Andrey S Kuznetsov

Miftakh F Zamaletdinov

Yaroslav V Bershatsk

Anatoly S Urban

Olga V Bocharova

Amar Bennasroune

Pascal Maurice

Eduard V Bocharov

Roman G Efremov
email: efremov@nmr.ru

Yaroslav V Bershatsky

Dimeric states of transmembrane domains of insulin and IGF-1R receptors: Structures and possible role in activation

Keywords: insulin receptor, transmembrane domain, dimerization, free energy of helix-helix association, protein-protein interactions in membrane, dimer structure prediction TM, transmembrane, IR, human insulin receptor, IGF-1R, human IGF-

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Insulin receptor (IR) family is a part of receptor tyrosine kinases (RTK) superfamily, that are bitopic integral proteins involved in signal transduction through the cell membrane via autophosphorylation of their intracellular domains. There are three members in IR family: insulin receptor (IR), insulin-like growth factor 1 receptor (IGF-1R), and insulin receptor-related receptor (IRR). Both IR and IGF-1R participate in regulation of cell metabolism, growth, differentiation and adaptation mechanisms. Being previously considered as an "orphan" receptor, IRR was recently found to be activated by alkaline medium and engaged in acid-base balance adjustment [START_REF] Deyev | Insulin receptor-related receptor as an extracellular alkali sensor[END_REF]. It is known that errors in normal processing of these receptors cause such severe diseases as type II diabetes mellitus, different tissues carcinomas and developmental disorders [START_REF] Belfiore | Insulin Receptor Isoforms and Insulin Receptor/Insulin-Like Growth Factor Receptor Hybrids in Physiology and Disease[END_REF][START_REF] Abuzzahab | IGF-I receptor mutations resulting in intrauterine and postnatal growth retardation[END_REF][START_REF] Juanes | Three novel IGF1R mutations in microcephalic patients with prenatal and postnatal growth impairment[END_REF]. Also, IR dysfunction was shown to correlate with Alzheimer disease [START_REF] Diehl | Insulin resistance in Alzheimer's disease[END_REF].

The main feature distinguishing the IR family from other RTKs is their special (αβ) 2heterotetrameric structure. The ECD of these receptors is represented by two disulfide-linked α-subunits, each associated with β-subunit, which consists of extracellular, TM and cytoplasmic segments [START_REF] Xu | How ligand binds to the type 1 insulin-like growth factor receptor[END_REF][START_REF] Croll | Higher-Resolution Structure of the Human Insulin Receptor Ectodomain: Multi-Modal Inclusion of the Insert Domain[END_REF][START_REF] Shier | Primary structure of a putative receptor for a ligand of the insulin family[END_REF][START_REF] Cai | Domain-dependent effects of insulin and IGF-1 receptors on signalling and gene expression[END_REF]. Amino acid sequences of ECD and TM parts differ dramatically between members of IR family (Fig. S1).

Nowadays, there is a serious lack of data on spatial structure, signal cascade and function mechanisms of IRR receptor. It is characterized by lower sequence identity values (Fig. S1) and has a deletion near functionally important juxtamembrane (JM) domain, that contains conservative substratebinding NPEY sequence (Table 1) [START_REF] Cai | Domain-dependent effects of insulin and IGF-1 receptors on signalling and gene expression[END_REF]. Also, IRR does not interact neither with insulin, nor with IGF-1. These issues can be explained by a specific mechanism of IRR activation, so this receptor was excluded from consideration in the present work.

IR and IGF-1R receptors transduce signal into the cell through the ligand-induced conformational change in ECD, followed by intracellular kinase domains autophosphorylation and kinase activity. The exact details of this process are still unknown but two main models have been proposed. The first one was based on the complex study of IGF-1R, including Förster resonance energy transfer (FRET) technique, and describes basal state with separated TM domains, that become close together and dimerize to transfer signal [START_REF] Kavran | How IGF-1 activates its receptor[END_REF]. Alternative model supposed dissociation of TM dimer upon activation, and thus, IR can be activated by artificial IR TM peptide [START_REF] Lee | Insulin Receptor Activation with Transmembrane Domain Ligands[END_REF]. Latest structural studies on IR and IGF-1R ECDs in basal and active states [START_REF] Xu | How ligand binds to the type 1 insulin-like growth factor receptor[END_REF][START_REF] Scapin | Structure of the insulin receptor-insulin complex by single-particle cryo-EM analysis[END_REF][START_REF] Weis | The signalling conformation of the insulin receptor ectodomain[END_REF][START_REF] Gutmann | Visualization of ligand-induced transmembrane signaling in the full-length human insulin receptor[END_REF] supported the first model.

Since RTK activation mechanism typically involves interaction of TM domains, the latter became a subject for a number of structural studies. Nowadays, a collection of TM dimers structures for different RTKs (e.g., ErbB1-4, PDGFRβ, FGFR3, GHR) was obtained using NMR spectroscopy in different membrane-mimicking systems. In the case of ErbB and GHR, these structures suppose activation mechanism with TM dimerization interfaces switching from hydrophilic N-terminal state to more hydrophobic C-terminal [START_REF] Bocharov | Conformational transitions and interactions underlying the function of membrane embedded receptor protein kinases[END_REF][START_REF] Bocharov | Structural basis of the signal transduction via transmembrane domain of the human growth hormone receptor[END_REF]. In contrast to mentioned RTKs, proteins from the IR family exist as preformed dimers of two subunits, and, probably, their TM domains do not interact in one of the receptor states. Within IR family, structural studies of TM domain have been done only for IR receptor -NMR spectroscopy in micelles revealed the helical structure of the monomer [START_REF] Li | Solution structure of the transmembrane domain of the insulin receptor in detergent micelles[END_REF]. This is in line with molecular dynamics (MD) simulations of the helical monomer in model lipid bilayer [START_REF] Mohammadiarani | All-Atom Structural Models of the Transmembrane Domains of Insulin and Type 1 Insulin-Like Growth Factor Receptors[END_REF]. However, the NMR data mentioned above did not permit direct detection of TM dimersthese were only found in crosslinking experiments [START_REF] Li | Solution structure of the transmembrane domain of the insulin receptor in detergent micelles[END_REF]. Finally, the dimerization of IR and IGF-1R TM domains was confirmed using different experimental techniques [START_REF] Lee | Insulin Receptor Activation with Transmembrane Domain Ligands[END_REF][START_REF] Scapin | Structure of the insulin receptor-insulin complex by single-particle cryo-EM analysis[END_REF][START_REF] Weis | The signalling conformation of the insulin receptor ectodomain[END_REF][START_REF] Gutmann | Visualization of ligand-induced transmembrane signaling in the full-length human insulin receptor[END_REF], excluding high-resolution structure determination methods.

Point mutagenesis assays revealed only one critical mutation V912E in the TM domain of IGF-1R -it was suggested to correspond to the well-known oncogenic mutation in TM domain of ErbB2, which leads to basal activation [START_REF] Takahashi | Insulin-like Growth Factor I Receptor Activated by a Transmembrane Mutation[END_REF]. Similar mutation (V938E/D) was proposed in IR TM sequence, but its influence on activation was detected only once [START_REF] Longo | Activation of insulin receptor signaling by a single amino acid substitution in the transmembrane domain[END_REF], while other experiments showed no effect [START_REF] Frattali | Evidence supporting a passive role for the insulin receptor transmembrane domain in insulin-dependent signal transduction[END_REF][START_REF] Yamada | Substitution of the insulin receptor transmembrane domain with the c-neu/erbB2 transmembrane domain constitutively activates the insulin receptor kinase in vitro[END_REF][START_REF] Cheatham | Substitution of the erbB-2 oncoprotein transmembrane domain activates the insulin receptor and modulates the action of insulin and insulin-receptor substrate 1[END_REF]. Replacement of the entire TM domain of IR by TM sequence of glycophorin A (GpA) makes the receptor non-functional [START_REF] Gardin | Substitution of the insulin receptor transmembrane domain with that of glycophorin A inhibits insulin action[END_REF], so one can suppose that the spatial structure of TM dimer of GpA does not allow JM and tyrosine kinase (TK) domains to reach their active configuration. At the same time, similar replacements with TM fragments of epidermal growth factor receptor (EGFR), ErbB2 and plateletderived growth factor receptor beta (PDGFRβ) do not interfere with activity of IR, thus assuming their structures being compatible with IR activation mechanism (sequences and their impacts on receptors functioning are listed in the Supplementary table S1) [START_REF] Yamada | Substitution of the insulin receptor transmembrane domain with the c-neu/erbB2 transmembrane domain constitutively activates the insulin receptor kinase in vitro[END_REF][START_REF] Cheatham | Substitution of the erbB-2 oncoprotein transmembrane domain activates the insulin receptor and modulates the action of insulin and insulin-receptor substrate 1[END_REF][START_REF] Yamada | Role of the Transmembrane Domain and Flanking Amino Acids in Internalization and Down-regulation of the Insulin Receptor[END_REF][START_REF] Bennasroune | Inhibition by transmembrane peptides of chimeric insulin receptors[END_REF].

