Comparative study of interaction energies between αIIbβ3 integrin and the peptidic, peptidomimetic and non-peptidic ligands by quantum mechanics FMO-PIEDA calculations

Integrins belong to a family of cell adhesion receptors. To better understand an adhesion mechanism of integrins, fragmented molecular orbital (FMO) method with pair interaction energy decomposition analysis (PIEDA) was applied for integrin:ligand complexes. Interaction energies were evaluated between the amino acid residues including Mg2+ and Ca2+ ions at ligand-binding site of αIIbβ3 integrin and two peptide chains with the Ala-Gly-Asp (AGD)- and the Arg-Gly-Asp (RGD)-binding motifs, a cyclic peptide (eptifibatide), peptidomimetic ligands (tirofiban and L-739758) and poly(l-lactic acid) chain (PLA). The results indicate that Mg2+ and Ca2+ ions together with Asp224A, Asn215B, Asp159A and Lys125B of αIIbβ3 are the most important residues for a binding of the peptidic ligands while for the peptidomimetic ligands and PLA, interactions with Ca2+ ions are less significant than those with amino acid residues of αIIbβ3. For all complexes, a dominant part of interaction energy comes from electrostatic interactions. New developed antagonists of αIIbβ3 should mimic not only the interactions of the RGD motif but also the interactions of the backbone of a longer peptidic sequence (RGDV or AGDV) with the focus on the interactions of the antagonists with the ADMIDAS Ca2+ ion. An interaction pattern predicted for PLA was compared with the native peptidic ligands.


Introduction
Integrins, selectins, cadherins, immunoglobulins and mucins belong to adhesion molecules (Harjunpää et al. 2019;Chothia and Jones 1997;Tvaroška et al. 2023). Integrins are heterodimeric molecules containing an α and a β subunit (Humphries 2000;Hynes 2002;Campbell and Humphries 2011) with large extracellular domains and short cytoplasmic domains Arnaout et al. 2005). |The ligand-binding site is formed in an interface between the α subunit and the β subunit (Fig. 1). Most integrins bind a wide variety of ligands (Humphries et al. 2006;Zheng and Leftheris 2020). The low affinity state-bent conformation of the integrins can change to the open active conformation forming the ligand-binding site in the β I domain (Luo et al. 2007;Zhu et al. 2013;Xiao et al. 2004). The β I domain has three metal ion-binding sites, with a Mg 2+ ion in the central metal ion-dependent adhesion site (MIDAS) flanked by two Ca 2+ ions, one of which is in a site termed adjacent to MIDAS (ADMIDAS). The other Ca 2+ ion is in a site termed as the ligand-associated metal ion-binding site (LIMBS) (Fig. 1).
Molecular dynamics (MD) simulations of integrins' conformational dynamics were reviewed recently (Tvaroška et al. 2023). The prevailing MD simulations have focused on understanding activation and transition from bent to extended conformations initiated by inside-out and outside-in signaling (Murcia et al. 2008;Puklin-Faucher and Vogel 2009;Ghitti et al. 2012;Craig et al. 2004;Mehrbod et al. 2013;Bidone et al. 2019;Gaillard et al. 2009;Chen et al. 2011;Puklin-Faucher et al. 2006;Wang et al. 2017). Recently, molecular dynamics simulations to the bidirectional adhesion signaling pathway of integrin α V β 3 were performed (Kulke and Langel 2020). From the results, the most likely mechanism for inside-out and outside-in signaling is the switchblade model with further separation of the transmembrane helices.
Integrins recognize protein ligands through Arg-Gly-Asp (RGD) sequence in flexible loop regions . However, the adhesion mechanism by which integrins differentiate among proteins with RGD motifs is not well understood (Dong et al. 2014). Based on available X-ray structures of RGD-binding integrins (Xiong et al. 2002;Springer et al. 2008;Dong et al. 2014;Zhu et al. 2008Zhu et al. , 2010Zheng and Leftheris 2020), a negatively charged carboxylate side chain of Asp directly coordinates with the MIDAS Mg 2+ ion and a positively charged side chain of Arg interacts with Asp residue of the integrin. Other amino acid residues of the protein ligand seems to play an important role for specific binding of the ligand since short peptides with different amino acid sequences with the RGD motif were not always effective antagonist for some studied RGD-binding integrins (Kapp et al. 2017;Kloczewiak et al. 1989). Additionally, isoDGR was found as a new natural recognition motif of the RGD-binding pocket of α v β 3 integrin (Spitaleri et al. 2008(Spitaleri et al. , 2011. Molecular dynamics simulations revealed that isoDGR-containing cyclopeptides are true α v β 3 antagonists which block integrin activation (Ghitti et al. 2012).
