Probing membrane protein association using concentration-dependent Number and Brightness

Abstract

We introduce concentration-dependent Number and Brightness (cdN&B), a fluorescence fluctuation technique which can be implemented on a standard confocal microscope and can report on the thermodynamics of membrane protein association in the native plasma membrane. It uses transient transfection to enable measurements of oligomer size as a function of receptor concentration over a broad range, yielding the association constant. We discuss artifacts in cdN&B that are concentration-dependent and can distort the oligomerization curves, and we outline procedures that can correct for them. Using cdN&B, we characterize the association of neuropilin 1 (NRP1), a protein which plays a critical role in the development of the embryonic cardiovascular and nervous systems. We show that NRP1 associates into a tetramer in a concentration-dependent manner, and we quantify the strength of the association. This work demonstrates the utility of cdN&B as a powerful tool in biophysical chemistry.

Graphical Abstract

INTRODUCTION

Membrane proteins are ubiquitous biomolecules which play critical roles in cell physiology. These proteins are important for cell signaling, cell adhesion, recognition, motility, differentiation, and organogenesis^1–3. Given these critical functions, it is not surprising that membrane proteins are popular drug targets. In fact, the majority of the drugs on the market are believed to act on membrane proteins^4–7. Yet, despite this importance, and despite many years of sustained progress, many open mechanistic questions remain. Notably, our understanding about membrane protein structure and function is still lagging behind our understanding of soluble proteins.

The function of membrane proteins is often regulated through their homointeractions^1,8–10. Studies of these interactions, however, pose unique challenges, as the membrane proteins reside in a complex hydrophobic environment. Relative to soluble proteins, membrane proteins are difficult to overexpress, difficult to purify, and their interactions are difficult to characterize using traditional biophysical methods^11–13. Fluorescence-based methods offer a unique opportunity to study membrane protein interactions in the natural environment of the plasma membrane, without the need for extraction and purification. In particular, fluorescence methods that use standard, commercially available equipment are broadly used to characterize processes occurring in the membranes of live cells.

Number and brightness (N&B) is one such technique. It measures the ratio of the variance due to the fluorescence intensity fluctuations over time to the average intensity, which is different for different oligomer sizes^14,15. Experimentally, N&B works by rapidly taking an image stack of the same region of a cell, and then computing the mean florescence intensity and the variance across the stack for each pixel. This allows for the calculation of the apparent molecular brightness, ϵ_app. The brightness does not depend on the concentration and scales linearly with the oligomer size, and this allows the apparent oligomer size to be easily calculated by normalizing the molecular brightness measured for a protein to the molecular brightness of a monomer control.

N&B has been used to gain insights into the behavior of membrane proteins. For example, N&B has been used to characterize how a soluble factor induces the dimerization of a GPI-anchored receptor, how self-association of annexins is affected by membrane binding, and how ligands control the oligomer size of the receptors EGFR and ErbB2^16–18. An exciting expansion of N&B is enhanced N&B (eN&B), which uses statistical resampling to gain insight into the oligomer size distribution within a pixel^19,20. eN&B has been used to reveal details about the time course of EphB2 clustering in response to its ligand^19,20. However, N&B has not been used to determine association constants for membrane proteins, a task which requires that measurements are made at equilibrium and as a function of protein concentration.

Here, we introduce a new tool, concentration-dependent N&B (cdN&B), which can characterize the thermodynamics of membrane protein association in the native plasma membrane of live cells. It enables the acquisition of an oligomerization curve by measuring the apparent oligomer size as a function of receptor concentration, and this allows for the determination of the association constant. Using this new tool, we study the homo-association of NRP1, a protein which plays an important role in the development of the embryonic cardiovascular and nervous systems^21,22, and which has been implicated in many diseases^23,24. NRP1 has been shown to oligomerize in the plasma membrane, but the exact type of oligomer that is formed is not known, and neither is the strength of the association²⁵. Using cdN&B, we construct an NRP1 oligomerization curve as a function of NRP1 concentration. We show that NRP1 associates into a tetramer, likely through a dimer intermediate, and we calculate the association constants.

