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 (Springer and Wang 2004; 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 Mg2+ ion in the central metal ion-dependent adhesion site (MIDAS) flanked by two Ca2+ ions, one of which is in a site termed adjacent to MIDAS (ADMIDAS). The other Ca2+ ion is in a site termed as the ligand-associated metal ion-binding site (LIMBS) (Fig. 1).

Fig. 1
figure 1

A 3-D structure of αIIbβ3 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 Mg2+ ion (blue ball) flanked by two Ca2+ ions (pink balls). The α subunit β-propeller domain is depicted in a gray color

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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 αVβ3 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 (Springer et al. 2008). 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. 2008, 2010; Zheng and Leftheris 2020), a negatively charged carboxylate side chain of Asp directly coordinates with the MIDAS Mg2+ 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 αvβ3 integrin (Spitaleri et al. 2008, 2011). Molecular dynamics simulations revealed that isoDGR-containing cyclopeptides are true αvβ3 antagonists which block integrin activation (Ghitti et al. 2012).

Fibrinogen binds to integrin αIIbβ3 on platelets during hemostasis and thrombosis and both proteins are mentioned in connection with cardiovascular and autoimmune diseases (Huang et al. 2019). αIIbβ3 integrin also plays a role in cancer progression. αIIbβ3 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, αvβ3 integrin binds fibrinogen via a non-terminal RGD motif in fibrinogen's α subunit. As was found by X-ray study (Springer et al. 2008), αIIbβ3 integrin also bound to a lamprey terminal AKQRGDV sequence with the RGD motif. Therefore, development of selective antagonists of αIIbβ3 and the closely related αVβ3 integrin was efforted in past decades (Xiao et al. 2004).

To compare an interaction pattern between αIIbβ3 integrin and the peptides with these two motifs, and better understand chemical nature of a complex ligand-binding site of αIIbβ3 consisted of the three metal ions, quantum mechanics calculations were performed in this study using the two-body fragmented molecular orbital (FMO) method (Kitaura et al. 1999; Fedorov and Kitaura 2009; Fedorov et al. 2012). Due to available X-ray structures (Springer et al. 2008; Xiao et al. 2004), the calculations were also performed for αIIbβ3 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 (IC50 = 2.44 nM) and tirofiban (IC50 = 1.3 nM) are nanomolar antagonist of αIIbβ3 (Kapp et al. 2017). L-739758, structurally similar to tirofiban, is an effective antagonist of αIIbβ3. The FMO-PIEDA calculations for these antagonists of αIIbβ3 will allow us to compare their interaction patterns with those of native peptidic ligands of αIIbβ3 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 αIIbβ3 specifically. In addition, FMO-PIEDA calculations were also performed for a complex of αIIbβ3 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 Mg2+ 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: αIIbβ3 complexes will show how well the polyester backbone of PLA mimics the interactions of the peptidic ligands of αIIbβ3 and which modifications of the structure of PLA could improve its adhesion properties for binging to integrins.

Fig. 2
figure 2

Structures of ligands used for FMO-PIEDA calculations. Protonation forms of carboxylate and amino groups, as used in the calculations, are shown

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Fig. 3
figure 3

a Schematic representation of interactions between αIIbβ3 integrin (green) and the peptide with the AGD motif; b and PLA interacted via terminal carboxylate with Mg2+ ion bound at the MIDAS site (PLA-01 or PLA-02 models); c and PLA interacted via backbone polyester groups (PLA-03 model) with the MIDAS, ADMIDAS and LIMBS sites