Fibrinogen binds to integrin α IIb β 3 on platelets during hemostasis and thrombosis and both proteins are mentioned in connection with cardiovascular and autoimmune diseases (Huang et al. 2019). α IIb β 3 integrin also plays a role in cancer progression. α IIb β 3 binds to RGD-lacking C-terminal region [the AKQAGDV sequence with an Ala-Gly-Asp (AGD) motif] of the γ subunit of fibrinogen (Yang et al. 2001) (Fig. 1). On the other hand, α v β 3 integrin binds fibrinogen via a non-terminal RGD motif in fibrinogen's α subunit. As was found by X-ray study , α IIb β 3 integrin also bound to a lamprey terminal AKQRGDV sequence with the RGD motif. Therefore, development of selective antagonists of α IIb β 3 and the closely related α V β 3 integrin was efforted in past decades (Xiao et al. 2004).
To compare an interaction pattern between α IIb β 3 integrin and the peptides with these two motifs, and better understand chemical nature of a complex ligand-binding site of α IIb β 3 consisted of the three metal ions, quantum mechanics calculations were performed in this study using the twobody fragmented molecular orbital (FMO) method (Kitaura et al. 1999;Fedorov and Kitaura 2009;Fedorov et al. 2012). Due to available X-ray structures Xiao et al. 2004), the calculations were also performed for α IIb β 3 complexes with peptidomimetic antagonists (eptifibatide, tirofiban and L-739758 ligand) (Fig. 2). Eptifibatide is a cyclic l-peptide with the homoarginine-Gly-Asp sequence, and together with tirofiban, they are used in treatment of thrombosis. Both eptifibatide (IC 50 = 2.44 nM) and tirofiban (IC 50 = 1.3 nM) are nanomolar antagonist of α IIb β 3 (Kapp et al. 2017). L-739758, structurally similar to tirofiban, is an effective antagonist of α IIb β 3 . The FMO-PIEDA calculations for these antagonists of α IIb β 3 will allow us to compare their interaction patterns with those of native peptidic ligands of α IIb β 3 and help better to understand their nanomolar biological activities. The calculations will show whether the synthetic antagonists mimic interactions of the native peptidic ligands or interact with α IIb β 3 specifically. In addition, FMO-PIEDA calculations were also performed for a complex of α IIb β 3 with a poly(l-lactic acid) (PLA) chain in two conformations (Fig. 3). In one conformation, mimicking terminal C-region of fibrinogen, PLA chains was modeled with its terminal carboxylate coordinated with the MIDAS Mg 2+ ion, while in the other conformation it interacted with an integrin ligand-binding groove and MIDAS by polyester groups as they were predicted by molecular docking calculations (mimicking the binding of a non-terminal region of a peptidic ligand). PLA is a thermoplastic polyester often used as medical implants in different forms (Suzuki and Ikada 2010). To improve cell adhesion properties of polymers, the integrin-targeting proteins were integrated in different polymeric scaffolds and implant materials (Zhao et al. 2020;Shekaran and García 2011;Kim and Park 2006;Dhavalikar et al. 2020). The FMO-PIEDA calculations for the PLA: α IIb β 3 complexes will show how well the polyester backbone of PLA mimics the interactions of the peptidic ligands of α IIb β 3 and which modifications of the structure of PLA could improve its adhesion properties for binging to integrins. Fig. 1 A 3-D structure of α IIb β 3 integrin with a bound peptide (with the AGD motif, green). The β subunit β3 I domain (red) has three metal ion-binding sites, with a Mg 2+ ion (blue ball) flanked by two Ca 2+ ions (pink balls). The α subunit β-propeller domain is depicted in a gray color Results and discussion