N&B in general is sensitive to movement and photobleaching, which can lead to errors in data processing and interpretation and can distort the oligomerization curve. We discuss the experimental and computational approaches that are necessary to correct for these artifacts in order to implement cdN&B. Moreover, we demonstrate the importance of making measurements over a wide concentration range for proteins whose oligomer size is concentration dependent. Provided that care is taken to accurately measure the protein concentration and correct for movement, cdN&B can be a powerful tool in membrane protein research.

Results

In cdN&B, one performs N&B measurements in a large number of cells expressing different amounts of the protein of interest tagged with a fluorescent protein. Here, experiments were performed with Chinese hamster ovary (CHO) cells that expressed membrane proteins labeled with mTurquoise (MT) on their C-termini. We used transient transfection to obtain cells expressing the labeled membrane protein over a broad concentration range. We then combined the cdN&B data for all the cells to obtain an oligomerization curve (apparent oligomer size versus concentration).

For a single cdN&B measurement, 150 images are taken of the same cell over approximately 90 seconds. The fluorescence of each pixel is measured over time. The fluorescence fluctuates due to the labeled proteins diffusing into and out of the pixel (see Figure S1). These fluctuations contain information about the oligomer size of the protein, as all the subunits of an oligomer diffuse together. Accordingly, the larger the oligomer size of the protein, the larger the fluorescence fluctuations; this is discussed in detail in Supporting Information, section I. However, cell movement, as well as photobleaching, will give rise to large, slow perturbations that need to be corrected. While such effects have been discussed in the N&B literature^14,26, we find that they scale nonlinearly with the concentration of the labeled protein, and can thus significantly distort the cdN&B oligomerization curve if they are not taken into account.

As a first step in implementing cdN&B, we sought to physically immobilize the cells during imaging by embedding them in an alginate gel (see Figure S2). Alginate is a polysaccharide derived from seaweed, which rapidly forms soft hydrogels (consisting of > 98% water) by interacting with divalent cations such as calcium ions. Alginate hydrogels have been widely used as biomaterials for drug delivery and tissue engineering, and as matrices for cell culture²⁷. The physical properties of alginate gels, such as stiffness, can be easily controlled by adjusting the polymer concentration, the crosslinking condition, and the gelling environment^28,29.The alginate gels used in this study are discussed in detail in Supporting Information, section II.

One fluorescence trace—in other words, the fluorescence as a function of image number (i.e., time)—acquired in the presence of the gel is shown in Figure 1A in blue. This trace represents the average fluorescence intensity across all the pixels in a membrane region selected for analysis (shown in Figure 1B). If there were cell movement or photobleaching, the overall trace would look like an exponential decay curve with fluctuations superimposed on it. This is shown in the fluorescence intensity versus image number trace in Figure S4, where the red line is the best fit to an exponential decay curve.

Figure 1.

Comparison of ϵ_app values for monomer (LAT) and dimer (E-cadherin) controls. A: Representative trace of fluorescence intensity versus image number (i.e., time) for a cell expressing LAT that did not require computational correction. The red line is the average fluorescence intensity. B: Representative image of a CHO cell expressing LAT, under reversible osmotic stress. In this geometry, the plasma membrane is perpendicular to the focal plane. Large continuous stretches of plasma membrane were manually selected for analysis. The region of plasma membrane selected for analysis is outlined in blue, and is constructed using membrane center selections (red stars). C&D: Apparent brightness values, measured for LAT-MT and E-cadherin-MT in individual cells, binned by concentration. The solid red lines are the median values for the bins, the bottom and top of the boxes are the 25^th and 75^th percentile values, and the red pluses are outlier values. A total of 185 cells were measured for LAT and 96 for E-cadherin. The average ϵ_app value for LAT is 0.032 ± 0.003 and for E-cadherin is 0.060 ± 0.004; errors represent standard errors of the mean.