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Results and discussion

αIIbβ3:peptide(GAKQAGDV). The complex of the integrin(αIIbβ3):peptide (GAKQAGDV) was used in this study as a template structure for comparison of ΔEint(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 αIIbβ3 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 Mg2+ ion (ΔEL:Mg2+  = − 350.2 kcal mol−1), the Ca2+ ion (ADMIDAS) (ΔEL:Ca(ADMIDAS)2+  = − 158.9 kcal mol−1), the Asp224A (ΔEL:Asp224A = − 90.5 kcal mol−1), the Ca2+(LIMBS) ion (ΔEL:Ca(LIMBS)2+  = − 75.8 kcal mol−1), the Asn215B (ΔEL:Asn215B = − 55.3 kcal mol−1), the Asp159A (ΔEL:Asp159A = − 52.1 kcal mol−1), the Lys125B (ΔEL:Lys125B = − 49.2 kcal mol−1) and the Arg214B (ΔEL: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 Mg2+ and both Ca2+ 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 Mg2+ and Ca2+ ions, and the repulsion with the ligand is decreased. The FMO-PIEDA analysis (Table S1 of ESI) of energy terms (ΔEels, ΔEexch, ΔEct+mix, ΔEdisp) of ΔEL:R-AA confirmed this trend where the electrostatic energy term, ΔEels, 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 αIIbβ3, the FMO-PIEDA analysis was also evaluated for every amino acid of the GAKQAGDV sequence (Table 2). ΔEL-AA:R energies between αIIbβ3 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 Mg2+ ion (Asp410, ΔEL-Asp410:Mg2+  = − 301.7 kcal mol−1), with the ADMIDAS Ca2+ ion (Val411, ΔEL-Val411:Ca(ADMIDAS)2+  = − 107.7 kcal mol−1) and with Asp224A (Lys406, ΔEL-Lys406:R-Asp224A = − 127.9 kcal mol−1). Val411 is the C-terminal residue terminated with negatively charged carboxylate. Thus, on both sides, on the integrin [Mg2+(MIDAS), Ca2+(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 most important role for a strong binding of the ligand. 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-CH3). In such peptide, interaction energy for Val411-CONH-CH3 fragment was decreased to − 6.5 kcal mol−1 (from − 92.8 kcal mol−1 found in GAKQAGDV-COO−, ΔEVal411:R). One of the reasons may be a repulsion between the Val411-CONH-CH3 and the ADMIDAS Ca2+ ion (ΔEVal411: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− (ΔEVal411: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 Ca2+ ion was demonstrated by experiments where γC peptides with the carboxylate substituted by amide blocked fibrinogen binding to αIIbβ3 (Kloczewiak et al. 1989). 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 (Kloczewiak et al. 1989; Kapp et al. 2017). We conclude that the interaction of αIIbβ3 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 Ca2+ ion and subsequent strong interactions of their backbones with αIIbβ3 and the ADMIDAS Ca2+ ion itself.

Table 1 Calculated total interaction energies (ΔEint(L:R), in kcal mol−1) between the bound ligand (L) and αIIbβ3 (Receptor, R) at the ab initio MP2/6-31G(d) and DFT-wB97X-D/6-31G(d) (in parentheses) levels
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Table 2 Interaction energies (ΔEL-AA:R, in kcal mol−1) between the amino acid residues of the bound peptides (Ligand, L)and αIIbβ3 integrin (Receptor, R) calculated at the ab initio MP2/6-31G(d) and DFT-wB97X-D/6-31G(d) (in parentheses) levels
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Fig. 4
figure 4

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the peptide with the AGD motif (GAKQAGDV-COO−) and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the bound peptide (ball-and-stick representation, green)

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The bound peptide does not directly coordinate with the ADMIDAS Ca2+ ion and interacts (via terminal carboxylate of Val411) with it via a water molecule [Peptide-Val411-COO−–H2O(254)–Ca2+(ADMIDAS), Fig. 4]. To see a role of the water molecule for the binding of the peptide, ΔEL:H2O(254) and ΔECa(ADMIDAS):H2O(254) were also analyzed. Both FMO-PIEDA interaction energies (ΔEL:H2O(254) =  − 37.3 kcal mol−1 and ΔECa(ADMIDAS):H2O(254) =  − 35.8 kcal mol−1) are with significant values; thus, they are significant contributors to a total interaction energy between the peptide and the ADMIDAS Ca2+ ion (ΔEL:Ca(ADMIDAS)2+  = − 158.9 kcal mol−1, Table 1). Similarly as it was for the ADMIDAS Ca2+ ion, the LIMBS Ca2+ ion is not in a direct contact with the bound ligand. Despite the larger distance between the ligand and the Ca2+ ions (> 4.5 Å), their interactions were significant. The PIEDA analysis (Table S1 of ESI) showed that the main contributor to total interaction energy between the ligand and the Ca2+ ions is the electrostatic energy term (ΔEelsL:Ca(ADMIDAS)2+  = − 202.5 kcal mol−1 of ΔEL:Ca(ADMIDAS)2+  = − 158.9 kcal mol−1; and ΔEelsL:Ca(LIMBS)2+  = − 116.7 kcal mol−1 of ΔEL:Ca(ADMIDAS)2+  = -75.8 kcal mol−1).