α IIb β 3 :peptide(GAKQAGDV). The complex of the integrin(α IIb β 3 ):peptide (GAKQAGDV) was used in this study as a template structure for comparison of ΔE int(L:R) with other complexes. The geometry of an X-ray structure (PDB ID: 2VDP) (Springer et al. 2007b) was firstly optimized at the DFT-QM/MM level. Then the FMO-PIEDA calculations were performed at both DFT (wB97X-D) and ab initio MP2 levels (Tables 1 and 2). Firstly, we wanted to understand which amino acid residues of α IIb β 3 are most important for binding a native peptide with the AGD motif (Table 1). Then, we also wanted to see which amino acid residues of the peptide (the GAKQAGDV sequence) are the most important for the binding ( Table 2). The FMO-PIEDA results of this complex are compiled in Fig. 4 and only results calculated at the MP2/6-31G(d) level are discussed. (The results calculated at the DFT-wB97X-D/6-31G(d) gave similar energy trends and are also given in Tables 1 and 2.) The calculations have revealed that the most significant interactions are between the peptide ligand and the Mg 2+ ion (ΔE L:Mg 2+ = − 350.2 kcal mol −1 ), the Ca 2+ ion (ADMIDAS) (ΔE L:Ca(ADMIDAS) 2+ = − 158.9 kc al mol −1 ), the Asp224A (ΔE L:Asp224A = − 90.5 kcal mol −1 ), the Ca 2+ (LIMBS) ion (ΔE L:Ca(LIMBS) 2+ = − 75.8 kcal m ol −1 ), the Asn215B (ΔE L:Asn215B = − 55.3 kcal mol −1 ), the Asp159A (ΔE L:Asp159A = − 52.1 kcal mol −1 ), the Lys125B (ΔE L:Lys125B = − 49.2 kcal mol −1 ) and the Arg214B (Δ E L:Arg214B = − 43.7 kcal mol −1 ). Thus, the most important interactions come from charged fragments of the integrin except for Asn215B. On the other hand, most severe repulsions come from negatively charged amino acid residues, namely Glu220B, Asp251B and Asp119B. These amino acid residues are directly coordinated with Mg 2+ and both Ca 2+ ions, and in the FMO calculations, they were modeled as the separate fragments. Thus, their predicted high repulsion with the peptide ligand is supposed to be overestimated, and in real chemical microenvironment, their negative charges are stabilized by coordination with the highly positive Mg 2+ and Ca 2+ ions, and the repulsion with the ligand is decreased. The FMO-PIEDA analysis (Table S1 of ESI) of energy terms (ΔE els , ΔE exch , ΔE ct+mix , ΔE disp ) of ΔE L:R-AA confirmed this trend where the electrostatic energy term, ΔE els , was the most significant part of the interaction energy. To understand which amino acid residues of the peptide are the most important for the binding to α IIb β 3, the FMO-PIEDA analysis was also evaluated for every amino acid of the GAKQ-AGDV sequence (Table 2). ΔE L-AA:R energies between α IIb β 3 and the residues of the bound peptide decrease (weaken) in order: Asp410 (− 251.8 kcal mol −1 ) > Lys406 (− 193.5 kcal mol −1 ) > Val411 (− 92.8 kcal mol −1 ) > Gln407 (− 62.1 kcal mol −1 ) > Gly409 (− 48.0 kcal mol −1 ) > Ala408 (− 20.0 kcal mol −1 ) > Gly404 (− 5.3 kcal mol −1 ) > Ala405 (4.0 kcal mol −1 ). The three most significant residues (Asp410, Val411 and Lys406) interact with the MIDAS Mg 2+ ion (Asp410, ΔE L-Asp410:Mg 2+ = − 301. 