Protein dimers and higher oligomers in detergent micelles

Vpu-WT and mutant Vpu proteins were expressed in HEK 293 cells (Fig. 1). SDS-Page analysis from cells expressing Vpu-WT revealed four bands (Fig. 2a, lane 1). The SDS-PAGE analysis of the double mutants Vpu-DD and Vpu-NN, which lack phosphate groups at the serines, showed only a single band each on the SDS-PAGE at various molecular weights due to the decreased migration rate of the negative charged Vpu-DD upon denaturation (Fig. 2a, lanes 3 and 9)2829. Vpu-52D and Vpu-56D each show two bands (Fig. 2a lanes 5 and 7). Taken together, these results indicate that the four bands of Vpu-WT represent the following from high to low molecular weight, (i) phosphorylation of both of the serines, Ser-52 and Ser-56, (ii) single phosphorylated serines at position 56 and (iii) position 52, and (iv) fully non-phosphorylated serines. The ratio between phosphorylated and non-phosphorylated Vpu remains the same as found in measurements directly from cell pellets using anti-strep-tag antibody for Vpu in Western blot (data not shown).

The thrombin enzyme cleaves the strep-His8 fusion tag from Vpu-WT and the mutants (Fig. 2a lanes 2, 4, 8 and 10 and Supplementary Fig. S1). The pattern mentioned for uncleaved Vpu does not seem to be affected by thrombin treatment.

The fusion tag-free Vpu was further purified by size-exclusion chromatography and eluted with four peaks (Fig. 2b). Vpu-WT showed two peaks, a smaller peak at 9.5 ml representing large protein/detergent complexes (P1 in Fig. 2b) and a larger peak representing smaller protein/detergent complexes (P2 in Fig. 2b) at 13.5 ml. Mutant Vpu-56D shows a similar pattern. For Vpu-52D and Vpu-DD the peak of the large complexes was not resolved. Vpu-NN showed the peak of the large complexes being larger than that of the smaller complexes. SDS-PAGE analysis identified the two peaks representing Vpu protein and its respective mutations (Fig. 2c). The third and fourth peaks correspond to thrombin and strep-His8 fusion tags, respectively.

Multi-angle light scattering analysis identified that P1 and P2 correspond to molecular weights of 174.7 ± 18.4 kDa and 18.0 ± 1.9 kDa, respectively (Table 1). The respective averaged oligomeric state was calculated to be around 19.0 ± 2.0 for P1 and 2.0 ± 0.2 for P2. Thus, Vpu is able to exist in two oligomeric states, which are most likely a dimer and higher oligomer.

Modulation of the dynamics of Vpu-WT, Vpu-NN and Vpu-DD oligomerization by the two phosphorylation sites

After purification of the proteins from a stock solution, the peak ratio between the higher oligomer (referring to P1) and the dimer (referring to P2) for Vpu-WT and Vpu-DD was in favor of the dimer for all ionic strengths investigated, 50, 150 and 300 mM NaCl (Fig. 3a). The peak of the higher oligomer is the largest at the highest ionic strength of 300 mM NaCl for the two proteins. The peak area of the higher oligomer was largest for Vpu-NN at all ionic strengths (Fig. 3b). Higher ionic strength screens the negative charges at the serine sites and even the partial charges of the amide group in asparagine indicating electrostatic type interaction modulates assembly.

Immediately after purification of Vpu-WT from a stock solution, the peak of the dimer was larger than that of the higher oligomer (Fig. 4a, top graph). Repeating the purification from the stock solution over a period of 12 days revealed a gradual increase in the higher oligomer. A slower increase in the peak of the higher oligomer was observed for Vpu-DD. Purification after 7 days showed just the beginning of a small peak for the dimer (Fig. 4a, middle graph, green line). In the case of Vpu-NN, the peak of the higher oligomer was larger than that of the dimer from the first day of the experiment and increased even more over three days, finally reaching a plateau over a longer period (Fig. 4a, lower graph).

