Spatial arrangement of proteins in planar and curved membranes by PPM 3.0

2.1. BAR domains

The Bin‐Amphiphysin‐Rvs167 (BAR) domain superfamily includes peripheral membrane proteins containing the BAR domain at N‐terminus (N‐BAR), the extended FCH (EFC)/FCH‐BAR domain (F‐BAR), or the IRSp53‐MIM homology domain (IMD)/inverse BAR domain (I‐BAR). ²¹ , ²² These proteins deform membranes to a geometry that corresponds to the structure of their membrane‐binding face. ²³ The BAR domain consists of an extended coiled‐coil structure forming a long “banana shaped” dimer. It has a curved membrane‐binding surface rich in positively charged residues that interacts with acidic phospholipids. N‐BAR domains of some proteins, such as endophilin and amphiphysin, also have hydrophobic amino acids in the amphiphilic N‐terminal helix that contribute to the membrane binding. ²⁴ Both N‐BAR and F‐BAR domains promote the positive membrane curvature and are involved in plasma membrane invaginations leading to endocytosis and phagocytosis. ²¹ Proteins with F‐BAR domains also regulate the formation of filopodium, lamellipodium, and podosome. ²⁵ In contrast, I‐BAR domains with inverted curvature likely sense or induce negative membrane curvature and stabilizes plasma membrane protrusions, such as filopodia, by interacting with the membrane from the inner side of the bend. ²⁶

The calculations with PPM 3.0 allowed us to evaluate radii of the intrinsic curvature for members of various families from the BAR domain superfamily. The radii vary widely, from around 120 Å for N‐BAR domains to around 410 and 540 Å for F‐BAR and I‐BAR domains, respectively (Tables 1, S2, and Figure 1a–d). These calculation results are consistent with previous estimates for these proteins. ²³ The calculated binding energies for many BAR domains are small, especially for protein structures with missing hydrophobic anchor residues. In such cases, the reliability of PPM 3.0 is lower.

2.2. Annexins

Annexins are a family of peripheral membrane proteins that bind to anionic membranes containing phosphatidylserine in the presence of Ca²⁺‐ions. In humans, this family has 12 members (ANXA1‐11, ANXA13) that are involved in plasma membrane vesiculation and repair. ²⁷ The conserved C‐terminal core domain of annexins consists of four similar repeats (eight in ANXA6), each having five α‐helices that form Ca²⁺‐binding sites. Some annexins act as monomers, other form dimers (ANXA1, ANXA2), trimer (ANXA4, ANXA5), or larger aggregates. It was shown that annexins can induce negative curvature on anionic membranes in Ca²⁺‐dependent manner, which leads to membrane aggregation, folding, blebbing, roll‐up, and fusion. ²⁷

Our calculations with PPM 3.0 demonstrated that available structures of monomers and trimers of different annexins have a negative intrinsic curvature (J <0) with average radii of around 100 Å (Figure 1e, Tables 1 and S2).

2.3. Mitochondrial ATP synthases

F‐type mitochondrial adenosine triphosphate (ATP) synthase is a multiprotein complex located in mitochondrial cristae that converts the proton motive force generated by proteins from the electron transport chain into ATP. In yeast and mammals, ATP synthase is composed of a soluble catalytic F₁ region containing α₃β₃γσε subunits and a TM F₀ region containing a, b, e, f, g, i/j, k, l, 8 subunits and a ring of 10 c‐subunits. During ATP synthesis, protons move across the mitochondrial inner membrane (MIM) from the intramembrane space into the matrix via F₀ region, which leads to rotation of the central rotor (γσεc₁₀), conformational changes in α₃β₃ subunits, and ATP synthesis from ADP and phosphate.

