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. 2018 Apr 11;3(4):4094–4104. doi: 10.1021/acsomega.8b00336

Charge-Transfer Knowledge Graph among Amino Acids Derived from High-Throughput Electronic Structure Calculations for Protein Database

Hongwei Wang †, Fang Liu †, Tiange Dong †, Likai Du †,*, Dongju Zhang ‡, Jun Gao †
PMCID: PMC6641752  PMID: 31458645

Abstract

graphic file with name ao-2018-00336g_0010.jpg

The charge-transfer coupling is an important component in tight-binding methods. Because of the highly complex chemical structure of biomolecules, the anisotropic feature of charge-transfer couplings in realistic proteins cannot be ignored. In this work, we have performed the first large-scale quantitative assessment of charge-transfer preference by calculating the charge-transfer couplings in all 20 × 20 possible amino acid side-chain combinations, which are extracted from available high-quality structures of thousands of protein complexes. The charge-transfer database quantitatively shows distinct features of charge-transfer couplings among millions of amino acid side-chain combinations. The overall distribution of charge-transfer couplings reveals that only one average or representative structure cannot be regarded as the typical charge-transfer preference in realistic proteins. This work provides us an alternative route to comprehensively understand the charge-transfer couplings for the overall distribution of realistic proteins in the foreseen big data scenario.

1. Introduction

Charge transfer is one of the simplest but fundamental reactions in life science.1−7 Electron- or hole-transfer reactions are possible between donors and acceptors separated by a long distance, that is, across protein–protein complexes.6,8−13 The charge-transfer effect is also suggested to be important to the protein folding or protein–water interactions.14−16 In biological molecules, the superexchange (tunneling) and hopping mechanisms are commonly used to interpret charge-transfer processes.5,6,17−19 The tunneling mechanism is a one-step process which exhibits a strong distance dependence, whereas the hopping mechanism provides an explanation for electron or hole transfer across long distances. Although the driving force of charge-transfer reactions is “encoded” in thousands of known protein structures, “decoding” them is challenging because of the complexity of natural proteins.20−23

The building blocks of proteins are only the twenty l-amino acids, which are distinguished by their distinct side-chain structures. Bioinformatics scientists have paid much attention to depict the structural significance of these protein complexes, and a large number of biological databases were constructed to classify protein structures in the past decades.24−31 In addition, the growing amount of high-quality experimental (X-ray, NMR, and cryo-electron microscopy) protein structures have opened space to improve our theoretical understanding of biological charge-transfer reactions. The relative abundance of various modes of amino acid contacts (van der Waals contacts and hydrogen bonds) could be completely exploited to understand the nature of electron transfer in proteins. Therefore, it becomes increasingly important to incorporate the available structural knowledge into our physical model development.32−36

Generally, in biomolecule charge-transfer reactions, the charge-transfer rate is proportional to the square of the donor/acceptor electronic coupling strength and the nuclear factor associated with the motion along the reaction coordinate.6,12,13,37,38 Electronic coupling elements as an important component for biological charge transfer can be derived from various empirical or semiempirical models20,38−42 and from direct electronic structure calculations.43−48 Nowadays, the computations with more advanced models are becoming increasingly possible to obtain the charge-transfer couplings for ensembles of structures. Therefore, it is desirable to go beyond the empirical parameters and directly calculate charge-transfer coupling parameters for millions of molecular fragments.

In this work, we derived the charge-transfer couplings from the single-electron motion equation of biomolecule systems under the tight-binding approximation. Then, a promising computational protocol is suggested to construct the charge-transfer coupling database, which is large enough to sufficiently represent possible occurrences of amino acid contacts in realistic proteins. The possible structural changes could significantly influence the electrical properties in bimolecular fragments, as revealed by differential analysis of charge-transfer couplings among millions of amino acid side-chain combinations. Thus, the pairwise charge-transfer interactions among discretized libraries of amino acid side-chain conformations, as a powerful look-up table, enable us to directly obtain the overall charge-transfer preferences for any structures, in the foreseen big data scenario.

