Symmetry-Based Self-Assembled Nanotubes Constructed Using Native Protein Structures: The Key Role of Flexible Linkers

Abstract

We construct nanotubes using native protein structures and their native associations from structural databases. The construction is based on a shape-guided symmetric self-assembly concept. Our strategy involves fusing judiciously-selected oligomerization domains via peptide linkers. Linkers are inherently flexible, hence their choice is critical: they should position the domains in three-dimensional space in the desired orientation while retaining their own natural conformational tendencies; however, at the same time, retain the construct stability. Here we outline a design scheme which accounts for linker flexibility considerations, and present two examples. The first is HIV-1 capsid protein, which in vitro self-assembles into nanotubes and conical capsids, and its linker exists as a short flexible loop. The second involves novel nanotubes construction based on antimicrobial homodimer Magainin 2, employing linkers of distinct lengths and flexibility levels. Our strategy utilizes the abundance of unique shapes and sizes of proteins and their building blocks which can assemble into a vast number of combinations, and consequently, nanotubes of distinct morphologies and diameters. Computational design and assessment methodologies can help reduce the number of candidates for experimental validation. This is an invited paper for a special issue on protein dynamics, here focusing on flexibility in nanotube design based on protein building blocks.

1. INTRODUCTION

Bio-nanotechnology aims to design novel biomaterials and molecular devices, often via self-assembly. In nature, proteins often self-assemble, spontaneously organizing in stable structures through non-covalent interactions. These create large complexes with well-defined structures that have specific functions [1–4]. Exploiting the ability of proteins to self-assemble in a specific manner can be useful for construction of novel structures [5–8]. Recently, there have been numerous reports describing the use of natural and artificial peptides in nanodesign [9–12]. Due to advances in peptide synthesis and molecular engineering techniques [13,14], peptide self-assembly can become a favorable route to obtain single or associated tubes, fibers, micelles and vesicles. Simulation methods and efficient modeling algorithms coupled with protein databases can accelerate the design via fast probing of many models, limiting experimentations to those with higher probability of success. While the number of methods increases, few general strategies address structural architectures and symmetries.

Padilla et al. [15] combined symmetric protein components for engineering self-assembling nanostructures with the assumption that natural proteins form from preferred self association of domains and that dimers, trimers, and tetramers are common. Hence, following certain geometric rules, two such domains can be covalently connected through a peptide linker into a single larger monomer. Such a fused monomer is therefore made of three segments, where those at both ends have a strong tendency to associate with identical copies of themselves into a symmetric nanostructure. In this manner, a vast range of symmetric nanostructures can be designed, such as cages, shells, unbounded layers, and filaments. The final 3D geometry of the molecular architecture depends on the oligomeric order of the original domains and on the preferred orientation of a helical linker. Raman et al. [16] substantiated this strategy, but introduced a new approach for fusing homo-oligomers: two monomers can be fused if both have cysteines adjacent to their termini. The termini are linked covalently via two glycines, and oxidative conditions lead to formation of a disulphide bond between the monomers. This bond rigidifies a desired orientation between the original monomers. Usui et al. incorporated cysteines into the binding elements by site-directed mutagenesis [17].

Tsai et al. presented an in silico strategy for constructing a protein nanotube [18]. The strategy involves optimal mapping of candidate protein building blocks (BBs) into a nanotube shape, leading to a complete atomic model of the protein nanotube. The procedure involves wrapping a planar sheet onto a tube surface. If the arrangement of the building blocks has a 2D repeating pattern, then the planar sheet can be shaped by the repeating 2D lattice. The lattice can be described by the three lattice constants {a,b,γ}. Two additional integers {n₁,n₂} define the wrapping of the planar sheet onto the tube surface, where n₁ defines the number of cells needed to wrap a full round of the tube, and n₂ defines the number of cells shifted after one complete round. This computational strategy was based on known experimental observed data [19–21].

Since self-assembled nanostructures are generally huge systems, earlier assessment methods that used MD simulations were limited by running time, and the protein region of interest [22,23]. Recently, we devised an all-atom molecular dynamics (MD) simulation method for validating protein nanotubes [24]. The method utilizes the observation from nature that a protomeric unit-cell self-assembles according to a predetermined symmetry. The mathematical transformations of the unit-cell to its identical neighbors are calculated in the preprocessing stage. The full atomic-coordinates of the unit-cell only are preserved throughout the simulation, and the cell non-bonded interactions with its neighboring images are constantly considered. This method allows accurate simulation of protein nanotubes in reasonable times.