The dynamics data was plotted as area of the peak of the higher oligomer (AP1), divided by the total area of AP1 and the peak area of the dimer (AP2), AP1/(AP1 + AP2), over time for Vpu-WT with a double logarithmic growth curve (Fig. 4b, black and Table 2). Vpu-DD (Fig. 4b, red) and Vpu-NN (Fig. 4b, blue) can both be fitted with a single function (see also Table 2). Vpu-NN (c = 1.05 day−1) and Vpu-DD (c = 0.56 day−1) mark a fast and slow increase in the area of the higher oligomer, respectively. Vpu-WT exhibited a fast increase (c = 2.35 day−1) first, followed by a slow increase (c = 0.31 day−1), similar to the afore-mentioned growth rates of Vpu-NN and Vpu-DD, respectively. As a result, Vpu-DD, due to their negative charges at the two serine sites tended to assemble very slowly reaching a final assembly ratio of a = 0.22, whilst Vpu-NN, having charges removed at the site of the two serines, assembled very quickly reaching the largest assembly ratio of a = 0.78. Therefore, the fast increase in the peak of the higher oligomer of Vpu-WT should be due to the assembly of non-phosphorylated Vpu, whilst the slower increase of that peak should be due to the assembly of both, single and double phosphorylated Vpu proteins. The single phosphorylated Vpu proteins obscure the plot in as much they show ‘mixed’ assembly dynamics. The negative charges of the phosphorylated serine site slowdown or even prevent oligomerization.

Sequence of mechanical events upon oligomerization by CGMD simulations of Vpu-WT and Vpu DD in hydrated lipid bilayers

The computational model of Vpu was generated by bending a helical motif of Vpu1–52 at the site of the EYR motif as reported previously30 (Fig. 5a, left). Sequence alignment shows that the strains used for building the computational models and the one used in the experimental study share 79% sequence identity (data not shown). Two copies of the kinked Vpu1–52 are run in a single lipid patch in an inverted orientation for 100 ns (Fig. S1). Both of the helices remain in both of the structures. Both of the structures (Fig. S1, black and red curves) show larger root mean square fluctuation (RMSF) values for residues Glu-28 to Ile-32. The structure shown by the red lines in Fig. S1, named Vpu1–52, was chosen for the next step, since the residues Leu-33 to Arg-40 of its second membrane-associated helix show lower RMSF values than those of the structure represented by the black curve. Residues Ile-38 to Ala-49 of the second, membrane-associated helix of Vpu1–52 are overlapped with the N terminal side of the NMR-based structure of Vpu36–8116 to finally generate full-length Vpu1–80 with united atoms. MD simulation of two copies of Vpu1–80 showed a leveling off of the root mean square deviation (RMSD) values after about 10 ns (Fig. S2, upper left). One of the Vpu1–80 structures showed large fluctuations of the amino acids in the kink region (Ile-32 to Gln-35, Fig. S2, upper right, red curve). These residues define the intermediate parts between the helices.

Based on these values and the leveling of the RMSD values this structure was considered further for CGMD simulations as Vpu-WT (Fig. 5a, left and Fig. S3). In Vpu-WT the serines are not phosphorylated. At this stage the CG mutant model Vpu-DD was generated by replacing the two serines with two aspartic acids. A total of 16 Vpu-WT and Vpu-DD are embedded in a hydrated lipid bilayer (0 ns, Fig. 5a, right) and simulated for 10 μs (Fig. 5b). The 16 Vpu-WT started to assemble into two large units consisting of 3 and 13 proteins (Fig. 5b, left). Vpu-DD at the end of the simulation shows three units of 1, 6 and 9 proteins (Fig. 5b, right).

After about 1 μs, Vpu-WT reached an oligomerization ratio of nearly 1 (a = 0.98, Table 2), compared to Vpu-DD which reached a value of about a = 0.58 (Fig. 6a and Table 2). The oligomerization ratio of Vpu-WT was due to large values of both TMD assembly (a = 0.68) and the cytoplasmic domain (a = 0.27) (Fig. 6b). For Vpu-DD as well, the TMD assembly contributed the most (a = 0.50) to the overall oligomerization compared to the cytoplasmic domain (a < 0.1) (Fig. 6c). Analysis of the growth curve showed that the growth rates c of the TMDs are almost independent of the phosphorylation state. The higher growth rate of the cytoplasmic domains of Vpu-DD compared to the rate of Vpu-WT is due to an almost sudden assembly of a few proteins (Table 2). In this state the growth rates were not compared with those of the experiments due to the different time scales.

Long lasting dimers of both Vpu-WT and Vpu-DD form close contact areas within the TMD along the line of valines (residues 6 to 13) of one monomer with the leucines and isoleucines of the other monomer31. Pore like structures with eventually serines (Ser-23 of the TMD) pointing towards the center of a putative pore have not been observed.

