(A) CaM-target complex exhibiting the conventional binding mode, where CaM is shown in pink and the target peptide in violet (PDB 3BXL). The common CaM-binding interface (20 positions in total) is highlighted in magenta, and ions are indicated as pink spheres. (B) Free CaM (center) can bind each of the 16 studied targets in the binding mode shown in panel A. (C) Multiple sequence alignment (ClustalW) and conservation logo of 16 peptide targets of CaM, for each of which the solved structure shows the conventional binding mode depicted in panel A. PDB codes and target descriptions are as listed. Note that the target peptides of 2BE6 and 2F3Y are derived from the same protein; however, we used both of them since they are of different lengths and the RMSD between the CaM molecules is significant (1.15 Å). (D) We methodically optimize CaM to bind each target (1-state), pairs of targets (2-state), and triplets of targets (3-state). Multiple-target design is implemented by minimizing the sum of the CaM sequence energies in each structure, with the constraint (denoted by arrows) that the same amino acid sequence be predicted for all structures.

(A) The number of mutations from the WT CaM sequence observed in the single lowest energy sequence when redesigning 20 positions in the CaM binding interface. The average number of mutations is 9.5 for single-state designs (52% native sequence recovery), 7 for the two-state designs (65% recovery), 6 for the three-state designs (70% recovery), and 4 for the design of all sixteen states (80% recovery). (B) Comparison of the 100 best designed CaM sequences to the evolutionarily observed sequences (HSSP profile of CaM). JSD dissimilarity between distributions of 100 designed sequences and HSSP was calculated according to Eq. 1, where lower JSD values indicate greater similarity between the predicted sequence profile and the HSSP profile. The average JSD is 0.48 for single-state designs, 0.37 for two-state designs, 0.35 for three-state designs, and 0.24 for design of all sixteen states.

(A) Dissimilarity between all pairs of sequence profiles designed for a single structural state was calculated for each of the interface position by computing the JSD dissimilarity score (Eq. 1). The results were binned for histogram analysis. Positions that exhibit low pairwise JSD scores with higher frequency (red) are most conserved between the various CaM single-state designs and hence are predicted to be affinity-defining. Positions that exhibit high pairwise JSD with higher frequency (cyan) differ for each single-state design and hence are specificity-defining. (B) Evolutionary logo with specificity and affinity-defining positions marked. (C) Structure of a CaM-target complex (PDB 3BXL) with affinity and specificity positions marked in red and cyan, respectively, and the target peptide is colored in violet. (D) Intramolecular and (E) intermolecular energetic contributions for the WT CaM sequence at each of the 20 interface positions. The intra- and intermolecular contributions were calculated in each of the 16 CaM-target complexes and were averaged over all cases. Positions are colored as above, and the dotted line indicates the average energy contribution for all positions.

(A) In comparing the amino acid distributions at each of the CaM interface positions obtained in single-state designs with those resulting from 2-state design calculations, five scenarios were observed. Dark blue - both individual states have similar profiles and the 2-state design chooses this profile. Light blue - two-state design yielded a profile that is a combination of the two distributions obtained for each single-state design. Green - two-state design yielded a distribution of amino acids that was similar to that of only one of the single-state designs. Orange - an amino acid distribution for the two-state design was chosen that is different from that of both of the individual single-state designs. Maroon - Despite the individual states having similar profiles, the two-state profile is different. Interface positions are marked on the horizontal axis. The analysis was performed only for cases where the particular position is in the binding interface for both of the combined CaM-target complexes (the number of such cases is shown in brackets below the interface position number). (B) Logos of sequence profiles individually optimized in the context of CaM-target complex structures with PDB identifiers 2F3Y and 3BXL (1-state design), compared to the profile resulting from simultaneous optimization for interaction with both targets (2-state design). Positions that demonstrate compromise scenarios are outlined in colors as in panel A.

Asterisks mark those amino acids with frequencies that significantly differ (, t-test with Bonferroni correction) between 1-state and both multistate designs, and change monotonically from 1-state to 2-state to 3-state (within a threshold of 90%).

(A) Designing CaM for binding an increasing number of partners progressively yields more native-like sequences. (B) The WT sequence has binding energies most similar to those of CaM sequences designed for multiple interactions. (C) We find that intramolecular interactions are critical for binding affinity, whereas intermolecular interactions determine specificity toward the various targets.

