Quantitative Analysis of Ligand Induced Heterodimerization of Two

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Quantitative analysis of ligand induced hetero-dimerization of two distinct receptors Chang Lu, and Zhi-Xin Wang Anal. Chem., Just Accepted Manuscript • Publication Date (Web): 20 Jun 2017 Downloaded from http://pubs.acs.org on June 20, 2017

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Analytical Chemistry

Quantitative analysis of ligand induced hetero-dimerization of two distinct receptors Chang Lu1 and Zhi-Xin Wang1, * 1

Key Laboratory of Ministry of Education for Protein Science, School of Life Sciences, Tsinghua University Beijing 100084 P.R. China

*

Corresponding author. E-mail: [email protected], Phone: 86-10-62785505, FAX: 86-10-62792826

ABSTRACT: The induced-dimerization of two distinct receptors through a hetero-bifunctional inducer is prevalent among all levels of cellular signaling processes, yet its complexity poses difficulty for systematic quantitative analysis. This paper firstly shows how to calculate the amount of any possible complex or monomer of hetero-ligand and two receptors present at equilibrium. The theory is subsequently applied to the determination of three independent equilibrium parameters involved in the rapamycin induced FKBP and FRB dimerization, in which all parameters were simultaneously estimated using one set of FRET experiments. A MATLAB script is provided for parametric fitting.

The functions of proteins in the complex intracellular environment are governed by their interactions with other proteins. Ligand-induced homo- and hetero-dimerization represent an important subset of protein-protein interactions and are frequently employed in transducing signals from the cell surface to the nucleus1 (Figure 1A). The dimerization or oligomerization of cell surface receptors by interaction with extracellular multivalent ligands has been shown to be an important event in triggering cellular responses in a number of cells 2,3. For instance, cytokine molecules, a large family of small proteins, can bind to specific cell surface receptors simultaneously and transmit a signal across the cell membrane 4-6. In a number of systems, the dimerization of soluble proteins by multivalent ligands has been shown to be an important event in triggering a cellular response. Scaffold proteins, for example, might facilitate signal transduction by preforming multi-molecular complexes that can be rapidly activated by incoming signal 7-9. Most extracellular signals are eventually transduced to the nucleus to elicit changes in gene expression. And the the dimerization of transcription factors is one of the most common natural events and artificial regulating mechanism in signal transduction 10-12. Chemically induced dimerization (CID) mediated by cell permeable, small molecules is an important tool in chemical biology for the analysis of protein function in cells 13-17. Genetically engineered CID systems are used in biological research to control protein localization, to manipulate signaling pathways and to induce protein activation11,12,16,17. In addition, small molecules can be (semi)rationally designed to bind simultaneously with two different proteins, and these molecules have proven to be powerful tools for therapeutic applications 12,18,19. For example, rapamycin has been widely used in technology developed to take advantage of the small molecule’s ability to hetero-dimerize proteins. Proteins of interest can be expressed as fusions to its interacting proteins, and then conditionally dimerized by the addition of rapamycin 11,16,19,20.

The model of ‘ligand-mediated’ dimerization of protein receptors can be generalized to an induced-dimerization scheme of three species (Figure 1B, Scheme 1). Based on the simplifying assumption that the concentration of total bivalent ligand is equal to the concentration of free or unbound bivalent ligands, Perelson and Delisi derived analytical expressions to calculate the fraction of dimerized proteins in a mixture of homo- or hetero- bifunctional ligands and monomeric proteins 21,22. Mack et.al. made the first attempt to derived an exact analysis for induced homo-dimerization without the inducer-in-excess assumption, and provided a detailed discussion of the parameter dependence23. However, their results cannot be trivially extended to the induced hetero-dimerization situation, which represents a large portion of scenarios in induced dimerization. More recently, Douglass et al. developed a comprehensive mathematical model for three-body binding equilibria, where they provided a detailed discussion of the model under special parametric conditions 24. Despite theoretical advances in the analysis of induced dimerization, there remains a gap between model building and experimental application. For instance, the equilibrium parameters in Scheme 1 has only been estimated by separated reactions, and the cooperativity involved in three-body binding has remained difficult to be quantitatively determined 18. In this paper, we analyzed the ligand induced heterodimerization of distinct proteins systematically, and derived algebraic expressions for the equilibrium concentrations of each of the individual state variables as a function of the parameters (the equilibrium constants and the total concentrations of each species). The whole model was further validated by in vitro experiments, using fluorescence resonance energy transfer (FRET) technology. It was applied to the well-studied system of rapamycin induced FKBP-FRB interaction18,25,26, and all parameters concerned in the system was estimated with one set of FRET experiments.

