Dimerisation of the Yeast K+ Translocation Protein Trk1 Depends on the K+ Concentration

In baker’s yeast (Saccharomyces cerevisiae), Trk1, a member of the superfamily of K-transporters (SKT), is the main K+ uptake system under conditions when its concentration in the environment is low. Structurally, Trk1 is made up of four domains, each similar and homologous to a K-channel α subunit. Because most K-channels are proteins containing four channel-building α subunits, Trk1 could be functional as a monomer. However, related SKT proteins TrkH and KtrB were crystallised as dimers, and for Trk1, a tetrameric arrangement has been proposed based on molecular modelling. Here, based on Bimolecular Fluorescence Complementation experiments and single-molecule fluorescence microscopy combined with molecular modelling; we provide evidence that Trk1 can exist in the yeast plasma membrane as a monomer as well as a dimer. The association of monomers to dimers is regulated by the K+ concentration.


Introduction
Trk1 is the main K + uptake system in baker's yeast (Saccharomyces cerevisiae). Deletion of TRK1 prohibits growth in/on medium containing low K + (see, e.g., [1,2]). Trk2 is a similar protein that, however, seems less important for promoting growth in limiting K + media because its expression level is much lower [3]. In addition to their main role, the uptake of K + , Trk1, and Trk2 are involved in several other processes, such as the regulation of membrane potential [4,5]; and Ca 2+ homeostasis [6]. Yeast Trks belong to the superfamily of K transporters (SKT), which is widespread in prokaryotes, fungi, and plants and consists of monovalent cation-translocation systems (for review, see, e.g., [7]). Most SKT proteins are thought to mediate passive ion translocation in the direction of the ions' electrochemical gradient, but the family also includes a subunit of the K + pump whose structure has been solved (KdpFABC; [8,9]). The cation-translocating parts of SKT proteins share the same principal architecture consisting of four Membrane-helix-Pore-Membrane helix (MPM) motifs (A-D) consisting of two transmembrane segments (M1 and M2) and a pore-forming region (P) between them ( Figure 1A). Each MPM motif is thus homologouss to a 2-Transmembrane domain (2-TM) K-channel α-subunit. As K-channel α subunits the MPM motifs of Trks are arranged around a central pore ( Figure 1B,C). It is worth mentioning that Stewart R. Durell and Robert H. Guy already proposed the similarity between SKT proteins and Kchannels in 1999 [10]. They detected the evolutionary relationship of MPM motives between SKT-proteins families and K-channels [11] and developed structural models for different SKT  SKT proteins might contain auxiliary subunits like TrkA, which is associated with TrkH, and KtrA, which is associated with KtrB. Yeast Trk1 and Trk2 instead possess a so called "large hydrophilic loop" (LHL) that is not necessary for ion translocation but modulates the cation selectivity of Trk1 [13].
We previously developed an atomic scale model of Trk1 [14] based on the available crystal structures of TrkH [15] and KtrB [16] that are both dimers. Consequently, our model is also a dimer. However, the architecture of Trks, like that of the other SKT proteins, indicates that they could be fully functional as monomers. On the other hand, because the second TM helix of MPM D is highly charged and might be unstable in a hydrophobic environment, even a tetrameric organisation in which these charges would be hidden within a complex with MPM D in the centre has been proposed from molecular modelling [10,11]. The presence of a central pore in the tetrameric arrangement was also proposed, which would allow for the observed anion permeability of Trk1 [17,18]. In order to elucidate the possible "multimeric" state(s) of Trk, we conducted a combined theoretical (molecular modelling and molecular dynamics (MD) simulations) and experimental study using bimolecular fluorescence complementation (BiFC) and single molecule fluorescence microscopy (SMFM).