When using the alginate gel, depending on the protein being expressed, we were able to immobilize 30–80% of the measured cells. This was judged by the stability of the fluorescence fluctuation time traces after applying an image alignment algorithm to the entire image stack³⁰. In the remaining cells, a mathematical correction known as “boxcar averaging” was applied to remedy the effects of the residual cell movement or any potential photobleaching. In this well-established approach²⁶, the brightness over a series of consecutive subsets of the image stack is calculated, and then the subset brightness values are averaged together to yield the corrected brightness value. Since changes in fluorescence intensity due to movement or photobleaching occur over a much longer time scale than those due to diffusion, boxcar averaging effectively filters out these slow contributions while preserving the fast fluctuations due to diffusion. Details about this process are described in Supporting Information, section II.

One final element of cdN&B is that we ensured that the concentrations in the plasma membrane could be accurately measured. It is challenging to determine such two-dimensional membrane protein concentrations in fluorescence experiments, because cells possess two to three times the membrane surface needed to sustain their shape, and thus the plasma membrane is highly “wrinkled” or “ruffled” ^31,32. While the effective 3D receptor concentrations can be determined by comparing the experimental fluorescence intensities to the fluorescence intensities of standard solutions of fluorescent proteins of known concentrations^33,34, the complex membrane topology prevents their conversion into 2D receptor concentrations within the plasma membrane³⁵.

However, cell membranes can be “un-wrinkled” in a reversible manner when the cells are subjected to controlled osmotic stress, as this leads to the disassembly and flattening of the caveolae³⁶. The cellular membrane acquires a spherical topology, and we image the equatorial cross-section of this sphere, ensuring that the plasma membrane is perpendicular to the focal plane (see Figure 1B). This process does not cause irreversible cell damage^37,38, and in published FRET studies, the reversible stress has been shown to not alter membrane protein interactions in a measurable way³⁹. In our experiments, the gel that we use to immobilize the cells also applies this reversible osmotic stress.

Monomer and dimer controls

In order to determine the apparent oligomer size of a protein, the brightness of a monomer, ϵ_monomer, must be determined first under a fixed set of imaging conditions used in the entire study. The monomer control that we used was linker for activation of T cells (LAT)—a single pass membrane protein that is important for T-cell receptor downstream signaling and has been used as monomer control in prior studies^40–44. The cell shown in Figure 1B expresses LAT-MT, with the region of plasma membrane selected for analysis outlined in blue. The fluorescence fluctuation trace in Figure 1A is acquired from this cell. The brightness is calculated from this trace using equations (s1) and (s3) in Supporting Information, section I. Brightness values calculated for LAT-MT in 185 cells are shown in Figure 1C. The data are binned by concentration and shown as box and whisker plots as a function of concentration. Since LAT is a monomer control, its brightness should not depend on the concentration. Noteworthily, a sharp increase in brightness with concentration was observed when the above protocol was not followed, i.e. the alginate gel was not used and the boxcar averaging was not applied (data not shown), unlike in Figure 1C, where there is no statistically significant difference in brightness between the lowest and highest LAT concentrations. The determined ϵ_monomer value is 0.032 ± 0.003; the error is the standard error of the mean (SEM).

To confirm that the oligomer size does scale linearly with ϵ_monomer in our experiments, we used Epithelial cadherin (E-cadherin) as a dimer control. E-cadherin supports cell-cell contacts and is responsible for the intercellular cohesion of epithelial tissues^45–47. Outside of adherent cell-cell junctions, E-cadherin exists in a constitutive dimeric form³⁹. The brightness values for E-cadherin as a function of concentration are shown in Figure 1D; the data are binned by concentration and shown as box and whisker plots. The mean molecular brightness values, ϵ_dimer, is 0.060 ± 0.004; errors bars are SEM. This gives an oligomer size of 1.9 ± 0.1, which is not significantly different from 2.0, the expected value for a dimer, based on one sample t-test.

