Abstract The neuronal protein Arc is a critical mediator of synaptic plasticity. Arc originated in tetrapods and flies through domestication of retrotransposon Gag genes. Recent studies have suggested that Arc mediates intercellular mRNA transfer and like Gag, can form capsid-like structures. Here we report that Drosophila proteins dArc1 and dArc2 assemble virus-like capsids. We determine the capsid structures to 2.8 Å and 3.7 Å resolution, respectively, finding similarity to capsids of retroviruses and retrotransposons. Differences between dArc1 and dArc2 capsids, including the presence of a structured zinc-finger pair in dArc1, are consistent with differential RNA-binding specificity. Our data support a model in which ancestral capsid-forming and RNA-binding properties of Arc remain under positive selection pressure and have been repurposed to function in neuronal signalling.
When characterizing biomolecular interactions, avidity, is an umbrella term used to describe the accumulated strength of multiple specific and unspecific interactions between two or more interaction partners. In contrast to the affinity, which is often sufficient to describe monovalent interactions in solution and where the binding strength can be accurately determined by considering only the relationship between the microscopic association and dissociation rates, the avidity is a phenomenological macroscopic parameter linked to several microscopic events. Avidity also covers potential effects of reduced dimensionality and/or hindered diffusion observed at or near surfaces e.g., at the cell membrane. Avidity is often used to describe the discrepancy or the “extra on top” when cellular interactions display binding that are several orders of magnitude stronger than those estimated in vitro . Here we review the principles and theoretical frameworks governing avidity in biological systems and the methods for predicting and simulating avidity. While the avidity and effects thereof are well-understood for extracellular biomolecular interactions, we present here examples of, and discuss how, avidity and the underlying kinetics influences intracellular signaling processes.
Scaffolding proteins serve to assemble protein complexes in dynamic processes by means of specific protein-protein and protein-lipid binding domains. Many of these domains bind either proteins or lipids exclusively; however, it has become increasingly evident that certain domains are capable of binding both. Especially, many PDZ domains, which are highly abundant protein-protein binding domains, bind lipids and membranes. Here we provide an overview of recent large-scale studies trying to generalize and rationalize the binding patterns as well as specificity of PDZ domains towards membrane lipids. Moreover, we review how these PDZ-membrane interactions are regulated in the case of the synaptic scaffolding protein PICK1 and how this might affect cellular localization and function.
Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract PDZ domain scaffold proteins are molecular modules orchestrating cellular signalling in space and time. Here, we investigate assembly of PDZ scaffolds using supported cell membrane sheets, a unique experimental setup enabling direct access to the intracellular face of the cell membrane. Our data demonstrate how multivalent protein-protein and protein-lipid interactions provide critical avidity for the strong binding between the PDZ domain scaffold proteins, PICK1 and PSD-95, and their cognate transmembrane binding partners. The kinetics of the binding were remarkably slow and binding strength two-three orders of magnitude higher than the intrinsic affinity for the isolated PDZ interaction. Interestingly, discrete changes in the intrinsic PICK1 PDZ affinity did not affect overall binding strength but instead revealed dual scaffold modes for PICK1. Our data supported by simulations suggest that intrinsic PDZ domain affinities are finely tuned and encode specific cellular responses, enabling multiplexed cellular functions of PDZ scaffolds. https://doi.org/10.7554/eLife.39180.001 eLife digest Inside a cell, many different signals carry information that is essential for the cell to remain healthy and perform its role in the body. It is, therefore, very important that the signals are sent to the right places at the right times. Scaffold proteins play an essential role in organizing these signals by bringing specific proteins and other molecules into close contact at particular times and locations within the cell. Defects in scaffolding proteins can lead to cancer, psychiatric