BiFC Indicates That Trk1[∆LHL] Can Exist as a Dimer with an Interface Formed by MPMs C and D
As was shown previously using BiFC, Trk1 can form at least dimers (Kale et al., 2019). When the N-and C-terminal parts of the YFP variant Venus (VN and VC) were fused to the C-termini of Trk1 monomers (Trk1/VC and Trk1/VN) and co-produced in yeast, BiFC was observed ( Figure 2A). Deletion of the long hydrophilic loop (LHL) did not affect fluorescence complementation, thus LHL is not required to form Trk1 dimers or multimers. On the contrary, co-expression of TRK1[∆LHL]/VN with TRK1[∆ LHL]/VC led to increased BiFC fluorescence, most likely due to the removal of steric hindrance caused by LHL (Figure 2A,B Figure 2E) as well as of two different monomers were close enough to produce BiFC (VN/Trk1[∆LHL] + Trk1[∆LHL]/VC, Figure 2C,D), whereas the combination of VN/Trk1[∆LHL] with VC/Trk1[∆LHL] did not give rise to fluorescence (cf. Supplementary Figure S6). Thus, the N-termini of different monomers seemed to be too far from each other for BiFC.
As mentioned above, the Trk1 polypeptide chain contains four MPM domains (A, B, C, and D), each homologous to a K-channel subunit, which are arranged around the central pore ( Figure 1). If Trk1 monomers were to form symmetric dimers, the interfaces between the monomers could be formed by domains A-B/B-A, B-C/C-B, C-D/D-C, or D-A/A-D (Figure 3A). If functional Trk1 were symmetric tetramers, the interface between the monomers could be formed by each of the four domains, i.e., the monomers would be symmetrically arranged with these domains in the centre (tetramers A, B, C, and D, Figure 3B).  Analysis of the electrostatic complementarity between the contact surfaces of dimers (Supplementary Figure S1) showed that the best complementarity was between the C-D and D-C surfaces. In addition, BC/CB and DA/AD dimers would be possible due to the presence of some complementary parts, whereas AB/BA interaction would be electrostatically unfavourable. All symmetric dimers and tetramers as well as a monomer were stable in the membrane in 100 ns MD simulations (Supplementary Figure S2). However, modelling and MD simulations did not allow for unambiguous differentiation between possible arrangements. Thus, atomic scale models based on a complete Trk1[ΔLHL] model ( Figure 1) were generated in which VN and VC were attached to the N-and C-termini of Trk1[ΔLHL], respectively. The ability of fluorescence complementation for symmetric dimers and tetramers was then analysed in silico by modelling the respective arrangements and measuring the distance between VN and VC fragments on different Trk1[ΔLHL] monomers. If it seemed likely that VN and VC came within a suitable distance (less than ~50 nm), fluorescence complementation was predicted. Trk1[ΔLHL] was used for modelling and MD as in the "wet-lab" experiments because BiFC was stronger than with full length Trk1 (see above). Furthermore, there is no structural model of LHL available. In Figure 4, the models for Trk1[ΔLHL]/VC and Trk1[ΔLHL]/VN (cf. Figure 3) arranged as symmetric dimers or tetramers are shown.
According to these models, BiFC which was observed with Trk1[ΔLHL]/VN + Trk1[ΔLHL]/VC ( Figure 2B  Analysis of the electrostatic complementarity between the contact surfaces of dimers (Supplementary Figure S1) showed that the best complementarity was between the C-D and D-C surfaces. In addition, BC/CB and DA/AD dimers would be possible due to the presence of some complementary parts, whereas AB/BA interaction would be electrostatically unfavourable. All symmetric dimers and tetramers as well as a monomer were stable in the membrane in 100 ns MD simulations (Supplementary Figure S2). However, modelling and MD simulations did not allow for unambiguous differentiation between possible arrangements. Thus, atomic scale models based on a complete Trk1[∆LHL] model ( Figure 1) were generated in which VN and VC were attached to the N-and C-termini of Trk1[∆LHL], respectively. The ability of fluorescence complementation for symmetric dimers and tetramers was then analysed in silico by modelling the respective arrangements and measuring the distance between VN and VC fragments on different Trk1[∆LHL] monomers. If it seemed likely that VN and VC came within a suitable distance (less thañ 50 nm), fluorescence complementation was predicted. Trk1[∆LHL] was used for modelling and MD as in the "wet-lab" experiments because BiFC was stronger than with full length Trk1 (see above). Furthermore, there is no structural model of LHL available. In  Therefore, we looked for internal positions in Trk1[ΔLHL] at which the insertion of a fluorescent "half-protein" and analysis of BiFC with the other part attached to another monomer would allow distinguishing between the remaining monomer arrangement options. Best suited were possibly exposed regions in intracellular loops of Trk1 that, were on the one hand, close to the membrane and, on the other hand, restricted the positioning of the fluorescent half-proteins, allowing BiFC only with certain arrangements. It turned out that the insertion of the C-terminal part of the fluorescent protein (GC, the C-terminal   Figure S3A,B). This combination could possibly also give rise to BiFC in the AD/DA dimer. However, the latter might be prevented by a potential sterical conflict between the loops connecting MPMs C and D. Taken together, the results left three possible arrangements of Trk1 monomers: CD/DC and DA/AD dimers, or a tetramer with four MPMs D in the centre (Table 1).
Therefore, we looked for internal positions in Trk1[∆LHL] at which the insertion of a fluorescent "half-protein" and analysis of BiFC with the other part attached to another monomer would allow distinguishing between the remaining monomer arrangement options. Best suited were possibly exposed regions in intracellular loops of Trk1 that, were on the one hand, close to the membrane and, on the other hand, restricted the positioning of the fluorescent half-proteins, allowing BiFC only with certain arrangements. It turned out that the insertion of the C-terminal part of the fluorescent protein (GC, the C-terminal fragment of GFP was used in this case, because BiFC was more easily detected by fluorescence microscopy visualisation with the setup used) into the intracellular loop three between MPM Figure 5A) would allow BiFC only for BC/CB and CD/DC dimers and tetramers with A or B in the centre but not with dimers AB/BA and DA/AD and with tetramers C and D ( Figure 5B). Therefore, the observed fluorescence complementation ( Figure 5C) excluded the tetramer D and the DA/AD dimer, leaving only the CD/DC dimer.  Figure 5A) would allow BiFC only for BC/CB and CD/DC dimers and tetramers with A or B in the centre but not with dimers AB/BA and DA/AD and with tetramers C and D ( Figure 5B). Therefore, the observed fluorescence complementation ( Figure 5C) excluded the tetramer D and the DA/AD dimer, leaving only the CD/DC dimer.

