Identification of correlated inter-residue interactions in protein complex based on the fragment molecular orbital method.

A theoretical scheme to systematically describe correlated (network-like) interactions between molecular fragments is proposed within the framework of the fragment molecular orbital (FMO) method. The method is mathematically based on the singular value decomposition (SVD) of the inter-fragment interaction energy (IFIE) matrix obtained by the FMO calculation, and can be applied to a comprehensive description of protein-protein interactions in the context of molecular recognition. In the present study we apply the proposed method to a complex of measles virus hemagglutinin and human SLAM receptor, thus finding a usefulness for efficiently eliciting the correlated interactions among the amino-acid residues involved in the two proteins. Additionally, collective interaction networks by amino-acid residues important for mutation experiments can be clearly visualized.

Introduction

Since its proposal in 1999 [1,2], the fragment molecular orbital (FMO) method [[3], [4], [5]] has provided a powerful and useful tool to perform ab initio electronic-state calculations for biomolecular and other related systems. One of very advantageous features in the FMO method for biomolecular analyses is its ability to evaluate “effective interactions” between “fragments” that are usually chosen to be an amino-acid residue or a (small) ligand molecule as a unit component in protein-ligand complex system, for instance. This inter-fragment interaction is referred to as IFIE (Inter-Fragment Interaction Energy) or PIE (Pair Interaction Energy) in the literature [[3], [4], [5], [6]], and plays a vital role in, e.g., docking analysis by specifying important interactions involved in the object system. In fact, the FMO-IFIE analysis has been extensively applied to the investigations of mechanisms of molecular recognition associated with protein-protein [[7], [8], [9], [10], [11]], protein-nucleic acid [[12], [13], [14]], protein-drug [[15], [16], [17], [18], [19]], and other [[20], [21], [22], [23], [24], [25]] intermolecular interactions.

In earlier studies, we applied the FMO-IFIE method to the analyses of intermolecular interactions of influenza virus hemagglutinin (HA) protein in complex with sialosaccharide receptors [23,25] and Fab fragment of antibody [7,8] for the investigation of mutation effects. Particularly, in the former analysis [25], we found an interesting phenomenon referred to as indirect effect in which the mutations of HA residues that do not strongly interact with the receptor significantly affect the change in binding affinity of complex, while the interactions between some unmutated residues in HA and the receptor often vary substantially due to the mutations at other residues. This unexpected effect has thus suggested a presence of correlated (network-like) inter-fragment interactions, whose detailed mechanism has remained to be elucidated.

In biomolecular complex systems, the inter-fragment interactions are multiple in essence. Although the electron-correlated FMO-IFIE itself refers to an effective, renormalized interaction between single fragments in which some many-body effects are included, the total complex interactions should be described as a whole in terms of the set of all the IFIEs. In earlier investigations on protein-protein interaction (PPI) [10,11], the network structure of IFIE (or PIE) was revealed in terms of the concept of Protein Residue Network (PRN). Concerning this issue of describing the correlated interactions due to multiple fragments, we have recently found a usefulness of the technique of singular value decomposition (SVD). In our previous study for protein-ligand systems [26], we applied the SVD for the calculated results of the IFIE matrix (amino-acid residues various ligand compounds) to elicit the essential interactions and consequently improve the correlation between FMO results and experimental ligand (small compound) binding affinities. Through this method, we obtained the improved correlation with experimental results by extracting important singular eigenvectors that play essential roles for ligand binding.

In the present study we extend this SVD methodology to the description of protein-protein interaction (PPI) in order to comprehensively identify the correlated interactions among residues. By means of the SVD that enables a data compression similar to the principal component analysis (see Sec. 2.3), the network structure of IFIEs is systematically extracted. We here employ a complex system of measles virus hemagglutinin (MVH) and human SLAM (signaling lymphocyte activation molecule) receptor as an example for the PPI analysis. Measles virus (MV) causes an acute and highly devastating contagious disease in humans. In a previous study [27], employing the crystal structures of three human receptors, SLAM, CD46, and Nectin-4, in complex with the measles virus hemagglutinin (MVH or HA), we computationally elucidated the details of binding energies between the amino-acid residues of HA and those of the receptors in terms of ab initio FMO method. The calculated IFIEs revealed a number of significantly interacting amino-acid residues of HA that played essential roles in binding to the receptors. As predicted from previously reported experiments, some important amino-acid residues of HA were shown to be common but others were specific to interactions with the three receptors. Further, we carried out FMO calculations for in silico experiments of amino-acid mutations, finding reasonable agreements with virological experiments concerning the substitution effect of residues. Thus, our study demonstrated that the electron-correlated FMO method is a powerful tool to exhaustively search for amino-acid residues that contribute to interactions with receptor molecules.