Despite the aforementioned experimental and structural data, pivotal details of the activation of IR-related receptors are still missing, especially from the structural and dynamic points of view. Particularly, although protein dimerization in lipid bilayer is commonly accepted, conformations of the membrane domains in the active and intermediate states remain puzzling. Obtaining the new data on TM dimer structure can help to understand the mechanism of signal transduction utilized by these receptors and propose possible ways to modulate it. In this work, we applied NMR spectroscopy to probe dimerization of TM segments of IR in membrane-mimicking medium. Furthermore, a battery of computational modeling techniques was used to predict possible TM dimer structures for IR and IGF-1R taking into account most of the available structural data used as constraints. Biological relevance of the models was further tested via comparison with known mutagenesis data related to modifications of TM domains of both receptors. The elaborated models can be used for rational design of new factors modulating insulin signaling.

Materials & methods

Dimerization of transmembrane segment of IR as probed by NMR spectroscopy.

In order to obtain the synthetic gene construct, IR TM domain sequence was assembled by PCR with overlapping primes, digested with BamHI and HindIII restrictases and cloned into pGEMEX1 vector (Promega). The final construct contained the sequence coding the IR TM segment and leading H6 tag T7 phage promoter (fragment named as IRtm): MHHHHHHG-925 SNIAKIIIGPLIFVFLFSVVIGSIYLFLRKR 953 . The 13 C/ 15 N-labeled peptide was expressed using continuous exchange cell-free expression system with E. coli S30 extract [START_REF] Bocharova | Cell-free expression of the APP transmembrane fragments with Alzheimer's disease mutations using algal amino acid mixture for structural NMR studies[END_REF]. After finalizing of the reaction, the peptide precipitate was separated from the reaction mixture by centrifugation. The pellet was solubilized in buffer containing 0.5% lauroyl sarcosine, 50 mM Tris/HCl, pH 8.0, 50 mM NaCl and size exclusion chromatography was carried out using the Tricorn 10/300 Superdex 200 Increase column at 0.5 ml/min flow rate. Fractions containing the peptide were combined, then the peptide was precipitated by addition of TCA and washed with cold acetone three times. The pellet was solubilized in 1:1 (v/v) trifluoroethanol-water mixture and lyophilized. In order to incorporate IRtm into membrane-mimicking micelles or bicelles, the peptide powder was first dissolved in 1:1 (v/v) trifluoroethanol-water mixture with the addition of n-dodecylphosphocholine (DPC) or the mixture of 1,2-dimyristoyl-d54-sn-glycero-3phosphocholine (DMPC) and 1,2-dihexanoyl-d22-sn-glycero-3-phosphocholine (DHPC), respectively, and then placed in an ultrasound bath for several minutes. The effective molar ratio q of long-chain and short-chain lipids in the DMPC/DHPC bicelle was ~0.3, assuming a free DHPC concentration of 7 mM in the bicellar suspension. The mixtures were lyophilized overnight and redissolved at pH 6.7 in 450 µl of water buffer solution containing 25 sodium phosphate, 0.3 мМ NaN 3 and 5% D 2 O (v/v). The selfassociation of IRtm in the micellar or bicellar environments was studied under variation of the detergent/peptide (D/P) or lipid/peptide (L/P) molar ratios within the range from 40 to 160 by the stepwise addition of concentrated micellar or bicellar suspensions followed by ultrasonication. NMR spectra were acquired at 313 K on 800 MHz AVANCE III spectrometer (Bruker BioSpin, Germany) equipped with triple-resonance with H/C/N triple resonance Z-gradient cryoprobe. The 1 H/ 13 C/ 15 N backbone resonances of IRtm were assigned (see Supplementary Table S2) with the CARA software [START_REF] Keller | The Computer Aided Resonance Assignment Tutorial[END_REF] using two-and three-dimensional heteronuclear NMR experiments [START_REF] Cavanagh | Protein NMR spectroscopy: principles and practice[END_REF]: 1 H/ 15 N-HSQC, 1 H/ 13 C-HSQC, 1 H/ 15 N-TROSY, 1 H/ 13 C/ 15 N-HNCO, 1 H/ 13 C/ 15 N-HNCA, 1 H/ 13 C/ 15 N-HN(CO)CA, 15 N-edited TOCSY-and NOESY-HSQC with mixing times of 40 and 80 ms, respectively. The BEST-TROSY version [START_REF] Favier | Recovering lost magnetization: polarization enhancement in biomolecular NMR[END_REF] of the triple resonance experiments was used, and the spectra were recorded with non-uniform sampling of indirect dimensions and processed using the qMDD software [START_REF] Kazimierczuk | A comparison of convex and non-convex compressed sensing applied to multidimensional NMR[END_REF]. Helical structure probability values (HSP) were obtained from the secondary structure probabilities estimated from the 1 H, 13 C, and 15 N chemical shift values using the web-based program TALOS-N [START_REF] Shen | Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks[END_REF].

General molecular dynamics parameters setup.

Gromacs molecular dynamics (MD) package version 5.1 [START_REF] Abraham | GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers[END_REF] was used with Gromos96 43a2 force field for protein, modified Berger lipid parametrization (for palmitoyloleylphosphatidylcholine, POPC) [START_REF] Berger | Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature[END_REF] and SPC water model, [START_REF] Berendsen | Interaction Models for Water in Relation to Protein Hydration[END_REF]. Verlet integration scheme was used with timestep 2 fs. Periodic boundary conditions in all dimensions were applied. Energy minimization was performed using steepest descent method. Temperature was kept constant at 315 K using V-rescale algorithm, pressure was controlled by Berendsen (during equilibration) and Parrinello-Rahman (in production runs) barostats [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF] at 1 bar with isotropic (for aqueous solutions) or semi-isotropic (for membranes) mode. Long-range Coulomb interactions were calculated by Ewald summation and van der Waals interactions were shifted to zero at 1.2 nm cut-off distance. Counterions were added to all systems to compensate the protein charge. All simulations are listed in supplementary table S3.

Extracellular domain movements analysis.

Molecular movements in IR ECD were studied using the principal component analysis (PCA) applied to MD trajectories of IR extracellular part (ectodomain) in aqueous solution. Its starting conformations were extracted from the crystal structure of ECD dimer of the IR isoform A in its basal state (PDB ID: 4zxb [START_REF] Croll | Higher-Resolution Structure of the Human Insulin Receptor Ectodomain: Multi-Modal Inclusion of the Insert Domain[END_REF]) and cryo-EM structure of the active state (PDB ID: 6sof [START_REF] Gutmann | Cryo-EM structure of the complete and ligand-saturated insulin receptor ectodomain[END_REF]). All carbohydrates / antibodies fragments and reconstructed missing regions were excluded. Then, to equilibrate conformations of insert domains (ID) and interdomain loops, 150 ns MD trajectories with restraints imposed on backbone atoms of rigid domains L1, CR, L2, FnIII-1,2,3 were calculated. Finally, 200 ns long trajectories were obtained without constraints.

Distance between centers of mass of D866 residues was selected as a measure of monomer closure, and PCA was applied to displacements of coordinates of C α atoms using tools implemented in the Gromacs package [START_REF] Abraham | GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers[END_REF]. Then, three MD trajectories for each state were compared by calculation of inner products of their first five eigenvectors of covariation matrix determined by PCA. Amplitude of the tweezer-like motion was estimated as a difference between the extreme values of the distance between D866 residues in MD trajectory filtered along the corresponding principal component. To visualize the results and detect hinge regions, we applied DynDom analysis [START_REF] Hayward | Systematic Analysis of Domain Motions in Proteins from Conformational Change; New Results on Citrate Synthase and T4 Lysozyme[END_REF] to filtered trajectories. Distance between inactive and active states in MD was estimated as a root-mean-square deviation (RMSD) of backbone atoms coordinates in domain pairs (L1+L2, FnIII-1+FnIII-2A, FnIII-2B+FnIII-3, L2+L2'), since changes of the entire structure are too large to analyze. In addition, we calculated RMSD values for residues forming the primary insulin binding site (site 1).

Spatial model of IR TM+JM : construction, MD simulation, analysis.