Single Molecule Fluorescence Microscopy and Stepwise Photobleaching
To test the proposed dimerisation, stepwise photobleaching (SP) analysis at the single-molecule level was performed. For these experiments, yeast cells were used, in which the TRK1 gene was replaced with either GFP/TRK1 or TRK1/GFP fusion genes. For SP analysis of the GFP signals 1000 frames with 10 ms illumination were captured (on average, a fluorescent GFP signal was observed in 223 ± 52 frames). Figure 6A displays a fluorescence image of a yeast cell with Trk1/GFP fluorescence signals. For SP analysis, sparsely distributed, diffraction-limited fluorescence signals ( Figure 6A) were determined from a sequence of images that were analysed. A time trace of a bleaching sequence is shown in Supplementary Figure S5, where the intensity decay corresponds to the signal

Single Molecule Fluorescence Microscopy and Stepwise Photobleaching
To test the proposed dimerisation, stepwise photobleaching (SP) analysis at the singlemolecule level was performed. For these experiments, yeast cells were used, in which the TRK1 gene was replaced with either GFP/TRK1 or TRK1/GFP fusion genes. For SP analysis of the GFP signals 1000 frames with 10 ms illumination were captured (on av-erage, a fluorescent GFP signal was observed in 223 ± 52 frames). Figure 6A displays a fluorescence image of a yeast cell with Trk1/GFP fluorescence signals. For SP analysis, sparsely distributed, diffraction-limited fluorescence signals ( Figure 6A) were determined from a sequence of images that were analysed. A time trace of a bleaching sequence is shown in Supplementary Figure S5, where the intensity decay corresponds to the signal of two emitters within a diffraction-limited spot. The signal of a single emitter blinking can be seen later in the trace. The summarised SP results showed that Trk1/GFP ( Figure 6B) and GFP/Trk1 ( Figure 6C) GFP fusion proteins incorporated in the plasma membrane were monomers (corresponding to a single GFP emitter per diffraction-limited spot) and dimers (corresponding to two GFP emitters per diffraction-limited spot), with a majority of monomers (Trk1/GFP~65%; GFP/Trk1~80%).