A striking feature is that assembly of Vpu-WT is driven by an early assembly of the cytoplasmic domain within 0.5 μs to an oligomerization ratio of ∼0.28 followed by an increasing rate of assembly due to the TMD within the first micro second of up to ∼0.70 (Fig. 6b). For Vpu-DD the sequence is reversed by assembly via TMDs of up to ∼0.50 oligomerization followed by cytoplasmic assembly which remains a ratio of ∼0.05 (Fig. 6c).

The oligomerization ratio of mixtures of Vpu-WT and Vpu-DD (12 Vpu-WT and 4 Vpu-DD, 8 Vpu-WT and 8 Vpu-DD as well as 4 Vpu-WT and 12 Vpu-DD) achieve maximum level at a later time step as for the ‘pure’ systems (Fig. 6d). Deriving the growth rate, c, from a fitting of the curves with a double logistic growth function indicates that in all the mixtures the first rate is faster than the second rate except for the mixture of 12 Vpu-WT and 4 Vpu-DD (Supplementary Table 2). Oligomerization of the TMDs does not follow this trend due to internal reorientations within the patches (Supplementary Table 2 and Supplementary Fig. S5).

Rate of oligomerizaion is driven by the assembly of the TMD of Vpu independent of negative charges due to phosphorylation of the two serines 52 and 56, while maximum degree of oligomerization depends on the negative charges.

Comparison of computational and experimental data

The Vpu model in respect to its cytoplasmic domain relies on NMR spectroscopic investigations in which the peptide is non-phosphorylated16. The structural feature is of two helices connected by a loop, which harbors the two serine sites 52 and 56. Another study in which a much shorter peptide, Vpu41-62, is used indicates that a short helical part towards the C terminal side disappears upon phosphorylation but the overall shape of a loop conformation remains3940. Thus, the CG models Vpu-WT and Vpu-DD reflect reliable structural features.

The computational system is designed to represent an estimate of the in vivo system. The proteins are embedded within a planar lipid bilayer of a single type of lipid molecule. Thus, the question of whether the Vpu proteins would oligomerize in the same way and with the same dynamics when embedded in a lipid bilayer can be addressed. In this study, the computational models exhibit the same behavior as found experimentally. The dimer is smallest unit to assemble. The level and growth rate of oligomerization of Vpu without the phosphate groups is bigger and faster than Vpu with phosphate groups. In addition, structural features taken from the simulation data allowed specification of the interaction dependent on the cytoplasmic domain and TMD with the latter contributing mostly to the oligomerization ratio. The coarse-graining investigations of conformational dynamics are limited to emphasizing the diffusive aspects of the protein in the bilayer. The computational data represent a semi-quantitative analysis of protein diffusivity which matches the experimental findings. The number of Vpu was chosen to be 16 instead of the putative 19 Vpu molecules calculated from the experimental analysis. This is done due to the need to use a squared lipid patch with regularly positioned molecules of 4 Vpu to build the larger patch.

In this paper the dynamics of oligomerization of the 16mer is segregated into contributions of the transmembrane and the cytoplasmic domain in a quantitative way to parallel the experimental data set in respect of growth rate and maximum oligomerization ratio. In an earlier computational study structural features of the assembly of two Vpu proteins either as Vpu-WT and Vpu-DD are reported31. The sequence of occurrence of individual oligomers of Vpu-WT and Vpu-DD during the simulation of lipid patches with up to 16mers and 36mers is explored on a qualitative level.

The sequence of protein assembly

The computational models were built alongside a biological pathway6. It is assumed that there is an equilibration of the monomeric unit of the membrane protein first, due to the distance between ribosomes (e.g., 500 Å apart from each other)3. The structure of the protein obtained in this state can be considered to be a ‘molten globule’ or ‘compact intermediate’, an intermediate state before the formation of a fully functional channel3. In a subsequent step larger assemblies are formed. A general feature is that the assembly of the host channels is in the minute to hour range41. Considerable time is dedicated to the folding of the subunits, a feature that is not explicitly considered in this study in as much CGMD simulation restrains the structure in its internal dynamics.