Here we use a new protocol for designing protein nanotubes from peptide building blocks based on experimental [15–17] and computational [18,24] works. Our method is based on two assumptions: (1) that a self-assembled peptide nanostructure can be virtually disassembled into identical asymmetric units that interact with each other through symmetry operations [25,26]; and (2) that most self-assembled lamellar sheets tend to wrap into cylindrical or fibrillar structures since a closed geometrical shape is energetically more favorable than its open planar state [1,27,28]. The revolving of a lamellar sheet into a tube, fibril or vesicle is dependent on the monomer concentration. The higher the concentration, the more globular is the geometry [29,30]. Since at low concentration a lamellar sheet would form a tube or a fibril, we focus on these geometries. Fig. (1) outlines the construction protocol. We demonstrate the strong relationship between our generalized protocol and the construction procedure of the human immunodeficiency virus type 1 (HIV-1) capsid protein [21], and construct novel protein nanotubes, based on the antimicrobial protein Magainin 2 [31]. Whereas in the HIV-1 capsid protein the linker is a short six amino-acid flexible loop, in our designed nanotube constructs we model different linkers of distinct lengths, flexibilities and dynamics, aiming to optimize geometrical and thermodynamic stability.

Figure 1.

An illustration of the procedure of fusing protein domains into a monomer that self-assembles into symmetric nanostructures. In this example, a single monomer taken from a dimeric protein (top left, in light gray) is covalently linked to a single monomer taken from a trimeric protein (top right, in dark gray) via a short linker (black). The fused monomer is now comprised of N-terminal and C-terminal domains. The monomer self-assembles into a unit-cell of P6 lattice symmetry, which finally self-assembles with identical cells to create a nanotube.

2. METHODS

Our design and construction protocol has several stages. First, we define a set of symmetries of a 2D lattice cell. This cell will eventually wrap around a cylinder surface. For each lattice symmetry, we select homo-oligomers from the PDB [32] and a specific linker to fuse the two oligomerization domains (ODs). In the last setup stage, we construct a unit-cell from the fused ODs and optimize the cell structure before wrapping it with identical entities into a tube. Finally, using CHARMM [33] we assess the stability of the model [24]. All minimizations, simulations and analysis use CHA-RMM22 force-field.

2.1. Defining Main Lattice Symmetries

Fig. (2) presents symmetric schemes of a unit-cell made of fused building blocks. In these typical schemes, the homo-oligomers that build a lattice cell include dimers, trimers, tetramers and hexamers. Table 1 summarizes the properties and constraints of each scheme.

Figure 2.

Typical plane group symmetries of a 2D unit-cell constructed from the fusion of two ODs. A light gray circle represents a dimer; a dark gray circle represents a trimer, tetramer or hexamer; a thick connector line represents a linker between two monomers. Light-gray numbers indicate the monomers that construct the cell, and dark-gray numbers show the monomers of the neighboring cells. (a) C4 symmetry built of dimers. (b) C4 symmetry built of tetramers and dimers. (c) P6 symmetry made of trimers and dimers. (d) P6 symmetry made of hexamers and dimers.

Table 1.

Properties of the 2D Unit-Cells Shown in Fig. (2)

Sub-Figure	Symmetry of Cell	Oligomers in Cell	Parallelism	Building Blocks
A	C4	4 dimers	anti-parallel	1a
B	C4	4 tetramers 4 dimers	identical	4
C	P6	2 trimers 5 dimers	The trimers are parallel	6
D	P6	4 hexamers 5 dimers	identicalb	6

^aThe building block is cyclic

^bThe parallelism constraint is imposed by the 1–4, 2–5, and 3–6 hexamer links

2.2. Selecting Oligomers and Linkers

The chain size of the selected oligomers is relatively small (here < 40 amino acids) due to the nanotube assessment times required by MD simulations. The linker that binds two ODs is short (here < 15 amino acids). In the setup phase the domains are placed on a plane according to the chosen symmetric scheme (Fig. (2)) with a minimal Euclidean distance between two adjacent termini, and no steric clashes. To model a flexible linker, we used ModLoop [34], which models a short peptide sequence between two fixed termini, or Modeller [35], such that the linker retains its predetermined conformation. We repeated this binding process for the construction of the whole unit-cell, and then minimized using “Steepest Decent” followed by “ABNR” (Adopted Basis Newton-Raphson). These were run by CHARMM [33].