disorders and other diseases, so these proteins represent potential new targets for medicinal drugs. Many scaffolding proteins assemble groups of proteins on the surface of the membrane that surrounds the cell. Previous studies have shown that scaffolding proteins are able to bind to several other proteins as well as the membrane itself at the same time. However, the precise way in which scaffolding proteins assemble such groups is not clear because it is technically challenging to study this process in living cells. To overcome this challenge, Erlendsson, Thorsen et al. used a new experimental setup known as supported cell membrane sheets – which provides direct access to the side of the cell membrane that usually faces into the cell – to study two scaffolding proteins known as PICK1 and PSD-95. The experiments show that PICK1 and PSD-95 bind to their partner proteins up to 100 times more strongly than previously observed using other approaches. This is due to the scaffolding proteins binding more strongly to both their partners and the membrane. Unexpectedly, the experiments show that the shape and physical characteristics of the partner protein have no effect on the increase in the strength of the binding. Further experiments suggest that altering the ability of the PDZ domain of PICK1 to bind to partner proteins changes the mode of action of the PICK1 protein so that it can activate different responses in the cell. Together these findings imply that the ability of scaffolding proteins to bind to their partner proteins is finely tuned to encode specific responses in cells in different situations – a hypothesis that Erlendsson, Thorsen et al. are planning to test in intact cells. https://doi.org/10.7554/eLife.39180.002 Introduction It is of fundamental importance for cell function to organize signaling processes in space and time. Scaffold proteins play a key role in these efforts by operating as versatile nanoscale modules capable of bringing distinct molecular components in close proximity to shape specificity in cellular signaling networks and regulate output (Good et al., 2011; Zeke et al., 2009). A broad variety of different protein-protein and protein-lipid interacting domains are found in scaffold proteins, enabling them to bind and direct localization and function of their diverse interaction partners, such as receptors, transporters, ion channels and kinases (Hung and Sheng, 2002; Zhu et al., 2016). Our current understanding of the dynamics and kinetics underlying scaffold interactions relies mostly on in vitro assays of single domains isolated form their native membrane environment (Vincentelli et al., 2015; Stiffler et al., 2007; Long et al., 2003; Ivarsson, 2012). Such approaches reduce the complexity and makes binding assays simpler to both perform and analyze. Nonetheless, the presence of several interaction domains in one protein, together with possible formation of higher order structures of both scaffold proteins and transmembrane interaction partners (Long et al., 2003; Ivarsson, 2012), strongly suggest that measurements in vitro cannot replicate the behavior of the native environment. Furthermore, scaffold proteins often function on, or in proximity, to lipid cellular membranes, and several scaffold protein domains directly interact with lipids (Egea-Jimenez et al., 2016; Pérez et al., 2013). PDZ (PSD-95/Discs Large/ZO-1) domains constitute one of the most common interaction domains in scaffold proteins (Feng and Zhang, 2009; Zhu et al., 2016; Ye and Zhang, 2013) and are characterized by an elongated binding groove that interacts with the last three to five C-terminal residues of the target proteins (Doyle et al., 1996). Scaffold proteins often contain several PDZ domains permitting them to serve as adaptors to assemble protein complexes (Doyle et al., 1996; Sheng and Sala, 2001; Feng and Zhang, 2009; Ye and Zhang, 2013). PICK1 (Protein Interacting with C Kinase 1), for example, forms a dimeric structure containing two spatially separated, identical PDZ domains and a lipid binding N-BAR (Bin/amphiphysin/Rvs) domain (Karlsen et al., 2015), enabling simultaneous binding of two interaction partners and tethering of the complex to the membrane (Xu and Xia, 2006). To perform its differential functions, PICK1 is believed to operate in two distinct modes of scaffolding; one required for clustering transmembrane interaction partners, such as the AMPA-type glutamate receptors (AMPARs), the metabotropic glutamate receptor 7 (mGluR7), ephrin and the monoamine transporters (Xia et al., 1999; Torres et al., 2001; Boudin et al., 