The AGD motif of the native ligand of αIIbβ3 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:αIIbβ3 complex, Gly409 of the peptidic ligand, seems also to play an important role for the binding. Its interaction energy with αIIbβ3 was predicted with a significant value of − 48.0 kcal mol−1 (ΔEGly409: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 (ΔEL-Gly409:R-Ala218B = − 8.5 kcal mol−1), three water molecules, two of them via carbonyl oxygen (ΔEL-Gly409:H2O(201) = − 13.9 kcal mol−1, ΔEL-Gly409:H2O(257) = − 14.5 kcal mol−1) and one via amide group (ΔEL-Gly409:H2O(258) = − 9.5 kcal mol−1) and the LIMBS Ca2+ ion (ΔEL-Gly409:Ca(LIMBS) = − 7.5 kcal mol−1). Similarly, as it was for Val411 of the peptidic ligand, the interaction of the Ala408-Gly409 backbone with αIIbβ3 seem to play an important role for the binding of the peptide with the AGD motif.

αIIbβ3:AKQRGDV peptide. Whereas ligands with the RGD motif binds to eight different integrins, the fibrinogen γC peptide with the AGD motif binds only to αIIbβ3. In contrast, the A408R mutation of the native γC peptide, which produced the RGD motif, did bind to αIIbβ3 (Springer et al. 2008). 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 αIIbβ3, while Lys406 interacts with Asp159A of αIIbβ3. We calculated a FMO-PIEDA energy profile for the αIIbβ3: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 αIIbβ3, the results are in Table 1. ΔEL-AA:R between the residues of the peptide and αIIbβ3 integrin decreases (weakens) in the following order: Asp410 (− 246.7 kcal mol−1) > Arg408 (− 183.7 kcal mol−1) > Val411 (− 127.13 kcal mol−1) > Gln407 (− 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 ΔEint(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 Mg2+ ion (Asp410, ΔEL-Asp410:Mg2+  = − 300.6 kcal mol−1), with the ADMIDAS Ca2+ ion (Val411, ΔEL-Val411:Ca(ADMIDAS)2+  = − 116.0 kcal mol−1) and with Asp224A (Arg408, ΔEL-Arg408:R-Asp224A = − 105.4 kcal mol−1). Thus, both the AKQAGDV and AKQRGDV sequences present an optimal 3-D structure for specific binding of γ subunit of fibrinogen to αIIbβ3. The total ΔEint(L:R) for the peptide with the RGD motif is stronger (ΔEint(L:R) =  − 736.0 kcal mol−1) compared with that for the peptide with the AGD motif (ΔEint(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 (Kloczewiak et al. 1989; Timmons et al. 1989). A similar result was obtained by Ruggeri et al., where the IC50 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 (Springer et al. 2008).