It is known that SLAM is the most important receptor for wild-type MV, because it is responsible for invasion and propagation, and also for pathogenesis in the infected animals [28]. Here, employing the IFIE matrix composed of the HA residues and the SLAM residues as the column and row elements, respectively, we assess the usefulness of the SVD analysis to comprehensively describe the PPIs. It is noted that we employ the result of FMO calculation in vacuo because the primary purpose of the present work is to propose a novel method and assess its validity, while the incorporation of solvent effect is actually feasible in explicit or implicit way [[29], [30], [31]]. In the following section, we first illustrate the theoretical framework to obtain the correlated inter-fragment interactions in the FMO scheme. Test calculations employing a protein complex MVH-SLAM are carried out in Sec. 3, and their implications are discussed. Concluding remarks are given in Sec. 4.

Methods

Fragment molecular orbital (FMO) method and inter-fragment interaction energy (IFIE)

The FMO method [[1], [2], [3], [4], [5]] is a computational method that divides large molecules such as proteins into relatively small units called fragments, and then calculates the energy of the whole molecule and the electron density quantum-chemically by molecular orbital (MO) calculations of fragment monomers and fragment dimers (sometimes, trimers and tetramers are also considered [5]). By using this method, we can apply an ab initio MO method that has been shown to succeed for small compounds to macromolecules such as proteins without a significant loss in accuracy.

When dividing a large molecule into fragments and letting the total electron energies of a fragment I and its pair be and , respectively, the total electron energy of a molecule can be approximated (FMO2 approximation) as [[3], [4], [5]]:

If is the difference matrix of the electron density of monomer () and dimer (), Eq. (1) can be transformed into the following equation:where and ; and are the electrostatic potentials that fragment I and fragment pair receive from surrounding fragments, respectively. We thus findwhere can be interpreted as the interaction energy between the fragment pair of I and J. This is referred to as inter-fragment interaction energy (IFIE) [[3], [4], [5]].

In the FMO method, the interaction between amino-acid residues in protein complex can be identified as an IFIE. Then, the total or partial summation of IFIEs (namely, IFIE-sum) is an index representing the strength of the binding between a specific residue and a set of other residues. This notion of IFIE-sum has played a significant role in the FMO analysis on biomolecular recognition [5]. However, in the present study, we propose an alternative approach to systematically extracting the collective interactions among clustered residues, as detailed below.

Structure preparation

To analyze the molecular interactions between MVH and human SLAM, we retrieved the crystal structures of the complex (Fig. 1 ) from the Protein Data Bank (PDB entry: 3ALZ) for the FMO calculation. In this structure, the complex of MVH-SLAM was composed of HA monomer (Chain A) and one SLAM molecule (Chain B).

Fig. 1

Complex structure of MVH (measles virus HA) and human SLAM (PDB code: 3ALZ).

In the present study, molecular interactions were analyzed [27] by the FMO method with electron-correlated MP2/6-31G∗ scheme using the software ABINIT-MP [5]. The preparation of the complex structure used for FMO calculation was carried out through molecular modeling by the Molecular Operating Environment (MOE, CCG Inc.) [32]. After complementation of missing atoms (for capping the missing residues) and addition of hydrogen atoms, the positions of the added atoms were energetically optimized with the AMBER force field [32]. The inter-fragment interaction energies (IFIEs) [[3], [4], [5]] which are obtained as effective interactions between fragments (residues) in the quantum-chemical FMO calculations then provide useful information about the important amino-acid pairs between MVH and the SLAM receptor. For example, the negative value of IFIE indicates an attractive interaction between the two fragments representing an amino acid pair. The summation of all the IFIEs between residue pairs of MVH and SLAM receptor gives the binding energy [5].

Singular value decomposition (SVD)

An matrix S with m and n-dimensional vectors as columns and rows can be related to an diagonal matrix that satisfies the following equation:Here, U is an orthogonal matrix, and V is an orthogonal matrix. If U and V are chosen appropriately, a pair of matrices can be made with satisfying the condition described below. When it is rewritten, the following equation is obtained:

This type of decomposition is called Singular Value Decomposition (SVD) [[33], [34], [35], [36]]. For simplicity of description, we assume . Otherwise, we can think of the transposed matrix of S.