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Figure 1. The model of ligand induced hetero-dimerization. (A) The dynamic schemes of a ligand (or protein or chemical inducer of dimerization) inducing two distinct proteins on the membrane/ in the cytosol/ inside nucleus. Induced hetero-dimerization can initiate or amplify signal transduction; it also serves as a mechanism to initiate gene transcription. (B) Thermodynamic scheme describing the reactions involved in induced dimerization. The equilibrium between ligand L and monomeric proteins P1 and P2 are characterized by the first step dissociation constants K1 and K2, and the equilibrium between monomeric protein (P1 or P2) and ligand-protein complex (LP2 or P1L) is characterized by the second step dissociation constants K3 or K4, respectively. α is the cooperativity parameter. (C) Example plots illustrating the concentration of different species present in the mixture versus increasing ligand concentration. When few ligand is present, the mixture contains mainly of monomeric proteins; when excessive inducer is added to the system, the mixture primarily consists of ligand-protein complexes. In the process of increasing ligand concentration, the fraction of hetero-dimer (P1LP2) increases first, and then decreases. (Parameters: K1 = K2/10, α=10, [P1]0 = [P2]0.)

n EXPERIMENTAL SECTION Constructs, protein expression and purification. Human FK506 binding protein (FKBP12, hereafter called FKBP) and a 100-amino acid domain (E2015 to Q2114) of the mammalian target of rapamycin (mTOR) known as the FKBP-rapamycin binding domain (hereafter called FRB) was subcloned into pET-Duet1 by BamH1/Not1 sites to give pETDuet1/FKBP and pETDuet1/FRB vectors. pCyPet-His and pYPet-His plasmids were gifts from Patrick Daugherty (Addgene plasmids #14030, #14031)27. The fluorophores were subsequently inserted into vectors by Not1/Xho1 sites to give pETDuet1/FKBP/CyPet and pETDuet1/FRB/YPet for generation of His-tagged FKBP-CyPet and FRB-YPet proteins. All constructs were verified by DNA sequencing. Both fusion proteins, overexpressed in E. coli BL21(DE3) cells at 20 oC, were purified over Ni-NTA (QIAGEN), ion-exchange and gel filtration chromatography (Source-15Q, Superdex-200; GE Healthcare). The SDSpage of the purified proteins are shown in Figure S1. The protein concentrations were determined using the BCA Assay Kit (Pierce). The purified proteins were stored at -80 oC. Fluorescence spectroscopy measurement. The fluorescence spectrum of fluorescently labeled proteins was measured using a microscopic spectrometer (Reinshaw) with a 438 nm argon laser (Spectra-Physics) as the excitation light source. Emission spectra (450600 nm) were recorded to confirm the fluorescence properties of the expressed fluorescent protein fusions (Figure S2). Upon addition of rapamycin, the spectrum shows decreased CyPet emission around 477 nm as well as a sharply increased YPet emission around 530 nm, indicating formation of (FKBP-CyPet)-rapamycin-(FRBYPet) complex and occurrence of resonance energy transfer between the two fluorophores (Figure S2). All proteins were diluted in PBS (pH 7.4) buffer, while rapamycin is solvated in EtOH. As