2000; Torres et al., 1998), and one required for recruiting protein kinase Cα (PKCα) to its transmembrane interaction partners to regulate their phosphorylation (Baron et al., 2002; Dev et al., 2000; Perez et al., 2001; Staudinger et al., 1995). The molecular mechanisms underlying these different scaffold modes remain nevertheless unknown. In contrast to neuronal scaffold interactions, drug-receptor or antibody interactions have been studied rigorously in tissues and cells uncovering molecular mechanisms of co-operativity and avidity in many biological systems (Varner et al., 2015). To enable similar studies of scaffold interactions with membrane proteins embedded in their natural membrane environment, we take here advantage of a supported cell membrane sheets (SCMS) technique (Perez et al., 2006a; Perez et al., 2006b). SCMS are prepared by pressing a glass cover-slip on an adherent cell culture. When the cover-slip is removed, the apical plasma membrane detaches from cells and a planar sheet exposing the inner surface of the membrane is exposed on the cover-slip. Binding of fluorescence labeled protein ligands to the membrane proteins exposed on the SCMS can be quantified by confocal laser scanning microscopy. Strikingly, our data reveal binding strengths for PICK1, as well as for the PDZ tandem domain from PSD-95 (Long et al., 2003; Cho et al., 1992), that are two to three orders of magnitude higher than the intrinsic affinities measured in vitro. The binding strength for PICK1 is strongly dependent on an intact PDZ domain binding groove and the membrane-binding N-BAR domain but, surprisingly, independent of the tertiary and quaternary structure of the transmembrane PDZ binding partners. To our further surprise, the binding strength for PICK1 is insensitive to discrete changes in the intrinsic affinities of the PDZ binding partners, which instead are reflected in changes of maximal binding. Mathematical modeling of homo-bivalent binding demonstrates that the observed behavior is consistent with a change in the binding mode from a scenario where one PICK1 dimer binds two membrane ligands to a scenario where one PICK1 dimer binds one membrane ligand and has one free PDZ domain available for other interactions. Altogether, by quantitatively illuminating binding kinetics of PDZ domain protein scaffolds on a cell membrane, our results reveal novel principles for how cellular scaffold proteins can operate to ensure specificity and selectivity in cellular signaling networks, and furthermore how these principles change our current understanding of cellular binding equilibria and mechanisms underlying the function of scaffold proteins in general. Results SCMS reveals nanomolar binding strength of scaffold interactions To investigate the interaction between PICK1 and the GluA2 subunit of the AMPAR in a semi-native environment, N-terminally flag-tagged GluA2 (SF-GluA2) was transiently expressed in HEK293 cells and labeled with Alexa-488 conjugated anti-FLAG M1 antibody before preparation of supported cell membrane sheets (SCMS) (Perez et al., 2006a) (Figure 1a–d). We incubated SCMSs, exposing the inner membrane leaflet and the intracellular parts of SF-GluA2, with increasing concentrations of purified PICK1, containing an N-terminal SNAP-tag fluorescently labeled with SNAP-surface 549 (PICK1) (Figure 1a,b), and measured the fluorescence intensity of bound PICK1 by confocal microscopy. By normalizing the intensities of the fluorescent signal from PICK1 (red) to the intensity of fluorescently labeled SF-GluA2 (green) and plotting this ratio as a function of increasing PICK1 concentration, we obtained a saturable binding curve (Figure 1f). The apparent affinity (Kd*) calculated from the binding curve was 67 ± 6 nM (mean ± s.e.m., n = 3), which, remarkably, is ~100 fold higher than the low micromolar intrinsic affinity (Kdint)determined for binding of the GluA2 C-terminus to the PICK1 PDZ domain using an in-solution based assay (Erlendsson et al., 2014). To test if the observed binding was specific and dependent on the C-terminal PDZ binding motif (-ESVKI) in GluA2, we added an alanine residue to the GluA2 C-terminus (-ESVKI + A) (SF-GluA2 +A) to compromise PDZ ligand binding (Madsen et al., 2005; Madsen et al., 2008). The apparent affinity and the maximal binding (Bmax) of PICK1 were significantly reduced compared to binding to SF-GluA2 for similar receptor expression levels (Figure 1b,e,f). This supports that PICK1 binding to SCMS from GluA2 expressing cells is specific and depends on the interaction with the GluA2 C-terminal PDZ motif. The results