Proper positioning of IR JM domain with respect to the inner membrane surface was recovered using structural alignment. First, we replaced IL-4 phosphopeptide in the NMR structure of intracellular substrate IRS-1 (PDB ID: 1irs [START_REF] Zhou | Structural basis for IL-4 receptor phosphopeptide recognition by the IRS-1 PTB domain[END_REF]) with the peptide IR JM , thus constructing the model of IRS-1 PTB +IR JM , which resembles the results described earlier [START_REF] Cai | Domain-dependent effects of insulin and IGF-1 receptors on signalling and gene expression[END_REF]. Taking into account that IRS-1 has also a pleckstrin homology (PH) domain, that is specific to phosphatidylinositol [START_REF] Abuzzahab | IGF-I receptor mutations resulting in intrauterine and postnatal growth retardation[END_REF][START_REF] Juanes | Three novel IGF1R mutations in microcephalic patients with prenatal and postnatal growth impairment[END_REF][START_REF] Diehl | Insulin resistance in Alzheimer's disease[END_REF]-trisphosphate, we superimposed our structure with IRS-1 PH+PTB (PDB ID: 1qqg [START_REF] Dhe-Paganon | Crystal structure of the pleckstrin homology-phosphotyrosine binding (PH-PTB) targeting region of insulin receptor substrate 1[END_REF], Fig. 1A). Finally, the model IRS-1 PH was structurally aligned with PH domain of Tandem Ph-Domain-Containing Protein 1 (PDB ID: 1eaz, [START_REF] Thomas | Crystal structure of the phosphatidylinositol 3,4-bisphosphate-binding pleckstrin homology (PH) domain of tandem PHdomain-containing protein 1 (TAPP1): molecular basis of lipid specificity[END_REF], RMSD = 0.14 nm), whose position on the membrane was taken from the OPM database [START_REF] Lomize | OPM database and PPM web server: resources for positioning of proteins in membranes[END_REF]. As a result, starting conformation of the complex IR JM +IRS-1 PH+PTB anchored on the model membrane was obtained (Fig. 1B). Since the relative position of TM and JM domains (their amino acid sequences are given in Table 1) is not known, three starting configurations of the model IR TM+JM were built by varying the rotation angle of IR JM +IRS-1 PH+PTB complex in the membrane plane around the G959 residue. Pre-equilibrated models of TM domain embedded into the membrane (slightly tilted) were used to attach other parts of the complex (Fig. 1C).

At these stages, MD simulations were carried out with the all-atom force field Amber99sb-ildn for protein, TIP3P water model and S-lipids parameters [START_REF] Jämbeck | An Extension and Further Validation of an All-Atomistic Force Field for Biological Membranes[END_REF] for POPC. Equilibration was done by 5 ns MD simulation with restrained positions of the protein backbone atoms. Finally, 200 ns MD trajectories were calculated. TM domain position in membrane was described by value of the helix tilt angle and its orientation in the membrane. Helix axis was determined locally based on coordinates of the nearest N, C, and Ca backbone atoms. This was done according to the method of Sugeta and Miyazawa [START_REF] Sugeta | General method for calculating helical parameters of polymer chains from bond lengths, bond angles, and internal-rotation angles[END_REF] and averaged. The helix tilt angle was determined as an angle between the membrane normal (Z-axis) and the helix axis vector. The orientation of the helical segment in the membrane was determined by the so-called "per-residue direction vectors" with origin on the local helix axis and pointed to the Ca atom of a given residue.

Receptor

Sequence IR TM domains and substrate binding site of JM sequence are highlighted in bold. Amino acid residues are colored according to their properties: aliphatic are black, small and polar -green, aromatic -pink, positively and negatively charged -blue and red, respectively. Amino acid numbering corresponds to protein without signal peptides, for IR sequence of its long isoform is used.

Prediction of TM helix-helix dimer structures with PREDDIMER algorithm.

Preliminary 3D models of TM dimers for IR and IGF-1R receptors were built using the PREDDIMER web-server (http://model.nmr.ru/preddimer, [START_REF] Polyansky | PREDDIMER: a web server for prediction of transmembrane helical dimers[END_REF]). To enhance sampling, multiple calculations were performed with varying amino acid sequences adding 1-2 residues to the N-or Cterminus. In total, eight variants for IR and six for IGF-1R were explored (Table S4). To select the most probable conformers, the resulting models were clustered based on similarity of the helix-helix interface and geometry of the dimer: the crossing angle between helices axes and intermonomer distance. Only clusters containing multiple models were further considered.

Prediction of TM helix-helix dimer structures via DAFT-modeling of their self-association.

An alternative method for predicting dimer structures was to simulate the self-assembly of TM peptides using a coarse-grained Martini forcefield [START_REF] Jong | Improved Parameters for the Martini Coarse-Grained Protein Force Field[END_REF], version 2.2P for protein with elastic bonds for preservation of the secondary structure. Here, polarizable water model and Martini version 2.0 for POPC lipids were used. For each receptor, 500 starting conformations were built using the DAFT software, as described in [START_REF] Wassenaar | High-Throughput Simulations of Dimer and Trimer Assembly of Membrane Proteins. The DAFT Approach[END_REF]. Fully helical peptides with sequences 926 NIAKIIIGPLIFVFLFSVVIGSIYLFLRKR 953 and 902 NFIHLIIALPVAVLLIVGGLVIMLYVFHR 930 were considered. The systems were then equilibrated and subjected to 500 ns MD simulations. Dimerized structures were selected based on the inter-monomer distance values. Residue-residue contact maps were built based on the solvent accessible surface area differences between dimeric and monomeric states (differences more than 0.001 nm 2 were considered as a contact).

Quality estimation for the predicted dimer models.

Selected dimer models were modified by addition of flanking residues at the N-and C-termini (resulting in 925 SNIAKIIIGPLIFVFLFSVVIGSIYLFLRKRQP 955 and 902 NFIHLIIALPVAVLLIVGGLVIMLYVFHRKRNN 934 peptides) and then subjected to energy minimization and 50 ns long MD simulations in explicit lipid environment (hydrated POPC). This was done to evaluate stability of the membrane-embedded dimers. Each dimer was oriented along the membrane normal (Z axis) and inserted into pre-equilibrated hydrated POPC bilayer. Then, overlapping lipid and water molecules were removed, and ions were added to get the system electrically neutral. Energy relaxation of the lipid environment was done via 5 ns MD simulation with the temperature increasing from 5 to 315 K (during first 200 ps) and restrained positions of protein backbone atoms. 50 ns MD production runs were performed without restraints. Stability of the structures was estimated in terms of the root-mean square deviation (RMSD) of coordinates of backbone atoms from the starting structure, secondary structure changes, comparison of the interaction interfaces before and after MD, and calculation of dimer geometry parameters (crossing angle, inter-monomer distance, tilt angle with respect to membrane normal).

Calculations of the free energy of TM helix-helix association.

To estimate the free energy of TM domains dimerization, umbrella sampling approach with harmonic restraining potential was employed. The distance between monomers centers of mass was the reaction coordinate varying from 0.75 to 2.20 nm with a step 0.05 nm, thus resulting in 32 simulation windows. Starting conformations were constructed by translation of the monomers in the membrane plane along the reaction coordinate. The first 50 ns of MD simulation with restrained protein segments were allocated to system equilibration, followed by 50 ns long production runs.

Free energy profiles were obtained using weighted histogram analysis method (WHAM) and bootstrap analysis to estimate statistical errors (implemented in Gromacs package) [START_REF] Hub | g_wham-A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates[END_REF]. The values of dimerization free energy were determined as the depth of the profile minima. To evaluate the effect of point mutations, the substitutions V938D and V912E were introduced into two previously generated structures of IR and IGF-1R TM dimers, respectively. Resulting models of the mutant forms were subjected to energy minimization and MD relaxation followed by free energy estimation with the same protocol as described above.

2D Surface hydrophobicity maps of TM helical peptides.

The molecular hydrophobicity potential (MHP) approach [START_REF] Efremov | Environmental characteristics of residues in protein: Three-dimensional molecular hydrophobicity potential approach[END_REF] was used to assess the spatial surface properties of TM α-helices of various RTKs. The MHP constants for peptide atoms were assigned according to [START_REF] Wildman | Prediction of Physicochemical Parameters by Atomic Contributions[END_REF]; calculations of the molecular surfaces of peptides and their interpolation onto a cylinder were performed as described in [START_REF] Polyansky | PREDDIMER: a web server for prediction of transmembrane helical dimers[END_REF]. Average MHP maps were generated using frame sets from 200 ns MD trajectories calculated for IR m7 , IGF-1R m5 and IR m7-V938D dimers, as well as for TM dimers of EGFR, ErbB2, GpA (PDB ID: 2kpf), and PDGFRβ (PDB ID: 2l6w) receptors. Two starting conformations were considered for both EGFR and ErbB2: N-terminal dimer of EGFR (PDB ID: 5lv6), C-terminal dimer of EGFR (PDB ID: 2m0b), N-terminal dimer of ErbB2 (PDB ID: 2jwa), and C-terminal dimer of ErbB2 (PDB ID: 2n2a). The maps were centered on the main dimerization interface of each protein. Other details of MHP analysis were described elsewhere [START_REF] Efremov | The hydrophobic nature of membrane-spanning α-helices as revealed by Monte Carlo simulations and molecular hydrophobicity potential analysis[END_REF].

Results

Flowchart of the study.

As discussed above, structural information about dimerization of TM domains of both IR and IGF-1R receptors is indirect and rather scarce. Hence, development of reliable models of the TM helical dimers requires that all available structural data is taken into consideration. The first constraint comes from the experimentally observed closure of TM segments of IR upon its activation [START_REF] Scapin | Structure of the insulin receptor-insulin complex by single-particle cryo-EM analysis[END_REF]. Are the membrane-proximal regions of the IR ectodomain capable of performing such high-amplitude tweezerlike movements? To address the question, we explored dynamics of this protein part via a series of MD simulations in water. The aim was to check if there are collective movements, bringing TM helices into direct contact. The second source of data for exploring organization of TM domain of IR is provided by the available 3D structures and membrane topology of the juxtamembrane (JM) region, which forms complex with the insulin receptor substrate 1 (IRS-1). Because the spatial arrangement of this complex near the cytoplasmic membrane surface can be reconstructed based on the experimental data, it gives a nice opportunity to check how autonomous this TM domain is. This was done via MD simulations of the isolated TM helix and the same helix conjugated with the JM / IRS-1 partsin order to explore conformational flexibility of the TM monomer in both cases. This issue is extremely valuable for subsequent TM dimer prediction for both receptorsthe more independent TM domain is, the more reliable the results of structural modeling for the TM dimer are. MD simulations performed for the aforementioned IR parts limiting its TM domain from the extra-and intracellular sides demonstrated that the membrane-spanning helices can be considered as relatively autonomous segments. This was an important justification for further modeling the structure of TM homodimers of IR and IGF-1R as autonomous objects.