2.3. Determining the Cell Parameters

The lattice constants {a,b,γ} affect the non-bonded interactions of the unit-cell with its identical neighboring images; setting too high values would cause weak non-bonded interactions, whereas setting lower values would cause geometric clashes or overlaps. We placed the unit-cell construct on the x-y plane so that its principal geometric axis coincides with the X-axis and the next largest coincides with the Y-axis. We then set a = Xmax-Xmin, b = Ymax-Ymin and c = ZmaxZmin. The constant γ is defined by the chosen lattice symmetry; γ = 90˚ for C2 or C4 symmetry (Fig. (2a and b)), and γ = 120˚ for P6 symmetry (Fig. (2c and d)). We solvated the constructed unit-cell in bulk water with dimensions corresponding to {a, b} while adding 9Å to both sides of c and counter-ions to a neutral pH. Then, after a few hundreds of local minimization steps, we ran constant pressure simulations with standard periodic boundary conditions for 0.5ns using NAMD [36]. We used the Nosé-Hoover Langevin piston method for pressure control [37], and the Langevin temperature control at 300K. This allowed a fine approximation of the volume of the unit-cell, from which we drew the refined lattice constants {a, b}. The result was used as an input for the next stage.

To wrap the unit-cell with its identical neighboring images into a cylinder, two additional wrapping parameters n₁ and n₂ had to be determined [18]. Based on the obtained lattice cell parameters {a,b,γ}, we ran local minimizations using cylindrical periodic boundary conditions with ascending n₁ values. For each n₁ we calculated the potential energy of the unit-cell. Fig. (3) depicts the potential energy values taken for different values of n₁ in two examples of observed nanotubes; the HIV-1 CA protein, and the surfactant-like peptide AcV₆D [19]. As n₁ increases the total energy decreases exponentially, indicating that a planar arrangement of cells is more favorable than cylindrical. However, our local minimization does not consider the non-bonded interactions between the two marginal cells that account for the closure of the cylinder. Instead, the cylindrical periodic boundary conditions only consider the non-bonded interactions of our unit-cell with its closest neighboring cells. Therefore, we picked the minimal value of n₁ for which the energy nearly reaches a plateau, as seen in both examples of Fig. (3). Once n₁ was obtained, we used the above method to find n₂. Since n₂ defines the helicity of the tube, its value is limited by n₁; a higher value suggests a more fibril-like structure rather than a tube. Finally, we obtained all five parameters that define the transformation of the unit-cell to its neighboring images. These parameters also define the outer radius of the tube, according to the following equation [18]:

$$r_{(\mathrm{tube})}=\frac{{\left[{\left(n_{1}a+n_{2}b\cos \mathrm{\gamma }\right)}^2+{\left(n_{2}b\sin \mathrm{\gamma }\right)}^2\right]}^{\frac{1}{2}}}{2\mathrm{\pi }}$$ (1)

Figure 3.

Obtaining the tube wrapping parameter n₁ using two examples of experimentally observed nanotubes; the HIV-1 CA protein nanotubes, and the surfactant-like AcV₆D nanotube. The potential energy of the unit-cell was measured for different values of the wrapping parameter n₁ which controls the tube curvature. The parameter n₂ was set to zero. In the HIV-1 CA protein case, the actual range of tube radii was obtained from the reconstruction of cryoEM images [21]. In the AcV₆D case, the range of tube radii was obtained from quick-freeze / deep-etch TEM image [19].

2.4. All-Atom MD Simulations

After obtaining the three lattice constants and the two wrapping parameters, we used our computational validation protocol [24] to assess the construct. This protocol uses explicit solvent together with cylindrical periodic boundary conditions to simulate a solvated unit-cell into a tube. Whilst the full atomic coordinates of the solvated unit-cell are preserved, the coordinates of the identical neighboring cells are calculated based on preprocessed transformation matrices. This enables measuring the non-bonded interactions of the unit-cell along the simulation. We carry out all-atom MD simulations into a nanotube, using the Image Facility of CHARMM [33].