The experimental part of this study verifies a “dimer” first step of oligomerization of Vpu as simulated in an earlier study31. This formation of a dimer is driven by the association of the TMDs as indicated from computer simulations. In the dimer the two phosphorylation sites are the furthest apart due to electrostatic charge repulsion. During assembly into larger units the exposed negative charges of the phosphate groups have to be taken care of. Whilst the cytoplasmic domain directs oligomerization, the TMDs are responsible for holding the oligomer together. Based on this study, how Vpu is assembled and how it eventually reaches a pore-like structure is shown in the schema in Fig. 7. Some of the individual monomers assemble into dimers via association of TMDs (Fig. 7a,b). Within a larger assembly or patch (Fig. 7c), dimers and additional monomers are able to adopt conformations, which can either be channel-like (as marked by the red circles) or not channel-like (as marked by the dashed grey circles). Conformational changes of the proteins will allow e.g., to the transformation of Vpu proteins from the not channel-like region into the channel-like regions. It is always possible that the assemblies can be made out of the dimers or a mixture of both dimers and monomers. The generation of protein patches for more than 16–20 proteins may be restricted due to thermodynamic considerations taking into account protein binding affinities and protein dynamics due to the membrane environment.

The phosphorylation sites are necessary for the role of Vpu in initiating the ubiquinone-dependent downregulation of the proteins to which it attaches. According to this study, those sites seem to have another role in the regulation of the assembly of Vpu itself. Whether the interaction of Vpu with host factors occurs with Vpu as a monomeric or dimeric unit still needs to be investigated. It is also possible that Vpu interacts with host proteins in its patch-like assembly.

Dimerization is generally an essential first step in the oligomerization of membrane proteins. Specific sites within the protein, such as the two phosphorylation sites in the cytoplasmic domain of Vpu, play a modulating role during the initial step of assembly whilst the TMD defines the stability of the oligomer.

In the special case of Vpu, the phosphorylated serines have an additional function. Besides functioning in the initiation of the downregulation of an attached host protein it also regulates the oligomeric state of Vpu.

Plasmids, cells and transfection

Human codon optimized Vpu genes derived from HIV-1 strain NL4-3 (P05923: MQPIQIAIAA10 LVVAIIIAIV20 VWSIVIIEYR30 KILRQRKIDR40 LIDRLIERAE50 DSGNESEGEI60 SALVEMGVEM70 GHHAPWDIDD80 L) were synthesized by multiple overlapping polymerase chain reaction (PCR) and cloned into the expression vector pTT-strep-his8 harboring a thrombin cleavage site for removing the tags. The cytoplasm domain mutants of single mutated Vpu, Vpu-S52D and -S56D, as well as double mutated Vpu, Vpu-S52/56D and Vpu-S52/56N were generated by quick-change site-directed mutagenesis and overlapping PCR respectively, by standard methods using the Phusion-II polymerase (New England BioLabs). For the single mutants, the second serine site is still available for phosphorylation during protein expression. Vpu with the mutations was also expressed using the vector pTT-strep-his8. All constructs were verified by sequencing analysis.

Protein expression

Human embryonic kidney (HEK) 293 cells were maintained under standard humidified conditions (37 °C and 5% CO2). The cells, medium and serum were purchased from Invitrogen. Plasmid transfection into suspension cells was performed with the Transfection System (Invitrogen) according to a previously reported protocol42.

Protein purification

Starting from a 1-liter culture, Vpu expressing HEK 293 cells were lysed by suspending in buffer (0.05 M Tris, pH8, 0.15 M NaCl, 20% glycerol, 1 mM PMSF (phenylmethanesulfonylfluoride) and 1 ng/ml DNAase). The fully suspended cells were disrupted twice on ice by Microfluidizer (M-110 L). Cell lysate was centrifuged in a JA25.5 rotor (Beckman Coulter) at 12,000 g for 35 min at 4 °C to remove unbroken cells and debris. The supernatant was then centrifuged in a Ti 45 rotor (Beckman Coulter) at 40,000 rpm for 1 h at 4 °C to separate the membrane pellet.

Vpu membrane pellets were homogenized with 0.5% (wt/vol) lauryldimethylamine-oxide (LDAO) detergents and incubated overnight at 4 °C. Detergent-solubilized membrane proteins were separated from insoluble material by centrifugation for 40 min at 12,000 g at 4 °C in JLA10.5 (Beckman Coulter). The supernatant was subjected into Strep-Tactin resin column by gravity. The resin was initially washed with high-salt buffer (0.05 M Tris, pH 8, 0.5 M NaCl, 1 mM ethylene diamine tetra acetate (EDTA), 0.05% (wt/vol) LDAO), then a low-salt buffer (0.05 M Tris, pH 8, 0.15 M NaCl, 1 mM EDTA, 0.05% (wt/vol) LDAO) and eluted with low-salt buffer containing 2.5 mM desthiobiotin (Sigma-Aldrich). The eluted protein was concentrated using an Amicon Ultra Centrifugal Filter (Millipore). The encoded protein contains a thrombin cleavage site (LVPRGS motif) cleavage site separating Strep-His8 tag from the C terminus of Vpu. Thus, a ratio of Thrombin (Sigma-Aldrich) was added to purified Vpu proteins at room temperature overnight. The mixture was concentrated using an Amicon Ultra Centrifugal Filter (Millipore).