7 kcal mol −1 ), with the ADMIDAS Ca 2+ ion (Val411, ΔE L-Val411:Ca(ADMIDAS) 2+ = − 107.7 kcal mol −1 ) and with Asp224A (Lys406, ΔE L-Lys406:R-Asp224A = − 127.9 kcal m ol −1 ). Val411 is the C-terminal residue terminated with negatively charged carboxylate. Thus, on both sides, on the integrin [Mg 2+ (MIDAS), Ca 2+ (ADMIDAS) and Asp224A] and on the peptide (Asp410, Val411 and Lys406), the highly polar amino acid residues and the metal ions seem to play The importance of the terminal carboxylate of Val411 for the binding was also confirmed by additional FMO-PIEDA calculations where in C-terminal Val411 of the bound peptide the charged carboxylate (GAKQAGDV-COO − ) was substituted by N-methyl amido group (GAKQAGDV-CONH-CH 3 ). In such peptide, interaction energy for Val411-CONH-CH 3 fragment was decreased to − 6.5 kcal mol −1 (from − 92.8 kcal mol −1 found in GAKQAGDV-COO − , ΔE Val411:R ). One of the reasons may be a repulsion between the Val411-CONH-CH 3 and the ADMIDAS Ca 2+ ion (Δ E Val411:Ca(ADMIDAS) 2+ = 20.4 kcal mol −1 ), which on the other hand is the major contributor of the interaction energy for the peptide with Val411-COO − (ΔE Val411:Ca(ADMIDAS) 2+ = − 107.7 kcal mol −1 ). Indeed, the importance of the free carboxylate group of the C-terminal residue Val411 for an interaction with the ADMIDAS Ca 2+ ion was demonstrated by experiments where γC peptides with the carboxylate substituted by amide blocked fibrinogen binding to α IIb β 3 ). Moreover, a substitution of Val411 by cysteine, tyrosine or leucine led to a dramatic decreasing of the binding properties of the ligand, while the substitution with phenylalanine maintained the activity of γC peptides Kapp et al. 2017). We conclude that the interaction of α IIb β 3 with the backbone of Val411 is more significant compared with its side chain. In case of the substitution with cysteine, tyrosine or leucine, the structure of their side chains may be more important for a tight binding to the ADMIDAS Ca 2+ ion and subsequent strong interactions of their backbones with α IIb β 3 and the ADMIDAS Ca 2+ ion itself.
The bound peptide does not directly coordinate with the ADMIDAS Ca 2+ ion and interacts (via terminal carboxylate of Val411) with it via a water molecule  Table 1). Similarly as it was for the ADMIDAS Ca 2+ ion, the LIMBS Ca 2+ ion is not in a direct contact with the bound ligand. Despite the larger distance between the   The AGD motif of the native ligand of α IIb β 3 contains the glycine residue. Glycin does not contain a side chain and may be most flexible part of the backbone of the peptides and proteins. Thus, it is important in conformational changes and folding in proteins. Here in the peptide:α IIb β 3 complex, Gly409 of the peptidic ligand, seems also to play an important role for the binding. Its interaction energy with α IIb β 3 was predicted with a significant value of − 48.0 kcal mol −1 (ΔE Gly409:R , Table 2). It should be noted that a FMO fragmentation technique with the shifted backbone definition was used in this study (Sladek and Fedorov 2022). It means that the Gly409 fragment includes the amide bond consisted of amine group of Gly409 and carbonyl group of Ala408. Detailed analysis of the FMO results showed that this backbone amide bond (Ala408-Gly409) interacts with Ala218B (ΔE L-Gly409:R-Ala218B = − 8.5 kcal mol −1 ), three water molecules, two of them via carbonyl oxygen (ΔE L-Gly409:H2O(201) = − 13.9 kcal mo l −1 , ΔE L-Gly409:H2O(257) = − 14.5 kcal mol −1 ) and one via amide group (ΔE L-Gly409:H2O(258) = − 9.5 kcal mol −1 ) and the LIMBS Ca 2+ ion (ΔE L-Gly409:Ca(LIMBS) = − 7.5 kcal mo l −1 ). Similarly, as it was for Val411 of the peptidic ligand, the interaction of the Ala408-Gly409 backbone with α IIb β 3 seem to play an important role for the binding of the peptide with the AGD motif. α IIb β 3 :AKQRGDV peptide. Whereas ligands with the RGD motif binds to eight different integrins, the fibrinogen γC peptide with the AGD motif binds only to α IIb β 3 . In contrast, the A408R mutation of the native γC peptide, which produced the RGD motif, did bind to α IIb β 3 ). In the X-ray structure (PDB ID: 2VDR) (Springer et