We ran local minimization steps as described above to adjust the solvated cell into a wedge of a cylinder. Langevin Dynamics was used to restrain the water molecules at the exterior boundaries from escaping to the outside and inside vacuum with a low friction coefficient of 1.0 at 300°K, applying image centering. SHAKE was added to restrain the carbon-hydrogen bonds, with a 1fs timestep. The Verlet leap-frog integrator was used, and an isotropic periodic sum method was employed for calculating the long-range interactions. The non-bonded lists and the image lists were updated as necessary. These were calculated using the input transformation matrices. The minimum analysis period was set to 20ns and was varied according to the system size; small systems were run for a longer period of time. The CHARMM utility [33] was also used for trajectory analyzes. The system images were viewed by VMD [38].

3. RESULTS

3.1. P6 Plane Group Symmetry of Dimers and Hexamers

In vitro, the HIV-1 CA protein was observed to self-assemble into conical shapes as well as single-walled cylinders [39]. Recently, a 9Å resolution atomic model of the full-length wild-type monomer was reconstructed from cryoEM (cryo-electron microscopy) images [21]. Each monomer has two domains connected covalently by a short linker. The N-terminal domain (NTD) is the largest domain with seven α-helices, the linker is a loop of six amino acids and the C-terminal domain (CTD) contains four -helices. The monomers are arranged in an approximate P6 lattice symmetry [40], such that the NTDs self-associate to form a hexameric ring, whereas the CTDs self-associate to form a dimer. The dimerization of two CTDs connects each ring to its six neighboring hexameric rings. Thus, this natural example fully complies with the scheme illustrated in Fig. (2d).

The actual lattice constants of the HIV-1 CA protein hexamer were determined by Ganser-Pornillos and coworkers [21] to be {a=92.7Å, b=92.7Å, γ =120˚}. Experimental observations also revealed a wide range of nanotube radii (20nm-25nm). Altogether, using the tube radius equation [18], we set the wrapping parameters to {n₁=14,n₂=0}, which corresponds to an exterior radius of ~20.6nm. The construction of the HIV-1 CA protein nanotube was discussed in [24]. Fig. (4) presents the construction of the unit-cell according to our protocol and approximately a fourth round of the resulting nanotube.

Figure 4.

The construction of the HIV-1 CA Protein single-walled nanotube, according to the design scheme presented in figure (2d). (a) The monomer (PDB code:3dik) is comprised of a large N-terminal domain (NTD, in red) and a smaller C-terminal domain (CTD, in green) which are connected covalently by a short linker (blue) of six amino acids. (b) The unit-cell consists of six monomers. The NTDs (red) are on the tube outer surface, and the CTDs (green) protrude toward the tube interior. The lattice constants {a,b,γ} are depicted. (c) A perspective view of three rows of the CA protein tube as seen from the tube exterior. The NTDs are in red whereas the CTDs are in green. The wrapping parameters are {n₁=14,n₂=0} and the lattice constants are {a=92.7Å, b=92.7Å, γ =120˚}. The outer tube radius is therefore 206Å. A unit-cell is highlighted in a dashed line. (d) Approximately a fourth round of the tube, as seen from the tube axis perspective.

3.2. C4 Plane Group Symmetry of Anti-Parallel Dimers

We constructed a single-walled protein nanotube with a C4 symmetry lattice cell, comprised of dimers only. Fig. (2a) illustrates the corresponding 2D scheme. The building block is cyclic, and is made of four antimicrobial Magainin 2 dimers (PDB code 1dum) [41]. Each monomer is an α-helix, and all helices are anti-parallel. Each monomer has 23 amino acids. The structure is shown in Fig. (5). In the Magainin 2 dimeric crystal structure, the monomers bind to each other through hydrophobic residues, whereas the charged and polar residues point toward the exterior environment (Fig. (5a)). Most of the charged residues are positive. Therefore, a C4 symmetry construct of four monomers ensures high level of electrostatic repulsion in the central cavity of the cell (Fig. (5b)). Such repulsion may aid in the geometrical stabilization of the cell (and hence nanotube) over time. Three different types of Magainin 2 based systems were constructed. These types differ by the linker secondary structure. In type 1 we modeled a poly-glycine loop to reflect a very flexible linker. Type 2 linker is comprised of poly-prolines and type 3 is comprised of a short helix from the PDB - both types rigidify the system. Fig. (5c) presents the three types of linkers.

Figure 5.