2. Methods and Computational Details

2.1. Tight-Binding Method for Biomolecules and Charge-Transfer Couplings

The tight-binding model is an effective approach to study complicated molecular systems with large sizes. Here, the single-electron motion equation for biomolecule systems is derived according to the idea of tight-binding approximation. Here, we provide a brief introduction of the tight-binding method for biomolecules, following the previous work of Liu49−51 and others.52,53 The time-independent Schrödinger equation for the many-electron problem of large biomolecules can be written as

2.1. 1

where H is the Hamiltonian operator for the biomolecular system of nuclei and electrons. In atomic units, the Hamiltonian for n electrons and m nuclei can be expressed as

2.1. 2

In eq 2, Ma is the ratio of the mass of nucleus a to the mass of an electron and Za is the atomic number of nucleus a. The Laplacian operators ∇i2 and ∇a2 involve differentiation with respect to the coordinates of the ith electron and the ath nucleus. The first term in the equation is the operator for the kinetic energy of the electrons; the second term is the operator for the kinetic energy of the nuclei; the third term represents the Coulomb attraction between electrons and nuclei; and the fourth and fifth terms represent the repulsion between electrons and between nuclei, respectively.

Note that the kinetic energy of the nuclei can be neglected within the Born–Oppenheimer approximation. The remaining terms in eq 2 are called the electronic Hamiltonian or Hamiltonian describing the motion of n electrons in the field of m nuclei,

2.1. 3

The building blocks of biomolecules are simply a few repeated structural units, that is, amino acids for proteins, nucleotides for DNA, and so on, and the many-electron Hamiltonian in this physical picture can be written as

2.1. 4

In eq 4, L and M refer to the repeated structural units or sites. The last term refers to the repulsion between the nuclei, which has no effect on the electronic structure of the biomolecules. Equation 4 can be rewritten as the sum of one-electron operators:

2.1. 5

and

2.1. 6

The corresponding many-electron Schrödinger equation can be solved via the one-electron Schrödinger equation,

2.1. 7

whereas ψ is the one-electron wave function for the biomolecules, and the one-electron Hamiltonian can be expressed as

2.1. 8

The first step to solve eq 7 is to calculate the one-electron Schrödinger equation of the isolated structural unit at the nonperturbation state.

2.1. 9

In eq 9, ϕlis the molecular orbital of one structural unit L and εl0 is the corresponding orbital energy. Equation 9 can be solved by available electronic structure methods, such as the Hartree–Fock or density functional theory method. In addition, the electronic orbital for the entire biomolecules can be expanded as the linear combination of site orbitals for repeated structural units.

2.1. 10

Substituting the above equation into eq 8, we can obtain the following equation:

2.1. 11

According to the tight-binding approximation, the electrons in this model are tightly bound to each structural unit to which they belong and they should have limited interaction with states and potentials on surrounding sites. Thus, the potential of the neighboring sites can be treated as perturbations. The tight-binding Hamiltonian is usually written as

2.1. 12

where c and c+ are the annihilation and creation operators for electrons or holes, respectively, ε is the on-site energy, and t is the transfer integral between sites.

In the tight-binding approximation, the electron has limited interaction with the non-neighboring sites. Thus, we can get the following expression:

2.1. 13

After comparing eqs 12 and 13, the formulas for the on-site energy and transfer integral can be given as

2.1. 14
2.1. 15

The summation runs over all possible sites L; however, only the neighboring sites are required to be considered in the tight-binding approximation. Thus, the on-site energy for site n only needs the potential information of site n and its closest neighboring sites C; the related formula of on-site energy can be simplified as

2.1. 16

It is obvious that the on-site energy in eq 16 is not fully equal to the orbital energy of the site n; at least, the first neighboring sites should be considered. The transfer integral only requires the potentials of sites n and n + 1, that is

2.1. 17

The transfer integral describes the ability to perform charge transfer among neighbor sites; meanwhile, the on-site energy describes the ability to move or inject an electron from a specific site. The use of amino acid dimers is sufficient for the construction of a charge-transfer coupling matrix.