NRP1 forms a tetramer

The development of cdN&B was driven by our research goal to uncover the oligomerization behavior of NRP1 in the plasma membrane. Neuropilin 1 (NRP1), a 140 kDa transmembrane receptor, plays a key role in two critically important biological processes: angiogenesis, the growth of new blood vessels from preexisting ones, and axon pathfinding during neuronal development^21,22. Angiogenesis starts with the activation and migration of endothelial cells lining the blood vessel. NRP1 is expressed in endothelial cells, where it interacts with and controls the behavior of a membrane receptor called VEGFR2, a primary regulator of angiogenesis. NRP1 is also expressed in sensory neurons, where it interacts with receptors called plexins, to regulate guidance signals that lead to axon repulsion. Furthermore, NRP1 is found in many tumors, and its overexpression has been linked to tumor growth^23,24.

NRP1 is believed to not only interact with VEGFR2 or plexins, but also engage in homooligomerization in the plasma membrane^48–50. NRP1 oligomerization is not well understood, but its role may be to exert control over NRP1 heterointeractions with either VEGFR2 or plexins, in accordance with the law of mass action. We previously used FRET to show that NRP1 forms an oligomer greater than a dimer, but we were unable to determine the exact oligomer size²⁵. We hypothesized that with cdN&B, we could measure the apparent oligomer size as a function of the concentration. The measured NRP1 apparent molecular brightness is shown as a function of concentration in Figure 2A on the left y-axis. Dividing the NRP1 apparent molecular brightness by ϵ_monomer gives the apparent oligomer size, shown as a function of the concentration on the right y-axis of Figure 2A. At low concentrations, the apparent oligomer size is between one and two, and at high concentration, the apparent oligomer is between three and four. This suggests that NRP1 undergoes a transition from a monomer to an oligomer as the concentration of NRP1 increases.

Figure 2.

cdN&B analysis of NRP1-MT lateral association in the plasma membrane of CHO cells. In total, 213 cells were analyzed, and the data were binned by concentration. A: Apparent molecular brightness (left) and oligomer size (right) values, where the solid red lines are the median values for the bins, the bottom and top of the boxes are the 25^th and 75^th percentile values, and the red pluses are outlier values. B&C: Apparent oligomer size of NRP1 as a function of concentration, where the black dots are the average values, and the error bars are the standard errors of the mean. B: The solid blue, red, and cyan curves are the best fit monomer-trimer, monomer-tetramer, and monomer-pentamer models, respectively. Fitting procedure is described in Supplemental Information, section IV. C: The best fit monomer-dimer-tetramer model (solid magenta line) is compared to the best fit monomer-tetramer model. Fitting procedure is described in Supplemental Information, section V.

Further knowledge about the oligomer size can be gained by fitting these data to different monomer-oligomer-models, as described in detail in Supporting Information, Section IV. Figure 2B shows the best-fit oligomerization curves, along with the binned apparent oligomer size data, now depicted as averages with the error bars representing the standard errors. We see that a monomer-tetramer model provides the best fit to the data. This conclusion is supported by a mean squared error (MSE) analysis, as the monomer-tetramer has the lowest error (Figure S7). The best fit association constant from the monomer-tetramer model is shown in Table 1.

Table 1.

Comparison between the measured association constants using cdN&B and FRET. EphA2 and EGFR are known to form dimers^51,52. The NRP1 oligomer order, i=4, was determined in this study and was used to fit previously published FRET NRP1 data²⁵ and determine the association constant. The errors are the 95% confidence intervals of the fits.

	cdN&B	FRET
EphA2 (μm2/rec)	0.0043±0.0025	0.0049±0.0017
ECTM EGFR (μm2/rec)	0.00063±0.00035	0.00036±0.00003
NRP1 ((μm2/rec)3)	2.7*10−9 ± 2*10−9	6.3*10−10± 2.6*10−10

Having established that NRP1 associates into tetramers, we next asked whether a monomer-dimer-tetramer equilibrium model (i.e., a dimer-of-dimer model) may provide a similarly good, or even better, description of the data. This more complex model is described in detail in Supporting Information, Section V. Figure 2C compares the fit of this model to the simpler monomer-tetramer model fit. We see that the monomer-dimer-tetramer model provides a good fit to the data, and has the lowest MSE of all the models which were evaluated (Figure S8). A comparison of the oligomeric fractions for the monomer-tetramer and monomer-dimer-tetramer models is shown in Figure S9.