The construction of a fused cyclic peptide from the antimicrobial homodimer Magainin 2 (PDB code: 1dum) according to the scheme shown in figure (2a). The cyclic peptide has C4 plane group symmetry. (a) The homo-dimer crystal structure. Each monomer is in different color (red and black). The side-chains are colored by their polarity; basic – blue, acidic – red, polar – green, hydrophobic – light gray. The inter-monomer interactions are hydrophobic, whereas the charged and polar side-chains point to the surface. (b) The four monomers are on a planar surface such that their center of mass lies on the origin. The black monomers are to be covalently linked through identical short linkers. The charged side-chains point towards the central cavity of the cell. (c) Three types of linkers were used to join adjacent monomers: poly-glycine (left), poly-proline (center) and α-helix (right). These linkers represent different levels of backbone flexibility. The backbone atoms are in green ribbons and the residual atoms are in blue.

3.2.1. Glycine Loops

Based on the Euclidean distance between the termini of two adjacent monomers, we constructed a cyclic peptide of four monomers connected by four poly-glycine linkers. Five residues were the minimum required to close the gaps. After solvation, ionization and minimization, we applied Langevin Dynamics keeping the pressure fixed for 0.5ns. The lattice constants obtained were {41Å, 41Å, 90˚}, and the wrapping parameters - {16,0}. Unfortunately the subsequent simulation stopped after 12ns due to steric hindrance within the cyclic unit-cell. Repeating the procedure with very flexible poly-glycine linkers of 12 residues obtained the lattice constants {42Å, 42Å, 90˚} and wrapping parameters {16,0}. However, the simulation halted after 5ns, again due to steric hindrance. At this stage we decided to introduce a linker of higher rigidity, a poly-proline loop, to allow a relaxed conformation of the cyclic peptide, and at the same time, constrain the motion within the unit-cell.

3.2.2. Proline Loops

A left-handed poly-proline II helix (PPII) is formed when sequential residues adopt backbone dihedral angles of roughly (φ=−75˚, ψ=150˚) and have trans isomers of their peptide bonds [42,43]. The PPII helix contains exactly three residues per turn, and the rise per turn is approximately 3.1Å. After measuring the Euclidean distance between two adjacent monomer termini, we placed four poly-proline linkers of five residues each to fill the gaps between the termini and create a cyclic peptide.

Following the procedure as above, lattice constants of {38.2Å, 38.2Å, 90˚} were obtained. Using local minimization with cylindrical boundary conditions, we obtained the wrapping parameters {16,0}. Finally, Langevin Dynamics was run for 30ns. Fig. (6a) presents snapshots along the simulation. As can be seen during the simulation, adjacent or opposite fragments of the cyclic peptide tend to create intra-molecular interactions. Thus the initial 2D structure of the unit-cell which possesses a central pore is distorted. Nevertheless, the inter-molecular interactions with the neighboring images prevail, and therefore, the nanotube preserves its physicochemical stability. Approximately half round of the resulting nanotube is seen in Fig. (6b). The coordinates were produced by the Image Facility of CHARMM using the lattice constants and wrapping parameters of this specific tube. Fig. (6c) highlights the unit-cell position of the charged residues with regard to its neighboring cells. Almost all of these hydrophilic side-chains still point towards the central cavity of the cell, thus maintaining the hydrophobic interactions between the cells. To further rigidify the initial structure of the unit-cell and preserve the central cavity of the cyclic peptide, we introduced helical linkers [15].

Figure 6.

A cyclic peptide made of monomers from the antimicrobial Magainin 2 (PDB code: 1dum) joined by identical poly-proline linkers and simulated for 30ns. (a) The results of MD simulation into a nanotube. At time=0ns the unit-cell appears solvated in water (blue beads) with neutralizing counter-ions (yellow beads). The four monomers of the cyclic peptide are in red ribbon, whereas the poly-proline linkers are in gray. The left perspective is as viewed from the tube exterior, whereas the right perspective exhibits the unit-cell with the four-fold axis vertical. The central pore in the unit-cell changes its 3D shape along the first 20ns of simulation and preserves it later on. (b) Approximately half of the nanotube after 30ns of simulation. Schematic illustrations exhibit the corresponding perspectives. Each cell is in different color. (c) A close-up on the charged residues of the unit-cell (in blue ribbons) at 30ns, viewing from the tube exterior perspective. The positively charged residues are in blue sticks, negatively charged in red.