also establish the use of SCMS as a new, robust, quantitative method for investigating membrane proximal scaffold interactions. Figure 1 Download asset Open asset PICK1 PDZ binds with nanomolar binding strength to transmembrane interaction partners in semi-native membranes. (a) SCMS were prepared from HEK293 Grip tite cells transfected with a fluorescently labeled (green) membrane protein of interest (left) by pressing a pre-coated glass coverslip onto the cells (middle) and subsequently detaching the apical plasma membranes from the remains of the cells (right). Single bilayers were readily distinguished from undisrupted cells or organelles by their lack of three-dimensional structure. SCMS were incubated with buffer containing fluorescently labeled scaffolding protein (red). Binding was quantified by measuring the intensity of PICK1, IPICK1, relative to the intensity of the receptor, Irec, in a region of interest (dashed white lines). (b) Representative confocal images demonstrating concentration dependent binding of PICK1 (red) to SCMS expressing SF-GluA2 (green), or (c) endpoints for SF-GluA2 +A. (d) Schematic representation of SF-GluA2 constructs labeled with anti-FLAG M1-alexa 488 antibody. (e) Expression levels of SF-GluA2 and SF-GluA2 +A in SCMS were similar (p=0.66). (f) Quantification of concentration dependent binding of PICK1 on SCMS’s expressing SF-GluA2 (black) (Kd*=67 ± 6 nM), or SF-GluA2 +A (red), (n = 3, ****p≤0.0001). (g) Schematic representation of TAC-YFP-GluA2 constructs (h) Representative end points of PICK1 concentrations series. (i) Quantification of concentration dependent binding of PICK1 to TAC-YFP-GluA2 (Kd*=73 ± 19 nM) (n = 3). Scale bars 10 μm. https://doi.org/10.7554/eLife.39180.003 Membrane anchored protein tails are sufficient to enable strong binding of PICK1 on SCMS To test if the increased binding strength measured in the SCMS assay, compared to the micromolar affinity measured by in-solution assays (Erlendsson et al., 2014), was dependent on the tetrameric arrangement of subunits within the AMPARs, we transferred the 24 C-terminal residues of GluA2 onto the C-terminus of the single transmembrane spanning α-subunit of the IL-2 receptor (TAC) fused to YFP (TAC-YFP-GluA2) (Figure 1g). In contrast to the AMPARs, TAC is not believed to form higher order structures (Spangler et al., 2015). Strikingly, we obtained a Kd* of 73 ± 19 nM (mean ±s.e.m., n = 3) for binding of PICK1 to TAC-YFP-GluA2 (Figure 1h,i) suggesting that the high apparent affinity was achieved independently of the tetrameric complex as well as of the membrane embedded segments of the receptor. To address how different PDZ-binding motifs affect the binding strength, we next measured the interaction of PICK1 with the C-terminus of the dopamine transporter DAT (TAC-YFP-DAT C24) (Figure 2). According to in-solution binding assays, this peptide has a 10-fold higher intrinsic affinity for PICK1 than the GluA2 peptide (Erlendsson et al., 2014). We observed specific binding also for this construct (Figure 2—figure supplement 1) but only a minor increase in Kd* (47 ± 5 nM, mean ±s.e.m., n = 7), revealing that the binding strength measured in the SCMS assay correlates poorly with the intrinsic affinity (Figure 1a,c). Figure 2 with 3 supplements see all Download asset Open asset PICK1 binding on SCMS is specific and the binding strength is increased two orders of magnitude compared to in-solution affinities. Schematic and representative confocal images demonstrating saturation with labeled PICK1 (a) and competition between labeled PICK1 and unlabeled PICK1 (b) on SCMS expressing TAC-YFP-DAT. Brackets indicate the varied PICK1 pool. (c) Normalized binding as a function of unlabeled PICK1 concentration (black), left axis (Kd*=47 ± 5 nM) (n = 7) compared to in-solution based FP-measurements (grey), right axis (Kd = 9± 2 μM, n = 3, performed in triplicates). (d) Normalized binding as a function of unlabeled PICK1 concentration (black), left axis (IC50 = 29 ± 4 nM) (n = 5) compared to in-solution based FP-measurements (grey), right axis (Ki,app = 2 ± 0.4 μM, n = 3, performed in triplicates). Scale bars 10 μm. https://doi.org/10.7554/eLife.39180.004 To further confirm specificity and rule out effects of the SNAP-tag on PICK1, competition binding using a fixed concentration of labeled SNAP-PICK1 and an increasing concentration of unlabeled PICK1 was performed on SCMSs expressing TAC-YFP-DAT (Figure 2b,d). The binding strength determined from competition binding (Ki*=29 ± 5 nM (mean ±s.e.m., n = 5) was close to that from the direct binding saturation assay