cdN&B validation by measuring previously studied RTKs

To verify this methodology, we also measured the oligomerization curves for membrane proteins, known to form dimers, that have been previously studied using other methods, including FRET ^51,52. In particular, Figure S10 shows the cdN&B apparent oligomer size data for (A) EphA2 and (B) a version of EGFR where the intracellular domain has been replaced with a fluorescent protein, MT (termed “ECTM-EGFR-MT,” as it contains the entire extracellular [EC] and transmembrane [TM] domains). The association constants for these constructs are known from FRET studies^51,52. Here, we calculate the association constants using cdN&B, by fitting the apparent oligomer size versus concentration data to a monomer-dimer equilibrium model as discussed in Supporting Information, section IV. The results, shown in Table 1, show that both cdN&B and FRET produce similar results. These results for proteins of known association states provide a verification of the cdN&B method.

Discussion

Previously, membrane protein association curves have been acquired using two-color, steady state FRET^44,51,53,54, a technique that does not directly measure the apparent oligomer size. It has been shown that two-color, steady-state FRET is good at differentiating between monomers, dimers, and higher order oligomers in the membrane, but cannot identify the exact oligomer size (e.g., trimer, tetramer, pentamer)^55,56. In this work, we introduce cdN&B, and we demonstrate that unlike FRET, it can yield an oligomerization curve (i.e., apparent oligomer size versus concentration). We use cdN&B to study NRP1 association, and we show that NRP1 forms a tetramer—likely through a dimer intermediate—in a concentration-dependent manner. The apparent oligomer size increases with concentration, in a functional form that is well described by both monomer-tetramer and monomer-dimer-tetramer equilibrium models. Such information becomes accessible only if the NRP1 concentration is measured, along with the apparent oligomer size, in each individual cell, in a cell population with variable NRP1 expressions. If concentration is not taken into account, the cdN&B experiment may lead to a fundamentally incorrect conclusion.

In Figure 3A, we show the averages of all measured NRP1 apparent oligomer sizes in individual cells, irrespective of the concentrations, along with the LAT (monomer control) and E-cadherin (dimer control) averages. The average NRP1 oligomer size is 2.2 ± 0.1, which is similar to the apparent average oligomer size for E-cadherin, 1.9 ± 0.1. This result could be interpreted to mean that NRP1 forms a dimer, just like E-cadherin. However, the cdN&B data in Figure 1 reveal that the apparent brightness, and thus the apparent oligomer size, of E-cadherin does not change with concentration. On the other hand, NRP1 brightness increases with NRP1 concentration, as seen in Figure 2. Importantly, if the brightness/oligomer size data are not determined as a function of concentration, one would not know that the conclusion drawn from Figure 3A for NRP1 is incorrect.

Figure 3.

A demonstration of cdN&B utility. A: Comparison of the average apparent oligomer sizes of LAT (1.00±0.04), E-cadherin (1.9±0.1), and NRP1 (2.2±0.1), when all the data are averaged irrespective of the protein concentration. Errors represent the SEM. These data may be misinterpreted to mean that NRP1 forms a dimer. B: NRP1 monomer, dimer, and tetramer fractions and the apparent oligomer size as a function of NRP1 concentration, on the semilog scale. The plot is for the best fit association constants, assuming a monomer-dimer-tetramer equilibrium. Blue: Monomer (dotted line), dimer (dashed line), and tetramer (solid line) fractions (left axis). Orange: Apparent oligomer size (right axis). These predictions, derived from the cdN&B measurements, define NRP1 lateral association for any concentration (expression level).

The oligomerization curve that we collect in cdN&B can also yield information about the strength of the interaction. This is accomplished by fitting the curves to obtain the best-fit association constant. Different models, which are consistent with prior knowledge about the protein, can be evaluated. Here, we show that while a simple monomer-tetramer equilibrium model provides a good fit for the NRP1 data, so does a more complicated model that includes dimers as intermediates. It is important to note that the more complicated model has two fit parameters rather than one, and thus it is not straight-forward to directly compare the two models. However, we expect that the probability of four independent monomers encountering each other simultaneously to form a tetramer is low. This argument, and the fact that the monomer-dimer-tetramer model provides the best fit to the experimental data, supports the existence of a dimer intermediate.