Amino acids found in the 100 best CaM binding interface sequences optimized for one (1-state), two (2-state), three (3-state), and sixteen (16-state) targets simultaneously, compared to the evolutionary profile of CaM (HSSP). The size of the displayed amino acid is proportional to its frequency of occurrence. Color coding: black - hydrophobic amino acids, green - polar non-charged, purple - amide, red - negatively charged, blue - positively charged. Results for all sixteen one-state CaM designs are shown. For clarity, only 15 out of 120 calculations and 14 out of 560 calculations are shown for the two-state and three-state designs, respectively. Numbers in parentheses denote the mean positional dissimilarity score (calculated according to Eq. 1) compared to HSSP, where lower values indicate greater similarity to the evolutionary profile.

(A) For each position in the CaM binding interface (horizontal axis), dissimilarity with the evolutionary profile of CaM (HSSP) is calculated using the JSD score. Black - positions with the largest dissimilarity between the design and the HSSP. White - positions showing the largest similarity between the design and HSSP. Red boxes indicate positions that are not in the binding interface for a particular CaM-target complex but were included in the calculation as part of the common binding interface. On the right, the average per-position dissimilarity is given for the 20 interface positions in the particular CaM-target complex. In parentheses, the same number is calculated with the boxed (non-relevant) interface positions excluded, so that the dissimilarity tends to decrease for these more “relevant” positions. (B) Correlation between the number of relevant interface positions in a particular CaM-target complex structure and dissimilarity of the designed sequences with the evolutionary profile, as calculated by the mean per-position JSD score (right side of panel A, numbers in parentheses). (C) Correlation between the energy of the WT sequence threaded onto a particular CaM-target complex structure and dissimilarity of the designed sequences with the evolutionary profile, as calculated by the mean per-position JSD score (right side of panel A).

Total energies (intramolecular+intermolecular energies) for each of the 20 interface positions are averaged in all 16 structures for the native sequence (green bars) and the single-state design lowest energy sequences (blue bars). The dotted lines indicate the respective average energy contributions for all positions. The affinity- and specificity-determining positions are boxed in red and cyan, respectively.

(A) For each position in all 2-state designs, its dissimilarity with the evolutionary profile (JSD score with HSSP) is compared to the JSD dissimilarity with the distribution that is the average of the two respective 1-state design strategies (JSD score for 1-state design results). For each position, we only analyzed the scenarios in which the predicted profile preferred only one of its constituent states or contained novel amino acids (the number of such cases for each position is shown in brackets on the bottom). Three main outcomes were tallied: Gray - no significant change in the dissimilarity score. Blue - the two-state design significantly improves the JSD of the single-state designs, i.e., two-state design is beneficial. Red - the two-state design performs significantly less well than the single-state designs in recovering the HSSP profile, i.e., two-state design results in greater dissimilarity with the evolutionary profile. Interface positions are marked on the horizontal axis. (B) Logos of sequence profiles individually optimized for CaM interaction states 2F3Y and 3BXL (1-state design) and simultaneously optimized for both states (2-state design), compared to the evolutionary profile (HSSP). Mean dissimilarities with the evolutionary profile (JSD from HSSP) are noted in parentheses. Positions that demonstrate the effect of the multispecific compromise, vis-a-vis HSSP, are outlined in colors as in panel A.

We evaluate the compatibility of various sequences with the structure of CaM in complex with target A (denoted as “state A”), where the choice of A ranges over all sixteen CaM-target complex structures; B, C, and D denote the structures of other CaM-target complexes. The sequence energies compared in the context of CaM in complex with A are those predicted by our protocol while considering CaM interactions with various combinations of targets, e.g., A+B. Each plot is a histogram of changes in energy resulting from the comparison between such design scenarios. All energy differences are normalized relative to the lowest energy sequence designed for interactions with target A and capped at 25% for purposes of depiction. (A) Gain in stability of state A due to its incorporation in multispecific design. Top: indicates that energies in state A were compared between the sequences resulting from CaM design that considers only interactions with target B and the design that simultaneously considers interactions with A and B. Middle: compares the sequences designed for state C and those designed for states A+B+C. Bottom: compares those designed for B+C with those designed for A+B+C. (B) Energetic non-optimality of state A not included in a particular multispecific design scenario. The energy differences are calculated between sequences designed for interactions with the marked combination of targets (B, B+C, and B+C+D, respectively) and those designed only for interaction with target A. (C) Loss of stability of state A due to incorporation of additional states in the design. Top: compares the energies of the sequences designed for interaction with target A alone with those designed for both A and B simultaneously. Middle: compares the sequences designed for A with those designed for A, B, and C. Bottom: compares the sequences designed for both states A and B with those designed for A, B, and C. (D) Energetic non-optimality of the WT CaM sequence in state A, as compared to the lowest energy sequence predicted in the respective design scenario, including designing only for interactions with A (top), for interactions with A and B (middle), and for interactions with A, B, and C (bottom).