3.2.3. Helical Linkers

Insertion of short linker helices to create a cyclic peptide is challenging since the covalent links at both ends are constrained by the limited range of backbone dihedral angles of α-helix. We cut a short α-helix of 13 residues from the structure of Follistatin (PDB code: 2p6a:c). The helix was chosen at random, and its length was determined by the Euclidean distance between the adjacent monomers in the unit-cell. We used Modeller [35] to bind each helix on both ends, while keeping the Magainin monomers still and allowing only the linkers to move. According to Table 1 the cyclic peptide illustrated in Fig. (2a) is organized in anti-parallel fashion. As a result, the covalent linkage of four helices to create a cyclic peptide produces an asymmetric square (Fig. (7)).

Figure 7.

A cyclic peptide comprised of monomers from the antimicrobial Magainin 2 (PDB code: 1dum) joined by helical linkers. The four identical linkers (in gray) are short -helices of 13 amino acids extracted from the structure of Follistatin (PDB code: 2p6a:c). The unit-cell appears in two perpendicular perspectives; as seen from the tube exterior (left) and when the four-fold axis is vertical (right). At 0ns, the unit-cell is locally minimized, and presented in bulk water (blue beads) with neutralizing ions (yellow beads). The cell shape is asymmetric due to the anti-parallel constraint induced by the design of a cyclic peptide (Table 1).

We followed our protocol by obtaining the lattice constants as {43.55Å, 43.55Å, 90˚}, followed by the wrapping parameters {16,0}. Finally, we applied Langevin Dynamics using cylindrical boundary conditions for 30ns. Fig. (7) presents the simulation snapshots every 10ns. The asymmetric 3D structure of the cyclic peptide maintains its structure along the simulation. As a result, the central pore does not collapse or gets distorted. Moreover, the fused monomers, which are initially classified as helices, also maintain their initial conformation. However, as in the poly-proline case, there is still a slight tendency along the simulation to create intra-molecular interactions while preserving the inter-molecular interactions with the neighboring images.

We compared the root mean-square deviations (RMSD) of poly-proline linkers and helical linkers systems. (Fig. (8a)) depicts the C RMSD of the unit-cells along the simulation. Since the reference structure is the minimized system, the high RMSD value at time 0 reflects a structural change the unit-cell has gone through during the first few picoseconds of equilibration. Neglecting the first few nanoseconds, it is clear that the helical linkers system preserves its original structure and orientation the most. This is also evident from the non-bonded energy of the unit-cell with its neighboring cells (Fig. (8b)). Here, the poly-proline linkers system fluctuates more than the helical linkers system and therefore exhibits a lower physicochemical stability over time.

Figure 8.

Structural and energetic analyzes of the poly-proline linkers system and the helical linkers system along 30ns of simulation. (a) The C RMSD calculated with regard to the systems structures after minimization. (b) The non-bonded energy of the unit-cell with its neighboring images.

4. DISCUSSION

We devised a shape-guided computational strategy to construct protein nanotubes without limitations on their size or diameter. The strategy is based on creating monomers by fusing two identical or distinct domains from native homo-oligomers and retaining their native association. The resulting fused monomers therefore possess two domains which self-assemble with identical copies of themselves. Via self-assembly a vast range of nanostructures can be obtained. This mechanism can be tailored to create nanotubes with variable shapes, sizes and diameters for various biological and non-biological applications.

Our strategy utilizes the natural repertoire of peptides and protein building blocks whose structures are available. This repertoire is extensive, and the combinations it can produce are vast. The challenge is to correctly engineer these in predefined geometries and chemical bonding while retaining their preferred associations. The innovative scheme of Padilla et al. [15] coupled with the powerful strategy of Tsai et al. [18] and our computational protocol [24] suggest a useful strategy to explore.

In this work we examined the already observed HIV-1 CA protein which self-assembles into conical shapes and single-walled nanotubes in vitro. Noteworthy, other retroviruses capsid proteins have also been observed to form nanotubes, in vitro. These include the Rous Sarcoma Virus (RSV) [44], the Murine Leukemia Virus (MLV) [45] and the Equine Infectious Anemia Virus (EIAV) [46]. Together with HIV-1 CA protein, these proteins share a common structure of a monomer comprised of a large NTD and small CTD which are covalently linked by a short flexible loop. Moreover, all these monomers were observed to self-assemble in the same manner, where the NTDs form a homo-hexamer and the CTDs form a homo-dimer. Thus, we hypothesize that this family of retroviruses can be attributed to our 2D assembly scheme, presented in Fig. (2d). To assemble them correctly we need the 3D structures of both interfaces: hexamer and dimer. Currently, both structures exist for HIV-1 CA protein only. Once both interfaces of the other retroviruses are available, their nanotubes could similarly be constructed as described here.