The mitochondrial ATP synthase complexes from plants, fungi, and mammals assemble into dimers forming rows along the ridges of the cristae. ²⁸ Dimer organization in long ribbons stabilizes the highly curved cristae ridges, which is essential for MIM morphology. ²⁹

PPM 3.0 was used to calculate spatial positions in membranes of V‐shaped dimers of F₁F₀‐ATP synthases from different organisms. It appeared that dimers from unicellular organisms (protozoa and algae), which are held together by hydrophilic helices, can be arranged in a spherical membrane bent toward the mitochondrial matrix (J >0) with average radii of 140 Å (Figure 1g, Tables 1 and S3). In contrast, two halves of the yeast ATP synthase dimer, which associate via the membrane‐embedded F₀ region, can be optimally positioned in two separate planar membrane sections that intersect under nearly a right angle (Figure 1m, Tables 2 and S4). These calculations agree with the previous analysis of cryo‐EM‐maps. ²⁸

Noteworthy, ATP synthase of chloroplasts predominantly exist as monomers and can be generally accommodated in flat membranes. Indeed, localization of chloroplast ATP synthase is confined to minimally curved membrane regions at the grana end and stroma lamellae. ³⁰

2.4. Mechanically activated Piezo and MscS ion channels

The mechanically activated Piezo channels are key eukaryotic mechanotransducers that convert mechanical force into cation permeation. ³¹ They mediate touch perception, mechanical nociception, proprioception, and vascular development. Piezo1 and Pezo2 are mainly expressed in nonsensory and sensory tissues of vertebrates, respectively. They are evolutionary and structurally unrelated to mechanosensitive channels of prokaryotes.

Several atomic models based on cryo‐EM density maps have been constructed for the mouse Piezo 1 ³¹ , ³² and Piezo 2 channels. ³³ Each channel represents a propeller‐like trimeric complex, where each subunit consists of 38 TM α‐helices organized in nine 4‐TM α‐bundles (first 12 TM α‐helices are not resolved in EM maps of Piezo 1; PDB ID: 6b3r) and two central helices connected by a regulatory C‐terminal extracellular domain. Pairs of central TM α‐helices form a narrow pore that deforms the membrane into a dome. ³¹

Calculation with PPM 3.0 demonstrated that all available structures of trimetric complexes of Piezo channels can be accommodated in a spherically deformed membrane bent toward the cytoplasm (J >0, R ~114 Å; Figure 1h). Similar results were obtained for heptameric bacterial mechanosensitive channels of small‐conductance, MscS (Tables 1 and S3).

2.5. Mitochondrial import receptor complex

The translocase of the outer membrane (TOM) represents the mitochondrial protein‐conducting channel that coordinates translocation of nuclear‐encoded proteins with mitochondrial target sequences from cytosol into mitochondria. ³⁴ The core TOM complex is a dimer of 10 TM subunits composed of two β‐barrels of TOM40 pore, each surrounded by single‐α‐helical TM subunits: TOM5, TOM6, TOM7, and TOM22. Recently, cryo‐EM structures of TOM complexes from Homo sapiens and Saccharomyces cerevisiae have been reported. ³⁵ , ³⁶ Further, dimeric TOM complexes were shown to associate in tetramers ³⁶ , ³⁷ or trimers. ³⁵

Calculations with PPM 3.0 demonstrated that the dimeric and tetrameric complexes of TOM bend MOM toward the intermembrane space, away from the cytoplasm, thus inducing a significant negative curvature (J <0). Importantly, the hydrophobic thickness of MOM was calculated as being reduced from ~30 to ~22 Å in the area of TOM40 β‐barrels (Figure 1I, Tables 1 and S2). The shallow membrane depression at the cytoplasmic site of the TOM complex may help preprotein binding and guiding to TOM40 translocation pores.

2.6. Mitochondrial calcium uniporter

Mitochondrial calcium uniporter (MCU) is a highly selective calcium channel localized in MIM. It mediates Ca²⁺‐uptake by mitochondria, which is critical for the regulation of Ca²⁺‐homeostasis in eukaryotes. MCU was found in all major eukaryotic taxa. However, only in metazoa, MCU forms a functional complex with EMRE and MICU1‐MICU2 heterodimer that blocks the channel at low Ca²⁺ concentration. ³⁸ , ³⁹ Several structures of dimeric forms of human MCU‐EMRE and MCU‐EMRE‐MICU1‐MICU2 complexes have been recently determined. ³⁸ , ³⁹ , ⁴⁰ , ⁴¹

Positioning of these structures in membranes by PPM 3.0 showed that monomeric MCU complexes can be accommodated in the flat lipid bilayer. However, the dimeric forms of MCU‐EMRE and MCU‐EMRE‐MICU1‐MICU2 complexes did not fit well to a single flat or a spherically deformed membrane. Apparently, they are located in a strongly bent region of mitochondrial cristae where they can be approximated by two flat membrane sections intersecting at an obtuse angle (Figure 1n, Tables 2 and S4).