Because the tight-binding model is corresponding to the orthogonal basis, the Löwdin method is performed to minimize the orbital overlap. In addition, the effective transfer integral can be transformed to

2.1. 18

In eq 18, s is the orbital overlap integral between sites. This transformation shows minor effects on the on-site energy and therefore can be ignored in our code implementation.

As two basic variables, the on-site energy and transfer integral are the diagonal and off-diagonal elements of the tight-binding Hamiltonian, respectively, which are basic physical variables in the study of DNA damage and respiration, photosynthesis, and the design of molecular electronic devices and charge-transfer problems.

The matrix elements of the overlap and Fock matrices are extracted from Gaussian 09 output, and then they are used to calculate the on-site energy and charge-transfer coupling. Once the tight-binding Hamiltonian is constructed, we may directly solve the well-known eigenvalue equation (HC = EC) for the electronic structure calculations of biomolecules. Also, the implementation of this workflow can be found in http://github.com/dulikai/bioX. Further work on the application of the charge-transfer database can be found in our recent work.54 This work is not aimed to deal with the charge-transfer interactions in complex proteins. In addition, we hope to understand the big picture of the tight-binding Hamiltonian elements from millions of possible amino acid combinations.

2.2. Construction of the Charge-Transfer Knowledge Graph

The Protein Data Bank (PDB) contains a wealth of data on nonbonded biomolecule interactions. This information is useful for us to develop a data-driven or informatics-based model. Here, the data collection procedure is accomplished by extracting the structural data from an improved version of the “Atlas of Protein Side-Chain Interactions”, which are derived from thousands of unique structures of protein complexes.55 This database is at its mature state. As of June 2017, the Atlas comprised 482 555 possible amino acid side-chain combinations for 20 × 20 sets of amino acid contacts. Note that the snapshot of this database on June 2017 can be directly obtained from us upon request. Each type of amino acid combinations has been carefully classified up to six clusters based on geometric similarity. In this fashion, each cluster has a clear-cut representative structure. The procedure to extract each dimer complex has been described in the work of Singh and Thornton.56

The initial structures in the amino acid side-chain database contain only the coordinates of heavy atoms, and the missing hydrogen atoms were added using the tleap module in AmberTools package.57 In addition, we mainly focus on the big picture of the charge-transfer couplings for millions of amino acid side-chain combinations. For simplicity, only one representative protonation state is considered for each amino acid because the protonation states of amino acids should only be reasonable in the realistic proteins. Therefore, we would assume that the amino acids adopt only a single protonation state, which can be regarded as the data washing procedure in big data. In addition, we believe that such a rough representation is very necessary for millions of amino acids combinations. In the language of cheminformatics, the side chains in the database present reasonable molecular descriptors for the differential analysis. The general trends can be extracted from millions of amino acid side-chain combinations in this fashion. The workflow to derive the charge-transfer couplings is summarized in Scheme 1.

Scheme 1. Work Flow of Calculating the Charge-Transfer Coupling for Any Amino Acid Side-Chain Combination.

Scheme 1

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The frontier orbitals of amino acids with large side chains are mainly located at the amino acid side-chain atoms, whereas the backbone atoms may be involved in the frontier orbitals for amino acids with small side chains. Therefore, the backbone of amino acids has been incorporated for amino acids with small side-chain groups, such as Gly and Ala. The point of cutting covalent bond is saturated with hydrogen atoms (i.e., either the Cα or Cβ atom). To eliminate any potential nonspecific interactions, the positions of hydrogen atoms were first optimized for each dimer at the semiempirical PM6 level with subsequent optimization with B3LYP/6-31G* calculations. The coordinates of the heavy atoms were kept fixed during the optimization procedure. The quantum chemistry calculations are performed with Gaussian 09 package.58 The optimized structures are used for our subsequent calculations of charge-transfer couplings at the B3LYP/6-31G* level and statistical analysis. The entire work flow requires 482 555 geometric optimizations at the PM6 level and 482 555 geometric optimizations at the B3LYP/6-31G* level, with subsequent 1 447 665 single-point calculations at the B3LYP/6-31G* level. Considering the geometric optimization generally requires 10–30 cycles; we need at least 10 millions of B3LYP calculations.