Quantification of BiFC Fluorescence
To further analyse this finding, a semi-quantitative BiFC analysis was performed by recording BiFC-fluorescence emission spectra from cultures of yeast cells expressing TRK1[ΔLHL] fusion genes with VN and/or VC from high copy number plasmids in order to reach a sufficient signal-to-noise ratio. As positive control, Trk1[ΔLHL]/YFP cells were used. Recording emission spectra instead of measuring fluorescence only at one emission/excitation pair allowed assessing the quality of the measurements and rule out non-specific fluorescence or contaminations. For all measurements, the same number of cells (as determined by OD measurements) was used.  Figure S6). A set of such spectra in the exponential growth phase (12 h growth and ~ 2.75 × 10 7 cells/mL in the original culture) in medium with 1 mM KCl is shown in Figure 7

Quantification of BiFC Fluorescence
To further analyse this finding, a semi-quantitative BiFC analysis was performed by recording BiFC-fluorescence emission spectra from cultures of yeast cells expressing TRK1[∆LHL] fusion genes with VN and/or VC from high copy number plasmids in order to reach a sufficient signal-to-noise ratio. As positive control, Trk1[∆LHL]/YFP cells were used. Recording emission spectra instead of measuring fluorescence only at one emission/excitation pair allowed assessing the quality of the measurements and rule out non-specific fluorescence or contaminations. For all measurements, the same number of cells (as determined by OD measurements) was used.  Figure S6). A set of such spectra in the exponential growth phase (12 h growth and~2.75 × 10 7 cells/mL in the original culture) in medium with 1 mM KCl is shown in Figure 7 Sets of such spectra were taken with media containing different concentrations of KCl during exponential and stationary growth phases. To quantify fluorescence as one data point per strain and measurement time, the average background-corrected "peak" fluorescence (530-534 nm) was taken. In Figure 8A    Sets of such spectra were taken with media containing different concentrations of KCl during exponential and stationary growth phases. To quantify fluorescence as one data point per strain and measurement time, the average background-corrected "peak" fluorescence (530-534 nm) was taken. In Figure 8A Figure 8B), the YFP and BiFC fluorescence also increased during the exponential growth phase but decreased after reaching a peak in the late exponential phase. Under these conditions, the intermolecular BiFC fluorescence observed with Trk1[∆LHL]/VN + Trk1[∆LHL]/VC was lower than the BiFC fluorescence observed with VN/Trk1[∆LHL]/VC throughout the whole experiment. In Figure 9A, the ratios of Trk1[∆LHL]/VN + Trk1[∆LHL]/VC fluorescence to VN/Trk1[∆LHL]/VC as an estimate for the relative abundance of dimers and monomers in low (0.1 mM) and moderate (1 mM) KCl-containing media are plotted vs. growth time. Whereas in medium containing 0.1 mM KCl, this ratio is smaller than one and rather constant during the full time of the experiment, in medium containing 1 mM KCl, this ratio strongly increased during stationary phase, indicating an increase in dimers. The results of these experiments are summarised in Figure 9B, in which the average ratios in the exponential growth phase (from~5 to~25 h) and stationary growth phase (from~50 to~150 h) are shown. The data confirmed that, regardless of the KCl concentration, intramolecular BiFC fluorescence (VN/Trk1[∆LHL]/VC), indicating monomers, seemed to be predominant in exponential growth phase. However, with higher [KCl], when the availability of K + is not growth limiting, dimerization occurs during the stationary phase.
KCl during exponential and stationary growth phases. To quantify fluorescence as one data point per strain and measurement time, the average background-corrected "peak" fluorescence (530-534 nm) was taken. In Figure 8A Figure 9B, in which the average ratios in the exponential growth phase (from ~5 to ~25 h) and stationary growth phase (from ~50 to ~150 h) are shown. The data confirmed that, regardless of the KCl concentration, intramolecular BiFC fluorescence (VN/Trk1[ΔLHL]/VC), indicating monomers, seemed to be predominant in exponential growth phase. However, with higher [KCl], when the availability of K + is not growth limiting, dimerization occurs during the stationary phase.