the extinction coefficient and quantum yield of fluorophores are sensitive to buffer composition, addition of EtOH is shown to influence the spectrum of CyPet and YPet. Therefore, we prepare each sample by combining 200 µL FKBP-CyPet and FRB-YPet mixture and 5 µL EtOH of various concentrations of rapamycin (including a 5 µL EtOH without rapamycin as control). All FRET experiments were conducted within one day to ensure that the systematical error remains essentially the same for all data. For each spectrum scanning, the samples were equilibrated for 20 min at 25 oC to ensure that the samples were in the equilibrium state and that the spectrum is stable. The fluorescence signals were obtained by averaging emission signal at 520~530nm. In the absence of rapamycin, the solution contains FKBP-CyPet and FRBYPet, and the emission fluorescence is given by: F0 = Φ D (λAem )QD0 ε D (λDex )[ D]0 + Φ A (λAem )QA0ε A (λDex )[ A]0 = f D [ D]0 + f A [ A]0

(1)

D stands for donor fluorophore (FKBP-CyPet) and A stands for the acceptor fluorophore (FRB-YPet). Q0D and Q0A are the quantum yield (without any energy transfer) of donor and acceptor, respectively. ε" and ε# are the extinction coefficients, Φ% and Φ& are the fraction of emitted fluorescence at given wavelength. We use fD and fA to denote the fluorescence per mol donor or acceptor concentration under given conditions. [D]0 and [A]0 denotes the total concentration of donor and acceptor fluorophores, respectively. With addition of rapamycin, the solution contains a mixture of protein-ligand complex (DL and AL) and protein-ligand-protein complex (DLA) and the fluorescence is given by (assuming that the properties of the fluorophore does not change upon binding of ligand):


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F = f D ([ D] + [ DL]) + f A ([ A] + [ AL]) + f f [ DLA] where f f = ΦD (λAem )QD0 ε D (λDex )(1 − E) + Φ A (λAem )QA0 {ε A (λDex ) + Eε D (λDex )}

(2)

E is the FRET efficiency, and f f denotes the fluorescence per mol concentration of donor-acceptor complex. FFRET is obtained by subtraction of control fluorescence: FFRET = F − F0 = f D ([ D] + [ DL] − [ D]0 ) + f A ([ A] + [ AL] − [ A]0 ) + f f [ DLA] = ( f f − f D − f A )[ DLA]

(3)

Therefore, the difference in fluorescence with or without rapamycin is directly proportional to the concentration of heterodimer.

n RESULTS AND DISCUSSION The induced dimerization can be generalized to a reaction scheme, composed of one ligand (denoted by ‘L’) and two binding proteins (denoted by ‘P1’ and ‘P2’) (Figure 1B). According to the principle of detailed balance, chemical equilibrium is attained when each reaction illustrated in Figure 1B is separately at equilibrium. Thus the dissociation constants for the four reactions are not independent and K1 K4 = K2 K3 . This is a formal consequence of the energy conservation principle. A cooperativity factor is introduced for the binding of second protein to protein-ligand complex: K3 = K1/α and K4 = K2/ α. This cooperativity factor (α) determines whether the formation of the ternary complex P1LP2 is more or less favorable than in the case of independent binding, which has been also discussed in previous literature23,24. Combining equilibria and mass conservation equations yields a quintic equation (see SI, Section I): a0 [ L]5 + a1[ L]4 + a2 [ L]3 + a3 [ L]2 + a4 [ L] + a5 = 0