al. 2007a), this arginine substitute a 3-D position of Lys406 and interacts with Asp224A of α IIb β 3, while Lys406 interacts with Asp159A of α IIb β 3. We calculated a FMO-PIEDA energy profile for the α IIb β 3 :peptide complex to see how presence of Arg408 and 3-D reorganization of the peptide change interactions with the integrin. The FMO-PIEDA results for every amino acid of the AKQRGDV sequence of the peptide are compile in Table 2, and for the most important amino acid residues of α IIb β 3 , the results are in Table 1. ΔE L-AA:R between the residues of the peptide and α IIb β 3 integrin decreases (weakens) in the following order: Asp410 (− 246.7 kcal mol −1 ) > Arg408 ( − 1 8 3 . 7 k c a l m o l − 1 ) > V a l 4 1 1 ( − 1 2 7 . 1 3 k c a l m o l − 1 ) > G l n 4 0 7 (− 50.4 kcal mol −1 ) > Gly409 (− 44.9 kcal mol −1 ) > Lys406 (− 33.3 kcal mol −1 ) > Ala405 (− 12.7 kcal mol −1 ). Thus, the order of significance is almost the same, as for the native peptide with the AGD motif, with an exception of Arg408, which now is a better contributor to total ΔE int(L:R) as Val411 and Lys406 ( Figure S1 of ESI). Again, as it was for the peptide with the AGD motif, the three most significant residues (Asp410, Arg408 and Val411) interact with the MIDAS Mg 2+ ion (Asp410, ΔE L-Asp410:Mg 2+ = − 30 0.6 kcal mol −1 ), with the ADMIDAS Ca 2+ ion (Val411, ΔE L-Val411:Ca(ADMIDAS) 2+ = − 116.0 kcal mol −1 ) and with Asp224A (Arg408, ΔE L-Arg408:R-Asp224A = − 105.4 kcal mo l −1 ). Thus, both the AKQAGDV and AKQRGDV sequences present an optimal 3-D structure for specific binding of γ subunit of fibrinogen to α IIb β 3 . The total ΔE int(L:R) for the peptide with the RGD motif is stronger (ΔE int(L:R) = − 736.0 kcal mol −1 ) compared with that for the peptide with the AGD motif (ΔE int(L:R) = − 708.6 kcal mol −1 ) (Fig. 5). This supports the finding that the substitution of Ala408 by Arg in human fibrinogen γC chain (dodecapeptide γC 400-411) led to gain 6 times on binding potency Timmons et al. 1989). A similar result was obtained by Ruggeri et al., where the IC 50 for γC 400-411 was 48-180 μM and only 14.5 μM for the A408R mutant (Ruggeri et al. 1986). Indeed, lamprey and xenopus, in contrast to human, γC sequences of fibrinogen contain the RGD motif .
Complexes α IIb β 3 :peptidomimetic ligands. Based on available X-ray structures Springer et al. 2007c, e, d), complexes of α IIb β 3 with cyclic peptide eptifibatide, nanomolar blocker tirofiban and the L-739758 ligand FMO-PIEDA interaction patterns were calculated (Figs. 7, 8 and 9) and compared with the results of the complexes of α IIb β 3 with the previously discussed peptides with the AGD and the RGD motifs. For these three ligands, the interactions with the MIDAS Mg 2+ ion, the ADMIDAS Ca 2+ ion and the LIMBS Ca  2+ is strongly repulsive (31.7 kcal mol −1 ). This finding is also supported by steered molecular dynamics (SMD) simulations where the ADMIDAS Ca 2+ ion had the lowest effect on SMD force profiles of the unbinding of eptifibatide from α IIb β 3 (Murcia et al. 2008).
Overall, the interactions of the ligands with the MIDAS Mg 2+ ion calculated in this study are the most significant (Fig. 5). The dominant part of ΔE L:Mg 2+ is an electrostatic  (Table 1, Figs. 6,7 and 8) are also the most important contributors to total ΔE int(L:R) for the α IIb β 3 complexes with the peptidomimetic ligands . In conclusion, eptifibatide, tirofiban and the L-739758 ligand interact with α IIb β 3 with similar interaction patterns as native peptidic ligands of α IIb β 3 . These may explain why they bind α IIb β 3 at the nanomolar level (Kapp et al. 2017).
