In vivo, most Na⁺ channel α subunits (Nav1.1–Nav1.9) are associated with one or more β subunits; nowadays, four distinct isoforms (β1∼β4) and two splice variants (β1A, β1B) have been discovered [1,2]. Structure/function studies have identified the P loop of domain IV of the Na⁺ channel α subunit as a likely interaction point for the extracellular domain of β1, accounting for the fine-tuning of Na⁺ channel activation and inactivation gating [3]. More recently, people began to focus on the studies of β subunits and their mutants, as experiments showed that many diseases were associated with β subunits changes, especially in the extracellular domain (ECD), which is in charge of the electrophysiological properties of the sodium channel and cell adhesion or migration [4].

As we all know, the β subunits share a common structure: a single membrane domain, an intracellular C-terminal domain, and a large extracellular N-terminal domain (Fig. 1). The ECD contains four potential N-glycosylation sites, which were modified with sialic acid; in this domain, they all have an immunoglobulin-like fold [5,6]. Among these subunits, β1 and β3 are non-covalently linked to VGSC α subunits, while β2 and β4 associate with disulfide connection. Particularly, β1 and β3 have compact relations; they are structurally similar, with 57% sequence identity and related to the same diseases, such as epilepsy and cardiac arrhythmia [4,7,8]. Recent studies reveal that the β1 and β3 subunits are always co-expressed in many tumour cells and involved in epilepsy, cardiac arrhythmia [6,9]. So, we speculate that there must be a special interaction mode between β1 and β3. To prove this inference, we have to know the crystal structure model of β1 and β3; however, there have been so far no published studies about 3-dimensional structure and interaction analysis between β1 and β3.

Therefore, in the present study, we provide a hypothesis that β1 has certain relationship with β3 subunit, which is different from the results of McEwen et al., who studied the interaction between β subunits and other CAMs in glial cells [10]. Moreover, this paper screened out the homologous mode template of β1 and did the docking studies of β1 and β3 subunits, which provides a strong basis for the further research of β subunits on structure and functional drug targeting.

3.1 Molecular modelling

3.2 Dynamics and PROCHECK

3.3 Protein–protein docking

4.1 Molecular modelling of β1 and β3

Analysis of the Ramachandran plot showed that 73.3% and 80.6% of the residues were in the most favourable regions, with 21.6% and 14.8% in the additional allowed regions for β1 and β3, respectively; the dynamic optimization results also indicated that the models are suitable for studies. The 3D structures and the Ramachandran plots of β1 and β3 are shown in Fig. 2A and B, respectively. Fig. 2C shows the evolution of the RMSD during the dynamic process of β1 structure.

4.2 Docking study between β1 and β3

Protein–protein dockings of β1–β1 and β1–β3 were carried out (as shown in Fig. 3A and B) for studying the interaction of molecules involved in potential energy, hydrogen bond, hydrophobic contacts. The potential energies were –593.32725 (kcal/mol) and –1068.48017 (kcal/mol), respectively for β1–β1, β1–β3, and showed that the β1–β3 heterogeneous di-polymer form was more stable than the β1–β1 homologous di-polymer form (see Table 2).

Table 2

Molecular interaction parameters between β1 and β3 subunit.

Items	β1–β1	β1–β3
Force field	CHARMm	CHARMm
Potential energy (kcal/mol)	–593.32725	–1068.48017
VDW energy (kcal/mol)	–134.90669	–402.55395
Electrostatic energy (kcal/mol)	–458.42056	–665.92622
Hydrogen bonding (pairs)	1	10
Residues involved in hydrophobic contacts	a: Ser137 Thr64 Thr136 Cys43 Asn135 b: Leu39 Leu127 Phe67 Phe128 Val139 c: Glu29 Glu66 Glu133 Glu145 d: Lys44 Lys62 Lys141 Arg45 Arg46 His143	Thr64 Thr136 Leu117 Leu127 Leu140 Pro133 Pro142 Phe126 Phe129 Glu65 Glu67 Asp130 Arg144

Currently, at least four VGSC β subunits have been cloned and characterized, but little research has been done about their structure and function. Therein most of the studies focused on β1, since many mutations involving β1 have been reported in neurological diseases, such as epilepsy, EGFS+ [17].

So far, only a model of β3 structure has been elaborated by homology modelling. However, our research brought in another hypothesis using a protein–protein model for docking β1 and β3, respectively, which is more likely to form a heterodimer (β1–β3). The results based on the pairs of hydrogen bonds between β subunits and including numbers of hydrophobic groups and potential energy as an important index of the investigation were considered as well. Meaningfully, the position of the hydrogen bond (122His–140Lys) between β1 subunits was just located in disulfide linkage area in the topological structure where the GEFS + mutations sites are centralized. We can conclude that His122 and Lys140 may play an important role in the function of β1 subunit.

From the potential energy results (–593.32725 kcal/mol and –1068.48017 kcal/mol) respectively for β1–β1, β1–β3, and the number of hydrogen bonds and hydrophobic groups (between β1 and β3, there exist 9 more additional hydrogen bonds than in the β1–β1 case), we can clearly prove that the combination β1–β3 is more stable than β1–β1. Also, we can predict many additional functions for the amino acid within the binding areas for β1 or β3, for example, cell surface migration and adhesion or regulation of Na⁺ current.

The authors have not supplied their declaration of conflict of interest.