ty than rapamycin to FRB (K2). Determination of the FKBPrapamycin complex and the FRB is difficult due to the non-covalent nature of the original FKBP-rapamycin complex. Here, we describe an experimental application of measuring the three parameters involved in rapamycin induced FKBP and FRB dimerization using one set of FRET experiments. In order to monitor the amount of hetero-dimers, fluorescent proteins CyPet and YPet are attached to the C-terminus of FKBP and FRB, respectively. FRET experiments were performed by adding various concentrations of rapamycin (all solvated in the same amount of EtOH) to FKBP-CyPet and FRB-YPet mixture of fixed total concentrations (Figure 2A). With increasing amount of rapamycin, the spectra show decreasing donor emission at 477 nm and increasing acceptor emission around 530 nm indicating the increasing amount of rapamycin induced hetero-dimer (Figure 2B). After a certain threshold, further addition of rapamycin leads to increased donor emission and decreased acceptor emission, suggesting decreased level of FRET and inhibition of hetero-dimer formation (Figure 2B).

(4)

where a0 = 1 −

1

α

( )(

a1 = −[ L ]0 + 1 −

1

α

K 1 + K 2 − [ L ]0 + [ P1 ]0 + [ P2 ]0 )

( )[ ( ) ( ) ( )

a 2 = ( K 1 − [ L ]0 + [ P1 ]0 )( K 2 − [ L ]0 + [ P2 ]0 ) − 1 − a3 = K 2 ( K 1 − [ L ]0 + [ P1 ] )0 a4 = K1 K 2 a5 = −

1

α

(

K1

− [ L ]0 + [ P1 ]0

α 2

(

K1

α

)(

1

K 2 [ L ] 0 − [ P1 ]0 ) + K 1 ([ L ] 0 − [ P2 ] 0 )]

α

− [ L ]0 + [ P1 ]0 + K 1 K 2 − [ L ]0 + [ P2 ] 0 ) K2

α

− [ L ]0 + [ P2 ]0 +

1

α

1−

1

α

2

K1 K 2

(

K2

α

)

− [ L] 0 + [ P2 ] 0 + 2

K1 K 2

α

[ L] 0

2

2

K 1 K 2 [ L ]0

Eq. 4 can be solved for [L] numerically if the total concentrations of proteins and ligand, and parameters K1, K2 and cooperativity factor α are assigned. The equilibrium concentrations of [P1], [P2], [P1L], [LP2] and [P1LP2] can then be expressed as functions of free ligand [L] (Eq. S11), which were then used to examine how the binding curves depend upon the affinities and stoichiometry (Figures S3-S6). The supporting information provides further details on deriving the equations and a MATLAB program for using them. The behavior of the system is illustrated in Figure 1C for a representative set of specific values and concentrations. In this study, we applied the above theory to measure equilibrium parameters of the well-studied system of rapamycin induced hetero-dimerization between FKBP and FRB 18,25. Rapamycin binds with high affinity (0.1-1 nM, denoted as K1) to FKBP and with low affinity (1-10 µM, denoted as K2) to FRB. This system has a high level of positive cooperativity, where FKBP-rapamycin complex binds to FRB (10-100 nM, denoted as K4) with much higher affini-

Figure 2. Simultaneous determination of equilibrium parameters involved in rapamycin-induced hetero-dimerization. (A) Schematic illustration of the hetero-dimer formation monitored via FRET signal change. FKBP is labeled by CyPet (the Donor fluorophore) and FRB is labeled by YPet (the Acceptor fluorophore). (B) Fluorescence spectra of FKBP-CyPet (55.4 nM) and FRB-YPet (39 nM) mixture under various concentrations of rapamycin. Left: from green to red, [rapamycin]t=0-20,475 nM; right: from red to green, [rapamycin]t=20,475546,000 nM. (C) This experiment is repeated for FRB-YPet (39 nM) and three different concentrations of FKBP-CyPet: 39.6 nM (black), 55.4 nM (blue) and 71.2 nM (orange). The FRET fluorescence obtained by subtraction of F0 is fitted to Eq. 4 (solid lines). (D) Experimentally determined values for all constants. The detailed statistics of non-linear fitting is provided in Table S1.