The membrane deformation caused by dimerization of MCU‐EMRE complexes is a likely reason of MCU enrichment at the curved surfaces of MIM between the inner boundary membranes and the cristae membranes that are close to contact points with MOM. ⁴¹ , ⁴² Such localization of uniporter complexes may increase their accessibility to Ca²⁺ ions from the cytosol.

2.7. Cation‐chloride cotransporters

The cation‐chloride cotransporters (CCCs) move Cl⁻ ions into or out of cells using the Na⁺ and/or K⁺ gradients generated by the Na⁺‐K⁺‐ATPase. NKCC1, the most experimentally studied CCC, participates in chloride homeostasis, regulation of cell volume, and neuronal excitability. ⁴³ Each CCC assembles into a dimer, where each subunit has the first 10 TM α‐helices forming the transport core and TM11‐TM12 helices participating in the dimerization interface. Similar to other members of the amino acid‐polyamine‐organocation (APC) superfamily of secondary active transporters, CCCs display the pseudo‐symmetric topology of two inverted repeats of five TM α‐helices (with broken TM1 and TM6) that form the central ligand binding cavity of the 10‐helical TM core. Cryo‐EM models of CCC dimers in the inward‐facing state demonstrate a similar architecture, with the peripheral TM4‐TM5 α‐helices located ~9 Å above the central TM11–TM12 α‐helices. ⁴³

Our calculations with PPM 3.0 demonstrated that all 23 available structures of CCCs can be better accommodated in highly curved sphere‐shaped membranes that are bent toward the cytoplasmic side of the PM (J >0, R ~105 Å; Figure 1j, Tables 1 and S3). Perhaps the local membrane deformation that appears as a “depression” in the middle of these protein complexes facilitates the TM transport.

2.8. Proton‐coupled K⁺ transporter

K⁺‐uptake permeases (KUPs) represent another family of the APC superfamily. KimA, a high affinity proton‐coupled K⁺ importer from Bacillus subtilis, shares a similar fold with CCCs. ⁴⁴ It functions as a homodimer, where each subunit is composed of 10‐helical core and TM11‐TM12 helices, which together with C‐terminal cytoplasmic domains form the dimerization interface. PPM 3.0 calculations revealed that, similar to CCCs, KimA in the inward‐facing state can be better accommodated in the significantly curved membrane bent toward the cytoplasm (J >0, R = 70 Å; Tables 1 and S3). Based on results of CG and MD simulations, it was suggested that the extent of the membrane bending by KimA dimer could be altered during transporter activity. ⁴⁴

2.9. Respiratory complex I

Mitochondrial respiratory complex I (NADH:ubiquinone oxidoreductase) is an essential enzyme for mitochondrial energy metabolism. It converts energy released by electron transfer from NADH to ubiquinone to the proton flux out of the matrix across the MIM, which is used for ATP synthesis. Mammalian respiratory complex I is the largest of respiratory complexes; it is composed of 45 subunits: 14 “core” subunits conserved in prokaryotes and eukaryotes that are sufficient for catalysis, and 31 “supernumerary” species‐specific subunits that are required for complex assembly, stability, and regulation. ⁴⁵ The L‐shape of the complex I is created by the matrix‐exposed hydrophilic part, which provides electron transfer between NADH and ubiquinone, and the TM domain, which is responsible for proton translocation.