Fig. 5
figure 5

FMO-PIEDA interaction energies (ΔEint(L:R), in kcal mol−1, blue) between the bound ligands and αIIbβ3 calculated at the ab initio MP2/6-31G (d) level. Also interaction energies (ΔEL:Mg(MIDAS)2+, red; ΔEL:Ca(ADMIDAS)2+, gray; and ΔEL:Ca(LIMBS)2+, yellow) between the ligand and the MIDAS Mg2+, ADMIDAS Ca2+ and LIMBS Ca2+ ions are also compiled

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The most important contributors of αIIbβ3 to ΔEint(L:R) are the MIDAS Mg2+ ion (ΔEL:Mg(MIDAS)2+  = − 352.0 kcal mol−1), the ADMIDAS Ca2+ ion (ΔEL:Ca(ADMIDAS)2+  = − 169.4 kcal mol−1), Asp224A (ΔEL:Asp224A = − 63.7 kcal mol−1), the LIMBS Ca2+ ion (ΔEL:Ca(LIMBS)2+  = 75.63 kcal mol−1), Asn215B (ΔEL:Asn215B = − 52.6 kcal mol−1), Asp159A (ΔEL:Asp159A = 25.7 kcal mol−1), Lys125B (ΔEL:Lys125B = − 49.2 kcal mol−1) and Arg214B (ΔEL:Arg214B = − 42.2 kcal mol−1) (Fig. 6). The detailed PIEDA analysis showed that electrostatic interactions are a dominant part of ΔEint(L:R) (Table S2 of ESI).

Fig. 6
figure 6

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the peptide with the RGD motif (AKQRGDV-COO−) and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the bound peptide (ball-and-stick representation, green)

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Complexes αIIbβ3:peptidomimetic ligands. Based on available X-ray structures (Springer et al. 2008; Springer et al. 2007c, e, d), complexes of αIIbβ3 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 αIIbβ3 with the previously discussed peptides with the AGD and the RGD motifs. For these three ligands, the interactions with the MIDAS Mg2+ ion, the ADMIDAS Ca2+ ion and the LIMBS Ca2+ ion are dominant except for eptifibatide. For this ligand only interactions with the MIDAS Mg2+ ion and the LIMBS Ca2+ ion are significant [ΔEL:Mg(MIDAS)2+  = − 265.2 kcal mol−1 and ΔEL:Ca(LIMBS)2+  = − 42.3 kcal mol−1], in opposite, with the ADMIDAS Ca2+ ion are repulsive (ΔEL:Ca(ADMIDAS)2+  = 3.2 kcal mol−1). The detailed analysis of the PIEDA energy contributors has showed that although ΔEelsL:Ca(ADMIDAS)2+ is attractive (− 26.1 kcal mol−1), ΔEdispL:Ca(ADMIDAS)2+ is strongly repulsive (31.7 kcal mol−1). This finding is also supported by steered molecular dynamics (SMD) simulations where the ADMIDAS Ca2+ ion had the lowest effect on SMD force profiles of the unbinding of eptifibatide from αIIbβ3 (Murcia et al. 2008).

Fig. 7
figure 7

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the eptifibatide and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the bound peptidomimetic ligand (ball-and-stick representation, green)

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Fig. 8
figure 8

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the tirofiban and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant terms of ΔEL:R-AA are visualized (tube representation, gray) as well as the bound peptidomimetic ligand (ball-and-stick representation, green)

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Fig. 9
figure 9

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the peptidomimetic ligand (L-739758) and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the bound peptidomimetic ligand (ball-and-stick representation, green)

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Overall, the interactions of the ligands with the MIDAS Mg2+ ion calculated in this study are the most significant (Fig. 5). The dominant part of ΔEL:Mg2+ is an electrostatic term (ΔEelsL:Mg(MIDAS)2+  = − 254.5 kcal mol−1 of ΔEL:Mg(MIDAS)2+  = − 265.2 kcal mol−1 for eptifibatide; ΔEelsL:Mg(MIDAS)2+  = − 235.2 kcal mol−1 of ΔEL:Mg(MIDAS)2+  = − 248.4 kcal mol−1 for tirofiban; and ΔEelsL:Mg(MIDAS)2+  = − 250.3 kcal mol−1 of ΔEL:Mg(MIDAS)2+  = − 265.5 kcal mol−1 for the L-739758 ligand). As it was for the peptides, Asp224A, Asn215B, Tyr122B, Lys125B and Tyr190A of αIIbβ3 (Table 1, Figs. 6, 7 and 8) are also the most important contributors to total ΔEint(L:R) for the αIIbβ3 complexes with the peptidomimetic ligands. In conclusion, eptifibatide, tirofiban and the L-739758 ligand interact with αIIbβ3 with similar interaction patterns as native peptidic ligands of αIIbβ3. These may explain why they bind αIIbβ3 at the nanomolar level (Kapp et al. 2017).