However, before such modeling, it was necessary to test in an experiment whether TM peptides themselves are able to form oligomers in membrane-like environment. So, series of NMR experiments with a peptide corresponding to the IR TM segment embedded into membrane-mimicking detergent micelles and lipid bicelles were carried out. Only after reliable confirmation of IR TM peptides interaction, atomistic simulations of the TM dimers of both receptors were performed. Two independent conformational search strategies were employed. First, the packing of TM dimers was predicted based on complementarity of the lipophilic/landscape properties of their individual TM helices [START_REF] Polyansky | PREDDIMER: a web server for prediction of transmembrane helical dimers[END_REF]. Then, spontaneous dimer assembly was carried out in a coarse-grained representation. Based on cluster analysis of the resulting dimers, several of the most populated states were selected and subjected to MD simulations in explicit hydrated lipid bilayerin order to keep only stable models for further analysis. The most energetically favorable TM dimers were elucidated based on the calculated free energies of helix-helix association. Biological relevance of the best models obtained for IR and IGF-1R TM domains was tested via comparison of the hydrophobic organization of TM helices and their homodimers for both wild-type receptors and two their mutants. Based on these data, the role of several TM segments from other proteins in activation of IR and/or IGF-1R was also discussed. Finally, available information about naturally occurred point mutations in the TM domains of both proteins was used to assess the elaborated models.

NMR spectroscopy of IR TM domains in micelles reveals multiple dimeric conformations.

In order to probe possible dimerization of the IR TM domains, the recombinant fragment IRtm, which included IR TM segment S925-R953, was dissolved in the aqueous suspensions of DPC micelles or DMPC/DHPC bicelles at detergent/peptide (D/P) or lipid/peptide (L/P) molar ratios varied from 40 to 160 (the latter corresponds to an average of one peptide per two micelles or bicelles). The pattern of helical structure probabilities (HSP) derived from the backbone chemical shift distribution of IRtm (Fig. 2C-F) indicates distinct TM helical structure from A928 to L952 in both membrane-mimicking environments. Line shapes of the signals in the NMR spectra (Fig. 2A,B) acquired at different D/P or L/P proved rather complex, implying that IRtm participates in several slow conformational exchange processes upon folding into multiple self-assembled structures, while its helical structure is preserved (as indicated by the similar chemical shifts). In the micellar environment, this apparently includes slow transitions between monomer, dimer, and another oligomer (e.g., second dimer, trimer or tetramer) detected as signal doubling and farther signal splitting (appearance of an additional satellite signal near some cross-peaks for the IRtm amide groups) observed within the D/P range used in the NMR experiments (Fig. 2A). The minimal distinguishable chemical shift difference between the signals of the IRtm states in the NMR spectra is ~20 Hz. Therefore, the transitions between multiple oligomerization states of IRtm in the micelles are a slow process (on a millisecond timescale or slower) with an occupancy of the states dependent on the D/P ratio. The transitions of IRtm embedded into the bicelles are also complex and presumably faster than in the micellar environment, as revealed by the L/P-dependent signal shifting and the appearance of signal multiplicity at low L/P (Fig. 2B). It is noteworthy that the patterns of NMR signal perturbation observed for the IRtm amide groups in the micellar and bicellar environment are apparently different. This is typical for weakly interacting TM domains of RTK-related receptors [START_REF] Bocharov | Structural basis of the signal transduction via transmembrane domain of the human growth hormone receptor[END_REF][START_REF] Bocharov | The Conformation of the Epidermal Growth Factor Receptor Transmembrane Domain Dimer Dynamically Adapts to the Local Membrane Environment[END_REF][START_REF] Polyansky | Atomistic mechanism of the constitutive activation of PDGFRA via its transmembrane domain[END_REF]. Thus, the NMR data show the principal ability of the IR TM domain to dimerize / oligomerize in different modes via alternative helix packing interfaces. 13 Cα chemical shifts, Δδ( 13 Cα) P-C , as the difference between the measured chemical shift and the typical chemical shift in a random coil conformation for IRtm embedded into the micelles and bicelles, respectively. E, F. Helical structure probabilities (HSP) derived from the backbone 1 H, 13 C, and 15 N chemical shifts for a given residue of IRtm embedded into the micelles and bicelles, respectively. Pronounced positive Δδ( 13 Cα) P-C values along with the HSP pattern are indicative of the helical structure distribution and its stability along the peptide sequence in the both membrane-mimicking environments.

Extracellular domain of IR is capable of tweezer-like motions of its membrane-proximal parts.

Analysis of three 200 ns long MD trajectories of IR ECD taken in its inactive form (PDB ID: 4zxb) showed notable conformational changes in two of them. These movements were accompanied by displacements of FnIII-3 segments located close to the membrane (residues D866-K876), but the overall character of the movement of mobile ectodomain units was different. The distance between the D866 residues located near the C-termini revealed different fluctuation pattern with mean values of 8.3±1.1, 8.4±0.8, and 6.8±2.4 nm, while for the active state this distance was 0.7±0.1, 1.1±0.2 and 1.9±0.3 nm in three independent runs (the distance plots are shown in Fig. S2A). No significant conformational changes were detected in the first 200-ns MD simulation performed for ectodomain initially taken in the active conformation (PDB ID: 6sof), and two other runs resulted in a non-symmetrical conformation with the "head domains" tilted, but no changes in FnIII-2 and FnIII-3 domains (Fig. 3A,B). This was the only high-amplitude intermolecular movement in the case of the active state model that did not change its structure sufficiently towards an inactive conformation. Using PCA technique, intramolecular movements were decomposed into a set of correlated motion modes along the eigenvectors of covariance matrix formed by displacements of coordinates for C α atoms. The eigenvectors were ranked by the value of their positional variance. In this decomposition, in the case of inactive ECD, we looked for the modes that bring the C-termini together, and such a tweezerlike motion was found to be the first (in two MD trajectories) or the second (in another one) eigenvector. This means that the found movement is significantits contributions to overall displacements of C α atoms were 13, 74, and 44%, respectively. Three variants of this motion mode have high degree of identity (aside from pushing C-termini together) that was approved by the calculation of their pairwise inner products (0.89, 0.91, and 0.62 for pairs 1-2, 2-3 and 1-3, respectively, see pairwise maps of inner products for the first five motions in Fig. S2B). Also, it was noted that there are no other highly similar motion modes observed in all three simulations of inactive ECD. However, the scale of these conformational changes is not enough to form a closely packed TM dimer in the inactive state. These motions look similar to that proposed by Uchikawa et. al. based on direct structure comparison between active and inactive states of IR [START_REF] Uchikawa | Activation mechanism of the insulin receptor revealed by cryo-EM structure of fully liganded receptor-ligand complex[END_REF]. To estimate structural similarity of the studied ectodomain model with its active state (Fig. 3A), we compared it with the MD-relaxed model of the latter, as tilted conformation (Fig. 3B) differs only in the "head" position with respect to FnIII "legs". First, we found that the hinge regions (shown in green in Figs. 3C,3D,3E) in two trajectories are located near the insulin binding site 1, although the latter is not correctly formed: FnIII-1 domain (residues Y493-D499, R539-K544) stays apart from the region formed by L1 moiety (marked with violet arrows on Fig. 3). Also, another hinge in the L2 domain is responsible for large structural rearrangements. Such changes were described by RMSD values calculated for backbone atoms of the domain pairs (Fig. S2C). These plots show that while the fit on the L2-L2' "core" is pretty good, the exact conformations of the inactive IR ectodomain are still very different from its active form. We observe correlated changes in domain behavior inside the FnIII domains and within the insulin binding pocket 1 in all trajectories, but only for MD2 there was a significant convergence towards the active conformation, except for the L1-L2 part (Fig. S2D). Hinge regions are widely distributed over the ectodomain: in two simulations we found them near the primary insulin binding sites 1/1', but in MD2 an alternative hinge was observed in the receptor "head", between L2 domains. This hinge region includes residues G463-C468 and the loop V515-C524 and also was proposed in [START_REF] Uchikawa | Activation mechanism of the insulin receptor revealed by cryo-EM structure of fully liganded receptor-ligand complex[END_REF]. It allows large-scale complex rotational motions. Interestingly, this is not the only hinge found for this simulation, and L1-L2 evolution showed the opposite direction of conformational changes, but still the overall shape of the ectodomain was closest to the active conformation (Figs. 3A,3C).

The intracellular part of IR is weakly structurally coupled to its TM domain.

