square error (RMSE) [23]. Models were further validated using cross-validation (CV) [25, 26], validation by response permutations [27], and validation by external prediction.
In cross-validation, one divides the data into several fractions. Seven were used in this study. Each fraction is repeatedly excluded once and then predicted from the model developed on the remaining data. The goodness of prediction of the CV is assessed by the Q^{2} measure [23].
In response permutation validation, many models are created using randomly permuted response data. Twenty permutations were used here. For each permuted model, the R^{2}, Q^{2}, and correlation coefficients between the original and permuted response values are estimated. The correlation coefficients are plotted against the R^{2} and Q^{2} values. The two corresponding linear correlation lines are estimated, one for R^{2} and one for Q^{2}, and the intercepts iR^{2} and iQ^{2} of the two regression lines with the zero correlation coefficient line are calculated [5, 23]. These intercept values indicate the R^{2} and Q^{2} of random response data. For example, a negative Q^{2} intercept shows that it is not possible to obtain predictive models with random data, and indicates that a high Q^{2} value of the original model is not obtained by pure chance.
External prediction assesses a model's stability when a substantial fraction of the data is excluded (e.g., more than one-third). External prediction may aim to predict the properties of new entities, in other words, entities that are entirely excluded from the data set. In the present case we predicted pKs for the S-set receptors using only data for F-set receptors. The goodness of external prediction was assessed by the external Q^{2} (eQ^{2}) value [5]. Further details on these model validation approaches and how to interpret their results have been previously reported [28].
Computation of the selectivity contribution of amino acids
The contributions of individual amino acids to the selectivity of peptide binding between pairs of receptors were computed using Eq. 5. In order to apply Eq. 5, the regression coefficients for the individual z-scales of the receptor's amino acids were computed from the corresponding PLS and PCA models. Nine amino acids (Q43, P48, I66, A89, I102, I129, L141, I251, Y268, according to the numbering in the MC_{4} receptor) contributed most to the selectivity of α-MSH (see Table 4) and were selected for site-directed mutagenesis. Moreover, upon analyzing the 3D model of the MC_{1} receptor it was deemed that S83 (corresponding to A89 in the MC_{4} receptor) had a strong H-bond interaction with S130 (A135 in the MC_{4} receptor). Since the amino acid positions A89/A135 (MC_{4} receptor numbering) showed identical co-variance in the receptor library, A135 was also selected for site-directed mutagenesis.
Statistical tests
The distribution of measured affinity for MC_{4} receptor and mutant receptors presented here as well as its logarithm values (pK) did not correspond to normal distribution. Therefore we decided to use nonparametric Wilcoxon Rank Sum statistical test [29] to verify the hypothesis that affinity for corresponding mutant receptor differs from wild-type MC_{4} receptor. The test was performed using R program [30].
Declarations
Acknowledgements
Supported by the Swedish Research Council (04X-05957 and 621-2002-4711). We thank Santa Veiksina for technical assistance.
Authors’ Affiliations
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