Complexes αIIbβ3:PLA. The PLA chains with a terminal carboxylate group (the PLA-COO− configuration) as well as with a terminal methyl ester group (the PLA-COOCH3 configuration) were docked into the ligand-binding site of αIIbβ3. The PLA-COO− chain was found to bind with terminal carboxylate to the MIDAS Mg2+ ion [d(PLA-COO−:Mg2+) = 2.13 Å] and with the polyester chain bound along a groove flanked by Asp159A, Asp224A and Ser226A on the one side and Arg214B, Tyr122B, Asn215B and the MIDAS Mg2+ ion on the other side (Fig. 10, PLA-01 model). PLA-COOCH3 bound in a similar conformation, however, interacting with the MIDAS Mg2+ ion [d(PLA-COOCH3:Mg2+) = 3.66 Å] with one of the ester groups at a middle of its chain, and with the terminal methyl ester group positioned at a hydrophobic groove flanked by Val156A and Met180B (Fig. 11, PLA-03 model). This groove was not filled by any conformations with the PLA-COO− configuration. For the subsequent QM/MM geometry optimizations and FMO-PIEDA calculations, two conformations with the best docking scores (PLA-01 and PLA-02) with the PLA-COO− configuration and one conformation (PLA-03) with PLA-COOCH3 were selected. The FMO-PIEDA results are compiled in Figs. 12, 13 and S3 and Table 1. The total ΔEint(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, ΔEint(L:R)(PLA-01) = − 272.1 kcal mol−1 or ΔEint(L:R)(PLA-03) = − 127.1 kcal mol−1 versus ΔEint(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 Mg2+ ion, the ADMIDAS Ca2+ ion and the LIMBS Ca2+ 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 αIIbβ3 (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 αIIbβ3 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.

Fig. 10
figure 10

Superposition of the PLA-01 ligand (yellow) with the peptide (the GAKQAGDV sequence, green) at the ligand-binding site of αIIbβ3 (QM/MM optimized integrin:ligand complexes)

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Fig. 11
figure 11

Superposition of the PLA-01 ((PLA-COO−, yellow) with the PLA-03 ligand ((PLA-COOCH3, magenta) at the ligand-binding site of αIIbβ3 (QM/MM optimized ligand:integrin complexes)

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Fig. 12
figure 12

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the PLA-01 ligand (PLA-COO−) and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the PLA-01 ligand (ball-and-stick representation, green)

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Fig. 13
figure 13

FMO-PIEDA interaction energies (ΔEL:R-AA, in kcal mol−1) between the PLA-03 (PLA-COOCH3) ligand and the amino acid residues of αIIbβ3 calculated at the ab initio MP2/6-31G(d) level. The attraction terms of ΔEint(L:R) present ΔEL:R-AA with the negative values, while repulsion terms are with the positive values. The amino acid residues with the most significant ΔEL:R-AA are visualized (tube representation, gray) as well as the bound PLA-03 ligand (ball-and-stick representation, green)

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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 αIIbβ3 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 Mg2+, the ADMIDAS Ca2+ (except for eptifibatide in which dispersion repulsion was dominant) and the LIMBS Ca2+ ions; (ii) all three ions at the ligand-binding site of αIIbβ3 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 αIIbβ3 two free carboxylate groups at the end of the ligand are necessary; (iv) Asp224A, Asn215B, Asp159A and Lys125B of αIIbβ3 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 αIIbβ3. The reason why some peptides with the AGD or RGD motif did not bind to αIIbβ3 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 αIIbβ3 while AGDC or AGDY not) (Kloczewiak et al. 1989).