Complexes α IIb β 3 :PLA. The PLA chains with a terminal carboxylate group (the PLA-COO − configuration) as well   Table 1. The total ΔE int(L:R) for the complexes with the PLA chain was 2-5 times weaker compared with the complexes with the native peptides or peptidomimetic ligands (Fig. 5). For example, ΔE int(L:R) (PLA-01) = − 272.1 kcal mol −1 or ΔE int(L:R) (PLA -03) = − 127.1 kcal mol −1 versus ΔE int(L:R) (GAKQAGDV peptide) = − 708.6 kcal mol −1 . One of the reasons for the weakening of the interaction energy is in weaker interactions of the PLA chain with the MIDAS Mg 2+ ion, the ADMIDAS Ca 2+ ion and the LIMBS Ca 2+ ion (Fig. 5). This is mainly evident for the PLA chain without the terminal carboxylate group (PLA-03). Therefore, the adhesion of PLA surface on a cell may be more efficient when free carboxylates are available on polymer surfaces in repeated intervals. This conclusion is clearly evident from FMO-PIEDA analysis comparing the PLA-01 (or PLA-02) and PLA-03 interaction patterns (Fig. 12, 13 and S3 of ESI). For PLA-03, key interactions with amino acid residues of α IIb β 3 (Asp159A, Phe160A, Tyr190A, Arg214B and Asp224A) are diminished compared with those found for the peptides, peptidomimetic antagonist and PLA-01 and PLA-02. This indicates that the ligand-binding site of α IIb β 3 is structurally design to bind a C-terminal peptide with two negatively charged carboxylate groups positioned close to each other (approximately 6 Å, a distance between carboxylate of Val411 and Asp410 of the native γC peptide), while in PLA-01 (or PLA-02) is only one terminal carboxylate group and in PLA-03 no free carboxylate or a negatively charged group.

Conclusion
The FMO-PIEDA calculations were performed to add, beside available structural and biochemical data, next physicochemical properties of two peptidic, three peptidomimetic ligands and the poly(l-lactic acid) chain bound to α IIb β 3 integrin. The predicted interaction profiles of the integrin:ligand complexes may be described by several basic features: (i) dominant interactions are electrostatic, including interactions of the ligands with the MIDAS Mg 2+ , the ADMIDAS Ca 2+ (except for eptifibatide in which dispersion repulsion was dominant) and the LIMBS Ca 2+ ions; (ii) all three ions at the ligand-binding site of α IIb β 3 are key contributors to total interaction energy; (iii) terminal free carboxylate of Val411 and side chain carboxylate of Asp410 play an important role for the strong binding of the γC peptidic ligand; thus, for effective adhesion of fibrinogen to α IIb β 3 two free carboxylate groups at the end of the ligand are necessary; (iv) Asp224A, Asn215B, Asp159A and Lys125B of α IIb β 3 are the most important amino acid residues for binding of the C-terminal octapeptide part of fibrinogen; and (v) both the KQAGDV and KQRGDV peptidic sequences are structurally and chemically adopted to bind effectively α IIb β 3 . The reason why some peptides with the AGD or RGD motif did not bind to α IIb β 3 is in structural and chemical nature of the C-terminal amino acid residue (X) in the AGDX or RGDX sequence rather than the AGD (or RGD) structure itself (e.g., AGDV or AGDF bind to α IIb β 3 while AGDC or AGDY not) .
From the X-ray structures of α IIb β 3 with the non-peptidic tirofiban and the L-739758 ligand it is evident that these antagonists mimic interactions of arginine and aspartic acid residues of the RGD motif of the peptidic ligands (contacts of tirofiban and L-739758 ligand with Asp224A and Mg 2+ ion). Other hidden interactions were revealed by the FMO-PIEDA calculations in this work. As it was for the peptides, the MIDAS Mg 2+ ion, the ADMIDAS Ca 2+ ion, the LIMBS Ca 2+ ion, Asp224A, Asn215B, Tyr122B, Lys125B and Tyr190A of α IIb β 3 are the most important contributors to total ΔE int(L:R) for the α IIb β 3 complexes with the antagonists. In conclusion, new synthetically developed antagonists of α IIb β 3 should mimic not only the interactions of the RGD motif but also the interactions of the backbone of a longer peptidic sequence (RGDV or AGDV) with the focus on the interactions of the antagonists with the ADMIDAS Ca 2+ ion.