Due to the complexity raised by multiple parameters, a single curve is not sufficient to obtain a reliable estimation of all parameters. Therefore, we measured three sets of data using fixed FRBYPet concentration and three different concentrations of FKBPCyPet (Figure 2C). After subtraction of non-FRET fluorescence,



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these data were simultaneously fitted to Eq. 4 to estimate four parameters, namely, dissociation constants K1, K2, K4 (or cooperativity factor α) and a scaling factor C (Figure 2D, Table S1). Specifically, FKBP to rapamycin interaction was found to be K1 =2.1 nM, the low confidence in this parameter and the difference from literature value (~0.3 nM18,26,28) may due to the relatively high concentrations we are using (40~71 nM). Moreover, fixing K1 = 0.3 nM during the non-linear fitting process results in an equally nice overall fit to experimental data, in which the other parameters remain essentially unchanged (Figure S8, Table S2). The FKBP-rapamycin to FRB dissociation constant was found to be K4 = 12 nM, which is in accordance with the literature value (12 or 24 nM18,26). Rapamycin to FRB dissociation constant has been suggested to be difficult to measure as the interaction is relatively weak (on the order of µM). Fitting of FRET experiment data to our model directly yields rapamycin to FRB dissociation constant K2 to be 1.4 µM, which is smaller than the value obtained by Banaszynski et al. using Surface Plasmon Resonance (26 µM)18. However, unlike in the case of K1, this parameter has a relatively high confidence (Table S1) and fixing K4 = 26 µM would not result in an acceptable non-linear fitting. Further analysis shows that this dissociation constant cannot be as large as ~20 µM due to the decrease of the hetero-dimer concentration at ~6 µM rapamycin (Figure 2C, S9). Our method is further tested on an induced dimerization system developed by Braun and Wandless 29, where the appropriate experimental condition for precise estimation of the involved parameters was analyzed using theoretical simulation (Figure S11). Generally speaking, the choice of protein concentrations used in the experiment is critical for accurate estimation of parameters. If the protein concentration in the solution is much larger or lower than the corresponding dissociation constant, some parameters may not be precisely determined by our method. It is always advisable, therefore, to carry out several sets of experiments at different protein concentrations. A detailed discussion of the problem is provided in the revised Supporting Information (see SI, Section II). In summary, the present study relates the concentrations of each species to equilibrium parameters without any approximations. These exact expressions allow us to conduct the first experiment to quantitatively analyze the ligand induced hetero-dimerization as an ‘intact system’, as opposed to the general practice of analyzing each reaction involved separately. Traditional biochemical methods, such as fluorescence polarization or SPR, can analyze the reactions involved in the induced hetero-dimerization system by isolation of the rest of reactants or by competitive binding 18,19,26,29, yet at the expense of designing assay specifically for each measurement. In comparison, this study demonstrates the potential to systemically screen for appropriate dimerizer that most efficiently induces receptor dimerization in a quantitative aspect.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Additional information includes the theoretical derivation of equilibrium concentration expressions, the results and discussion of theoretical experiments, the guidelines for choosing experimental conditions, the statistical analysis of the non-linear fitting results and supplementary figures for experiments and theoretical simulations (PDF)

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MATLAB program and data processing demo(ZIP)

AUTHOR INFORMATION Corresponding Author * Corresponding author. E-mail: [email protected], Phone: 86-10-62785505, FAX: 86-10-62792826.

ORCID Chang Lu: 0000-0002-3272-0120

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported in part by grant 2016YFA0502004 from the Ministry of Science and Technology of the People’s Republic of China. The FRET experiment was done in Prof. Xin Sheng Zhao’s lab. We also thank Dr. Zhi Xin Lyu for his technical assistance.

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Figure 1. The model of ligand induced hetero-dimerization. 127x70mm (300 x 300 DPI)



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Figure 2. Simultaneous determination of equilibrium parameters involved in rapamycin-induced heterodimerization. 84x87mm (300 x 300 DPI)


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Quantitative Analysis of Ligand Induced Heterodimerization of Two

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