3. Results and Discussion

First, the charge-transfer integrals are calculated for millions of amino acid side-chain combinations to reveal the richness of biological charge-transfer reactions in realistic proteins. This database is helpful to describe how the conformation ensemble influences charge-transfer couplings within distinct protein structures. Here, without losing any generality, we will restrict our study to electron- and hole-transfer coupling between highest occupied molecular orbitals of each amino acid side-chain combination. To facilitate our following discussions, the words “hot” and “cold” are used to describe the residues with larger and smaller charge-transfer coupling values, respectively.

Traditionally, the charge-transfer coupling was often assumed to be a constant or an empirical formula for each type of residue combinations in modeling realistic biomolecule systems.38,41,49−51,59 Thus, Table 1 presents the average charge-transfer couplings as constants of the overall 20 × 20 possible amino acid pairs, which reveals that most charge-transfer couplings are nonzero and below 0.05 eV. The 20 amino acids can be divided into several groups according to the chemical compositions of their side chains, that is, nonpolar/hydrophobic groups, nonpolar/aromatic groups, polar/neutral groups, polar/basic groups, and polar/acidic groups. In general, the transfer couplings for the polar/polar or basic/acidic combinations are greater than those of the pairwise hydrophobic combinations,60 with only minor exceptions.

Table 1. Average Transfer Coupling Matrix for the 20 × 20 Possible Pairs over Their Representative Structuresa.

3.

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a

The filled colors are used to distinguish residue types. White refers to nonpolar, purple refers to aromatic, green refers polar and neutral, blue refers to polar and basic, and red refers to polar and acidic amino acids. Significant charge-transfer couplings are highlighted with blue (0.05–0.1 eV) and red (>0.10 eV) fonts.

The knowledge graph is applied to visualize charge-transfer couplings for 20 × 20 possible amino acid combinations. In Figure 1a, the edge weights in our graph are assigned as the average values of the unsigned charge-transfer couplings between two types of amino acids (see Table 1). Each vertex represents an amino acid. The edge width between the nodes is linearly corresponding to the absolute value of the charge-transfer couplings. This graph representation provides a self-explanation of the significant charge-transfer interactions among amino acids, such as Glu/Ser and Lys/Pro. Note that the remarkable charge-transfer couplings between cysteine residues are mainly caused by the possible disulfide bonds in realistic proteins.

Figure 1.

Figure 1

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Knowledge graph of the charge-transfer couplings among residues. (a) Charge-transfer knowledge graph connected by their average charge-transfer couplings. (b) Number distribution graph connected by the number of amino acid pairs with charge-transfer couplings larger than 0.05 eV. (c) Residues with significant charge-transfer couplings are highlighted with blue (<0.05 eV) and red (≥0.05 eV) backgrounds.

In Figure 1b, we try to go beyond the analysis of average charge-transfer couplings, and details of the entire 482 555 amino acid pairs are exploited. The edge weights are assigned as the number of structures with charge-transfer couplings larger than 0.05 eV in each kind of amino acid combinations. This graph retains most topological features of charge-transfer couplings in Figure 1a, which indicates that the average structures of each amino acid pair provide a reasonable approximation to interpret the charge-transfer couplings in realistic proteins. Figure 1c summarizes the charge-transfer significance of each amino acid, which is consistent with our common sense that most remarkable residues for charge-transfer reactions are those polar residues, such as Ser and Lys. This one-dimensional representation may be useful as a reference material to qualitatively understand the possible charge-transfer features in proteins.