Discussion
The primary aim of this study was to find out whether yeast Trk1 exists in the plasma membrane in monomeric, dimeric, or even in a higher multimeric form. Trk1 could be fully functional as a monomer because its structure is homologous to a concatemer of four K-channel α-subunits and thus equivalent to a full K-channel. However, the related SKT

Discussion
The primary aim of this study was to find out whether yeast Trk1 exists in the plasma membrane in monomeric, dimeric, or even in a higher multimeric form. Trk1 could be fully functional as a monomer because its structure is homologous to a concatemer of four K-channel α-subunits and thus equivalent to a full K-channel. However, the related SKT proteins KtrB and TrkH, which work as K-channels, have been crystallised as dimers [15,16], and for Trks, a tetrameric structure has been proposed by earlier modelling [10].
We addressed this question by using BiFC with fusion proteins carrying a partial fluorescent protein (VN or VC) fused either to the N-or the C-terminus of Trk1[∆LHL] monomers and co-expressing combinations of these fusion genes. It turned out that (i) the Ctermini of Trk1 and the version lacking the long hydrophilic loop (LHL) and (ii) the N-and C-termini of separate monomers are close enough to give rise to BiFC (Figure 2), whereas BiFC was never observed (measured) when the parts of the fluorescent proteins were fused to the N-termini of separate Trk1 or Trk1[∆LHL] monomers. The latter finding did not only show that the N-termini of Trk1 monomers were too far away for BiFC but also proved that the observed BiFC was not due to non-specific interaction/aggregation. Thus, Trk1 monomers can at least form dimers. However, the presence of such dimers does not exclude the additional presence of monomers or higher-order multimers (tetramers). It also does not tell which parts (MPMs) of Trk1 form the interface between the monomers. The possible (and most likely) arrangement would be symmetrical dimers or tetramers. Dimer interfaces could be formed by MPMs AB/BA, BC/CB, CD/DC, or DA/AD. Tetramers would be arranged with one of the four MPMs in the centre (Figure 3). Using molecular modelling and MD simulation, it was analysed which of the possible arrangements were consistent with the BiFC results that showed close proximity of the C-termini as well as the N-and C-termini of separate monomers but not of the N-termini (Figure 2). It turned out that these results were consistent with a tetramer around MPMs D and dimers CD/DC and DA/AD ( Table 1). The insertion of a fluorescent protein fragment (GC) into Trk1[∆LHL] intracellular loop three, connecting MPMs C and D (Trk1[∆LHL][G1010/GC/E1011]) and the co-expression of the fusion gene with TRK1[∆LHL]/VN, allowed to exclude the Dcentred tetramer and the AD/DA dimer. Thus, the non-monomeric form of Trk1 is most likely a dimer, with the interface formed by MPMs C and D. This is consistent with the crystal structures of TrkH and KtrB, which also consist of dimers with a CD/DC interface.
Trk1 can also mediate anion translocation [17], and it was proposed that the permeation path was formed by the central interface of a D-tetramer [18]. Our results argue against this hypothesis and indicate that the anion-selective "pore" of Trk1 is formed either by the CD interface or even within one monomer. During MD simulations, an increased density of Cl − ions was observed close to the intracellular pore exit (Supplementary Figure S4). This could be explained by the presence of positively charged residues (Arg and Lys) in this region or simply by interactions with K + ions in the pore region. However, Cl − ions were attracted to this region even in the absence of K + . Additionally, an increase in the density of Cl − was seen close to the intracellular part of the CD interface. However, the simulations never showed the formation of a water-filled cavity or pore in the CD/DC contact surface that would allow Cl − translocation. One might consider the possibility of a dimer of CD/DC dimers. However, this seems unlikely because in that case an interaction of the N-termini of Trk1[∆LHL] (in VN/Trk1[∆LHL] + VC/Trk1[∆ LHL]) located in different dimers would be possible. Thus, the Cl − path via Trk1 remains elusive.
The fact that Trk1 as observed can exist as a dimer but not as a tetramer in the plasma membrane does not exclude the existence of monomers. Strictly speaking, it also does not exclude the existence of trimers or even higher-order multimers. However, this has never been observed for any K-channel-related protein (i.e., possessing four MPM motifs) and thus seems very unlikely. Therefore, single molecule fluorescence microscopy (SMFM) was used as an independent method. For these experiments, yeast cells were used in which the Trk1 gene was replaced with a TRK1/GFP or a GFP/TRK1 fusion gene. It turned out that, as expected, often two GFP molecules were in close proximity, indicating dimers. However, the majority of Trk1/GFP and GFP/Trk1 fluorescence was caused by single GFP molecules, showing the presence of monomers ( Figure 6). In addition, very few fluorescent particles consisting of three fluorophores were observed that might have been caused by non-specific aggregation.