and increased 100-fold compared to the intrinsic affinity of the PICK1 PDZ interaction with the DAT C-terminus obtained in solution using a fluorescence polarization competition assay (2.1 ± 0.4 μM) (Figure 2b,d). To complement the results for PICK1, we also probed the binding strength of fluorescently labeled PSD-95 PDZ 1–2 tandem domain on SCMS expressing the ß1-adrenergic receptor (Hu et al., 2000). Indeed, the measured binding strength (EC50 = 3 ± 2 μM) was two orders of magnitude increased compared to the intrinsic affinities previously measured in solution for either of the two domains (430 ± 47 µM and 120 ± 20 µM for PDZ1 and PDZ2, respectively) (Møller et al., 2013) (Figure 2—figure supplement 2a,b). These findings further support that the binding strengths of PDZ domain scaffolding interactions are substantially higher than intrinsic PDZ affinities. Intrinsic affinities of PDZ ligands control maximal binding of PICK1 Despite similar high binding strength, comparison of the binding curves for PICK1 binding to TAC-YFP-GluA2 and TAC-YFP-DAT revealed a surprising two-fold difference in total maximal binding (Bmax) (TAC-YFP-DAT Bmax = 100%; TAC-YFP-GluA2 Bmax = 44 ± 9%) (Figure 2—figure supplement 3a,b). Note that this difference unlikely is due to different expression levels as the maximum binding was normalized to the YFP signal for the two different constructs. To address whether the difference was a consequence of the different intrinsic affinities of the DAT C-terminus compared to the GluA2 C-terminus, we exploited that the intrinsic affinity of PICK1 for the DAT C-terminus depends on the C-terminal valine and that substitution of the aliphatic side-chain of the C-terminal valine decrease its intrinsic affinity for PICK1; Val (WT) (2.3 ± 0.1 µM)>Ile (9.5 ± 0.9 µM)>Ala (49 ± 3 µM) (Madsen et al., 2005). Because DAT plasma membrane targeting is compromised by alterations in the extreme C-terminus (Bjerggaard et al., 2004), we introduced the mutation series into a previously characterized fusion construct in which the DAT C-terminus is fused to β2 adrenergic receptor (flagβ2-DAT8) (Madsen et al., 2012) yielding three constructs: LKV, LKI and LKA, respectively (Figure 3—figure supplement 1a). The apparent affinity of PICK1 to LKV (Kd*=37 ± 5 nM, n = 8) (mean ±s.e.m.) (Figure 3a,b) was essentially the same as that seen for TAC-YFP-DAT (Figure 2). Moreover, despite a decrease in intrinsic affinity of up to >20 fold, we observed no differences in apparent affinity in the SCMS assay upon mutating the valine to isoleucine (LKI Kd*=39 ± 4 nM, n = 7) or alanine (LKA Kd*=59 ± 11 nM, n = 5) (Figure 3a,b). Instead, we observed an unexpected reduction in maximal binding (Bmax LKI: 56 ± 2%, LKA: 41 ± 4%; (means ±s.e.m.) relative to LKV (Figure 3a,b and Table 1) for similar receptor surface expression levels (Figure 3—figure supplement 1b). Figure 3 with 1 supplement see all Download asset Open asset The intrinsic PDZ affinity does not translate directly to avidity but determines maximal binding. (b) Normalized binding derived from SCMS as a function of PICK1 concentration to LKV (black) (Kd*=37 ± 5 nM, Bmax = 100%), LKI (dark grey) (Kd*=29 ± 4 nM, Bmax = 56 ± 2%), LKA (light grey) (Kd*=59 ± 11 nM, Bmax = 41 ± 4%) LKV +A (white) (Kd*not fitted, Bmax = 21 ± 3). n = 8, 7, 5 and 3, respectively (**p<0.01; ****p≤0.0001). (b) Representative images demonstrating concentration dependent binding of PICK1 to SCMS expressing LKV, LKI and LKA constructs. (c) Representative PICK1 binding to SCMS expressing LKV or LKI as a function of incubation time. PICK1 concentration is 100 nM. Half maximum binding values are 24 ± 14 min for LKV, and 11 ± 4 min for LKI (means ±s.e.m, n = 3). (d) Representative images showing time dependent PICK1 binding to LKV and LKI. (e) Representative PICK1 dissociation curves from SCMS expressing LKV or LKI (points are means ±SD). LKV is fitted to a two-state dissociation with estimated fast and slow half-life of 21 ± 8 and 373 ± 51 min., respectively. LKI is fitted to a one-state dissociation with a half-life of 431 ± 16 min. (means ± S.E, n = 3). (f) Representative images showing time dependent PICK1 dissociation from LKV and LKI. Scale bars 10 μm. https://doi.org/10.7554/eLife.39180.008 Table 1 PICK1 WT binding statistics. https://doi.org/10.7554/eLife.39180.010 LigandEC50 (nM)Bmax (% of max)NTac-yfp dat c2447±5100 §7TAC-YFP DAT C24 + An.d-3TAC-YFP GluA2 C2473±1944 ± 9 §3TAC-YFP GluA2 C24 + An.d-3SF-GluA267±6100 and 3SF GluA2 + An.d*33 ± 4 and 3β2-DAT WT (LKV)37±5100 #8β 2-DAT LKI29±456 ± 2 #7β 2-DAT LKA59±1141 ± 4 #5β 2-DAT + A201±10221 ± 3#3 Dissociation studies reveal two distinct binding modes for PICK1 To obtain better insight into the molecular mechanism underlying the different maximal binding levels we turned to kinetic experiments. Association experiments did not show any striking difference between LKV and LKI (Figure 3c–d). Both constructs displayed slow (half-bound maxima; LKV: 24 ± 8 min, LKI: 14 ± 6 min; (means ±s.e.m., n = 3)), but saturable binding. PICK1 dissociation, on the other hand, revealed that whereas PICK dissociated very slowly when bound to LKI (t½=431 ± 16 min; mean ±s.e.m., n = 3), a distinct fast component of dissociation was observed from LKV on top of the slow dissociation rate (t½=21 ± 8 and 373 ± 51 min; mean ±s.e.m., n = 3), (Figure 3e–f). This suggests that the unbinding of LKV consists of two kinetically distinct processes and that PICK1 therefore might engage in two different binding configurations depending on the concentration of PICK1 and the intrinsic affinity for the membrane embedded ligand. That is, when the concentration of PICK1 is low and the intrinsic affinity for the membrane embedded ligand is low, PICK1 might adopt the intuitive binding mode with both PDZ domains of the dimer bound to a membrane embedded ligand (slow dissociation rate). However, when the concentration of PICK1 is high and the intrinsic affinity for the membrane embedded ligand is high, PICK1 might gradually switch to a binding mode with only one PDZ domain engaged in binding of the membrane embedded ligand (fast dissociation rate). To probe the feasibility of this hypothesis, we turned to thermodynamic simulations. Simulations support dual binding modes for PICK1 The principle of bivalency is well known to endow high affinity (often denoted as ‘avidity’) and the two individual steps in the bivalent PDZ-binding of PICK1 (aa) to two identical membrane embedded ligands (e.g. a receptor) (A) can be represented as shown in the scheme in Figure 4a (leading to formation of the ‘red complex’, aAAa). Indeed, bivalency increases the overall affinity and residence time since this permits multiple partial unbinding and rebinding events to take place before the protein fully dissociates (Vauquelin and Charlton, 2013; Vauquelin and Charlton, 2013). However, when the bulk concentration of PICK1 [aa] is sufficiently high, the free bivalent PICK1 would be expected to outpace binding of the second PDZ domain, thereby preventing formation of the ‘red complex’ (aAAa) and instead leading to formation of the ‘blue complex’ (aaAAaa) (Figure 4a). Under these conditions, the rate for formation of the blue ‘ternary’ complex (V2) is larger than the rate for formation of the red complex, (V3), because V2 relies on the free bulk concentration of ligand [aa], whereas V3 relies on the local concentration [L] of the second domain for binding, which in turn depends on the distance (r) between the individual domains (Figure 4a). Moreover, V3 might be compromised by steric hindrance, restricted rotation freedom and entropic penalty jointly denoted, f (Figure 4a) (Vauquelin, 2013; Vauquelin and Charlton, 2013). The effect of this empiric factor is to scale the effective concentration [L] of the free end of the PICK dimer in the AAaa complex (the ‘green complex’). The proposed model is the simplest model explaining our data. However, additional reaction steps can be envisioned for the binding of PICK1 for example the binding of the amphipathic helix in PICK1 to the cell membrane (vide infra) or putative long-range allosteric structural changes induced by the first binding event. None of such effects are necessary explicitly to describe our data, but may be encompassed by the f value. By simultaneously solving the system of differential equations related to formation of all of the involved complexes (Figure 4—figure supplement 1a–b), and using k1 and k-1 values derived of from the in-solution PDZ binding to soluble ligands (Erlendsson and Madsen, 2015; Erlendsson et al., 2014) together with an inter PDZ distance (r) of 180 Å determined from the structure of PICK1 based on Small-Angle X-ray Scattering (Karlsen et al., 2015)) and an f value of 185, we obtained a biphasic saturation binding curve (Figure 4b) that overall was in good agreement with the experimentally derived saturation binding curve observed for PICK1 binding to LKV. Importantly, the biphasic shape results from the population of the ternary blue complex (aaAAaa) outpacing the binary red complex (aAAa) at concentrations above 100 nM of PICK1. Note that in the averaged experimental data shown in Figure 3a and c, the biphasic