Next, we focus on the top 16 amino acid pairs with significant charge-transfer couplings in 400 possible amino acid pairs. In Figure 2, the box plots are used as a quick way of examining the variation in statistical population of charge-transfer couplings. Each box plot refers to the distinct geometric clusters for a specific type of the amino acid pair. The median values of the charge-transfer couplings for each geometric cluster are significantly different. The spacings between the different parts of the box indicate the degree of dispersion (spread) and skewness of the data. The overall charge-transfer couplings are widely distributed among geometric clusters within a specific amino acid combination. These observations are consistent with our calculated median and standard deviation of the charge-transfer coupling database (Tables S1–S3). In summary, each type of amino acid pair or even each geometric cluster may contain widespread charge-transfer couplings. Thus, it is not always a good choice to assume that the charge-transfer coupling is the same for one type of amino acid combinations in realistic proteins and their dynamics studies.

Figure 2.

Figure 2

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Box plots are used to depict the character of charge-transfer couplings. Each plot shows the distinct clusters for a specific amino acid pair. The bottom and top of the box are the first and third quartiles, respectively, and the band inside the box is the second quartile (the median). Note that the scale of the y-axis is not the same to enhance the comparison within each box plot.

Figure 3 presents three-dimensional structure distributions for the Glu/Glu and His/Glu pairs as typical systems, which have an intermediate total number of observed contacts (2475 and 2583) in the protein amino acid side-chain atlas. Figure 3a,b shows the geometric distributions for each amino acid pair, for which the amino acids have distinct interaction patterns, indicating that their packing is not entirely random.61−63 The population of charge-transfer couplings is encoded in various models of geometric contacts, that is, the hydrogen bonds or van der Waals contacts. The geometric distributions with charge-transfer couplings greater than 0.05 eV are shown in Figure 3c,d. A few geometric clusters completely disappear in the Glu/Glu and His/Glu pairs, which indicates their minor contribution to the possible charge-transfer events. These results suggest that the charge-transfer coupling distribution of overall geometric clusters cannot be simply described by only one representative structure. In addition, one must pay close attention when dealing with the geometric ensemble of amino acid pairs in realistic proteins, and the appropriate transfer coupling parameters should be applied only after performing tests on similar geometric features.

Figure 3.

Figure 3

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Example distribution and its associated geometric clusters for Glu/Glu (a) and His/Glu (b) pairs. The selective structural distributions for Glu/Glu (c) and His/Glu (d) pairs with the charge-transfer coupling greater than 0.05 eV.

As mentioned above, the charge-transfer coupling parameters are found to be very sensitive to the structural orientation of the amino acid pairs,3,64−66 in the context of overall geometric distribution. The relative abundance of various modes of amino acid contacts leads to a very different charge-transfer coupling distribution. Thus, several geometric clusters can be assigned as hot contacts, whereas the others can be assigned as cold contacts. The plots of charge-transfer coupling distributions of all amino acid pairs are available at http://github.com/dulikai/bidiu.

In Figure 4, the charge-transfer coupling population is summarized for the Ser/Glu pair, which can be classified into six geometric clusters. The Ser/Glu pair is used as an illustrated example, with enough geometric contacts (3277 contacts) and charge-transfer couplings strengths. First, the selected cluster representatives (red lines) are not always related to the largest peak position in the charge-transfer coupling distributions. In addition, the cluster representative structures may even represent the extreme charge-transfer coupling values in a few cases. Second, the charge-transfer coupling distribution curves usually exhibit more than one peak, beyond the peak position near the zero value. Third, the charge-transfer coupling distribution can be widespread in the same geometric clusters, although the root-mean-square deviation values of these structures in each cluster are only within 1.5 Å.56 In summary, further geometric variables should be applied to measure the charge-transfer coupling distribution in realistic proteins.

Figure 4.

Figure 4

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Distributions of charge-transfer couplings (eV) for the six geometric clusters of the Ser/Glu pair are shown, where Ser is the center fragment. The red line refers to the charge-transfer couplings for the representative structure of each geometric cluster.

The explicit geometric correlation with the charge-transfer couplings is investigated. The electronic coupling is usually supposed to decay exponentially with the distance between donors and acceptors67−69Figure 5 shows the charge-transfer couplings along the center to center distance between the two amino acid pairs. Because of the anisotropic feature of amino acids, it is hard to say that the amino acid pairs with larger charge-transfer couplings show relatively shorter pairwise distances. In most cases, the values of charge-transfer couplings can differ by 1 order of magnitude at the median range (4.0–5.0 A). The charge-transfer couplings remarkably decay to nearly zero beyond the median range. In addition, the overall charge-transfer coupling distribution is strongly related to the physicochemical properties of amino acids. In addition, each type of amino acid pairs exhibits its specific charge-transfer coupling feature or fingerprint.