Once the association constants are determined, we can predict the association state of NRP1 for any concentration. In Figure 3B, we plot the apparent oligomer size for NRP1, along with the monomer, dimer, and tetramer fractions, as a function of concentration on a semi-log plot. We see that NRP1 is predominately monomeric for expressions up to 100 NRP1/μm², and it becomes 50% tetramer at a concentration of approximately 1800 NRP1/μm². Thus, the oligomerization state of NRP1 is now known for any NRP1 expression level.

It is important to keep in mind that artifacts in cdN&B can distort oligomerization curves and lead to erroneous results. These artifacts have been discussed in the literature for N&B, and they arise mainly due to cell movement, photobleaching, and/or incomplete fluorophore maturation^26,57. While we see no indication for incomplete maturation in this study, as the monomer and dimer controls give an apparent oligomer size of one and two respectively, we note that there exists a correction protocol that can be applied if incomplete maturation is a concern⁵⁷. In our case, artifacts are primarily caused by cell movement, as we minimize photobleaching by imaging at low laser power. Importantly, the artifacts increase as the protein concentration increases, as discussed in Supporting Information, Section II. Movement is a particular problem in experiments that involve overexpressing proteins which promote cell migration, such as NRP1 and many RTKs. These artifacts are seen as a sharp increase in the oligomerization curve as the protein concentration increases. This is demonstrated in Figure S6, where the results are derived from the same NRP1 data set as in Figure 2, but the data have not been computationally corrected.

The first step in solving this technical issue was to physically inhibit cell movement (see Figure S11 for a summary of all cdN&B steps). Although chemical fixation is commonly used in N&B and similar experiments, we were concerned that this process could alter membrane protein interactions⁵⁸. Instead, we embedded the live cells in an alginate hydrogel, which led to a significant decrease in cell movement. The second step was to use boxcar averaging coupled with simulations to computationally correct for the artifacts in cells with residual cell movement or photobleaching. These two steps ensured that the fluctuations we analyze are due to molecules diffusing in and out of a pixel, rather than due to collective movement involving the entire plasma membrane. We were able to eliminate the artifacts in the cdN&B oligomer size curves, as judged by the fact that the apparent brightness, and thus the apparent oligomer size, for both a monomeric protein, LAT, and a constitutively dimeric protein, E-cadherin, do not depend on their concentrations (Figure 1C and D).

Many of the experimental details in cdN&B are similar to previous FRET investigations^44,51,53,54, as both techniques rely on (i) transient transfection to ensure a broad range of receptor expressions, and (ii) analysis of individual cells. Since FRET cannot generally distinguish between trimers, tetramers, pentamers, etc.^55,59, cdN&B can be viewed as a better alternative to FRET for assessment of membrane protein oligomerization. However, FRET results are not generally affected by cell movement, as only three scans are performed in the confocal microscope^53,60, as compared to 150 in cdN&B. Thus, no cell immobilization is needed in the FRET experiments, resulting in faster data collection.

We envision, therefore, that it may be beneficial to collect both FRET and cdN&B data sets for a membrane protein and analyze the data globally. The utility of this approach is demonstrated in Supporting Information, section VI, where the oligomerization curve for the combined data is shown in Figure S12. Other fluctuation methods can also be used together with cdN&B. These include fluorescence intensity fluctuation spectroscopy (FIF)^61,62 and spatial intensity distribution analysis (SpIDA)^63,64, which utilize spatial, rather than temporal fluctuation analysis,. Moreover, cdN&B could be combined with other N&B techniques such eN&B^19,20 in order to improve resolution. All of these methods have some limitations. This is why, answers to seemingly simple questions about the oligomer size of a protein in the membrane are often controversial in the literature. In order to overcome these limitations and resolve these controversies, we believe that it is best to always use at least two methods in parallel to answer the important biological questions. We believe that cdN&B should be one such method, due to its unique strengths.