As mentioned before, it is important to estimate the influence of the intracellular juxtamembrane (JM) domain on dynamics of TM domain. Although there is no direct structural data on JM domain position with respect to the membrane, we reconstructed it via step-by-step homology modeling (see Methods). Resulting model is schematically shown in Fig. 1C. It has two sites of membrane attachment: IR TM domain and pleckstrin homology (PH) domain of IRS-1, which interacts with IR JM via phosphotyrosine-binding (PTB) domain. To assess, whether the membrane-proximal cytoplasmic regions of the IR effect behavior of its TM domain or the latter can be considered autonomous, we compared the dynamics of the TM helix in the lipid membrane with and without the intracellular complex. In such a comparison, we used the following parameters: residue flexibility (expressed in terms of root-meansquare flexibility (RMSF) values), tilt angle θ of the TM helix axis with respect to the membrane plane, side chain directional angle α (this determines, whether a given residue is exposed towards the extracellular space or to cytoplasm).

It was shown that the JM region almost does not restrain flexibility of the TM helix with the exception of residues adjacent to the cytoplasmic membrane surface (Fig. 4A). We found that tilt angle θ fluctuates between 20° and 40° in all simulations, and Z coordinates of selected amino acid residues are the same in isolated TM helix and in complex (Figs. S3A,S3B). Moreover, in three independent MD simulations, distribution of θ in complex shows the same main maximum as for the isolated IR TM helix (Fig. 4B). Positioning of TM helix in bilayer is determined not only by the tilt angle of the helix axis and the shift along the membrane normal (Z), but also by the rotation angle φ. However, it can be described by side chain direction vectors or their Z projections or set of directional angles α i (Fig. 4C). Side chain direction vectors analysis confirmed identical behavior of the TM helix in both cases (Figs. 4D,S3C). Thus, the side chains of residues I930, F937, V938, F941, I945, I948, and Y949 were found to be turned towards the cytoplasm. In the presence of intracellular complex, this orientation is a bit more stable.

Figure 4. MD-derived structural/dynamic characteristics of isolated monomeric TM domain of IR (IR TM ) and IR TM+JM in complex with PH and PTB intracellular domains of the IRS-1 substrate (IR TM+JM / IRS-1 PH+PTB ).

A. Residue flexibility expressed in terms of the root-mean-square fluctuation (RMSF) values for IR TM (black) and IR TM+JM / IRS-1 PH+PTB (red). B. Distribution of the TM-helix tilt angle θ for IR TM (black) and IR TM+JM / IRS-1 PH+PTB (red). C. Definition of the angles describing helix position in the membrane. α-Helix and its directional vector (h) are shown in red and blue, side chain and its radius-vector are in green, membrane border and its normal vector (Z) -black. Angle θ determines helix tilt with respect to the membrane, angle φ accounts for helix rotation around its own axis, and α determines direction of amino acid side chain. D. Side chains direction angles (α) for residues in IR TM (black) and IR TM+JM (red). The data are averaged over three MD simulations. Positive values of α correspond to residues pointing towards the extracellular surface.

Spatial models of TM dimers and their stability in lipid environment.

Models of the dimers obtained de novo using the PREDDIMER program [START_REF] Polyansky | PREDDIMER: a web server for prediction of transmembrane helical dimers[END_REF] were clustered into seven and six main groups for IR and IGF-1R, respectively. All representative structures from these clusters had symmetric dimerization interface (Table S5), as non-symmetrical ones are less favorable due to the scoring function implemented in the PREDDIMER algorithm (This approximation looks quite realistic, since the vast majority of the homodimers with a known 3D structure have a symmetrical dimerization interface). To select the models well adapted to the membrane environment, they were subjected to MD simulations in hydrated lipid bilayer. Only four dimers for each receptor were stable in the membrane-mimicking environmentthey demonstrated small fluctuations of RMSD values calculated for protein backbone atoms with respect to the starting conformation. In addition, helical structure and helix packing geometry of the dimers were well preserved in the course of MD. As a result, only these eight models were selected for further consideration (Table 2).

Despite different starting conformations (parallel and glycophorin-like, or crossed), two IR models (IR m1 and IR m2 ) revealed similar dimer packing parameters after 50 ns MD run. These models differ by the conformation of the N-terminal segments that are highly flexible due to the kink at the Pro934 residue. The calculated RMSD values for these two models were: 0.3 nm for the whole dimer and 0.1 nm for the C-terminal segments. Thus, it was reasonable to suppose that these models represent the same state, which is stabilized by intermolecular interactions on the C-termini of TM helices having glycophorin-like SxxxG pattern. The model IR m6 has similar dimerization interface, but positive value of the crossing angle between the helical axes. Finally, the model IR m7 exhibits stable symmetric helix-helix interface with parallel packing of the monomers.

Analysis of the resulting four stable dimer models of IGF-1R revealed that all of them possess non-glycophorin-like type and have different values of the crossing angle. So, at this stepbased on structural/dynamic data only -there is no means to give preference to any of the structure. Further differentiation and ranking can be done only upon assessment of their dimerization free energy.

Self-association of TM domains as probed by coarse-grained MD simulations.

Although PREDDIMER proved its effectiveness [START_REF] Polyansky | PREDDIMER: a web server for prediction of transmembrane helical dimers[END_REF], it (like any predictive approach for proteins) has a number of limitations. First, as mentioned above, the resulting structures of homo-dimers are symmetrical. Second, it is assumed a priori that two helices necessarily form a complex -the only question is the value of the corresponding scoring function. Finally, in PREDDIMER the membrane is implicitly taken into account. Therefore, an independent prediction approach is required to assess the reliability of the generated 3D dimeric models of the TM domains of IR and IGF-1R. This was done using coarse-grained MD simulations in a hydrated lipid bilayer.

Such approximation limits the conformational mobility of peptides, but allows their lateral movements in the membrane and association. At the end of 500-ns long MD simulations, 83% of IR (414/500) and 72% of IGF-1R (360/500) pairs of monomers dimerized spontaneously. In order to see, what dimeric structures were formed, 2D residue contact maps were calculated (Fig. 5). The maps were averaged over the whole set of the resulting helix-helix models. As seen in Fig. 5, TM domains of IGF-1R prefer parallel helix packing within the dimer, that is characterized by a number of frequently formed symmetric contacts V912-V912', L915-L915', V922-V922', and Y926-Y926'. In contrast, IR dimers showed a wider distribution of residue-residue contacts, which lie outside the diagonal on the map, indicating a high population of asymmetric structures.

Compared to the selected PREDDIMER models (see above), reproducibility rates of these selfassembled dimers were 36% (128 of 360 models have backbone RMSD < 0.3 nm with one of PREDDIMER models) for IR and 55% (228 of 414) for IGF-1R. In the case of IR, we observed multiple modes of helix packing in dimers: 58 dimers were close to the IR m6 model, and 38 others -to IR m7 . However, these two groups cover the majority of the self-assembled structures that can be clustered based on geometry. By contrast, most part of the assembled IGF-1R dimers (122 of 228) reproduced the single model IGF-1R m5 with parallel packing of monomers (see color markers on Fig. 5). So, at this step, no new candidate models compared to PREDDIMER predictions were found. Color markers show dimerization interfaces found in PREDDIMER models IR m1 and IGF-1R m1 (green), IR m2 and IGF-1R m5 (magenta), IR m7 and IGF-1R m4 (red), IR m6 and IGF-1R m6 (blue).

Free energy of TM α-helix dimerization in IR and IGF-1R.

The evaluated dimerization free energy (ΔΔG) data for IR and IGF-1R reveal that the unified IR models (IR m1 and IR m2 , green and black curves in Fig. 6A, respectively) have similar shape of the energy profile and almost identical values of the potential of mean force (PMF). This supports an assumption of the feasibility of the SxxxG interaction motif. In contrast, the model IR m6 is not energetically favorable (blue curve in Fig. 6A), while the model IR m7 represents an alternative variant of packing -it has the opposite interface, which includes the conservative residue Pro934. For the latter model, the free energy of helix-helix association is comparable to that of IR m1/m2 (red curve).

In the case of IGF-1R, the deepest ΔΔG minimum -41±4 kJ/mol is revealed by the model IGF-1R m5 (Figure 6B, black line). Moreover, its PMF profile is well separated from those obtained for alternative states IGF-1R m1 , IGF-1R m4 , and IGF-1R m6 . We therefore propose this model with parallel packing of helices and residues P911 lying on the interface as a potential dimeric state of IGF-1R. a Color mapping corresponds to that used in Table 1. Underscores correspond to residues that do not participate in protein-protein interactions. b Crossing angles between helices axes. c,d Distances and free energy values correspond to minima on the calculated PMF profiles (values with standard deviations were taken from data shown in Fig. 6). Comparison of the resulting favorable dimer models of IR and IGF-1R (fragments A927-L951 and H905-H929, respectively) in terms of RMSD between protein backbone atoms, shows that the model IGF-1R m5 is structurally close to IR m7 (RMSD = 0.16 nm, Fig. 6C), while for the dimers IR m1 and IR m2 the corresponding RMSDs with IGF-1R m5 are 0.32 and 0.30 nm, respectively.

3D models of TM dimers explain the effect of point mutations IR V938D and IGF-1R V912E .