If is an element of , in the case of , ; in the case of , for , . At this time, , where is called a singular value of S, a column vector of U is a left singular vector, and a row of is a right singular vector [[33], [34], [35], [36]].

When the original matrix S is , the size of each matrix is the following; , and . When we consider a complex of protein A with m residues and protein B with n residues, the column vector of U is an orthonormal basis for each amino-acid residue in protein A and the row vector of is an orthonormal basis for each amino-acid residue in protein B, where each singular vector has an independent meaning. In this paper, we analyze the singular vectors of U and , and call them singular vectors 1, singular vectors 2, …and so forth in order according to the associated singular values. To execute the singular value decompositions, we have used numpy.linalg.svd in NumPy (www.numpy.org).

In this way, through the application of SVD to the IFIE matrix S for protein complex, we can extract the correlated inter-residue interactions specified as singular components.

Results and discussion

SVD component analysis based on IFIEs

Through the FMO calculation for MVH-SLAM complex [27], we obtained an IFIE matrix composed of the residue components of MVH and those of SLAM, where and fragments were considered for MVH and SLAM, respectively. (The numbers of amino-acid residues contained in MVH and SLAM were 421 and 111, respectively, in which the disulfide bonds were divided.) Then, performing the SVD for the IFIE matrix, we have obtained the singular vectors for MVH and SLAM each with the corresponding singular values, which represent the modes of collective interaction pattern. The singular vectors 1–10 for MVH (HA) and SLAM are depicted in Fig. 2 and they are represented by color on the binding interface of the complex in Fig. 3 . In particular, the first singular vectors of HA and SLAM are depicted in Fig. 4 for the complex form, thus showing particularly important interactions for complex formation. It is noted that the signs of the components of singular vectors do not necessarily correspond to those of the electric charges or the interaction energies associated with the amino-acid residues, due to the arbitrariness of the total phase (positive/negative) of the singular vectors.

Fig. 2

Singular vectors 1–10 with decreasing singular values for SLAM (left, –) and HA (right, –). The abscissa refers to the amino-acid numbers and the ordinate represents the values of singular vector components normalized by the maximum value. The IFIE values were obtained by the FMO calculation in which Hie536 (an unprotonated form of His536) was employed.

Fig. 3

Residues with large magnitude in each singular vector 1–10 for SLAM (left) and HA (right). The IFIE values used for the SVD analysis were the same as those in Fig. 2. Blue and red colors indicate positive and negative values, respectively, whose deepness of the hue refers to the normalized magnitude. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4

(A) Residues with large magnitude in the first singular vector 1 for the complex of HA (right) and SLAM (left). The IFIE values used for the SVD analysis were the same as those in Fig. 2. Blue and red colors indicate positive and negative values, respectively, whose deepness of the hue refers to the magnitude. The suffixes “H” and “S” indicate the residues of HA and SLAM, respectively. The position of H536 (Hie536) is highlighted by the yellow dotted circle. (B) Interaction surfaces of HA (right) and SLAM (left) depicted by opening out the interfaces of the complex with rotation. (C) Interacting residues of the target molecules depicted by the ball-and-stick representation on the surface of partner proteins. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

As seen in Fig. 2, Fig. 3, Fig. 4, we can detect D505, D507, D530 and R533 on the HA side as important residues, which corresponds well to experimental findings [[37], [38], [39]]. On the other hand, we observe important residues of E75, K77 and E123 on the SLAM side, as was remarked in the previous study [27]. For singular vectors of top five rank 1–5 with higher singular values, the main components are predominantly composed of charged residues, showing the importance of electrostatic interactions especially in the case of MVH-SLAM complex [27]. It is also noted that the interaction patterns given by each component of singular vectors 1–5 vary slightly but distinctively, thus showing their proper meanings. For the first singular vectors, we observe the tendency that the positively and negatively charged residues have the opposite signs and interact with the opposite-sign partners at the MVH-SLAM interface (Fig. 4). Interestingly, the relative phase (positive versus negative signs) of the dominant components is different between the singular vectors of 2 and 3, while the similar residues (e.g., K77, E123, D505, D507 and R533) are involved, thus representing the complex mixture of attractive and repulsive interactions among charged residues. As for the rank 6–10 singular vectors, on the other hand, we find important contributions from neutral (polar and hydrophobic) residues, some of which are related to the hydrogen bond or dispersion interactions. In addition to the interactions associated with polar residues such as Ser and Thr, we observe those by Tyr, Phe, Leu and Ile in the eigenvectors 6–10. These charged and neutral residues significantly affect the binding affinity of MVH-SLAM complex when they are mutated [27].