Calculations by PPM 3.0 of mitochondrial respiratory complexes I of plant and mammals demonstrate that the difference between transfer energies for curved and flat membranes is smaller (∆∆G ~12%) than for other calculated membrane‐deforming proteins (∆∆G from 20% to 80%). Therefore, respiratory complexes I can be accommodated either in flat or slightly curved membranes that bend toward the intermembrane space (J <0, R ~450 Å; Figure 1k, Tables 1 and S3). Such results are consistent with localization of these complexes in flat or slightly curved regions of inner membranes of cristae. ²⁸ On the other hand, the bacterial respiratory complex I (PDB ID: 3rko) has a slightly larger curvature (J <0, R = 270 Å) compared to the mitochondrial complex I. The structures of all other components of the respiratory chain (complexes II, III, and IV) were found to be planar.

2.10. Photosystems I and II

Photosystem I and II (PSI and PSII) are two multisubunit pigment‐protein complexes embedded in the thylakoid membranes of higher plants, algae, and cyanobacteria that capture light energy and transform it to photochemical reactions of oxygenic photosynthesis. In higher plants and algae, the core complexes of PSI and PSII form large supercomplexes with peripheral antennae, the light‐harvesting complexes (LHCs): PSI‐LHCI, PSII‐LHCII (or PSII‐FCPII), and PCI‐LHCI‐LHCII at state 2. ⁴⁶ In plant and algae, PSI exists as monomers, while in bacteria, it usually forms trimers, but also may exist as tetramers, possibly as adaptation to high light levels. ⁴⁷ PSII‐LHCs supercomplexes are formed by two protomers, each composed of multisubunits PSII core and a complex antenna systems. ⁴⁸

Calculation by PPM 3.0 of all available structures of PSI and PSII complexes with or without LHCs revealed that almost all of them fit to a planar lipid bilayer. A few exceptions are: the tetrameric PSI from cyanobacteria (PDB ID: 6tcl ⁴⁷ ), the PSI‐LHCI‐LCHII supercomplex from green algae (PDB ID: 7d0j ⁴⁶ ), and the PSII‐FCPII supercomplex of diatoms (PDB ID: 6jlu ⁴⁸ ). These complexes can be better arranged in slightly curved membranes (average R of 490 Å) than in a flat lipid bilayer (Figure 1l, Tables 1 and S3). The physiological relevance of a small intrinsic curvature of these proteins is not completely clear, but it might reflect the slight bend of thylakoids in unicellular algae and cyanobacteria.

2.11. Tripartite multidrug efflux pumps

In Gram‐negative bacteria, tripartite multidrug efflux pumps export biological metabolites and antimicrobial compounds out of the cell, thereby contributing to bacterial resistance. Models of three such pumps, which span both inner (IM) and outer (OM) bacterial membranes, were experimentally determined: AcrAB‐TolC efflux pump of Escherichia coli, MexAB‐OprM complex of Pseudomonas aeruginosa, and MacAB–TolC assembly of Escherichia coli. AcrAB‐TolC and MexAB‐OprM belong to the Resistance‐Nodulation‐cell Division (RND) family, while MacAB‐TolC complex is a FtsX‐like permease. RND transporters operate as a secondary proton/drug antiporter using the energy of proton transport in TM domains located in the IM to power the export of substrates through the periplasm and the OM. ⁴⁹ , ⁵⁰ MacAB‐TolC contains the dimeric MacB ATPase, an ABC‐transporter from IM that energizes the drug transport. ⁵¹ The boundaries of both membranes of the bacterial cell envelop were determined by PPM 3.0 for these structures (Figure 1o, Tables 2 and S4).

2.12. Gap‐junctions channels

Gap‐junction proteins, such as connexins, innexins, pannexins, leucine‐rich repeat‐containing 8 (LRRC8) proteins, and calcium homeostasis modulators (CALHM), are large‐pore channels with a pore diameter more than 14 Å. These proteins are composed of TM 4‐α‐helical bundles organized in multimers: 6‐mers (connexins, LRRC8), 7‐mers (pannexins), 8‐mers (innexines, CALHM1), and 9, 10, 11‐mers (CALHMs). Multimeric hemichannels connecting through their extracellular regions form gap‐junction channels between adjacent cells, while hemichannels of CALHM1 and CALMH4 interacting through their cytoplasmic regions may form channels between the plasma membrane and the organelle membrane. ⁵² Boundaries of two opposed membranes connected via gap‐junction channels were calculated by PPM 3.0 for 21 multimeric structures of connexins, CALHMs, innexins, and pannexins (Tables 2 and S4).