In order to analyse the distribution of Trk1 monomers and dimers under various conditions, "semi quantitative BiFC" analysis was performed. As indicators for dimers cells possessing Trk1[∆LHL]/VN and Trk1[∆LHL]/VC were used, and as a measure for monomers VN/Trk1[∆LHL]/VC cells were employed. The dimerisation of the latter could also lead to BiFC via N-terminus-C-terminus interactions between two separate monomers. However, BiFC in cells with Trk1[∆LHL]/VC plus VN/Trk1[∆LHL] was very low as compared to those with VN/Trk1[∆LHL]/VC, leading only to a small overestimation of the number of monomers. The results (Figure 8) showed that in medium with moderate and high [KCl] (≥1 mM), BiFC fluorescence (and YFP fluorescence in Trk1[∆LHL]/YFP) increased during the exponential and early stationary growth phases and remained constant for a long period ( Figure 8A). In contrast, in medium with low KCl (0.1 mM), YFP and BiFC fluorescence reached a maximum in the late exponential growth phase and decreased again during the stationary phase ( Figure 8B).
It has been shown that yeast cells grown in media with non-limiting [K + ] also contain higher internal [K] (see, e.g., [19]). Thus, a reason for this difference could be the increased stability of Trk1 in cells containing higher K + concentrations. Alternatively, the metallothionine promoter P CUP1 that drove the expression of the TRK1[∆LHL] fusion genes might be more active in the intracellular conditions present when cells are grown in higher [K + ] media. It also seems possible that the Trk1 dimers are protected against degradation/recycling, i.e., dimerisation could stabilise the complex in the membrane by "hiding" regions sensitive to proteolysis in the inner part of the complex, making them less accessible. Experiments with Trk1 concatemers, for example, could be carried out to differentiate between these possibilities. However, since the analysis of this observation was not the main topic of the study, this was not followed further.
Importantly An unusual feature of Trk1 is that this translocation system can change its affinity from high to low depending on K + [20][21][22]. It was thought that this change in affinity was caused by some molecular switch dependent on intracellular [K + ]. In a recent study, it was claimed that not only intracellular but also extracellular K + contributed to the affinity change and that affinity changes gradually [23].
Most microorganisms employ different high-and low-affinity membrane transport systems in order to cope with the changing availability of nutrients. A prominent example in yeast is glucose uptake. Here a wide variety of transporters with different affinities and transport capacities exist, and their expression is regulated according to the glucose availability determined intracellularly and via transmembrane sensors (for review, see, e.g., [24,25]. It is much less common that one transport protein changes its affinity in order to fulfil the transport requirements. Among them is a dual-affinity glucose uptake system, Igt1, that has recently been identified in Torulaspora delbrueckii [26]. AtKUP1 [27,28] from Arabidopsis thaliana is the only K + translocation system besides Trk1 that was proposed to be able to switch between high and low affinity modes dependent on the extracellular K + concentration. However, the mechanism of affinity change is still unknown. The best understood dual-affinity transporter is NRT1.1/CHL1 [29], which mediates nitrate transport in plants. The current model for NRT1.1 affinity shift is that in the presence of high NO 3− concen-trations, NRT1.1 is present as a dimer that mediates nitrate translocation with low affinity (Kd~2 mM). The switch of NRT1.1 to high affinity (Kd~100 µM) is caused by the phosphorylation of a single threonine residue. This in turn leads to a de-dimerisation, and both monomers then act as high-affinity NO 3− transporters [30]. It is tempting to speculate that the affinity change in Trk1 might be caused by a similar/analogous mechanism. The results presented here show that Trk1 dimers are the dominant form in high [K + ] in the stationary growth phase when no high velocity/high affinity uptake is needed. In the exponential growth phase and in the stationary phase, when [K + ] is low and high K + uptake is needed for growth, however, the fraction of monomers is dominant. MD simulations suggest that the pore of a single Trk1 monomer is more symmetrically built than the two pores in a dimer. This increased symmetry might lead to better coordination of the translocated ions and thus higher fluxes. At present, this explanation is still somewhat speculative. It remains to be determined in further studies whether the dimer-monomer ratio of Trk1 observed here is correlated to the K + -translocation capabilities of the protein.