A novel feature of the SVD methodology proposed in the present work is to explicitly elicit the correlated or cooperative IFIEs shared among multiple residue fragments. For example, as seen in Fig. 4, the cluster formed by E503, D505, D507 and R533 in HA and that by E75, K77, R90 and E123 in SLAM cooperatively interact with each other, thus yielding a collective interaction network for the formation of protein complex. Such a novel viewpoint would be essential when we describe the indirect interactions between fragments [25] as well as their direct interactions, which often play an important role in biomolecular complex formation but was difficult to detect by earlier analyses [27] based on the individual IFIE values for each residue pair. Thus, the present approach can provide a novel FMO-based tool for the PPI analysis as an alternative to the earlier attempts based on other viewpoints such as the 3D Scattered Pair Interaction Energies (3D-SPIEs) [9] and the PIE-PRN [10,11].

Effects of protonation state of His536

In some virological mutagenesis experiments, the importance of H536 residue in MVH on protein binding to SLAM was remarked [[37], [38], [39]]. However, in Fig. 2, Fig. 3, Fig. 4 above, we cannot detect the important contribution by H536 in the FMO calculation as well as in the earlier analysis [27]. One possible reason for the disagreement with experiments may be concerned with the protonation state of His536. Therefore, we have also performed the FMO calculation and subsequent SVD analysis on MVH-SLAM complex in which the protonated (positively charged) His, Hip536, was used instead of the unprotonated (neutral) His, Hie536, employed in the calculation above. The first singular vector components obtained in this case are depicted in Fig. 5, Fig. 6 , which have revealed the importance of Hip536 in the interaction between HA and SLAM in marked contrast to the case with Hie536. The calculated results for the rank 1–10 singular vectors for HA and SLAM are depicted in Figs. S1 and S2 in the Supplementary data. Thus, we should keep in mind the possibility that the protonation state of H536 may be varied due to some reasons such as those changes of surrounding environments associated with pH, ionic strength, charged states of other residues and structural change.

Fig. 5

(A) Residues with large magnitude in the first singular vector 1 for the complex of HA (right) and SLAM (left), where the IFIE values were obtained by the FMO calculation in which Hip536 was employed. Blue and red colors indicate positive and negative values, respectively, whose deepness of the hue refers to the magnitude. The suffixes “H” and “S” indicate the residues of HA and SLAM, respectively. The position of H536 (Hip536) is highlighted by the yellow dotted circle. (B) Interaction surfaces of HA (right) and SLAM (left) depicted by opening out the interfaces of the complex with rotation. (C) Interacting residues of the target molecules depicted by the ball-and-stick representation on the surface of partner proteins. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 6

First singular vectors for SLAM (left, ) and HA (right, ), where the IFIE values for the SVD analysis were obtained by the FMO calculation in which Hip536 was employed. The abscissa refers to the amino-acid numbers and the ordinate represents the values of singular vector components normalized by the maximum value.

SCIFIE analysis

It is well known that the FMO calculations performed in vacuo give the IFIE values that overestimate the electrostatic interactions at the far distances [5]. Although we may take explicit or implicit account of solvation effects [[29], [30], [31]] to overcome this difficulty, we here resort to a post-FMO processing scheme called Statistically Corrected IFIE (SCIFIE) [40] by which the effective screening (electrostatic shielding) in the long range is partially performed. The results for the singular vectors of top 10 rank for HA and SLAM are shown in Figs. S3 and S4 in the Supplementary data for the cases of Hie536 and Hip536, respectively. We also give the comparison of the first singular vectors obtained through IFIE with Hie536, IFIE with Hip536, SCIFIE with Hie536 and SCIFIE with Hip536 in Fig. 7 . As seen in these figures, the SCIFIE protocol relevantly remedies the screening (electrostatic shielding) issue by erasing the redundant long-range interaction components in protein complex. Fig. 8 clearly illustrates this point in terms of comparison between the IFIE and SCIFIE results for the first singular vectors, in which the long-range contributions are reduced without the significant influence on the interactions at the binding interface. Finally, we show in Table 1 the comparison of the contributions from each singular value component in all the four cases of IFIE with Hie536, IFIE with Hip536, SCIFIE with Hie536 and SCIFIE with Hip536. It is thus observed that the SVD contributions up to the 10th component give more than occupancy in the total sum, dominating the MVH-SLAM interactions. In this way, the present compression scheme for the original IFIE data would provide a computational basis to efficiently describe PPIs.