For each receptor, single functional mutation was described in the TM domain: V938D in IR and V912E in IGF-1R (Table S1). Both of them induce basal activity of the receptors. Therefore, availability of the constructed 3D models of TM domains provides a nice opportunity to check, how the mutations can affect the structure and dynamics of the dimers. These effects were explored via atomistic MD simulations of the dimers composed of TM peptides with the corresponding point replacements. Initial conformations of the dimers were built based on the structurally closest models IR m7 and IGF-1R m5 (see Methods). The results obtained permit the following conclusions: (1) In both dimeric models, the mutated residues lie on the helix-helix interface (Table 2, models IR m7 , IGF-1R m5 ). (2) In IR V938D , additional hydrogen bond appears between the introduced D938 residue and P934 of the opposite subunit, but no significant structure alternation was detected. (3) No additional hydrogen bonds were found in the IGF-1R V912E dimer, it was also stable in 50 ns MD simulation. (4) The calculated free energies of dimerization (ΔΔG) of mutant dimers (red profiles on Fig. 7) were surprisingly lower (especially, in case of IR) than those obtained for the wild-type dimers (black curves). ( 5) The free energy minima on the PMF profiles are equal to -69 ± 4 and -48 ± 4 kJ/mol for IR m7-V938D and IGF-1R m5-V912E , respectively.

Hydrophobic organization of TM segments of IR, IGF-1R and some other bitopic membrane proteins.

An additional opportunity to probe the resulting models of TM dimers of IR and IGF-1R is provided by the availability of data on functional activity of the full-length hybrid receptors, whose TM domains were artificially replaced by TM segments of a number of other bitopic membrane proteins. Among the latter are different growth factor receptors and their mutants: EGFR, ErbB2, PDGFRβ [START_REF] Yamada | Substitution of the insulin receptor transmembrane domain with the c-neu/erbB2 transmembrane domain constitutively activates the insulin receptor kinase in vitro[END_REF][START_REF] Cheatham | Substitution of the erbB-2 oncoprotein transmembrane domain activates the insulin receptor and modulates the action of insulin and insulin-receptor substrate 1[END_REF][START_REF] Yamada | Role of the Transmembrane Domain and Flanking Amino Acids in Internalization and Down-regulation of the Insulin Receptor[END_REF][START_REF] Bennasroune | Inhibition by transmembrane peptides of chimeric insulin receptors[END_REF] and GpA [START_REF] Gardin | Substitution of the insulin receptor transmembrane domain with that of glycophorin A inhibits insulin action[END_REF]. In the first three cases, both IR and IGF-1R demonstrated either normal or basal activity, while employment of TM GpA sequence resulted in significant drop of the hybrid receptor functioning (Table S1). Taking into account such an interchangeability of the TM segments, it seems reasonable to assume that appearance of the functional hybrid can be interpreted as a prove that the host and the guest TM segments have rather similar physico-chemical organization of their monomers, thus ensuring correct TM homodimer conformation in the active state. To check this, we compared 2D maps of distribution of hydrophobic/hydrophilic properties on the surfaces of the studied TM α-helical segments (Fig. 8). These properties were expressed in terms of the molecular hydrophobicity potential (MHP) values calculated in points of the solvent-accessible surface [START_REF] Efremov | The hydrophobic nature of membrane-spanning α-helices as revealed by Monte Carlo simulations and molecular hydrophobicity potential analysis[END_REF]. Upon considering the entire maps, special attention was given to the MHP-organization in the helix-helix interfacial zones (shown with contour lines in Fig. 8) because they play an important role in helix packing. The following conclusions were made. First, there are large differences between the maps of our models of IR and IGF-1R (Fig. 8A,8B) and GpA-like packing (Fig. 8C,8D). Boththe contact areas and the MHP distributions -are very different, namely all GpA-like structures (GpA itself and the N-terminal dimers of EGFR and ErbB2) have large hydrophilic areas lying on the interaction interface in its central (residues G79 and G83 for GpA) or the N-terminal parts (EGFR, ErbB2). In contrast, alternatively packed EGFR and ErbB2 Cterminal dimers (Fig. 8E) show no large hydrophilic contact areas. The same is true for IR m7 and IGF-1R m5 both having long hydrophobic patches. The unique mark is the small hydrophilic area formed by V938, S942 and G946 in IR and G919, G920 in IGF-1R lying near the dimerization interface. This area is also affected by V938D mutation in IR, but not V912E in IGF-1R, as shown in Fig. 8B. In addition, one can mention more hydrophilic C-terminal part of the interaction site for IR, IGF-1R, and also in EGFR and ErbB2 C-terminal dimers. This similarity may reflect the ability of these sequences to functionally replace IR and IGF-1R fragments. PDGFRβ stays apart (Fig. 8F), but it has also prolonged interface shifted towards the C-terminus.

Discussion

The latest structural data available for IR ectodomaintwo models representing the active state [START_REF] Weis | The signalling conformation of the insulin receptor ectodomain[END_REF][START_REF] Uchikawa | Activation mechanism of the insulin receptor revealed by cryo-EM structure of fully liganded receptor-ligand complex[END_REF] suggests a prominent closure of FnIII-3 domains, that allows dimerization of TM segments. MD simulations showed high degree of stability for such a conformation having the only hinge region between FnIII-1 and FnIII-2 domains that result in a "tilted" form with no significant changes in the D866-D866' distance. Such "tilted" and non-symmetrical structures have been previously mentioned in [START_REF] Gutmann | Cryo-EM structure of the complete and ligand-saturated insulin receptor ectodomain[END_REF]. In contrast, our MD simulations of the X-ray model of IR ectodomain in its ground state [START_REF] Croll | Higher-Resolution Structure of the Human Insulin Receptor Ectodomain: Multi-Modal Inclusion of the Insert Domain[END_REF] revealed several hinge regions. This determines a set of molecular motions, the most notable of which are the tweezer-like closure of the C-terminal "legs" and the complex rotation inside the L1-L2 "core". The accumulated two simulation sets were not enough to fill the gap between the inactive and active conformations and showed a large variety of hinge regions being available for conformational changes, so the activation process may have multiple steps. However, our results are in line with the experiments showing FnIII-3 and TM domains closure [START_REF] Kavran | How IGF-1 activates its receptor[END_REF][START_REF] Weis | The signalling conformation of the insulin receptor ectodomain[END_REF][START_REF] Gutmann | Visualization of ligand-induced transmembrane signaling in the full-length human insulin receptor[END_REF] and with previous assumptions made by structural alignment in [START_REF] Uchikawa | Activation mechanism of the insulin receptor revealed by cryo-EM structure of fully liganded receptor-ligand complex[END_REF]. Although we did not succeed in reproducing the complete association of the membrane-proximal domainsthis happens only upon insulin-induced IR activationwe found that both these types of motions are inherent already in the inactive state of the receptor. Hence, it seems that insulin acts as a triggerits binding ultimately shifts the active/ground state equilibrium inducing local conformational changes in these protein parts, which are then converted into large-scale rearrangements resulting in dimerization of TM segments. It is noteworthy that multiple hinge regions found in the ectodomain explain the ability of IR to bind different number of ligands in a step-wise manner that is in line with latest structural results describing liganded state of the ectodomain [START_REF] Hayward | Systematic Analysis of Domain Motions in Proteins from Conformational Change; New Results on Citrate Synthase and T4 Lysozyme[END_REF][START_REF] Uchikawa | Activation mechanism of the insulin receptor revealed by cryo-EM structure of fully liganded receptor-ligand complex[END_REF]. Finally, we assume that besides monomeric/dimeric forms of TM domain respectively in the ground/active states, there exist other intermediates with dimerized or dissociated TM helices. Because several favorable modes for IR TM dimerization were predicted in silico and detected in NMR experiments, the question of exact IR activation mechanism is still open. We suggest that this multi-step nature of the IR activation may be the reason that its TM dimer structure has not yet been solved by NMR and may indicate the existence of a potential intermediate state(s) [START_REF] Li | Solution structure of the transmembrane domain of the insulin receptor in detergent micelles[END_REF]. To summarize, we conclude that the available experimental data and the reported here computational results on dynamic behavior of the ECDs of IR and IGF-1R principally allow ligand-induced approaching of their terminal (membrane-proximal) FnIII-3 domains followed by dimerization of TM segments inside the lipid bilayer.

In addition, structural modeling of TM dimers requires an answer to the following question: "How autonomous are membrane domains?" In other words, do the intracellular parts of the receptors affect association of TM helices? To address this issue, spatial location of the cytoplasmic juxtamembrane (JM) region with respect to the lipid bilayer was reconstructed. Inspection of dynamic behavior of the membrane-embedded monomeric TM segment with/without the JM "anchor" shows that the latter does not strongly limit the conformational mobility of TM helix. So, the simulation data obtained for bothextra-and intra-cellular parts of the receptorswere considered in favor of computational modeling of TM dimers of IR and IGF-1R approximated simply by their membrane-spanning helices without neighboring protein regions. The concept of partially independent behavior of these domains is in line with recent experiments for other members of the RTK family [55]. Furthermore, because IR and IGF-1R can form functional hybrid receptor [START_REF] Belfiore | Insulin Receptor Isoforms and Insulin Receptor/Insulin-Like Growth Factor Receptor Hybrids in Physiology and Disease[END_REF], an assumption was made that these proteins have similar molecular mechanism of activation, or, at least, its final steps resulting in signal transduction and, therefore their TM dimers share common packing properties in active conformation.