Strains and Growth Conditions
Most Saccharomyces cerevisiae strains used in this study were generated by (co-) transformation of BY4741 [31] trk1, trk2, and tok1∆ (=BYT123 in [32]) with plasmids containing TRK1([∆LHL]) fusion constructs with the N-terminal fragment consisting of residues 1-155 (VN) or the C-terminal fragment 156-238 (VC) from the GFP variant "Venus" [33]. With the setup we used, bleaching of VN/GC BiFC fluorescence was subjectively reduced compared to VN/VC fluorescence and thus more easily detected by fluorescence microscopy visualisation. Therefore, the C-terminal fragment (residues 155-238) of yEGFP (GC) was used instead of VC for the construction of pYEX-[HIS3]-TRK1[∆LHL][G1010/GC/E1011], in which the BiFC-fragment was inserted in intracellular loop three, connecting MPMs C and D of Trk1 (cf. Figure 1). In all cases, high copy number plasmids (derived from pYEX; cf. Supplementary Table S1) were used to obtain a sufficient signal-to-noise ratio.

Plasmid Construction and Yeast Transformation
E. coli/S. cerevisiae shuttle plasmids derived from pYEX-BX (Clontech Laboratories, Mountain View, CA, USA). For co-expression experiments, pYEX-[LEU2] was used in combination with pYEX-[HIS3] [13]. All constructs carrying fusion genes of TRK1[∆LHL] YFP or BiFC fragments were generated by PCR using the overlap extension method [35]. A list of all plasmids is given in Supplementary Table S1. All PCR-derived parts of plasmids were verified by sequencing. Maps and full sequences of all plasmids used in this study are available from the corresponding author. Episomal plasmids used for producing Trk1([∆LHL]) fusion proteins are listed in Supplementary Table S1. For transformation, the LiCl/PEG method [36] was used.

Fluorescence Microscopy
Fluorescence microscopy was carried out as described in [37] using an epifluorescence microscope with a 100×/1.30 oil immersion lens and appropriate filter sets. Pictures were taken with a CCD camera. To distinguish YFP, VN/VC (Venus), and VN/GC fluorescence from non-specific fluorescence, two filter sets were used: λ ex : 450-490 nm, beam splitter 505 nm, λ em : 520 nm long pass for "specific" fluorescence, and λ ex : 510-560 nm, beam splitter 575 nm, λ em : 590 nm long pass for "non-specific" fluorescence. The fluorescent microscopy pictures shown were generated by subtracting non-specific fluorescence (λ ex 510-560 nm) from pictures taken with λ ex 450-490 nm and merging the result (green channel) with the corresponding bright field picture (red channel) using ImageJ [38].