Fig. 7

Comparison among the first singular vectors for SLAM (left) and HA (right) obtained in terms of SVD analyses on (A) IFIE with Hie536, (B) IFIE with Hip536, (C) SCIFIE with Hie536 and (D) SCIFIE with Hip536. The abscissa refers to the amino-acid numbers and the ordinate represents the values of singular vector components normalized by the maximum value.

Fig. 8

Comparison between the first singular vectors for the IFIE with Hie536 (A–C) and the SCIFIE with Hie536 (D–F). HA and SLAM are located on the right and left hand sides in each complex, respectively, and blue and red colors refer to the positive and negative values of each residue component, respectively, with their deepness of the hue representing the magnitude. (B)–(C) and (E)–(F) refer to the normalized values on the SLAM-HA interface in the cases of IFIE and SCIFIE, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Table 1

Comparison of top 10 singular values among the results for IFIE with Hie536, IFIE with Hip536, SCIFIE with Hie536, and SCIFIE with Hip536. Their contribution fractions and the accumulated occupancies are also shown.

Vector #	IFIE with Hie536			IFIE with Hip536
	Singular value	Fraction	Accumulated occupancy	Singular value	Fraction	Accumulated occupancy
1	449.315	0.448	0.448	454.644	0.450	0.450
2	116.423	0.116	0.564	116.755	0.115	0.565
3	103.481	0.103	0.668	103.951	0.103	0.668
4	54.745	0.055	0.722	56.152	0.056	0.723
5	41.031	0.041	0.763	41.672	0.041	0.764
6	33.864	0.034	0.797	33.840	0.033	0.798
7	26.555	0.026	0.824	26.636	0.026	0.824
8	20.892	0.021	0.844	21.317	0.021	0.845
9	16.677	0.017	0.861	16.755	0.017	0.862
10	15.722	0.016	0.877	15.739	0.016	0.877
Vector #	SCIFIE with Hie536			SCIFIE with Hip536
	Singular value	Fraction	Accumulated occupancy	Singular value	Fraction	Accumulated occupancy
1	230.852	0.308	0.308	233.106	0.308	0.308
2	102.076	0.136	0.444	103.161	0.137	0.445
3	93.085	0.124	0.568	92.962	0.123	0.568
4	49.857	0.066	0.634	50.687	0.067	0.635
5	37.755	0.050	0.685	38.480	0.051	0.686
6	32.755	0.044	0.728	32.722	0.043	0.729
7	25.730	0.034	0.763	25.701	0.034	0.763
8	20.975	0.028	0.791	20.996	0.028	0.791
9	17.845	0.024	0.814	17.969	0.024	0.815
10	15.743	0.021	0.835	15.757	0.021	0.836

Concluding remarks

In this study, we have proposed a novel methodology to efficiently obtain and visualize the correlated inter-fragment interactions in the FMO calculations for protein complex. With the aid of the SVD technique for the efficient data compression, the IFIE matrix composed of the residue components from each protein can be decomposed into the contributions from individual singular-value components that comprehensively describe the cooperative interaction network among amino-acid residues. We have applied this method to the analysis of molecular recognition between the measles virus HA and its SLAM receptor to assess its feasibility and usefulness. (The FMO calculation results which treat His536 as Hie and Hip are registered in the FMO database [41] (https://drugdesign.riken.jp/FMODB/) as FMODB ID entries 3NVVL and JM999, respectively.) Collective interaction patterns formed by some important residues, which could not be described in earlier FMO-IFIE studies based on individual fragment interactions, were thus identified in agreement with experimental observations. In addition, the significances of the protonation state of His536 and of the electrostatic screening effect were addressed in the present study, while the explicit or implicit inclusion of the solvation effects would be an important issue [[29], [30], [31]] in actual pharmaceutical applications. For the future development, the incorporation of the pair interaction energy decomposition analysis (PIEDA) [42] would be interesting to discriminate the contributions from various kinds of molecular interactions. The proposed method would also be applicable to the analysis of molecular recognition associated with the new coronavirus SARS-CoV-2, e.g., for a complex between the spike protein and the angiotensin-converting enzyme 2 (ACE2) [[43], [44]].

Declaration of competing interest

There is no conflict of interest among authors.