The first direct experimental evidence of the ability of the peptides representing helical TM segments of IR to associate in the membrane-mimicking environments (DPC micelles and DHPC/DMPC bicelles) by high-resolution method have been obtained in this work by NMR spectroscopy. Our results slightly differ from those obtained in [START_REF] Li | Solution structure of the transmembrane domain of the insulin receptor in detergent micelles[END_REF], possibly, due to different length of the studied peptide. We assume that having large fragment on the extracellular side, the dimerization is inhibited due to strong interaction of this amphiphilic JM sequence with the micelle surface observed in [START_REF] Li | Solution structure of the transmembrane domain of the insulin receptor in detergent micelles[END_REF], while the His-rich N-terminal part of IRtm is soluble. Shorter IRtm also showed higher degree of helicity in I931-I932 region proposing more elongated peptide conformation in the less perturbed micelle or bicelle. In addition, IRtm has a helical conformation in both monomeric and dimeric (oligomeric) states. This served as the basis for atomistic modeling of TM domain association for both IR and IGF-1R.

Using two independent techniques, for IGF-1R we found a single energetically favorable and spontaneously assembled dimeric state with parallel packing of the helices (model IGF-1R m5 in Fig. 6). We therefore propose this conformation as a prospective model for the active state. Interestingly, being applied to IR, similar computational approach yields multiple dimeric structures, and some of them are predicted independently by different algorithms, namely the models IR m6 and IR m7 . The latter was selected as a potential active dimer because it has the same parallel packing as the aforementioned IGF-1R m5 . The corresponding structural alignment is shown in Fig. 6C. Noteworthy, the calculated multi-state organization of TM domain in IR agrees well with our NMR data, where simultaneously several oligomeric conformations were observed. Having quite deep minima on PMF profiles, these TM dimers have a good tendency to form spontaneously as FnIII-3 domains come close enough, that is in line with current view on receptor activation process [START_REF] Kavran | How IGF-1 activates its receptor[END_REF][START_REF] Lee | Insulin Receptor Activation with Transmembrane Domain Ligands[END_REF][START_REF] Scapin | Structure of the insulin receptor-insulin complex by single-particle cryo-EM analysis[END_REF].

Having multiple favorable models for IR TM dimer, we focused on the inactive IR ectodomain modeling based on well determined X-ray structure to search for inactive TM dimer signs. Our analysis revealed several hinge regions inside IR ectodomain allowing a wide set of molecular motions, including both tweezer-like closure of the C-terminal "legs" and a complex rotation inside the L1-L2 "core". Despite we did not succeed in reproduction of whole ectodomain evolution, we propose that both L1-L2 rotation and tweezer-like motions are crucial for IR activation. Due to the presence of multiple hinge regions in ectodomain, the receptor can pass through a number of states with different TM dimer conformations. Finally, we assume that there is no TM dimer in fully-inactive receptor, and there is active TM dimer indeed. Despite the fact that we have found several favorable modes for IR TM dimerization and detected signal shifting, doubling and even more splitting in NMR spectra, the question of the exact IR activation mechanism is still open. Another question comes from the data on the active ECD movements showing non-symmetrical behavior during MD. This may indicate spontaneous formation of several TM dimer structures. However, this is in agreement with the experimental results.

How to evaluate the correctness of the elaborated dimeric models of TM domains of both receptors in the absence of direct structural data? First, we checked spatial disposition of two functionally important point mutations -V938D in IR and V912E in IGF-1R (Table S1). Both of these acidic residues are known to cause basal activity of the receptors [START_REF] Takahashi | Insulin-like Growth Factor I Receptor Activated by a Transmembrane Mutation[END_REF][START_REF] Longo | Activation of insulin receptor signaling by a single amino acid substitution in the transmembrane domain[END_REF]. Interestingly, in the best dimeric models, the mutations lie near the helix-helix interfaces. In addition, they result in intrusion of the polar side chains of Asp/Glu into the hydrophobic core of the dimers. As a rule, appearance of additional polar contacts in nonpolar environment has a stabilizing effect. Indeed, mutation V938D in IR dimer results in hydrogen bond formation of the carboxyl group of D938 with backbone of the second monomer, that resembles the mechanism of neu-mutation effect proposed in ErbB2 [55]. This was confirmed by calculations of the free energy of helix-helix association in lipid bilayerit is significantly lower for mutant peptides. For example, the free energy difference between IR and IR V938D dimers is close to the energy gain usually observed upon formation of a hydrogen bond in hydrophobic medium (~30 kJ/mol) [START_REF] Efremov | Dielectric-dependent strength of interlipid H-bonding in biomembranes: Model case study[END_REF].

Second, physico-chemical properties (e.g., distribution of surface hydrophobicity expressed in terms of MHP) of helical monomers and their mutual arrangement in the dimers (e.g., parallel vs crossed packing) of IR and IGF-1R was compared with analogous characteristics of TM helices of several other proteins, which are capable/uncapable of dimerizing with IR and/or IGF-1R, thus resulting in functional receptors. We assumed that in the case of experimentally proved interchangeability of TM segments, their surface MHP maps and packing in the dimers resemble each other, and vice versa. As it was shown here, such characteristics obtained for both studied receptors are very different from those in GpA, thus explaining inactivity of the IR/GpA hybridthe full-length insulin receptor with TM domain of GpA. By contrast, the ability of other RTKs -EGFR and ErbB2 -to switch between two dimerization interfaces may be a key feature explaining why these TM domains do not cause strong changes in functioning of such a hybrid IR/EGFR (or IR/ErbB2) receptor. Furthermore, TM helix of PDGFRβ has an extended dimerization interface, which resembles that predicted for IR and IGF-1R dimers. Being considered together with similar hydrophobic properties of the helices and the helix-helix interfacial area, this explains the experimentally observed functionality of the hybrid receptor. Finally, an interesting opportunity to probe dimeric models of IR and IGF-1R was provided by the recent experimental data on IR with ectodomain containing leucine zipper GCN4 on the С-terminus: this construct improved reproducibility of the ligand binding assay in water solution [START_REF] Weis | The signalling conformation of the insulin receptor ectodomain[END_REF]. It is important that such a modification mimics formation of a dimeric state in TM domain of the wild-type receptor. Experimentally derived 3D structure of the zipper was shown to be rather similar: compared to our IR m7 model, the structure of GCN4 zipper (PDB ID: 4dmd) used in the structural study [START_REF] Oshaben | The native GCN4 leucinezipper domain does not uniquely specify a dimeric oligomerization state[END_REF] show significant similarities having small positive crossing angle (~21°). This confirms that the predicted geometry of TM helix-helix dimer permits realization of the functionally active form of the IR ectodomain.

Based on the totality of experimental and calculated data obtained in this work, we come to the following conclusions (they are schematically summarized in Fig. 9): (1) In the full-size IR and IGF-1R, dimerization of TM segments does not contradict the available structural data. (2) According to NMR measurements in membrane mimic, the isolated TM segment of IR undergoes spontaneous selfassociation revealing multiple oligomeric states. This proves its high propensity for association in membrane-like environments. (3) Molecular modeling reveals that both proteins have structurally similar preferred conformation of TM dimers presumably representing the active state. (4) Modeling of extracellular and intracellular parts favors a step-wise transduction of conformational changes within the molecule starting with its ectodomain. We propose that there is no TM dimer in a completely inactive receptor (Fig. 9A), but finally -after ligand binding followed by closure of FnIII-3 domains -parallel packing of TM segments results in approaching of intracellular kinase domains. [START_REF] Diehl | Insulin resistance in Alzheimer's disease[END_REF] The IR dimer apparently has at least two conformations (intermediate + active (Fig. 9B,9C)). This may indicate that an ensemble of IR states occurs during activation, which is consistent with the different stoichiometry of known insulin-IR complexes. [START_REF] Xu | How ligand binds to the type 1 insulin-like growth factor receptor[END_REF] Mutations in the TM domain that cause basal receptor activity lie at the dimerization interface in the dimers and increase their stability. [START_REF] Croll | Higher-Resolution Structure of the Human Insulin Receptor Ectodomain: Multi-Modal Inclusion of the Insert Domain[END_REF] The hydrophobic organization of TM helix surfaces and their packing in IR and IGF-1R dimers are preserved among a group of receptors with interchangeable TM domains.

The proposed 3D models of receptor dimers provide a structural basis for the rational design of further ways to regulate the functioning of these key components of cell signaling. Among such "modulators" we outline the creation of artificial "interceptor peptides" targeting TM domains of receptors and alteration of membrane properties around the receptorsthis can affect the activation of such RTKs [55].

Figure 1 .