Figure 5.

Figure 5

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Charge-transfer couplings as a function of amino acid pairwise distance for top 16 amino acid pairs.

It is expected that more abundant electronic information can be derived from the orientation of amino acid side-chain contacts. Figure 6 provides the charge-transfer coupling distribution as a function of distance and angle between pairwise amino acids. The definition of the coordinate system can be found in Scheme S1. The overall view of heat maps suggests that each type of amino acid combinations contains its specific charge-transfer coupling distribution. In addition, the charge-transfer coupling shows strong anisotropic features among various clusters of amino acid side-chain combinations. We can find a few distinct hot regions, for which the unsigned charge-transfer couplings are larger than those of its surroundings. Thus, the angular variable should be considered in the analytical estimate of the charge-transfer couplings among amino acids. The anisotropic stacking of protein side chains could be a critical factor to determine the electronic properties of proteins. In addition, we suggest that the possible structural changes could significantly influence the electronic properties in proteins.64,66,70,71

Figure 6.

Figure 6

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Distance vs angular-dependent charge-transfer couplings for top 16 amino acid pairs.

Finally, we present the selected structures for top 16 amino acid pairs with most significant charge-transfer couplings in Figure 7. It is clear that the amino acid pair should have specific contacts to achieve high charge-transfer couplings. Various intermolecular interactions can be responsible for the significant charge-transfer reactions. The hydrogen bonds are most common in the available amino acid pairs, such as Asp/Thr, Asp/Ser, Glu/Ser, Glu/Glu, and Glu/Thr. This is consistent with our common sense.3,23,59,60 The π···π stacking or C–H···π interactions between the hydrophobic amino acid side chain and aromatic rings are also observed to be important for the charge-transfer reactions (i.e., Lys/Phe, Phe/His, and so on), although their absolute couplings values are not very large (∼0.05 eV). The role of C–H···π interactions in charge-transfer reactions is not commonly recognized,72,73 although the C–H···π interactions are reported to play an important role because of their significant occurrences in organic crystals, proteins, and nucleic acids.74−76 Further investigation of the role of C–H···π interactions in charge-transfer interactions is needed. In summary, the exploitation of the mega data sets allows us to rationalize the charge-transfer couplings and their structural characters on the same foot.

Figure 7.

Figure 7

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Selected structures for the top 16 amino acid pairs with the most significant charge-transfer couplings.

4. Conclusions

In summary, we present a promising protocol to construct a charge-transfer database at a residue level, which is derived from millions of electronic structure calculations among 20 × 20 possible amino acid side-chain combinations. In this fashion, the possible charge-transfer properties among residues could be understood in a more explicit and more intuitionistic fashion, without any requirement of the knowledge of chemical intuition about the chemical interactions or empirical formulas. In addition, the possible structural changes could significantly influence the electronic properties in proteins. On the basis of these observations, we suggest that the protein charge transfer can be accomplished by the selective arrangement of interacting amino acid orientations.

The construction of charge-transfer database for amino acids presents one of the key steps toward understanding the electronic structure information in proteins. Future work may be possible to enumerate the most common hot motifs that are suitable for charge-transfer reactions in proteins by reusing sophisticated charge-transfer parameters.

Acknowledgments

The work was supported by the National Natural Science Foundation of China (nos. 21503249, 21373124), Huazhong Agricultural University Scientific & Technological Self-innovation Foundation (program no. 2015RC008), and Project 2662016QD011 and 2662015PY113 supported by the Fundamental Funds for the Central Universities. The authors also thank the support of Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under grant no. U1501501.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b00336.

  • Statistical analysis of charge-transfer database and definition of the molecular system (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao8b00336_si_001.pdf (285.4KB, pdf)

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