behavior of the saturation binding curve is likely masked by experimental variation, as supported by the fact that we could extract a representative data set and fit this to a biphasic curve in good agreement with the simulated curve (Figure 4—figure supplement 2a–c). Figure 4 with 3 supplements see all Download asset Open asset Schematic representation of the thermodynamic model for homobivalent ligand-target interactions and thereon-based simulated saturation and dissociation curves. (a) Thermodynamic scheme for homobivalent ligand, ‘aa’- target, ‘AA’, interactions (see also Figure 4—figure supplement 1 for full scheme). The different binding modes in panel a are designated by ‘AAaa’ for the partially bound complexes (green), by ‘aAAa’ for the bivalently bound complex (red) and by ‘aaAAaa’ for ‘ternary’ complex with two partly bound ligands (blue). The rebinding kinetics is dependent the local concentration, [L], that is calculated as that of one molecule within a half-sphere with radius, r. Moreover, the rate constant is modified by f due to steric hindrance, restricted rational freedom and entropic cost. An f of 185 enables good qualitative simulation of our data (see also Figure 4—figure supplement 3 for behavior at other values of f). (b) Simulated saturation binding curve for binding of species. Input parameters: k1 = 1.85⋅105 M−1min−1, k-1 = 0.0085 min-−1, k2 = 0.136 min−1 (i.e. a composite rate constant such as defined in the figure). Total incubation time is 120 min. Analysis of the total signal according to a variable slope sigmoidal dose-response paradigm yields half-maximal signal at 50 nM. Note for these parameters the blue ‘ternary’ complex outpaces the red bivalent complex at bulk concentration of PICK1 above 100 nM. (c,d) Simulated dissociation curves after 120 min pre-incubation with 200 nM (c) and 20 nM (d) of the same homobivalent ligand as in panel c (corresponding to the affinity difference between LKV and LKI). [aa] is set and kept at 0 for simulating the ‘washout phase’. https://doi.org/10.7554/eLife.39180.011 The modeling also rationalizes the differential binding observed for LVK and LKI (Figure 3a–d). The lower intrinsic affinity for LKI reflects a change in the dissociation constant k-1, and as k-1 is equivalent for the three rates (V1, V2 and V3), the relative partitioning into the three different complexes will be unchanged. The absolute concentration dependence, however, will be parallel shifted when comparing LKV to LKI, as illustrated for a specific concentration [aa] by the arrow in Figure 4b. Consequently, a ligand with lower intrinsic affinity (such a LKI) will need a correspondingly higher concentration of bulk PICK1 to populate the ternary blue complex (Figure 4). This likely entails that what we observe when analyzing binding for the LKI ligand, that is the reduced apparent Bmax for LKI (Figure 3b) most likely represents a ‘plateau’ before transition to the blue complex, which would be observed if we experimentally were able to use even higher concentration of PICK1. Finally, it should be noted that increasing or decreasing the f parameter, affecting k2, would also have an important influence on the concentration-dependent formation of the blue complex (Figure 4—figure supplement 3). The discrimination between the different binding modes becomes even more perceptible in the simulation of the dissociation experiments; that is when free, labeled ligand molecules are removed and/or prevented to bind (Figure 4c,d). The observed dissociation for LKV is first dominated by the unbinding of one of the ligands in the blue complex. Being governed by a single off-rate, k-1, the initial component of the curve is fast, as would be expected from a monovalent binding event. Yet, since the so-obtained partially bound complexes (green) are more prone to form the bivalent red complex than to dissociate, the second component is governed by the slow dissociation of fully bound bivalent complexes (Figure 4c). For LKI or GluA2, which have lower intrinsic affinities (numerically corresponding to lower PICK1 concentration on Figure 4b), the ternary ‘blue’ complex is not favored and only the slow second component is observed in the simulation (Figure 4d). Importantly, the simulations are in very good agreement with the actual dissociation experiment (Figure 3e,f). Dual binding modes for PICK1 relies on two functional PDZ domains The model described above and in Figure 4 relies on two independent PDZ domain ligand-binding sites in the PICK1 dimer, and consequently it predicts that no differences in the apparent maximal b