Single Molecule Fluorescence Microscopy (SMFM)
For the experiments, yeast cells expressing TRK1/GFP or GFP/TRK1 were grown in medium supplemented with 0.1 mM KCl and used for measurements in the late exponential growth phase. For the measurements, a suspension of living yeast cells was transferred into a reservoir prepared with a two-component adhesive on a glass cover slip. To immobilise the cells, the cover slip surface was coated with poly-D-lysine (1 mg/mL; incubation time: 10 min).
Image acquisition was performed as described previously [39,40] using a modified Olympus IX81 inverted epifluorescence microscope with an oil-immersion objective (UApo N 60×/1.49 NA, Olympus, Vienna, Austria). The sample was positioned on a XYZ piezo stage (P-733.3DD, Physical Instruments, Karlsruhe, Germany) with nanometer precision on top of a mechanical stage with a range of 1 × 1 cm. The sample was illuminated in the blue channel with 488 nm laser light from a diode laser (Toptica Photonics, Gräfelfing, Germany). The signal was detected using an Andor iXonEM+ 897 (back-illuminated) EMCCD camera (16 µm pixel size). The following filter sets were used: dichroic filter (ZT405/488/561/640rpc, Chroma, Olching, Germany), emission filter (446/523/600/677 nm BrightLine quad-band band-pass filter, Semrock, Rochester, NY, USA). Cell segmentation [41], localisation and stepwise photobleaching of GFPs were analysed using a software platform developed in-house. A detailed protocol can be found in the supplemental protocol "Analysis of stepwise photobleaching of GFP in cells".

Quantification of BiFC
Yeast cell cultures were inoculated to an OD600 = 0.1 (~1.1 × 10 6 cells/mL) and grown in SDAP medium with the required supplements and the appropriate amount of KCl at 28 • C, shaking at 180 rpm. For measurements, samples corresponding to 2.4 OD units were harvested by centrifugation (4000× g, 10 min, RT) and resuspended in 200 µL of water. Samples were transferred to 96-well microplates and after 2 h of settling to the bottom of the wells, emission spectra (λ ex 474 nm, bottom, bandwidth 12 nm) from 510 to 540 nm (bandwidth 5 nm) were recorded in 2 nm steps using a fluorescence reader (Safire, Tecan, Groedig, Austria). To correct for non-specific fluorescence, spectra from cells not possessing a fluorescent Trk1-protein (Trk1[∆LHL]/VC-L or Trk1[∆LHL]/VN-L) were subtracted.

Molecular Modelling and MD Simulations
Dimer and tetramer models of Trk1 were built from the published homology model of the Trk1 monomer (Zayats et al., 2015) in YASARA (Krieger, Koraimann, and Vriend, 2002) based on the crystal structure of the KtrB dimer (pdb 4j7c) [16] taking into account the position of the crystal structure in the membrane as predicted by the OPM server. Local clashes on contact surfaces were resolved by local energy minimisation in vacuum using YASARA with a Nova force field [42]. The potential energy of modelled dimeric and tetrameric complexes was minimised and equilibrated by MD. Complexes of Trk1 structures embedded in a POPC bilayer membrane and solvated in water (the TIP3P model) were built with the CHARMM-GUI server (https://charmm-gui.org/ (accessed on 1 February 2022)). MD simulations were run for all complexes for 100 ns with GROMACS 4.6.5 using the following MD parameters: NPT ensemble, temperature set to 310 K and controlled by a Nose-Hoover thermostat; constant pressure at X-Y direction was controlled by a Parrinello-Rahman barostat and a CHARMM36m force field [43]. The stability of complexes was analysed by RMSD calculations (Supplementary Figure S2). Electrostatic surface potentials were calculated with YASARA by a numeric method and visualized using atom radii for surface representation. The maximum electrostatic surface potential for the colour range is 80 kcal/mol. The "Particle Mesh Ewald Approach" was used to calculate electrostatic potential in vacuo [44]. Protein-protein docking based on shape complementarity was carried out using Patchdock [45]. BLAST was used to search for homologs [46]. Secondary structure predictions were performed by Jpred [47]. Ab initio modelling was run on the I-TASSER server [48]. YASARA geometry-based loop modelling [49] was used for modelling of N-and C-terminal "tails" and intracellular loops and re-sampling. Structure alignments were carried out using the MUSCLE method in YASARA [50].

Data Availability Statement:
The data presented in this study are presented in the article and the supplementary material. Molecular cloning data (plasmid maps and full sequences) are available from the authors upon request.