Protein analysis

Protein concentration in the samples was quantified by Nanotrop (Thermo). Protein purity was analyzed by SDS-PAGE on 16% acrylamide gels, stained by Rapid Stain. Size-exclusion chromatography was performed on a FPLC system (AKTA, GE) using a Superdex 200 10/30 size exclusion column pre-equilibrated in the buffer (0.05 M Tris, pH 8.0, 0.15 M NaCl and 0.05% (wt/vol) LDAO). The flow rate was set at 0.5 ml/min. Absorbance at 280 nm was monitored and recorded. The fraction from the major peak was collected in 0.5 ml fractions.

SEC/MALS measurement

The mass determination of purified Vpu protein and LDAO detergent in Vpu-LDAO micelle was measured by a combination of size exclusion chromatography (SEC) coupled with three detectors: Multi-Angle Light Scattering (MALS), Refractive Index Detection (RI) and UV280nm absorbance (Wyatt Technology). The whole system was pre-equilibrated with 50 mM Tris (pH 8.0), 150 mM NaCl and 0.05% LDAO buffer. Vpu-LDAO micelles were injected into a Superdex 200 10/30 column at 0.3 ml/min in buffer and then passed through the multi-angle light scattering detector and refractive index detector continuously. The data was analyzed by ASTRA software (Wyatt Technology).

Construction of full-length Vpu model

An ideal helical structure of the first 52 amino acids of Vpu (Vpu1–52, HV1S1, P19554) was generated using the MOE software suit (www.chemcomp.com). The sequence used for Vpu1–52 was:

The helix was bent around residues Glu-28 to Ile-32 so that the helical stretch from residues Leu-33 to Ser-52 aligned with the membrane surface as described earlier30. Asp-39 was pointing towards the bilayer surface and Arg-48 was pointing into the aqueous phase, according to experimental findings43. In this configuration, the ϕ/ψ values of the amino acids in the bend are as follows: Glu-28: ϕ/ψ = −70.4°/0.2°, Tyr-29: ϕ/ψ = −65.2°/−42.5°, Arg-30: ϕ/ψ = −84.7°/−13.8°, Lys-31: ϕ/ψ = −86.2°/10.0°, Ile-32: ϕ/ψ = −57.6°/−18.0°. Two of these structures (each 530 atoms including united atoms), were embedded in a hydrated lipid bilayer so that they were inverted to each other and simulated for 100 ns. The last frame of the 100 ns MD simulation of Vpu1–52 (see red RMSD and RMSF curves in Supplementary Fig. S2) was chosen to generate full-length Vpu1–81.

The first structure out of the 20 structures of the models deposited in the PDB data bank (PDB ID: 2K7Y, HV1H2, P05919; residues 36 to 81)16, GSIDR40 LIDRITERAE50 DSGNESEGDQ60 EELSALVERG70 HLAPWDVDDL80, was chosen to be merged with Vpu1–52 from the MD simulations as follows. Residues Ile-39 to Arg-45, which adopt a helical motif, were merged with the helical motif of residues Ile-38 to Arg-44 of Vpu1–52 on the level of the Cα atoms to generate full-length Vpu, Vpu1-80 henceforth referred to as Vpu-WT.

Two of these structures (790 atoms including united atoms) were embedded into a fully hydrated lipid bilayer as mentioned above. The last frame of the 100 ns MD simulation of Vpu1-80 (see red curves for root mean square deviation (RMSD) and root mean square fluctuation (RMSF) in Supplementary Fig. S3) was chosen to generate a coarse grained (CG) model Vpu-WT31.

A computational model of mutant Vpu-DD, was generated at the full-length structure prior to start the CGMD simulations by replacing Ser-52/56.