The FMO-PIEDA calculations of the complexes of α IIb β 3 with the poly(L-lactic acid) chain indicate that a terminal carboxylate or a free carboxylate on the PLA surface are essential to mimic the adhesion process of the RGD-binding integrins. The PLA ester groups themselves are not chemically so appropriate ligands for interactions with either Mg 2+ and Ca 2+ ions or amino acid residues at the ligand-binding site of α IIb β 3 . In general, the adhesion of PLA surface on a cell may be more efficient when free carboxylates are available on polymer surfaces in repeated intervals.

Methodology
Structural models and molecular docking. The X-ray structures ) of α IIb β 3 integrin with bound ligands (an octapeptide with the GAKQAGDV sequence, PDB ID: 2VDP (Springer et al. 2007b); a heptapeptide with the AKQRGDV sequence, PDB ID: 2VDR (Springer et al. 2007a); a cyclic peptide eptifibatide with the (HR)CCPWGDG sequence, PDB ID: 2VDN  (Springer et al. 2007c); peptidomimetic tirofiban, PDB ID: 2VDM (Springer et al. 2007e) and the L-739758 ligand; PDB ID: 2VC2 (Springer et al. 2007d)) were used as 3-D structural models for QM/MM geometry optimizations and subsequent FMO-PIEDA calculations. The complex integrin α IIb β 3 :poly(L-lactic acid) (C 3 H 4 O 2 ) n=7 was built based on the X-ray structure of α IIb β 3 with the octapeptide with the AGD motif, PDB ID: 2VDP (Springer et al. 2007b)). The peptide and most water molecules were removed and a PLA chain was added to the ligand-binding site using of molecular docking. PLA was docked either in a charged form (with free terminal carboxylate, PLA-COO − ) or in a neutral form (with terminal methyl ester group, PLA-COOCH 3 ). Then, two bound conformations of PLA-COO − in α IIb β 3 (PLA-01 and PLA-02) and one of the PLA-COOCH 3 (PLA-03) were selected based on a docking score for subsequent QM/MM and FMO-PIEDA calculations. The conformations PLA-01 and PLA-02 mimic the binding of a terminal C-region of fibrinogen to α IIb β 3 (Fig. 3). In these conformations terminal carboxylate of PLA was predicted to coordinate with the MIDAS Mg 2+ ion. In the case of PLA-03 the docked chain mimics the binding of a non-terminal region of a peptidic ligand along a ligand-binding groove and MIDAS (Fig. 3).
Molecular docking was performed with the GLIDE program, version 7.0 (Friesner et al. 2004), of the Schrödinger package. For prediction of protonation states of the amino acid residues of α IIb β 3 , the Propka version 2 empirical program (Li et al. 2005;Bas et al. 2008) was used (pH = 7.4). The receptor box with a size of 39 × 39 × 39 Å was centered at the Mg 2+ ion at MIDAS of α IIb β 3 using OPLS2005 partial atomic charges (Kaminski et al. 2001). Flexible docking in standard (SP) precision was used. The potential for nonpolar parts of the ligands was softened by scaling the Van der Waals radii by a factor of 0.8 for atoms of the ligands with partial atomic charges less than specified cutoff of 0.15. For 10 ligand poses with the best docking score the post-docking minimization was performed.
QM/MM geometry optimizations. For the protein complexes (α IIb β 3 :ligand), geometry optimizations at the QM/MM level were applied (BP86/LACVP*:OPLS2005) (Becke 1988;Wadt and Hay 1985;Kaminski et al. 2001) using the QSite (Murphy et al. 2000) program of the Schrödinger package. The QM part (more than 280 atoms) of the system included Mg 2+ ion, Ca 2+ ions and their coordinated ligands (amino acid residues and water molecules). The rest of the molecular system was calculated at the MM level described by the OPLS2005 force field (Kaminski et al. 2001). The QM/MM methodology (an additive scheme) with hydrogen caps on boundary QM atoms was used. Between the QM and MM regions, electrostatic treatment using Gaussian charge distributions was employed. The piperidine and carboxylate groups of tirofiban and the L-739758 ligand were modeled in ionized forms (as depicted in Fig. 2) according to the pK a Propka calculations (Li et al. 2005;Bas et al. 2008).