We addressed the challenge of ab initio construction of novel monomers which self-assemble into novel nanostructures focusing on the choice of the linker between the two ODs. The linker choice is critical, since it needs to fixate the fused domains in their relative positions. Therefore, as an example of ab initio construction, we chose the Magainin 2 homodimer [31] and followed a C4 symmetry scheme of fusing a cyclic peptide, while introducing three different types of linkers, one at a time. These types differ in their rigidity, and thus, in their ability to maintain their 3D structure throughout the simulation. Even though our simulations were successful with either poly-proline linkers or helical linkers, the helical linker maintained the initial 3D structure of the system best. Structural and thermodynamic studies validate this conclusion.

Nonetheless, we observed that in the natural case of the HIV-1 CA protein nanotube the linker is a short random loop. Looking at the HIV-1 CA nanotube Fig. (4) it is clear that the self-assembly of a single monomer creates a very compact nanostructure, with no cavities through which a small molecule could penetrate. Thus, the high flexibility of the linker has almost no dynamical effect on the overall conformation of the self-assembled nanotube. On the other hand, the Magainin 2 based cyclic peptide has a central pore which may allow such penetration into and out of the tube. To maintain the initial geometry of the pore during dynamics and to prevent a collapse, it is essential to rigidify the linkers which are the weak fragments of the cyclic peptide. Thus, it appears that when the 3D protomeric structure in the unit-cell is compact, a flexible dynamic linker may also be suitable, whilst a porous unit-cell requires a more rigid linker.

During the construction process, we faced the challenge of determining the optimal radius of the self-assembled tube. We realized that as the radius increments, the total potential energy of the system decreases exponentially. However, this behavior is deceiving since the cylindrical periodic boundary conditions method does not allow considering the non-bonded interaction energy between the two marginal cells. Hence, to overcome this problem, we chose radii values for which the energy nearly reached a plateau. This concept was reinforced by the analysis of the radii of the HIV-1 CA protein nanotube as well as the surfactant-like peptide nanotube AcV₆D which were both observed experimentally.

Here we constructed a fused protein monomer from Magainin 2 homo-dimer, and simulated its self-assembly into a single-walled nanotube. In principle, if there are identical protomeric monomers and the concentration of the solute is high, structural propagation can be indefinite. The surfactant-like peptide AcV₆D self assembles into a tube [19]; another example of tube formation is the microtubulin [47]. There, the interdigitation of the microtubulin building blocks prevents closure into a vesicle. A similar situation exists in other proteins, like the bacterial flagellar [48]. However, the non-functional diphenylalanine (FF) was observed in the test tube to form both a tube and a vesicle [49]. Thus, some monomers favor an association into either tubes or vesicles, whereas others can form both. For the latter case, it can be expected that the preferred organization is concentration-dependent. In the case of FF, experiments revealed that at high peptide concentration, a tube was formed; at low concentration, a vesicle. Moreover, a tube has a one-dimensional curvature, whereas a vesicle has two. At a low concentration, the limited extent of non-polar buried surface area in a short tube drives the system to closure since a vesicle has a larger buried surface area. On the other hand, when the concentration is high, there is no such chemical pressure on the system. A long tube buries extensive non-polar surface. Thus, when the concentration is high, there is a high chance of vesicles fusing together to form a long tube, or an elongated vesicle, as shown by coarse-grained Monte Carlo simulations [50]. Therefore, based on our simulations that exhibited geometrical and thermodynamic stability, we hypothesize that at a high enough concentration, our fused cyclic peptides can form long nanotubes.

Our ab initio construction was applied to systems with approximate local C4 lattice symmetry, but it is not limited to this symmetry and can be extended to assess other types of symmetrical systems where all the fused monomers are identical, and where these are assumed to assemble into cylinders. A future development of generic simulation protocols for handling other geometric structures might further facilitate the assessment of a broader range of novel protomeric structures which are assembled from such fused homo-oligomers.

Constructing novel protein nanostructures with desired properties is challenging. There is a great necessity for experimental and computational strategies toward this aim. A computational strategy is a valuable starting point, since it saves enormous time and resources by ruling out unlikely solutions. However, experimental validation is the next required step for any computational solution.

LIST OF ABBREVIATIONS

MD

Molecular dynamics simulations

HIV-1

Human immunodeficiency virus type 1

OD

Oligomerization domain