From the X-ray structures of αIIbβ3 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 Mg2+ ion). Other hidden interactions were revealed by the FMO-PIEDA calculations in this work. As it was for the peptides, the MIDAS Mg2+ ion, the ADMIDAS Ca2+ ion, the LIMBS Ca2+ ion, Asp224A, Asn215B, Tyr122B, Lys125B and Tyr190A of αIIbβ3 are the most important contributors to total ΔEint(L:R) for the αIIbβ3 complexes with the antagonists. In conclusion, new synthetically 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.

The FMO-PIEDA calculations of the complexes of αIIbβ3 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 Mg2+ and Ca2+ ions or amino acid residues at the ligand-binding site of αIIbβ3. 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 (Springer et al. 2008) of αIIbβ3 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 αIIbβ3:poly(L-lactic acid) (C3H4O2)n=7 was built based on the X-ray structure of αIIbβ3 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-COOCH3). Then, two bound conformations of PLA-COO− in αIIbβ3 (PLA-01 and PLA-02) and one of the PLA-COOCH3 (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 αIIbβ3 (Fig. 3). In these conformations terminal carboxylate of PLA was predicted to coordinate with the MIDAS Mg2+ 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 αIIbβ3, 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 Mg2+ ion at MIDAS of αIIbβ3 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 (αIIbβ3: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 Mg2+ ion, Ca2+ 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 pKa 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 (αIIbβ3:ligand) were reduced to ligand-binding site clusters consisted of more than 260 structural fragments (amino acid residues, Mg2+ and Ca2+ ions, structural water molecules and ligand. The cluster includes amino acid residues which are positioned in radius of 18 Å around Mg2+ 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 conductor-like 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):

$$\Delta E_{{{\text{L}}:{\text{R}}}}^{{{\text{int}}}} = \, \Delta E_{{{\text{L}}:{\text{R}}}}^{{{\text{els}}}} + \, + \, \Delta E_{{{\text{L}}:{\text{R}}}}^{{{\text{ct}} - {\text{mix}}}} + \, \Delta E_{{{\text{L}}:{\text{R}}}}^{{{\text{exch}}}} + \, \Delta E_{{{\text{L}}:{\text{R}}}}^{{{\text{disp}}}} + \Delta G_{{{\text{L}}:{\text{R}}}}^{{{\text{sol}}}}$$
(1)

The electrostatic energy ΔEL:Rels presents Coulomb-like interactions between the fragments. ΔEL:Rct−mix approximates polarization which originates from the charge transfer and the mixing part. The exchange energy ΔEL:Rexch grows for fermion particles, the electrons and answers for the Pauli repulsion of electrons between the fragments. Dispersion energy ΔEL:Rdisp arises from fluctuations of dipoles on the fragments due to electron correlation. ΔGR:Lsol 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. 2017, 2018; Takaya 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 integrin-binding 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 ΔEL-AA(n) with total ΔEint(L:R):

$$\Delta E_{{{\text{int}}({\text{L}}:{\text{R}})}} = \, \Delta E_{{{\text{L}} - {\text{AA}}:{\text{R}}}} \left( {1} \right) \, +_{{}} \Delta E_{{{\text{L}} - {\text{AA}}:{\text{R}}}} \left( {2} \right) \, + \, \ldots \, + \, \Delta E_{{{\text{L}} - {\text{AA}}:{\text{R}}}} \left( {\text{n}} \right)$$
(2)

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 αIIbβ3 [Receptor, R-AA(m)] on the ligand binding. Then, interaction energies between the ligand and the receptor will be marked as ΔEL:R-AA(m) with total ΔEint(L:R):

$$\Delta E_{{{\text{int}}({\text{L}}:{\text{R}})}} = \, \Delta E_{{{\text{L}}:{\text{R}} - {\text{AA}}}} \left( {1} \right) \, +_{{}} \Delta E_{{{\text{L}}:{\text{R}} - {\text{AA}}}} \left( {2} \right) + \, \ldots \, + \, \Delta E_{{{\text{L}}:{\text{R}} - {\text{AA}}}} \left( {\text{m}} \right)$$
(3)

where m is number of amino acid fragments of the receptor αIIbβ3. This FMO-PIEDA scheme was applied for all ligands calculated in this work.