FMO-PIEDA calculations. For the protein:ligand complexes, the two-body FMO method together with the pair interaction energy decomposition analysis (PIEDA) was used (Kitaura et al. 1999;Fedorov and Kitaura 2009;Fedorov et al. 2012). In FMO method, a biomolecular system is partitioned into fragments (with a fragment size-one amino acid residue). For modeling of the covalently bounded amino acids, the hybrid orbital projection operator (HOP) technique was applied. In the case of the peptidic ligands, the following two types of the fractioning were used in the FMO calculations: (i) the peptidic ligand was one large fragment consisted of all amino acid residues (i.e., for the octapeptide ligand with the AGD motif the fragment consists of 8 amino acid residues. The results are compiled in Table 1 and Figs. 4,5,6,7,8,9,12,13); and (ii) the peptidic ligand was fragmented into separate amino acid residues according to a default FMO fragmentation technique with the shifted backbone definition (results in Table 2) (Sladek and Fedorov 2022). The QM/MM optimized structures of complexes (α IIb β 3 :ligand) were reduced to ligand-binding site clusters consisted of more than 260 structural fragments (amino acid residues, Mg 2+ and Ca 2+ ions, structural water molecules and ligand. The cluster includes amino acid residues which are positioned in radius of 18 Å around Mg 2+ ion. Detailed information about amino acid fragments can be found in pdb files included in ESI). The Facio program was used to prepare inputs for the FMO calculations (Suenaga 2008). The second-order Møller-Plesset theory (MP2) (Møller and Plesset 1934;Frisch et al. 1990) and density functional theory (DFT) wBP97X-D method (Becke 1997) with Grimme's empirical dispersion correction (Grimme 2006) were used with the 6-31G(d) basis and the conductorlike polarizable continuum model (C-PCM (PCM < 1 > , keywords IFMO = -1, IEF = -10, SOLVNT = WATER) (Fedorov 2019). The Gamess package (Barca et al. 2020;Schmidt et al. 1993) [version 30 June 2021 (R1), linux version] was employed. The pair interactions between the two structural fragments of the molecular system were predicted within the electrostatic potential of the surroundings. In our case the interactions between the fragments of the ligand (L) and the fragments of the receptor (R) were predicted. The FMO-PIEDA method separates the interaction energy into physically interpretable terms (1): The electrostatic energy ΔE L:R els presents Coulomblike interactions between the fragments. ΔE L:R ct−mix approximates polarization which originates from the charge transfer and the mixing part. The exchange energy ΔE L:R exch grows for fermion particles, the electrons and answers for the Pauli repulsion of electrons between the fragments. Dispersion energy ΔE L:R disp arises from fluctuations of dipoles on the fragments due to electron correlation. ΔG R:L sol is solute-solvent solvation free energy. FMO-PIEDA was successfully used in various proteins complexes (Lim et al. 2019;Sogawa et al. 2020;Anan et al. 2019;Sladek et al. 2017Sladek et al. , 2018Takaya et al. 2020;Kalník et al. 2023;Mironov et al. 2022).
To better understand a role of amino acid residues of the peptidic ligands with AGD and RGD motifs in the integrinbinding process and compare differences in an interaction pattern, the peptides with the GAKQAGDV and AKQRGDV sequences, and eptifibatide were divided into amino acid fragments [Ligand, L-AA(n)] in similar manner as amino acids of αIIbβ3 [Receptor, R-AA(m)]. Then, interaction energies between the ligand and the receptor will be marked as ΔE L-AA (n) with total ΔE int(L:R) : where n = 8 is for the GAKQAGDV sequence, n = 7 is for the AKQRGDV sequence and n = 6 is for eptifibatide. Then, the FMO-PIEDA analysis was also performed for a fragmentation scheme with the ligand as one structural fragment (Ligand, L) to see roles of amino acid residues of α IIb β 3 [Receptor, R-AA(m)] on the ligand binding. Then, interaction energies between the ligand and the receptor will be marked as ΔE L:R-AA (m) with total ΔE int(L:R) : (1) where m is number of amino acid fragments of the receptor α IIb β 3 . This FMO-PIEDA scheme was applied for all ligands calculated in this work.