Classical MD simulations

MD simulations on the systems reported in the present study were carried out with GROMACS 4.5.5 using Gromos96 (ffG45a3) force field with an integration step size of 2 fs. The temperature of the protein, lipid, and the water molecules were separately coupled to a Berendsen thermostat at 310 K with a coupling time of 0.1 ps. A semi isotropic pressure coupling was applied with a coupling time of 1.0 ps and a compressibility of 4.5e−5 bar−1. Long-range electrostatics were calculated using the particle-mesh Ewald (PME) algorithm with grid dimensions of 0.12 nm and interpolation order 4. Lennard-Jones and short-range Coulomb interactions were cut off at 1.4 and 1 nm, respectively.

Vpu1–52 and Vpu1–80 proteins were put on either side of the lipid bilayer consisting of 228/228 lipids (11856/11856 atoms) and hydrated with 11671/11473 water molecules (35013/34419 atoms) (Supplementary Figs S2 and S3). Lipids which overlapped with the peptide were removed. The system was then minimized (5000 steps of steepest descent and 5000 steps of conjugate gradient) and equilibrated for a total of 8.65 ns. Equilibration was achieved by gradually increasing the temperature from 100 K to 200 K and then to 310 K, whilst keeping the peptide fully restrained (k = 1000 kJ mol−1 nm−2). The first two simulations (at 100 K and 200 K) were run for 200 ps, the last simulation (at 310 K) was run for 8.5 ns. It was verified that the space between helix 2 and lipid membrane did not contain any water molecules, since the hydrophobic residues were pointing toward to the lipids. Holding the system at 310 K, the restraints, imposed by a force constant k on the peptide, were released in two steps (k = 500 kJ mol−1 nm−2, k = 250 kJ mol−1 nm−2), running each of the steps for 500 ps. The unconstrained systems were submitted to production runs of 100 ns.

The last frame of the 100 ns MD simulation of Vpu1–80 was used to replace the serines at site 52 and 56 into aspartic acid (Vpu1–80-DD).

Coarse-grained MD simulations

Coarse-grained molecular dynamics (CGMD) simulations using the Gromacs software were performed using the MARTINI force field v2.0 for water and v2.1 for protein4445. The Martini script was used to convert Vpu1–80 and Vpu1–80-DD into coarse-grained structural models. A default elastic network was used46. The integration time step was Δt = 30 fs and periodic boundary conditions were applied. The non-bonded interaction had a cut off distance of 1.2 nm. The temperature of the protein, lipid, and the water molecules were separately coupled to a Berendsen thermostat at 310 K with a coupling time of 1.0 ps. A semi-isotropic pressure coupling was applied with a coupling time of 12.0 ps and a compressibility 3e-5 bar–1. For the lipid bilayer, a pre-equilibrated 2048 lipid POPC membrane hydrated by 33912 water molecules was used as a starting point. Sixteen full-length Vpu and Vpu-DD mutants were embedded in a POPC membrane (Supplementary Fig. S4) with a protein: lipid ratio of 1:931. Na-ions were added to neutralize the system. The systems consisted of 57064 and 57058 beats for the Vpu-WT and Vpu-DD system, respectively. The simulations with mixtures of Vpu-WT and Vpu-DD were generated by replacing 4 Vpu proteins in a row by the other type of protein. The simulation systems were then neutralized with the respective number of Na-ions. All the system were energy minimized (500 steps of steepest decent) and equilibration with protein restrain (k = 500 kJ mol−1 nm−2) for a total of 2.7 ns. The unrestrained systems were submitted to production runs of 10 μs.

Oligomerization analysis

The oligomerization rate of the computational data was calculated with the concentration of trimer or higher oligomers divided by the concentration of total oligomer, in order to quantify the oligomerization level the maximum value was 1 and the minimum was 0. The respective curves were fitted with a logarithmic growth function.

with a = maximum oligomerization ratio, b = initial value at time t = 0, and c = growth rate (time−1). Non-linear regression was performed by using non-linear curve fitting of OriginLab 9.0. The initial values were set to a = 1, b = 1, and c = 0.1. Iteration was conducted until the difference between reduced χ2 values of two successive iterations was less than a specified tolerance value, here 10−9 by default. Fitting the experimental Vpu-WT data two logistic growth functions were combined additively.

Structures are considered as oligomers when the distance between 10 pairs of CG-atoms of different Vpu structures was below 5 Å and observed continuously for more than 10 times steps between the proteins.

Additional Information

How to cite this article: Chen, C.-P. et al. Membrane protein assembly: two cytoplasmic phosphorylated serine sites of Vpu from HIV-1 affect oligomerization. Sci. Rep.

6, 28866; doi: 10.1038/srep28866 (2016).