 1 Figure 1. Step-by-step scheme of building the model of Insulin Receptor (IR) transmembrane (TM) and juxtamembrane (JM) domains in complex with intracellular insulin receptor substrate -1 (IRS-1) phosphotyrosine-binding (PTB) domain. A. Structural alignment of IRS-1 PTB domain from structure 1irs with IL-4 replaced by IR JM (IRS-1 PTB domain is yellow and bound IR JM domain is red) and 1qqg (IRS-1 PTB and pleckstrin homology (PH) domains shown in cyan). B. Subsequent alignment of the structure from previous step with a pleckstrin homology domain of Tandem Ph-Domain-Containing Protein 1 (1eaz, blue) with the predicted bilayer inner surface (orange spheres). C. Resulting structure of IR TM-JM segment (red) in complex with PTB and PH domains of IRS-1, located on lipid bilayer (only phosphorus atoms are shown as orange spheres).

  ------RTLYASVNPEYFSASD939

Figure 2 .

 2 Figure 2. NMR spectroscopy of IRtm in membrane-mimicking environments. A. Overlaid 1 H/ 15 N-HSQC NMR spectra of IRtm embedded into the DPC micelles at D/P of 40 (in red) and 120 (in blue), 313 K and рН 6.7. The 1 H-15 N backbone and side-chain resonance assignments are shown (cross-peaks from the N-terminal part of IRtm disappeared due to fast water-amide proton exchange in the H6 tag sequence). On the top, IRtm undergoes a slow monomer-dimer-oligomer (or second dimer) transitions, as proved by the comparison of the 1 H/ 15 N-HSQC spectra revealing the appearance of pronounced signal multiplicity at D/P of 40. sequential NMR spectra within four boxes present the cross-peaks of G933 and G946 of the NMR spectra acquired for IRtm embedded into micelles at D/P varied from 40 to 160. In micelles, IRtm undergoes a slow monomer-dimer-oligomer (or second dimer) transitions with an occupancy of the states dependent on D/P, as proved by the comparison of the 1 H/ 15 N-HSQC spectra revealing the gradual appearance of pronounced signal multiplicity at low D/P. The cross-peaks corresponding to monomer and dimer (oligomer) states of IRtm are marked by 'M' and 'D', respectively. B. Overlaid 1 H/ 15 N-HSQC NMR spectra of IRtm embedded into the DMPC/DHPC bicelles at L/P of 40 (in red) and 160 (in blue), 313 K and рН 6.7. On the top, sequential NMR spectra within four boxes present the cross-peaks of G933 and G946 of the NMR spectra acquired for IRtm embedded into bicelles at L/P varied from 40 to 160. In bicelles, IRtm undergoes the monomer-dimer-oligomer transitions faster than in the micellar environment, as proved by the comparison of the 1 H/ 15 N-HSQC spectra revealing the L/P-dependent signal shifting and the appearance of signal multiplicity at low L/P. The cross-peaks corresponding to monomer, dimer (oligomer) and mixed states of IRtm are marked by 'M',

Figure 3 .

 3 Figure 3. IR extracellular domain (ECD) structure and motions. A. Model of the active state constructed based on its cryo-EM structure [38]. Two monomers are shown in red and blue, respectively. Insulin molecules are colored in gray, and primary insulin binding sites are in violet with arrows pointing on them. Secondary structure elements are given in ribbon presentation. B. The tilt motion observed in two MD trajectories of the active ECD conformation with the hinge region between FnIII-1 and FnIII-2 domains. C, D, E. Schematic images of the "tweezer-like" and other motion types observed in three MD simulations filtered by the first/second principal component of the motion. Red and blue parts show moving and fixed parts of the molecule, hinge regions are colored in green, primary insulin binding sites 1 and 1' are shown in violet with violet arrows pointing towards their L1 and FnIII-1 parts. Black arrows indicate directions of motion for each trajectory. Flexible and unstructured regions are colored in gray. Orange line schematically represents the membrane surface.

Figure 5 .

 5 Figure 5. Contact occupancy maps for self-assembled TM dimers of insulin receptor (IR segment 930-951, panel A) and insulin-like growth factor receptor 1 (IGF-1R fragment 907-928, panel B) predicted via coarse-grained MD simulations. The maps were calculated for each of 414 (IR) and 360 (IGF-1R) dimerized structures and averaged.Color markers show dimerization interfaces found in PREDDIMER models IR m1 and IGF-1R m1 (green), IR m2 and IGF-1R m5 (magenta), IR m7 and IGF-1R m4 (red), IR m6 and IGF-1R m6 (blue).

Figure 6 .

 6 Figure 6. Free energy (ΔΔG) of helix-helix interaction calculated for selected models of TM dimers in IR and IGF-1R via MD simulations in lipid bilayer. A, B. Potential of mean force (PMF) profiles of IR (A) and IGF-1R (B) for dimer models IR m2 /IGF-1R m5 (black), IR m7 /IGF-1R m4 (red); IR m1 /IGF-1R m1 (green), and IR m6 /IGF-1R m6 (blue). Standard deviations on PMF profiles are shown with vertical error bars. C. Structural and sequence alignment of two energetically favorable models with parallel packing: IR m7 (cyan) and IGF-1R m5 (green). Conservative amino acid residues are shown with sticks and marked with bold letters.

Figure 7 .

 7 Figure 7. Free energy (ΔΔG) profiles calculated for TM dimers of IR m7 (A) and IGF-1R m5 (B) via MD simulations in lipid bilayer. PMF plots for the wild-type dimers and the related mutant forms are shown with black and red colors, respectively. Other details are the same as in the legend to Fig. 6.

Figure 8 .

 8 Figure 8. Molecular hydrophobicity potential (MHP) distribution maps for TM dimers of IR and IGF-1R TM (A), their mutant forms IR V938D and IGF-1R V912E (B), glycophorin A (C), N-terminal GpA-like TM dimers of EGFR and ErbB2 (D) and their alternative C-terminal dimers (E), and PDGFRβ TM segment (F). The cylindrical projection of the surface MHP distribution is used. Axis values correspond to the rotation angle around the helical axis (φ) and the distance along the latter (h), respectively. 2D maps are colored according to MHP arbitrary units [49] from blue (hydrophilic areas) to brown (hydrophobic ones). The maps were averaged over 200 ns MD simulations. Contact area between monomers in the corresponding TM dimers is marked by a black contour. Residual marks correspond to average positions of their C α atoms.

Figure 9 .

 9 Figure 9. Schematic illustration of the key stages of the proposed mechanism of signal transduction by IR. ECDextracellular domain, JMjuxtamembrane region, TMDtransmembrane domain, KDkinase domain. Left to right: structural rearrangements of the receptors inferred from structural information obtained in this work (indicated by numbers 1 and 2 in circles) and available literature data. A. Inactive state: disulfide-linked ECD is in unliganded U-shape conformation, TMD helices are separated. B, C. The ligand binding induces conformational changes in ECD that bring their C-termini closer together (1, indicated by black arrows) resulting in transient dimerization both of TMD and KD (marked with 2 in circle). Further switching of IR dimer accompanied by rearrangements of all domains into the active state allows phosphorylation of the target tyrosine residues (pY) followed by the stimulation of the downstream signaling cascades.

Table 1 .

 1 Sequence alignment for TM and JM domains of human IR, IGF-1R, and IRR receptors.

Table 2 .

 2 Parameters of the resulting stable TM dimer models for IR and IGF-1R.

	Receptor Model	Interaction interface a	Angle b , deg.	Distance c , nm	ΔΔG d , kJ/mol
		m1	___I___I__PL__V___S__IG__YLF___ ___I__II___L__VF__SV__G___L__R_	-25	0.9	-30.1 ± 4.7
	IR	m2 m6	___I__I___P___VF__S__IG__YLF_R_ P__I___I___L__VF__SV__GS_YL__R_ _S__AK__I__L___F__S___G__YL_LR_ _S__A___I__L__VF__S______Y__LR_	-17 29	0.9 0.8	-36.2 ± 3.5 -22.8 ± 5.0
		m7	______II__P___V__F___I__IY__L__ ___I__II__P___V__F___I__IY__L__	3	1.0	-33.9 ± 6.0
		m1	____H______V___LI__G___M___F__K _______I_______LI__G___M___F___	-27	1.2	-19.7 ± 3.5
	IGF-1R	m4 m5	________________I__GL__M_______ ________________I__GL_IM_______ ___I__II__P___L______V__LY__HR_ ___I__II__PV__L___G__V___Y__H__	44 5	1.2 1.0	-22.4 ± 3.2 -41.3 ± 4.1
		m6	_____________V______L___L__F___ __________P__V__IV__L___L______	35	1.3	-16.1 ± 2.7

Acknowledgments

Supercomputer calculations were supported within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project "5-100". Access to computational facilities of the Supercomputer Center "Polytechnical" at the St. Petersburg Polytechnic University and IACP FEB RAS Shared Resource Center "Far Eastern Computing Resource" equipment (https://cc.dvo.ru) is gratefully appreciated. Coarse-grained MD simulations were partially carried out using the equipment provided by the IBCH core facility (CKP IBCH, supported by Russian Ministry of Education and Science, grant RFMEFI62117X0018). The authors express their sincere thanks to Dr. K.A. Beyrit for helpful discussions.

Funding

This work was supported by the Russian Science Foundation (project #18-14-00375) in part of MD simulations and NMR spectroscopy. Protein engineering and MHP analysis were supported by the Russian Foundation for Basic Research (projects #18-54-15007 and #18-04-01289).