4.1. PPM 3.0 method

The PPM 3.0 method determines orientations in membranes of proteins and peptides by optimizing their transfer free energies from water to the membrane environment (∆G _transf). Since the PPM 2.0 method was previously extensively tested, ³ , ¹⁹ , ²⁰ we used the same approach for calculating ∆G _transf, but added the following new options: (a) fitting a protein structure into a sphere‐shaped bilayer with an adjustable radius of curvature and hydrophobic thickness; (b) positioning of proteins in several lipid bilayers; (c) using different membrane systems; and (d) positioning of peptides or small proteins in a spherical micelle.

The transfer free energy is calculated as a sum of short‐range ASA‐dependent contributions for all atoms (H‐bonds, van der Waals, and hydrophobic interactions with solvent), long‐range electrostatic contributions of dipole moments and charged groups, and the ionization penalty for ionizable groups. ¹⁹ The solvation properties of a membrane as an anisotropic solvent are described by hydrogen bonding capacity and dielectric permittivity profiles along the bilayer normal. These profiles were calculated based on the experimentally determined distributions of different lipid groups along the normal of the 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) bilayer. ⁵³

4.2. PPM 3.0 web server

The PPM 3.0 web server provides fast calculation of spatial positions and intrinsic curvatures of TM and peripheral proteins in flat and curved biological and artificial membranes. It also allows calculating boundaries of several membranes (or several independent sections of the same membrane) where the protein complex is located. The web server is located at the OPM database web site (https://opm.phar.umich.edu/ppm_server3).

The input includes: (a) a coordinate file (in pdb format) of a 3D structure of a protein or a peptide of interest that can be provided by a user or taken from the PDB or the OPM databases; (b) a choice between one to four membranes; (c) a choice of each membrane type (from 17 types of biological membranes, four types of lipid bilayer, and a DPC micelle); (d) lists of protein subunits assigned to each membrane in the multiple membranes option; (e) designation of protein topology (location of N‐terminus of the first subunit relative to the “in” or “out” membrane side); and (f) an option to include curvature in calculation. With the “curvature allowed” option selected, PPM 3.0 automatically defines whether a protein fits better to a planar or a spherically deformed bilayer. The option with positioning in a spherical micelle can be used only for peptides and small amphiphilic proteins, but not for TM proteins.

The output includes: (a) a downloadable coordinate file (in pdb format) of a protein structure supplemented by calculated membrane boundaries; (b) the membrane binding energy for peripheral proteins or the transfer free energies of TM proteins from water to flat (∆G _flat) and curved (∆G _curv) membranes; (c) the radius of curvature for proteins in curved membranes (R); (d) the membrane penetration depth for peripheral proteins or hydrophobic thickness (D) for TM proteins; and (e) the tilt angle between the membrane normal and the protein axis.

For structures with a single planar bilayer, the origin of the coordinates corresponds to the center of the lipid bilayer. Z axis coincides with the membrane normal; atoms with a positive sign for its Z coordinate are arranged in the outer leaflet as defined by the user‐specified topology. The center of the spherical vesicle or the micelle corresponds to the origin of coordinates. The radius of curvature of a sphere‐shaped membrane (R) denotes the distance from the origin of coordinates to the middle of the lipid bilayer, which includes only the inner leaflet and excludes the other leaflet with a 35 Å‐thicknesses (15 Å thick hydrophobic core plus 20 Å thick head group region). Thus, R of 100 Å would correspond to the diameter of a spherical vesicle of 270 Å. The protein axis is calculated as the sum of TM secondary structure segment vectors (for TM proteins) or as the principal inertia axis (for peripheral proteins).

Visualization of calculated protein structures positioned in planar or curved membranes is provided by Jmol, a platform‐independent Java‐viewer, and a WebGL‐based 3D viewer iCn3D.